Finite Group Databasebeta

← #72252743

Subgroups — #72252743

Order 3456.

6415 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 6415 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13164890C211yesmaximal, characteristic, complemented
2C2×C32⋊#997C211yesmaximal, characteristic, complemented
3C2×C32⋊#997C211yesmaximal, characteristic, complemented
4C3×#87547C313yesmaximal, complemented
5C32×H(7,𝔽2)C311yesmaximal, characteristic, complemented
6C32⋊#997C2211yescharacteristic, complemented
72−1+4⋊H(3,𝔽3)—42nomaximal
8D4×C22⋊H(3,𝔽3)—41nomaximal
9D4×C22⋊H(3,𝔽3)—42nomaximal
10C32×#585—32no—
11C32×#585—32no—
12C32×#585—32no—
13C32×#585—31no—
14C32×#585—32no—
15C32×#585C2×C311yescharacteristic, complemented
16C2×C32×H(5,𝔽2)—32no—
17C2×C32×H(5,𝔽2)—31no—
18C2×C32×H(5,𝔽2)—32no—
19C2×C32×H(5,𝔽2)—31no—
20C2×C32×H(5,𝔽2)—32no—
21C2×C32×H(5,𝔽2)—31no—
22C2×C32×H(5,𝔽2)—32no—
23C2×C32×H(5,𝔽2)C2×C311yescharacteristic, complemented
24C2×C32×H(5,𝔽2)C2×C311yescharacteristic, complemented
25C3×#5950C2×C313yescomplemented
26C2×C3×#997C2×C313yescomplemented
27C2×C3×#997C2×C313yescomplemented
28C22×C22⋊H(3,𝔽3)—41no—
29C22×C22⋊H(3,𝔽3)—42no—
30C22×C22⋊H(3,𝔽3)—41no—
31C22×C22⋊H(3,𝔽3)—42no—
32#41⋊H(3,𝔽3)—42no—
33C2×Q8⋊H(3,𝔽3)—42no—
34C2×Q8⋊H(3,𝔽3)—42no—
35C4×C22⋊H(3,𝔽3)—41no—
36C4×C22⋊H(3,𝔽3)—42no—
37C3×H(7,𝔽2)—31no—
38C3×H(7,𝔽2)C3211yescharacteristic
39#87547—33no—
40C32×2−1+4—32no—
41C32×2−1+4—34no—
42C32×2−1+4—34no—
43C32×2−1+4—32no—
44C32×2−1+4—32no—
45C32×2−1+4—32no—
46C32×2−1+4—32no—
47C32×2−1+4A412yescomplemented
48C32×H(5,𝔽2)—32no—
49C32×H(5,𝔽2)—32no—
50C32×H(5,𝔽2)—32no—
51C32×H(5,𝔽2)—34no—
52C32×H(5,𝔽2)—32no—
53C32×H(5,𝔽2)—34no—
54C32×H(5,𝔽2)—32no—
55C32×H(5,𝔽2)—32no—
56C32×H(5,𝔽2)—32no—
57C32×H(5,𝔽2)—32no—
58C32×H(5,𝔽2)—34no—
59C32×H(5,𝔽2)—34no—
60C32×H(5,𝔽2)—32no—
61C32×H(5,𝔽2)—34no—
62C32×H(5,𝔽2)—34no—
63C32×H(5,𝔽2)—34no—
64C32×H(5,𝔽2)—34no—
65C32×H(5,𝔽2)—34no—
66C32×H(5,𝔽2)—34no—
67C32×H(5,𝔽2)—34no—
68C32×H(5,𝔽2)—34no—
69C32×H(5,𝔽2)—34no—
70C32×H(5,𝔽2)—32no—
71C32×H(5,𝔽2)—34no—
72C32×H(5,𝔽2)—32no—
73C32×H(5,𝔽2)—34no—
74C32×H(5,𝔽2)—32no—
75C32×H(5,𝔽2)—31no—
76C32×H(5,𝔽2)—32no—
77C32×H(5,𝔽2)—31no—
78C32×H(5,𝔽2)—31no—
79C32×H(5,𝔽2)—32no—
80C32×H(5,𝔽2)—32no—
81C32×H(5,𝔽2)C22×C311yescharacteristic
82C2×C32×#41—34no—
83C2×C32×#41—34no—
84C2×C32×#41—34no—
85C2×C32×#41—34no—
86C2×C32×#41—34no—
87C2×C32×#41—34no—
88C2×C32×#41—32no—
89C2×C32×#41—34no—
90C2×C32×#41—32no—
91C2×C32×#41—34no—
92C2×C32×#41—34no—
93C2×C32×#41—32no—
94C2×C32×#41—34no—
95C2×C32×#41—31no—
96C2×C32×#41—32no—
97C2×C32×#41—31no—
98C2×C32×#41—32no—
99C2×C32×#41—31no—
100C2×C32×#41—32no—
101C2×C32×#41—31no—
102C2×C32×#41—32no—
103C2×C32×#41—32no—
104C2×C32×#41—32no—
105C2×C32×#41—32no—
106C2×C32×#41—31no—
107C2×C32×#41—32no—
108C2×C32×#41—31no—
109C2×C32×#41—32no—
110C22×C32×D4—34no—
111C22×C32×D4—34no—
112C22×C32×D4—34no—
113C22×C32×D4—31no—
114C22×C32×D4—32no—
115C22×C32×D4—31no—
116C22×C32×D4—32no—
117C22×C32×D4—32no—
118C22×C32×D4—31no—
119C22×C32×D4—31no—
120C22×C32×D4—31no—
121C22×C32×D4—32no—
122C22×C32×D4—31no—
123C22×C32×D4—32no—
124C22×C32×D4—31no—
125C22×C32×D4—32no—
126C22×C32×D4—31no—
127C22×C32×D4—32no—
128C22×C32×D4A411yescharacteristic, complemented
129C22×C32×D4A412yescomplemented
130C3×#997C22×C313yescomplemented
131C3×2−1+4⋊C3—46no—
132C3×D4×A4—43no—
133C3×D4×A4—46no—
134C2×C22⋊H(3,𝔽3)—41no—
135C2×C22⋊H(3,𝔽3)—42no—
136C2×C22⋊H(3,𝔽3)—81no—
137C2×C22⋊H(3,𝔽3)—82no—
138C2×C22⋊H(3,𝔽3)—81no—
139C2×C22⋊H(3,𝔽3)—82no—
140D4×H(3,𝔽3)—161no—
141Q8⋊H(3,𝔽3)—42no—
142C3×#585—32no—
143C3×#585—32no—
144C3×#585—36no—
145C3×#585—36no—
146C3×#585—36no—
147C3×#585—33no—
148C3×#585—36no—
149C3×#585—32no—
150C3×#585—31no—
151C3×#585—32no—
152C3×#585—31no—
153C3×#585C2×C3211yescharacteristic
154C2×C3×H(5,𝔽2)—32no—
155C2×C3×H(5,𝔽2)—36no—
156C2×C3×H(5,𝔽2)—33no—
157C2×C3×H(5,𝔽2)—36no—
158C2×C3×H(5,𝔽2)—33no—
159C2×C3×H(5,𝔽2)—36no—
160C2×C3×H(5,𝔽2)—33no—
161C2×C3×H(5,𝔽2)—36no—
162C2×C3×H(5,𝔽2)—31no—
163C2×C3×H(5,𝔽2)—32no—
164C2×C3×H(5,𝔽2)—31no—
165C2×C3×H(5,𝔽2)—32no—
166C2×C3×H(5,𝔽2)—31no—
167C2×C3×H(5,𝔽2)—32no—
168C2×C3×H(5,𝔽2)—31no—
169C2×C3×H(5,𝔽2)—31no—
170C2×C3×H(5,𝔽2)C2×C3211yescharacteristic
171C2×C3×H(5,𝔽2)C2×C3211yescharacteristic
172#5950—33no—
173C2×#997—33no—
174C2×#997—33no—
175C24×C32—31no—
176C24×C32—32no—
177C24×C32—31no—
178C24×C32—32no—
179C24×C32—31no—
180C24×C32—31no—
181C24×C32C2×A411yescharacteristic, complemented
182C24×C32C2×A412yescomplemented
183C24×C32C2×A411yescharacteristic, complemented
184C24×C32C2×A412yescomplemented
185C22×C3×A4—43no—
186C22×C3×A4—46no—
187C22×C3×A4—43no—
188C22×C3×A4—46no—
189C32×#41—32no—
190C32×#41—34no—
191C32×#41—32no—
192C32×#41—34no—
193C32×#41—34no—
194C32×#41—32no—
195C32×#41—32no—
196C32×#41—32no—
197C32×#41—34no—
198C32×#41—34no—
199C32×#41—34no—
200C32×#41—34no—
201C32×#41—32no—
202C32×#41—32no—
203C32×#41—34no—
204C32×#41—34no—
205C32×#41—34no—
206C32×#41—34no—
207C32×#41—34no—
208C32×#41—34no—
209C32×#41—34no—
210C32×#41—34no—
211C32×#41—34no—
212C32×#41—34no—
213C32×#41—34no—
214C32×#41—34no—
215C32×#41—34no—
216C32×#41—34no—
217C32×#41—34no—
218C32×#41—32no—
219C32×#41—34no—
220C32×#41—34no—
221C32×#41—32no—
222C32×#41—32no—
223C32×#41—34no—
224C32×#41—34no—
225C32×#41—32no—
226C32×#41—32no—
227C32×#41—34no—
228C32×#41—34no—
229C32×#41—34no—
230C32×#41—34no—
231C32×#41—34no—
232C32×#41—34no—
233C32×#41—34no—
234C32×#41—34no—
235C32×#41—34no—
236C32×#41—34no—
237C32×#41—34no—
238C32×#41—32no—
239C32×#41—32no—
240C32×#41—32no—
241C32×#41—32no—
242C32×#41—32no—
243C32×#41—32no—
244C32×#41—32no—
245C32×#41C2×A412yescomplemented
246C2×C32×Q8—32no—
247C2×C32×Q8—34no—
248C2×C32×Q8—32no—
249C2×C32×Q8—34no—
250C2×C32×Q8—31no—
251C2×C32×Q8—32no—
252C2×C32×Q8—31no—
253C2×C32×Q8—32no—
254C2×C32×Q8—32no—
255C2×C32×Q8—32no—
256C2×C32×Q8C2×A412yescomplemented
257C2×C32×Q8C2×A412yescomplemented
258C2×C32×D4—32no—
259C2×C32×D4—34no—
260C2×C32×D4—34no—
261C2×C32×D4—32no—
262C2×C32×D4—34no—
263C2×C32×D4—32no—
264C2×C32×D4—34no—
265C2×C32×D4—34no—
266C2×C32×D4—34no—
267C2×C32×D4—34no—
268C2×C32×D4—34no—
269C2×C32×D4—34no—
270C2×C32×D4—34no—
271C2×C32×D4—34no—
272C2×C32×D4—34no—
273C2×C32×D4—34no—
274C2×C32×D4—34no—
275C2×C32×D4—34no—
276C2×C32×D4—34no—
277C2×C32×D4—34no—
278C2×C32×D4—34no—
279C2×C32×D4—34no—
280C2×C32×D4—34no—
281C2×C32×D4—34no—
282C2×C32×D4—31no—
283C2×C32×D4—32no—
284C2×C32×D4—31no—
285C2×C32×D4—32no—
286C2×C32×D4—34no—
287C2×C32×D4—34no—
288C2×C32×D4—34no—
289C2×C32×D4—34no—
290C2×C32×D4—34no—
291C2×C32×D4—34no—
292C2×C32×D4—31no—
293C2×C32×D4—32no—
294C2×C32×D4—31no—
295C2×C32×D4—32no—
296C2×C32×D4—31no—
297C2×C32×D4—32no—
298C2×C32×D4—31no—
299C2×C32×D4—32no—
300C2×C32×D4—34no—
301C2×C32×D4—34no—
302C2×C32×D4—34no—
303C2×C32×D4—34no—
304C2×C32×D4—34no—
305C2×C32×D4—34no—
306C2×C32×D4—31no—
307C2×C32×D4—32no—
308C2×C32×D4—31no—
309C2×C32×D4—32no—
310C2×C32×D4—32no—
311C2×C32×D4—34no—
312C2×C32×D4—34no—
313C2×C32×D4—32no—
314C2×C32×D4—32no—
315C2×C32×D4—34no—
316C2×C32×D4—31no—
317C2×C32×D4—32no—
318C2×C32×D4—31no—
319C2×C32×D4—32no—
320C2×C32×D4—31no—
321C2×C32×D4—31no—
322C2×C32×D4—31no—
323C2×C32×D4—32no—
324C2×C32×D4—32no—
325C2×C32×D4—32no—
326C2×C32×D4—31no—
327C2×C32×D4—32no—
328C2×C32×D4—31no—
329C2×C32×D4—32no—
330C2×C32×D4—31no—
331C2×C32×D4—32no—
332C2×C32×D4—31no—
333C2×C32×D4—32no—
334C2×C32×D4—31no—
335C2×C32×D4—32no—
336C22×C32×C4—34no—
337C22×C32×C4—34no—
338C22×C32×C4—34no—
339C22×C32×C4—31no—
340C22×C32×C4—32no—
341C22×C32×C4—31no—
342C22×C32×C4—32no—
343C22×C32×C4—31no—
344C22×C32×C4—31no—
345C22×C32×C4—32no—
346C22×C32×C4—32no—
347C22×C32×C4—31no—
348C22×C32×C4—32no—
349C22×C32×C4—31no—
350C22×C32×C4—32no—
351C22×C32×C4—31no—
352C22×C32×C4—32no—
353C22×C32×C4—31no—
354C22×C32×C4C2×A411yescharacteristic, complemented
355C22×C32×C4C2×A412yescomplemented
356C3×#41⋊C3—46no—
357C2×C3×SL(2,𝔽3)—46no—
358C2×C3×SL(2,𝔽3)—46no—
359C3×C4×A4—43no—
360C3×C4×A4—46no—
361H(7,𝔽2)H(3,𝔽3)11yescharacteristic, complemented, Sylow
362C22×H(3,𝔽3)—161no—
363C22×H(3,𝔽3)—161no—
364C22⋊H(3,𝔽3)—41no—
365C22⋊H(3,𝔽3)—42no—
366C4×H(3,𝔽3)—161no—
367C3×2−1+4—34no—
368C3×2−1+4—32no—
369C3×2−1+4—32no—
370C3×2−1+4—34no—
371C3×2−1+4—312no—
372C3×2−1+4—36no—
373C3×2−1+4—36no—
374C3×2−1+4—312no—
375C3×2−1+4—36no—
376C3×2−1+4—36no—
377C3×2−1+4—36no—
378C3×2−1+4—32no—
379C3×2−1+4—32no—
380C3×2−1+4—32no—
381C3×2−1+4—32no—
382C3×2−1+4C3×A412yes—
383C3×H(5,𝔽2)—32no—
384C3×H(5,𝔽2)—32no—
385C3×H(5,𝔽2)—36no—
386C3×H(5,𝔽2)—36no—
387C3×H(5,𝔽2)—32no—
388C3×H(5,𝔽2)—34no—
389C3×H(5,𝔽2)—32no—
390C3×H(5,𝔽2)—34no—
391C3×H(5,𝔽2)—36no—
392C3×H(5,𝔽2)—312no—
393C3×H(5,𝔽2)—36no—
394C3×H(5,𝔽2)—312no—
395C3×H(5,𝔽2)—36no—
396C3×H(5,𝔽2)—36no—
397C3×H(5,𝔽2)—36no—
398C3×H(5,𝔽2)—36no—
399C3×H(5,𝔽2)—312no—
400C3×H(5,𝔽2)—312no—
401C3×H(5,𝔽2)—36no—
402C3×H(5,𝔽2)—312no—
403C3×H(5,𝔽2)—312no—
404C3×H(5,𝔽2)—312no—
405C3×H(5,𝔽2)—312no—
406C3×H(5,𝔽2)—312no—
407C3×H(5,𝔽2)—312no—
408C3×H(5,𝔽2)—312no—
409C3×H(5,𝔽2)—312no—
410C3×H(5,𝔽2)—312no—
411C3×H(5,𝔽2)—36no—
412C3×H(5,𝔽2)—312no—
413C3×H(5,𝔽2)—36no—
414C3×H(5,𝔽2)—312no—
415C3×H(5,𝔽2)—32no—
416C3×H(5,𝔽2)—32no—
417C3×H(5,𝔽2)—32no—
418C3×H(5,𝔽2)—32no—
419C3×H(5,𝔽2)—34no—
420C3×H(5,𝔽2)—34no—
421C3×H(5,𝔽2)—32no—
422C3×H(5,𝔽2)—34no—
423C3×H(5,𝔽2)—34no—
424C3×H(5,𝔽2)—34no—
425C3×H(5,𝔽2)—34no—
426C3×H(5,𝔽2)—34no—
427C3×H(5,𝔽2)—34no—
428C3×H(5,𝔽2)—34no—
429C3×H(5,𝔽2)—34no—
430C3×H(5,𝔽2)—34no—
431C3×H(5,𝔽2)—32no—
432C3×H(5,𝔽2)—34no—
433C3×H(5,𝔽2)—32no—
434C3×H(5,𝔽2)—34no—
435C3×H(5,𝔽2)—36no—
436C3×H(5,𝔽2)—33no—
437C3×H(5,𝔽2)—36no—
438C3×H(5,𝔽2)—33no—
439C3×H(5,𝔽2)—33no—
440C3×H(5,𝔽2)—36no—
441C3×H(5,𝔽2)—36no—
442C3×H(5,𝔽2)—32no—
443C3×H(5,𝔽2)—31no—
444C3×H(5,𝔽2)—32no—
445C3×H(5,𝔽2)—31no—
446C3×H(5,𝔽2)—31no—
447C3×H(5,𝔽2)—32no—
448C3×H(5,𝔽2)—32no—
449C3×H(5,𝔽2)—31no—
450C3×H(5,𝔽2)C22×C3211yescharacteristic
451C2×C3×#41—32no—
452C2×C3×#41—34no—
453C2×C3×#41—36no—
454C2×C3×#41—312no—
455C2×C3×#41—312no—
456C2×C3×#41—312no—
457C2×C3×#41—312no—
458C2×C3×#41—312no—
459C2×C3×#41—312no—
460C2×C3×#41—312no—
461C2×C3×#41—36no—
462C2×C3×#41—312no—
463C2×C3×#41—36no—
464C2×C3×#41—312no—
465C2×C3×#41—312no—
466C2×C3×#41—33no—
467C2×C3×#41—36no—
468C2×C3×#41—33no—
469C2×C3×#41—36no—
470C2×C3×#41—33no—
471C2×C3×#41—36no—
472C2×C3×#41—33no—
473C2×C3×#41—36no—
474C2×C3×#41—34no—
475C2×C3×#41—34no—
476C2×C3×#41—34no—
477C2×C3×#41—34no—
478C2×C3×#41—34no—
479C2×C3×#41—34no—
480C2×C3×#41—32no—
481C2×C3×#41—34no—
482C2×C3×#41—32no—
483C2×C3×#41—34no—
484C2×C3×#41—34no—
485C2×C3×#41—31no—
486C2×C3×#41—32no—
487C2×C3×#41—31no—
488C2×C3×#41—32no—
489C2×C3×#41—31no—
490C2×C3×#41—32no—
491C2×C3×#41—31no—
492C2×C3×#41—32no—
493C2×C3×#41—36no—
494C2×C3×#41—36no—
495C2×C3×#41—36no—
496C2×C3×#41—33no—
497C2×C3×#41—36no—
498C2×C3×#41—33no—
499C2×C3×#41—36no—
500C2×C3×#41—32no—
501C2×C3×#41—32no—
502C2×C3×#41—32no—
503C2×C3×#41—31no—
504C2×C3×#41—32no—
505C2×C3×#41—31no—
506C2×C3×#41—32no—
507C22×C3×D4—34no—
508C22×C3×D4—34no—
509C22×C3×D4—34no—
510C22×C3×D4—312no—
511C22×C3×D4—312no—
512C22×C3×D4—312no—
513C22×C3×D4—33no—
514C22×C3×D4—36no—
515C22×C3×D4—33no—
516C22×C3×D4—36no—
517C22×C3×D4—36no—
518C22×C3×D4—33no—
519C22×C3×D4—33no—
520C22×C3×D4—31no—
521C22×C3×D4—32no—
522C22×C3×D4—31no—
523C22×C3×D4—32no—
524C22×C3×D4—32no—
525C22×C3×D4—31no—
526C22×C3×D4—31no—
527C22×C3×D4—33no—
528C22×C3×D4—36no—
529C22×C3×D4—33no—
530C22×C3×D4—36no—
531C22×C3×D4—33no—
532C22×C3×D4—36no—
533C22×C3×D4—33no—
534C22×C3×D4—36no—
535C22×C3×D4—31no—
536C22×C3×D4—32no—
537C22×C3×D4—31no—
538C22×C3×D4—32no—
539C22×C3×D4—31no—
540C22×C3×D4—32no—
541C22×C3×D4—31no—
542C22×C3×D4—32no—
543C22×C3×D4—31no—
544C22×C3×D4—32no—
545C22×C3×D4C3×A411yescharacteristic
546C22×C3×D4C3×A412yes—
547#997—33no—
5482−1+4⋊C3—126no—
549D4×A4—123no—
550D4×A4—126no—
551C23×C32—31no—
552C23×C32—31no—
553C23×C32—32no—
554C23×C32—32no—
555C23×C32—34no—
556C23×C32—34no—
557C23×C32—34no—
558C23×C32—31no—
559C23×C32—31no—
560C23×C32—32no—
561C23×C32—31no—
562C23×C32—32no—
563C23×C32—31no—
564C23×C32—32no—
565C23×C32—31no—
566C23×C32—32no—
567C23×C32—31no—
568C23×C32—32no—
569C23×C32—81no—
570C23×C32—82no—
571C23×C32—241no—
572C23×C32—241no—
573C23×C32—241no—
574C23×C32—242no—
575C23×C32—241no—
576C23×C32—242no—
577C23×C32—241no—
578C23×C32—242no—
579C23×C32C22×A411yescharacteristic
580C23×C32C22×A412yes—
581C2×C3×A4—43no—
582C2×C3×A4—46no—
583C2×C3×A4—83no—
584C2×C3×A4—86no—
585C2×C3×A4—83no—
586C2×C3×A4—86no—
587C32×Q8—32no—
588C32×Q8—32no—
589C32×Q8—34no—
590C32×Q8—32no—
591C32×Q8—32no—
592C32×Q8—34no—
593C32×Q8—32no—
594C32×Q8C22×A412yes—
595C32×D4—32no—
596C32×D4—34no—
597C32×D4—34no—
598C32×D4—34no—
599C32×D4—34no—
600C32×D4—34no—
601C32×D4—34no—
602C32×D4—32no—
603C32×D4—34no—
604C32×D4—32no—
605C32×D4—34no—
606C32×D4—32no—
607C32×D4—34no—
608C32×D4—34no—
609C32×D4—32no—
610C32×D4—34no—
611C32×D4—32no—
612C32×D4—32no—
613C32×D4—32no—
614C32×D4—32no—
615C32×D4—34no—
616C32×D4—32no—
617C32×D4—34no—
618C32×D4—34no—
619C32×D4—34no—
620C32×D4—32no—
621C32×D4—32no—
622C32×D4—31no—
623C32×D4—32no—
624C32×D4—32no—
625C32×D4—31no—
626C32×D4—31no—
627C32×D4—32no—
628C32×D4—163no—
629C32×D4C22⋊A411yescharacteristic
630C2×C32×C4—31no—
631C2×C32×C4—31no—
632C2×C32×C4—32no—
633C2×C32×C4—32no—
634C2×C32×C4—34no—
635C2×C32×C4—32no—
636C2×C32×C4—34no—
637C2×C32×C4—32no—
638C2×C32×C4—34no—
639C2×C32×C4—34no—
640C2×C32×C4—34no—
641C2×C32×C4—34no—
642C2×C32×C4—34no—
643C2×C32×C4—34no—
644C2×C32×C4—34no—
645C2×C32×C4—31no—
646C2×C32×C4—32no—
647C2×C32×C4—34no—
648C2×C32×C4—32no—
649C2×C32×C4—31no—
650C2×C32×C4—32no—
651C2×C32×C4—32no—
652C2×C32×C4—32no—
653C2×C32×C4—32no—
654C2×C32×C4—31no—
655C2×C32×C4—32no—
656C2×C32×C4—31no—
657C2×C32×C4—32no—
658C3×SL(2,𝔽3)—46no—
659#585—32no—
660#585—32no—
661#585—32no—
662#585—31no—
663#585—32no—
664#585C2×H(3,𝔽3)11yescharacteristic, complemented
665C2×H(5,𝔽2)—32no—
666C2×H(5,𝔽2)—31no—
667C2×H(5,𝔽2)—32no—
668C2×H(5,𝔽2)—31no—
669C2×H(5,𝔽2)—32no—
670C2×H(5,𝔽2)—31no—
671C2×H(5,𝔽2)—32no—
672C2×H(5,𝔽2)C2×H(3,𝔽3)11yescharacteristic, complemented
673C2×H(5,𝔽2)C2×H(3,𝔽3)11yescharacteristic, complemented
674C2×H(3,𝔽3)—161no—
675C2×H(3,𝔽3)—321no—
676C2×H(3,𝔽3)—321no—
677C24×C3—33no—
678C24×C3—36no—
679C24×C3—33no—
680C24×C3—36no—
681C24×C3—33no—
682C24×C3—33no—
683C24×C3—31no—
684C24×C3—32no—
685C24×C3—31no—
686C24×C3—32no—
687C24×C3—31no—
688C24×C3—31no—
689C24×C3—31no—
690C24×C3—32no—
691C24×C3—31no—
692C24×C3—32no—
693C24×C3C2×C3×A411yescharacteristic
694C24×C3C2×C3×A412yes—
695C24×C3C2×C3×A411yescharacteristic
696C24×C3C2×C3×A412yes—
697C22×A4—123no—
698C22×A4—126no—
699C22×A4—123no—
700C22×A4—126no—
701C3×#41—32no—
702C3×#41—34no—
703C3×#41—32no—
704C3×#41—34no—
705C3×#41—34no—
706C3×#41—32no—
707C3×#41—32no—
708C3×#41—32no—
709C3×#41—34no—
710C3×#41—34no—
711C3×#41—34no—
712C3×#41—34no—
713C3×#41—32no—
714C3×#41—32no—
715C3×#41—36no—
716C3×#41—312no—
717C3×#41—36no—
718C3×#41—312no—
719C3×#41—312no—
720C3×#41—36no—
721C3×#41—36no—
722C3×#41—36no—
723C3×#41—312no—
724C3×#41—312no—
725C3×#41—312no—
726C3×#41—312no—
727C3×#41—36no—
728C3×#41—36no—
729C3×#41—312no—
730C3×#41—312no—
731C3×#41—312no—
732C3×#41—312no—
733C3×#41—312no—
734C3×#41—312no—
735C3×#41—312no—
736C3×#41—312no—
737C3×#41—312no—
738C3×#41—312no—
739C3×#41—312no—
740C3×#41—312no—
741C3×#41—312no—
742C3×#41—312no—
743C3×#41—312no—
744C3×#41—34no—
745C3×#41—34no—
746C3×#41—34no—
747C3×#41—34no—
748C3×#41—34no—
749C3×#41—34no—
750C3×#41—34no—
751C3×#41—34no—
752C3×#41—34no—
753C3×#41—34no—
754C3×#41—34no—
755C3×#41—34no—
756C3×#41—34no—
757C3×#41—34no—
758C3×#41—34no—
759C3×#41—36no—
760C3×#41—312no—
761C3×#41—312no—
762C3×#41—36no—
763C3×#41—36no—
764C3×#41—312no—
765C3×#41—312no—
766C3×#41—36no—
767C3×#41—36no—
768C3×#41—312no—
769C3×#41—312no—
770C3×#41—312no—
771C3×#41—312no—
772C3×#41—312no—
773C3×#41—312no—
774C3×#41—312no—
775C3×#41—312no—
776C3×#41—312no—
777C3×#41—312no—
778C3×#41—312no—
779C3×#41—36no—
780C3×#41—32no—
781C3×#41—34no—
782C3×#41—34no—
783C3×#41—32no—
784C3×#41—32no—
785C3×#41—34no—
786C3×#41—34no—
787C3×#41—32no—
788C3×#41—32no—
789C3×#41—34no—
790C3×#41—34no—
791C3×#41—34no—
792C3×#41—34no—
793C3×#41—34no—
794C3×#41—34no—
795C3×#41—34no—
796C3×#41—34no—
797C3×#41—34no—
798C3×#41—34no—
799C3×#41—34no—
800C3×#41—32no—
801C3×#41—36no—
802C3×#41—36no—
803C3×#41—36no—
804C3×#41—36no—
805C3×#41—36no—
806C3×#41—36no—
807C3×#41—32no—
808C3×#41—32no—
809C3×#41—32no—
810C3×#41—32no—
811C3×#41—32no—
812C3×#41—32no—
813C3×#41—32no—
814C3×#41C2×C3×A412yes—
815C2×C3×Q8—32no—
816C2×C3×Q8—36no—
817C2×C3×Q8—32no—
818C2×C3×Q8—34no—
819C2×C3×Q8—32no—
820C2×C3×Q8—34no—
821C2×C3×Q8—36no—
822C2×C3×Q8—312no—
823C2×C3×Q8—36no—
824C2×C3×Q8—312no—
825C2×C3×Q8—33no—
826C2×C3×Q8—36no—
827C2×C3×Q8—33no—
828C2×C3×Q8—36no—
829C2×C3×Q8—31no—
830C2×C3×Q8—32no—
831C2×C3×Q8—31no—
832C2×C3×Q8—32no—
833C2×C3×Q8—36no—
834C2×C3×Q8—32no—
835C2×C3×Q8—32no—
836C2×C3×Q8—32no—
837C2×C3×Q8C2×C3×A412yes—
838C2×C3×Q8C2×C3×A412yes—
839C2×C3×D4—32no—
840C2×C3×D4—34no—
841C2×C3×D4—34no—
842C2×C3×D4—32no—
843C2×C3×D4—34no—
844C2×C3×D4—32no—
845C2×C3×D4—36no—
846C2×C3×D4—312no—
847C2×C3×D4—312no—
848C2×C3×D4—36no—
849C2×C3×D4—312no—
850C2×C3×D4—36no—
851C2×C3×D4—312no—
852C2×C3×D4—312no—
853C2×C3×D4—312no—
854C2×C3×D4—312no—
855C2×C3×D4—312no—
856C2×C3×D4—312no—
857C2×C3×D4—312no—
858C2×C3×D4—312no—
859C2×C3×D4—312no—
860C2×C3×D4—312no—
861C2×C3×D4—312no—
862C2×C3×D4—312no—
863C2×C3×D4—34no—
864C2×C3×D4—34no—
865C2×C3×D4—34no—
866C2×C3×D4—34no—
867C2×C3×D4—34no—
868C2×C3×D4—34no—
869C2×C3×D4—34no—
870C2×C3×D4—34no—
871C2×C3×D4—34no—
872C2×C3×D4—34no—
873C2×C3×D4—34no—
874C2×C3×D4—34no—
875C2×C3×D4—33no—
876C2×C3×D4—36no—
877C2×C3×D4—33no—
878C2×C3×D4—36no—
879C2×C3×D4—312no—
880C2×C3×D4—312no—
881C2×C3×D4—312no—
882C2×C3×D4—312no—
883C2×C3×D4—312no—
884C2×C3×D4—312no—
885C2×C3×D4—33no—
886C2×C3×D4—36no—
887C2×C3×D4—33no—
888C2×C3×D4—36no—
889C2×C3×D4—312no—
890C2×C3×D4—312no—
891C2×C3×D4—312no—
892C2×C3×D4—312no—
893C2×C3×D4—312no—
894C2×C3×D4—312no—
895C2×C3×D4—33no—
896C2×C3×D4—36no—
897C2×C3×D4—33no—
898C2×C3×D4—36no—
899C2×C3×D4—312no—
900C2×C3×D4—312no—
901C2×C3×D4—312no—
902C2×C3×D4—312no—
903C2×C3×D4—312no—
904C2×C3×D4—312no—
905C2×C3×D4—33no—
906C2×C3×D4—36no—
907C2×C3×D4—33no—
908C2×C3×D4—36no—
909C2×C3×D4—36no—
910C2×C3×D4—312no—
911C2×C3×D4—312no—
912C2×C3×D4—36no—
913C2×C3×D4—36no—
914C2×C3×D4—312no—
915C2×C3×D4—33no—
916C2×C3×D4—36no—
917C2×C3×D4—33no—
918C2×C3×D4—36no—
919C2×C3×D4—31no—
920C2×C3×D4—32no—
921C2×C3×D4—31no—
922C2×C3×D4—32no—
923C2×C3×D4—34no—
924C2×C3×D4—34no—
925C2×C3×D4—34no—
926C2×C3×D4—34no—
927C2×C3×D4—34no—
928C2×C3×D4—34no—
929C2×C3×D4—31no—
930C2×C3×D4—32no—
931C2×C3×D4—31no—
932C2×C3×D4—32no—
933C2×C3×D4—34no—
934C2×C3×D4—34no—
935C2×C3×D4—34no—
936C2×C3×D4—34no—
937C2×C3×D4—34no—
938C2×C3×D4—34no—
939C2×C3×D4—31no—
940C2×C3×D4—32no—
941C2×C3×D4—31no—
942C2×C3×D4—32no—
943C2×C3×D4—34no—
944C2×C3×D4—34no—
945C2×C3×D4—34no—
946C2×C3×D4—34no—
947C2×C3×D4—34no—
948C2×C3×D4—34no—
949C2×C3×D4—31no—
950C2×C3×D4—32no—
951C2×C3×D4—31no—
952C2×C3×D4—32no—
953C2×C3×D4—32no—
954C2×C3×D4—34no—
955C2×C3×D4—34no—
956C2×C3×D4—32no—
957C2×C3×D4—32no—
958C2×C3×D4—34no—
959C2×C3×D4—31no—
960C2×C3×D4—32no—
961C2×C3×D4—31no—
962C2×C3×D4—32no—
963C2×C3×D4—33no—
964C2×C3×D4—36no—
965C2×C3×D4—33no—
966C2×C3×D4—33no—
967C2×C3×D4—33no—
968C2×C3×D4—36no—
969C2×C3×D4—36no—
970C2×C3×D4—36no—
971C2×C3×D4—33no—
972C2×C3×D4—36no—
973C2×C3×D4—33no—
974C2×C3×D4—36no—
975C2×C3×D4—33no—
976C2×C3×D4—36no—
977C2×C3×D4—33no—
978C2×C3×D4—36no—
979C2×C3×D4—31no—
980C2×C3×D4—32no—
981C2×C3×D4—31no—
982C2×C3×D4—31no—
983C2×C3×D4—31no—
984C2×C3×D4—32no—
985C2×C3×D4—32no—
986C2×C3×D4—32no—
987C2×C3×D4—31no—
988C2×C3×D4—32no—
989C2×C3×D4—31no—
990C2×C3×D4—32no—
991C2×C3×D4—31no—
992C2×C3×D4—32no—
993C2×C3×D4—31no—
994C2×C3×D4—32no—
995C22×C3×C4—312no—
996C22×C3×C4—312no—
997C22×C3×C4—312no—
998C22×C3×C4—34no—
999C22×C3×C4—34no—
1000C22×C3×C4—34no—
1001C22×C3×C4—33no—
1002C22×C3×C4—36no—
1003C22×C3×C4—33no—
1004C22×C3×C4—36no—
1005C22×C3×C4—33no—
1006C22×C3×C4—33no—
1007C22×C3×C4—36no—
1008C22×C3×C4—36no—
1009C22×C3×C4—33no—
1010C22×C3×C4—36no—
1011C22×C3×C4—33no—
1012C22×C3×C4—36no—
1013C22×C3×C4—33no—
1014C22×C3×C4—36no—
1015C22×C3×C4—33no—
1016C22×C3×C4—31no—
1017C22×C3×C4—32no—
1018C22×C3×C4—31no—
1019C22×C3×C4—32no—
1020C22×C3×C4—31no—
1021C22×C3×C4—31no—
1022C22×C3×C4—32no—
1023C22×C3×C4—32no—
1024C22×C3×C4—31no—
1025C22×C3×C4—32no—
1026C22×C3×C4—31no—
1027C22×C3×C4—32no—
1028C22×C3×C4—31no—
1029C22×C3×C4—32no—
1030C22×C3×C4—31no—
1031C22×C3×C4—31no—
1032C22×C3×C4—32no—
1033C22×C3×C4C2×C3×A411yescharacteristic
1034C22×C3×C4C2×C3×A412yes—
1035#41⋊C3—126no—
1036C2×SL(2,𝔽3)—126no—
1037C2×SL(2,𝔽3)—126no—
1038C4×A4—123no—
1039C4×A4—126no—
1040C22×C32—31no—
1041C22×C32—32no—
1042C22×C32—31no—
1043C22×C32—32no—
1044C22×C32—31no—
1045C22×C32—32no—
1046C22×C32—32no—
1047C22×C32—41no—
1048C22×C32—121no—
1049C22×C32—122no—
1050C22×C32—121no—
1051C22×C32—122no—
1052C22×C32—121no—
1053C22×C32—122no—
1054C22×C32—121no—
1055C22×C32—122no—
1056C22×C32—121no—
1057C22×C32—121no—
1058C22×C32—121no—
1059C22×C32—121no—
1060C22×C32—124no—
1061C22×C32—122no—
1062C22×C32—122no—
1063C22×C32—124no—
1064C22×C32—124no—
1065C22×C32—122no—
1066C22×C32—122no—
1067C22×C32—163no—
1068C22×C32—163no—
1069C22×C32C2×C22⋊A411yescharacteristic
1070C22×C32C2×C22⋊A411yescharacteristic
1071C3×A4—43no—
1072C3×A4—46no—
1073C32×C4—32no—
1074C32×C4—32no—
1075C32×C4—32no—
1076C32×C4—32no—
1077C32×C4—31no—
1078C32×C4—163no—
1079C32×C4C2×C22⋊A411yescharacteristic
10802−1+4—34no—
10812−1+4—32no—
10822−1+4—32no—
10832−1+4—34no—
10842−1+4—32no—
10852−1+4—32no—
10862−1+4—32no—
10872−1+4C22⋊H(3,𝔽3)12yescomplemented
1088H(5,𝔽2)—32no—
1089H(5,𝔽2)—32no—
1090H(5,𝔽2)—32no—
1091H(5,𝔽2)—34no—
1092H(5,𝔽2)—32no—
1093H(5,𝔽2)—34no—
1094H(5,𝔽2)—32no—
1095H(5,𝔽2)—32no—
1096H(5,𝔽2)—32no—
1097H(5,𝔽2)—32no—
1098H(5,𝔽2)—34no—
1099H(5,𝔽2)—34no—
1100H(5,𝔽2)—32no—
1101H(5,𝔽2)—34no—
1102H(5,𝔽2)—34no—
1103H(5,𝔽2)—34no—
1104H(5,𝔽2)—34no—
1105H(5,𝔽2)—34no—
1106H(5,𝔽2)—34no—
1107H(5,𝔽2)—34no—
1108H(5,𝔽2)—34no—
1109H(5,𝔽2)—34no—
1110H(5,𝔽2)—32no—
1111H(5,𝔽2)—34no—
1112H(5,𝔽2)—32no—
1113H(5,𝔽2)—34no—
1114H(5,𝔽2)—32no—
1115H(5,𝔽2)—31no—
1116H(5,𝔽2)—32no—
1117H(5,𝔽2)—31no—
1118H(5,𝔽2)—31no—
1119H(5,𝔽2)—32no—
1120H(5,𝔽2)—32no—
1121H(5,𝔽2)C22×H(3,𝔽3)11yescharacteristic
1122C2×#41—32no—
1123C2×#41—34no—
1124C2×#41—34no—
1125C2×#41—34no—
1126C2×#41—34no—
1127C2×#41—34no—
1128C2×#41—34no—
1129C2×#41—34no—
1130C2×#41—32no—
1131C2×#41—34no—
1132C2×#41—32no—
1133C2×#41—34no—
1134C2×#41—34no—
1135C2×#41—31no—
1136C2×#41—32no—
1137C2×#41—31no—
1138C2×#41—32no—
1139C2×#41—31no—
1140C2×#41—32no—
1141C2×#41—31no—
1142C2×#41—32no—
1143C2×#41—32no—
1144C2×#41—32no—
1145C2×#41—32no—
1146C2×#41—31no—
1147C2×#41—32no—
1148C2×#41—31no—
1149C2×#41—32no—
1150C22×D4—34no—
1151C22×D4—34no—
1152C22×D4—34no—
1153C22×D4—31no—
1154C22×D4—32no—
1155C22×D4—31no—
1156C22×D4—32no—
1157C22×D4—32no—
1158C22×D4—31no—
1159C22×D4—31no—
1160C22×D4—31no—
1161C22×D4—32no—
1162C22×D4—31no—
1163C22×D4—32no—
1164C22×D4—31no—
1165C22×D4—32no—
1166C22×D4—31no—
1167C22×D4—32no—
1168C22×D4C22⋊H(3,𝔽3)11yescharacteristic, complemented
1169C22×D4C22⋊H(3,𝔽3)12yescomplemented
1170H(3,𝔽3)—161noSylow
1171C23×C3—33no—
1172C23×C3—33no—
1173C23×C3—33no—
1174C23×C3—36no—
1175C23×C3—36no—
1176C23×C3—33no—
1177C23×C3—36no—
1178C23×C3—312no—
1179C23×C3—312no—
1180C23×C3—312no—
1181C23×C3—31no—
1182C23×C3—31no—
1183C23×C3—31no—
1184C23×C3—32no—
1185C23×C3—32no—
1186C23×C3—31no—
1187C23×C3—32no—
1188C23×C3—34no—
1189C23×C3—34no—
1190C23×C3—34no—
1191C23×C3—33no—
1192C23×C3—36no—
1193C23×C3—33no—
1194C23×C3—36no—
1195C23×C3—33no—
1196C23×C3—36no—
1197C23×C3—33no—
1198C23×C3—36no—
1199C23×C3—31no—
1200C23×C3—32no—
1201C23×C3—31no—
1202C23×C3—32no—
1203C23×C3—31no—
1204C23×C3—32no—
1205C23×C3—31no—
1206C23×C3—32no—
1207C23×C3—31no—
1208C23×C3—32no—
1209C23×C3—81no—
1210C23×C3—82no—
1211C23×C3—241no—
1212C23×C3—242no—
1213C23×C3—241no—
1214C23×C3—242no—
1215C23×C3—241no—
1216C23×C3—242no—
1217C23×C3—241no—
1218C23×C3—241no—
1219C23×C3—241no—
1220C23×C3—242no—
1221C23×C3—241no—
1222C23×C3—242no—
1223C23×C3—243no—
1224C23×C3—243no—
1225C23×C3—243no—
1226C23×C3—246no—
1227C23×C3—243no—
1228C23×C3—246no—
1229C23×C3C22×C3×A411yescharacteristic
1230C23×C3C22×C3×A412yes—
1231C2×A4—123no—
1232C2×A4—126no—
1233C2×A4—243no—
1234C2×A4—246no—
1235C2×A4—243no—
1236C2×A4—246no—
1237C3×Q8—32no—
1238C3×Q8—32no—
1239C3×Q8—36no—
1240C3×Q8—36no—
1241C3×Q8—36no—
1242C3×Q8—312no—
1243C3×Q8—312no—
1244C3×Q8—36no—
1245C3×Q8—32no—
1246C3×Q8—34no—
1247C3×Q8—34no—
1248C3×Q8—32no—
1249C3×Q8—36no—
1250C3×Q8—32no—
1251C3×Q8—32no—
1252C3×Q8C22×C3×A412yes—
1253C3×D4—32no—
1254C3×D4—36no—
1255C3×D4—312no—
1256C3×D4—36no—
1257C3×D4—36no—
1258C3×D4—312no—
1259C3×D4—312no—
1260C3×D4—36no—
1261C3×D4—312no—
1262C3×D4—312no—
1263C3×D4—312no—
1264C3×D4—312no—
1265C3×D4—312no—
1266C3×D4—312no—
1267C3×D4—36no—
1268C3×D4—312no—
1269C3×D4—36no—
1270C3×D4—312no—
1271C3×D4—312no—
1272C3×D4—312no—
1273C3×D4—312no—
1274C3×D4—36no—
1275C3×D4—36no—
1276C3×D4—36no—
1277C3×D4—312no—
1278C3×D4—36no—
1279C3×D4—34no—
1280C3×D4—32no—
1281C3×D4—32no—
1282C3×D4—34no—
1283C3×D4—34no—
1284C3×D4—32no—
1285C3×D4—34no—
1286C3×D4—34no—
1287C3×D4—34no—
1288C3×D4—34no—
1289C3×D4—34no—
1290C3×D4—34no—
1291C3×D4—32no—
1292C3×D4—34no—
1293C3×D4—32no—
1294C3×D4—34no—
1295C3×D4—34no—
1296C3×D4—34no—
1297C3×D4—34no—
1298C3×D4—32no—
1299C3×D4—32no—
1300C3×D4—32no—
1301C3×D4—34no—
1302C3×D4—32no—
1303C3×D4—36no—
1304C3×D4—36no—
1305C3×D4—33no—
1306C3×D4—36no—
1307C3×D4—36no—
1308C3×D4—33no—
1309C3×D4—33no—
1310C3×D4—36no—
1311C3×D4—32no—
1312C3×D4—32no—
1313C3×D4—31no—
1314C3×D4—32no—
1315C3×D4—32no—
1316C3×D4—31no—
1317C3×D4—31no—
1318C3×D4—32no—
1319C3×D4—31no—
1320C3×D4—483no—
1321C3×D4C3×C22⋊A411yescharacteristic
1322C2×C3×C4—33no—
1323C2×C3×C4—36no—
1324C2×C3×C4—36no—
1325C2×C3×C4—312no—
1326C2×C3×C4—36no—
1327C2×C3×C4—312no—
1328C2×C3×C4—312no—
1329C2×C3×C4—36no—
1330C2×C3×C4—33no—
1331C2×C3×C4—33no—
1332C2×C3×C4—36no—
1333C2×C3×C4—36no—
1334C2×C3×C4—312no—
1335C2×C3×C4—312no—
1336C2×C3×C4—312no—
1337C2×C3×C4—312no—
1338C2×C3×C4—312no—
1339C2×C3×C4—312no—
1340C2×C3×C4—312no—
1341C2×C3×C4—33no—
1342C2×C3×C4—36no—
1343C2×C3×C4—31no—
1344C2×C3×C4—32no—
1345C2×C3×C4—32no—
1346C2×C3×C4—34no—
1347C2×C3×C4—32no—
1348C2×C3×C4—34no—
1349C2×C3×C4—34no—
1350C2×C3×C4—32no—
1351C2×C3×C4—31no—
1352C2×C3×C4—31no—
1353C2×C3×C4—32no—
1354C2×C3×C4—32no—
1355C2×C3×C4—34no—
1356C2×C3×C4—34no—
1357C2×C3×C4—34no—
1358C2×C3×C4—34no—
1359C2×C3×C4—34no—
1360C2×C3×C4—34no—
1361C2×C3×C4—34no—
1362C2×C3×C4—31no—
1363C2×C3×C4—32no—
1364C2×C3×C4—36no—
1365C2×C3×C4—36no—
1366C2×C3×C4—36no—
1367C2×C3×C4—33no—
1368C2×C3×C4—36no—
1369C2×C3×C4—33no—
1370C2×C3×C4—36no—
1371C2×C3×C4—32no—
1372C2×C3×C4—32no—
1373C2×C3×C4—32no—
1374C2×C3×C4—31no—
1375C2×C3×C4—32no—
1376C2×C3×C4—31no—
1377C2×C3×C4—32no—
1378SL(2,𝔽3)—126no—
1379C2×C32—21no—
1380C2×C32—21no—
1381C2×C32—61no—
1382C2×C32—61no—
1383C2×C32—62no—
1384C2×C32—61no—
1385C2×C32—62no—
1386C2×C32—62no—
1387C2×C32—62no—
1388C2×C32—163no—
1389C2×C32—323no—
1390C2×C32—323no—
1391C2×C32C22×C22⋊A411yescharacteristic
1392C24—31no—
1393C24—32no—
1394C24—31no—
1395C24—32no—
1396C24—31no—
1397C24—31no—
1398C24C2×C22⋊H(3,𝔽3)11yescharacteristic, complemented
1399C24C2×C22⋊H(3,𝔽3)12yescomplemented
1400C24C2×C22⋊H(3,𝔽3)11yescharacteristic, complemented
1401C24C2×C22⋊H(3,𝔽3)12yescomplemented
1402#41—32no—
1403#41—34no—
1404#41—32no—
1405#41—34no—
1406#41—34no—
1407#41—32no—
1408#41—32no—
1409#41—32no—
1410#41—34no—
1411#41—34no—
1412#41—34no—
1413#41—34no—
1414#41—32no—
1415#41—32no—
1416#41—34no—
1417#41—34no—
1418#41—34no—
1419#41—34no—
1420#41—34no—
1421#41—34no—
1422#41—34no—
1423#41—34no—
1424#41—34no—
1425#41—34no—
1426#41—34no—
1427#41—34no—
1428#41—34no—
1429#41—34no—
1430#41—34no—
1431#41—32no—
1432#41—34no—
1433#41—34no—
1434#41—32no—
1435#41—32no—
1436#41—34no—
1437#41—34no—
1438#41—32no—
1439#41—32no—
1440#41—34no—
1441#41—34no—
1442#41—34no—
1443#41—34no—
1444#41—34no—
1445#41—34no—
1446#41—34no—
1447#41—34no—
1448#41—34no—
1449#41—34no—
1450#41—34no—
1451#41—32no—
1452#41—32no—
1453#41—32no—
1454#41—32no—
1455#41—32no—
1456#41—32no—
1457#41—32no—
1458#41C2×C22⋊H(3,𝔽3)12yescomplemented
1459C2×Q8—32no—
1460C2×Q8—32no—
1461C2×Q8—34no—
1462C2×Q8—32no—
1463C2×Q8—34no—
1464C2×Q8—31no—
1465C2×Q8—32no—
1466C2×Q8—31no—
1467C2×Q8—32no—
1468C2×Q8—32no—
1469C2×Q8C2×C22⋊H(3,𝔽3)12yescomplemented
1470C2×Q8C2×C22⋊H(3,𝔽3)12yescomplemented
1471C2×D4—32no—
1472C2×D4—34no—
1473C2×D4—34no—
1474C2×D4—32no—
1475C2×D4—34no—
1476C2×D4—32no—
1477C2×D4—34no—
1478C2×D4—34no—
1479C2×D4—34no—
1480C2×D4—34no—
1481C2×D4—34no—
1482C2×D4—34no—
1483C2×D4—34no—
1484C2×D4—34no—
1485C2×D4—34no—
1486C2×D4—34no—
1487C2×D4—34no—
1488C2×D4—34no—
1489C2×D4—31no—
1490C2×D4—32no—
1491C2×D4—31no—
1492C2×D4—32no—
1493C2×D4—34no—
1494C2×D4—34no—
1495C2×D4—34no—
1496C2×D4—34no—
1497C2×D4—34no—
1498C2×D4—34no—
1499C2×D4—31no—
1500C2×D4—32no—
1501C2×D4—31no—
1502C2×D4—32no—
1503C2×D4—34no—
1504C2×D4—34no—
1505C2×D4—34no—
1506C2×D4—34no—
1507C2×D4—34no—
1508C2×D4—34no—
1509C2×D4—31no—
1510C2×D4—32no—
1511C2×D4—31no—
1512C2×D4—32no—
1513C2×D4—34no—
1514C2×D4—34no—
1515C2×D4—34no—
1516C2×D4—34no—
1517C2×D4—34no—
1518C2×D4—34no—
1519C2×D4—31no—
1520C2×D4—32no—
1521C2×D4—31no—
1522C2×D4—32no—
1523C2×D4—32no—
1524C2×D4—34no—
1525C2×D4—34no—
1526C2×D4—32no—
1527C2×D4—32no—
1528C2×D4—34no—
1529C2×D4—31no—
1530C2×D4—32no—
1531C2×D4—31no—
1532C2×D4—32no—
1533C2×D4—31no—
1534C2×D4—32no—
1535C2×D4—31no—
1536C2×D4—31no—
1537C2×D4—31no—
1538C2×D4—32no—
1539C2×D4—32no—
1540C2×D4—32no—
1541C2×D4—31no—
1542C2×D4—32no—
1543C2×D4—31no—
1544C2×D4—32no—
1545C2×D4—31no—
1546C2×D4—32no—
1547C2×D4—31no—
1548C2×D4—32no—
1549C22×C4—34no—
1550C22×C4—34no—
1551C22×C4—34no—
1552C22×C4—31no—
1553C22×C4—32no—
1554C22×C4—31no—
1555C22×C4—32no—
1556C22×C4—31no—
1557C22×C4—31no—
1558C22×C4—32no—
1559C22×C4—32no—
1560C22×C4—31no—
1561C22×C4—32no—
1562C22×C4—31no—
1563C22×C4—32no—
1564C22×C4—31no—
1565C22×C4—32no—
1566C22×C4—31no—
1567C22×C4C2×C22⋊H(3,𝔽3)11yescharacteristic, complemented
1568C22×C4C2×C22⋊H(3,𝔽3)12yescomplemented
1569C22×C3—33no—
1570C22×C3—36no—
1571C22×C3—33no—
1572C22×C3—36no—
1573C22×C3—33no—
1574C22×C3—36no—
1575C22×C3—36no—
1576C22×C3—31no—
1577C22×C3—32no—
1578C22×C3—31no—
1579C22×C3—32no—
1580C22×C3—31no—
1581C22×C3—32no—
1582C22×C3—32no—
1583C22×C3—31no—
1584C22×C3—31no—
1585C22×C3—41no—
1586C22×C3—121no—
1587C22×C3—121no—
1588C22×C3—122no—
1589C22×C3—121no—
1590C22×C3—122no—
1591C22×C3—122no—
1592C22×C3—121no—
1593C22×C3—122no—
1594C22×C3—121no—
1595C22×C3—122no—
1596C22×C3—123no—
1597C22×C3—126no—
1598C22×C3—123no—
1599C22×C3—126no—
1600C22×C3—122no—
1601C22×C3—123no—
1602C22×C3—126no—
1603C22×C3—123no—
1604C22×C3—126no—
1605C22×C3—123no—
1606C22×C3—123no—
1607C22×C3—123no—
1608C22×C3—123no—
1609C22×C3—126no—
1610C22×C3—126no—
1611C22×C3—126no—
1612C22×C3—1212no—
1613C22×C3—1212no—
1614C22×C3—1212no—
1615C22×C3—121no—
1616C22×C3—121no—
1617C22×C3—121no—
1618C22×C3—121no—
1619C22×C3—122no—
1620C22×C3—122no—
1621C22×C3—122no—
1622C22×C3—124no—
1623C22×C3—124no—
1624C22×C3—124no—
1625C22×C3—483no—
1626C22×C3—483no—
1627C22×C3C2×C3×C22⋊A411yescharacteristic
1628C22×C3C2×C3×C22⋊A411yescharacteristic
1629A4—123no—
1630A4—126no—
1631C3×C4—36no—
1632C3×C4—36no—
1633C3×C4—36no—
1634C3×C4—36no—
1635C3×C4—33no—
1636C3×C4—32no—
1637C3×C4—32no—
1638C3×C4—32no—
1639C3×C4—32no—
1640C3×C4—31no—
1641C3×C4—31no—
1642C3×C4—483no—
1643C3×C4C2×C3×C22⋊A411yescharacteristic
1644C32—163no—
1645C32#8754711yescharacteristic, complemented
1646C23—31no—
1647C23—31no—
1648C23—31no—
1649C23—32no—
1650C23—32no—
1651C23—31no—
1652C23—32no—
1653C23—34no—
1654C23—34no—
1655C23—34no—
1656C23—31no—
1657C23—32no—
1658C23—31no—
1659C23—32no—
1660C23—31no—
1661C23—32no—
1662C23—31no—
1663C23—32no—
1664C23—81no—
1665C23—82no—
1666C23—241no—
1667C23—242no—
1668C23—241no—
1669C23—241no—
1670C23—241no—
1671C23—242no—
1672C23—241no—
1673C23—242no—
1674C23C22×C22⋊H(3,𝔽3)11yescharacteristic
1675C23C22×C22⋊H(3,𝔽3)12yes—
1676Q8—32no—
1677Q8—32no—
1678Q8—32no—
1679Q8—34no—
1680Q8—34no—
1681Q8—32no—
1682Q8—32no—
1683Q8C22×C22⋊H(3,𝔽3)12yes—
1684D4—32no—
1685D4—34no—
1686D4—32no—
1687D4—32no—
1688D4—34no—
1689D4—34no—
1690D4—32no—
1691D4—34no—
1692D4—34no—
1693D4—34no—
1694D4—34no—
1695D4—34no—
1696D4—34no—
1697D4—32no—
1698D4—34no—
1699D4—32no—
1700D4—34no—
1701D4—34no—
1702D4—34no—
1703D4—34no—
1704D4—32no—
1705D4—32no—
1706D4—32no—
1707D4—34no—
1708D4—32no—
1709D4—32no—
1710D4—32no—
1711D4—31no—
1712D4—32no—
1713D4—32no—
1714D4—31no—
1715D4—31no—
1716D4—32no—
1717D4C32⋊(C22⋊A4)11yescharacteristic
1718C2×C4—31no—
1719C2×C4—32no—
1720C2×C4—32no—
1721C2×C4—34no—
1722C2×C4—32no—
1723C2×C4—34no—
1724C2×C4—34no—
1725C2×C4—32no—
1726C2×C4—31no—
1727C2×C4—31no—
1728C2×C4—32no—
1729C2×C4—32no—
1730C2×C4—34no—
1731C2×C4—34no—
1732C2×C4—34no—
1733C2×C4—34no—
1734C2×C4—34no—
1735C2×C4—34no—
1736C2×C4—34no—
1737C2×C4—31no—
1738C2×C4—32no—
1739C2×C4—32no—
1740C2×C4—32no—
1741C2×C4—32no—
1742C2×C4—31no—
1743C2×C4—32no—
1744C2×C4—31no—
1745C2×C4—32no—
1746C2×C3—21no—
1747C2×C3—21no—
1748C2×C3—31no—
1749C2×C3—61no—
1750C2×C3—61no—
1751C2×C3—63no—
1752C2×C3—66no—
1753C2×C3—66no—
1754C2×C3—63no—
1755C2×C3—66no—
1756C2×C3—63no—
1757C2×C3—66no—
1758C2×C3—61no—
1759C2×C3—62no—
1760C2×C3—62no—
1761C2×C3—61no—
1762C2×C3—62no—
1763C2×C3—61no—
1764C2×C3—62no—
1765C2×C3—483no—
1766C2×C3—963no—
1767C2×C3—963no—
1768C2×C3C22×C3×C22⋊A411yescharacteristic
1769C22—31no—
1770C22—32no—
1771C22—31no—
1772C22—32no—
1773C22—31no—
1774C22—32no—
1775C22—32no—
1776C22—41no—
1777C22—121no—
1778C22—122no—
1779C22—121no—
1780C22—122no—
1781C22—122no—
1782C22—121no—
1783C22—122no—
1784C22—121no—
1785C22—122no—
1786C22—121no—
1787C22—121no—
1788C22—121no—
1789C22—121no—
1790C22—122no—
1791C22—122no—
1792C22—122no—
1793C22—124no—
1794C22—124no—
1795C22—124no—
1796C22C2×C32⋊(C22⋊A4)11yescharacteristic
1797C22C2×C32⋊(C22⋊A4)11yescharacteristic
1798C4—32no—
1799C4—32no—
1800C4—32no—
1801C4—32no—
1802C4—31no—
1803C4C2×C32⋊(C22⋊A4)11yescharacteristic
1804C3—31no—
1805C3—483no—
1806C3C3×#8754711yescharacteristic
1807C2—21no—
1808C2—21no—
1809C2—61no—
1810C2—62no—
1811C2—62no—
1812C2—61no—
1813C2—62no—
1814C2—61no—
1815C2—62no—
1816C2C22×C32⋊(C22⋊A4)11yescharacteristic
subgroupG/H
center, Frattini, socleC2×C3C22×C3×C22⋊A4
commutator, cosocleC3×H(5,𝔽2)C22×C32
FittingC32×H(7,𝔽2)C3
hypercenterC32×D4C22⋊A4
hypocenterH(5,𝔽2)C22×H(3,𝔽3)
LCSG ▷ C3×H(5,𝔽2) ▷ H(5,𝔽2)
UCSC1 ◁ C2×C3 ◁ C32×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13164890C2semidirect
2. C2×C32⋊#997C2semidirect
3. C2×C32⋊#997C2semidirect
4. C3×#87547C3semidirect
5. C32×H(7,𝔽2)C3semidirect
6. C32⋊#997C22semidirect
15. C32×#585C2×C3semidirect
23. C2×C32×H(5,𝔽2)C2×C3semidirect
24. C2×C32×H(5,𝔽2)C2×C3semidirect
25. C3×#5950C2×C3semidirect
26. C2×C3×#997C2×C3semidirect
27. C2×C3×#997C2×C3semidirect
47. C32×2−1+4A4semidirect
128. C22×C32×D4A4semidirect
129. C22×C32×D4A4semidirect
130. C3×#997C22×C3semidirect
181. C24×C32C2×A4semidirect
182. C24×C32C2×A4semidirect
183. C24×C32C2×A4semidirect
184. C24×C32C2×A4semidirect
245. C32×#41C2×A4semidirect
256. C2×C32×Q8C2×A4semidirect
257. C2×C32×Q8C2×A4semidirect
354. C22×C32×C4C2×A4semidirect
355. C22×C32×C4C2×A4semidirect
361. H(7,𝔽2)H(3,𝔽3)semidirect
664. #585C2×H(3,𝔽3)semidirect
672. C2×H(5,𝔽2)C2×H(3,𝔽3)semidirect
673. C2×H(5,𝔽2)C2×H(3,𝔽3)semidirect
1087. 2−1+4C22⋊H(3,𝔽3)semidirect
1168. C22×D4C22⋊H(3,𝔽3)semidirect
1169. C22×D4C22⋊H(3,𝔽3)semidirect
1398. C24C2×C22⋊H(3,𝔽3)semidirect
1399. C24C2×C22⋊H(3,𝔽3)semidirect
1400. C24C2×C22⋊H(3,𝔽3)semidirect
1401. C24C2×C22⋊H(3,𝔽3)semidirect
1458. #41C2×C22⋊H(3,𝔽3)semidirect
1469. C2×Q8C2×C22⋊H(3,𝔽3)semidirect
1470. C2×Q8C2×C22⋊H(3,𝔽3)semidirect
1567. C22×C4C2×C22⋊H(3,𝔽3)semidirect
1568. C22×C4C2×C22⋊H(3,𝔽3)semidirect
1645. C32#87547semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131648902
C2×C32⋊#9972
C3×#875473
C32×H(7,𝔽2)3
2−1+4⋊H(3,𝔽3)4
D4×C22⋊H(3,𝔽3)4