Finite Group Databasebeta

← #11810348

Subgroups — #11810348

Order 1152.

1771 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic, complemented
2C2×#63977C211yesmaximal, characteristic
3C2×D3×#217C211yesmaximal, characteristic, complemented
4C2×#63881C211yesmaximal, characteristic, complemented
5C3×#4955C211yesmaximal, characteristic, complemented
6C3×#4952C211yesmaximal, characteristic, complemented
7#10591712C211yesmaximal, characteristic, complemented
8#10591703C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591379C211yesmaximal, characteristic, complemented
11#10591369C211yesmaximal, characteristic, complemented
12#10591364C211yesmaximal, characteristic, complemented
13#10591316C211yesmaximal, characteristic, complemented
14#10591303C211yesmaximal, characteristic, complemented
15#10591292C211yesmaximal, characteristic, complemented
16#77669—31nomaximal
17#73826—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C2×#3750C2211yescharacteristic, complemented
30#64092—24no—
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39#63977—24no—
40D3×#217—24no—
41C2×#3724C2211yescharacteristic, complemented
42C2×Dic3⋊Dic3C2211yescharacteristic, complemented
43C2×#3722C2211yescharacteristic, complemented
44C2×#3722C2211yescharacteristic, complemented
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic, complemented
50#63881—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#953—31no—
58C22×#217—31no—
59C2×#893—31no—
60C2×#883—31no—
61C2×#883—31no—
62C2×#883—61no—
63C2×#882—31no—
64C2×#67⋊C4—31no—
65C2×D3×C22⋊C4—31no—
66C3×#397—31no—
67C3×#379—31no—
68#4993—31no—
69#4961—31no—
70#4959—31no—
71#4959—31no—
72#4958—31no—
73#4956—31no—
74#4955D311yescharacteristic, complemented
75#4952D311yescharacteristic, complemented
76#4951—31no—
77#4950—31no—
78#4949—31no—
79#4945—31no—
80#4944—31no—
81#4942—31no—
82#4672—31no—
83#4670—31no—
84#4668—31no—
85#4667—31no—
86#4665—31no—
87#4665—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—22no—
102C2×#638—22no—
103C2×#638—41no—
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—41no—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—41no—
121C2×#626D414yes—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—41no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—22no—
129#3757D414yescomplemented
130#3752—22no—
131C4⋊(C3⋊Dic3)—22no—
132#3750—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—41no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—41no—
140C3×Dic3⋊C4—22no—
141#3724—41no—
142Dic3⋊Dic3—41no—
143#3722—22no—
144#3722—41no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149Dic32—22no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—61no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C22×D12—31no—
161C22×D12—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—61no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—21no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4C2×D311yescharacteristic
177C2×C3×C22⋊C4C2×D311yescharacteristic
178#953—64no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—61no—
186C2×#217—64no—
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189C2×#217C2×D311yescharacteristic
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—61no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—61no—
215C2×Dic3⋊C4C2×D311yescharacteristic, complemented
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218#893—64no—
219#883—64no—
220#883—64no—
221#883—68no—
222#882—64no—
223#67⋊C4—64no—
224D3×C22⋊C4—64no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2×D412yes—
244C23×C32C2411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3C2×D412yes—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—28no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3—44no—
269C22×C3×D3C2×D412yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C22×C3×D3#4112yes—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279#638—44no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3C2×D412yes—
288C2×C3⋊Dic3C2×D412yes—
289C4×C3⋊D3—44no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D412yes—
308#626—28no—
309#626—44no—
310D3×Dic3—44no—
311D3×Dic3—44no—
312C2×#123—91no—
313C2×#120—91no—
314C2×C4×D4—91no—
315C22×C22⋊C4—91no—
316#399—91no—
317#397—31no—
318#394—91no—
319#394—91no—
320#388—91no—
321#388—91no—
322#386—91no—
323#386—91no—
324#385—91no—
325#380—91no—
326#379—31no—
327C24×C3—21no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—31no—
345C23×D3—31no—
346C23×D3—41no—
347C23×D3—41no—
348C23×D3—61no—
349C23×D3C22×D311yescharacteristic
350C23×D3C22×D311yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C2×#67—34no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—64no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—122no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—122no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3—62no—
391C22×Dic3—121no—
392C22×Dic3—121no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×D12—34no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—121no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—64no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—122no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—122no—
420C3×C4⋊C4—62no—
421C3×C22⋊C4—24no—
422C3×C22⋊C4—22no—
423C3×C22⋊C4—22no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—62no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—121no—
430C3×C22⋊C4—121no—
431#217—22no—
432#217—22no—
433#217—34no—
434#217—34no—
435#217—41no—
436#217—64no—
437#217—62no—
438#217—62no—
439#217—62no—
440#217—62no—
441(C2×D3)⋊C4—22no—
442(C2×D3)⋊C4—22no—
443(C2×D3)⋊C4—22no—
444(C2×D3)⋊C4—41no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—64no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—121no—
455(C2×D3)⋊C4—121no—
456C4⋊Dic3—62no—
457C4⋊Dic3—62no—
458C4⋊Dic3—64no—
459C4⋊Dic3—121no—
460Dic3⋊C4—22no—
461Dic3⋊C4—62no—
462Dic3⋊C4—62no—
463Dic3⋊C4—64no—
464Dic3⋊C4—121no—
465Dic3⋊C4—121no—
466Dic3⋊C4—121no—
467C4×Dic3—62no—
468C4×Dic3—62no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32C22×D411yescharacteristic
477C22×C32C22×D411yescharacteristic
478C22×C32C2×#4111yescharacteristic
479C22×C32C2×#4111yescharacteristic
480C22×C32C2×#4111yescharacteristic
481C22×C32H(5,𝔽2)11yescharacteristic
482C22×C32H(5,𝔽2)11yescharacteristic
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—41no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—416no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3#12314yescomplemented
505C32×C4—41no—
506C32×C4—41no—
507C3⋊Dic3—22no—
508C3⋊Dic3—22no—
509C3⋊Dic3—41no—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C25—31no—
517C22×D4—91no—
518C22×D4—91no—
519C22×D4—91no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523#123—184no—
524#120—184no—
525C4×D4—184no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—184no—
547C2×C22⋊C4D3211yescharacteristic
548C2×C42—91no—
549#95—31no—
550#95—31no—
551#95—31no—
552#95—91no—
553#95—91no—
554#95—91no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—22no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—68no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3—124no—
595C23×C3—124no—
596C23×C3D3×D412yes—
597C23×C3D3×D412yes—
598C23×C3C23×D311yescharacteristic
599C23×C3C23×D311yescharacteristic
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—28no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—44no—
614C22×D3—44no—
615C22×D3—44no—
616C22×D3—44no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—121no—
635C22×D3—121no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3#23512yes—
639C22×D3D3×D412yes—
640C22×D3#23712yes—
641C22×D3#23712yes—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—32no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678#67—68no—
679#67—124no—
680#67—124no—
681#67—124no—
682#67—128no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—62no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—124no—
728C2×Dic3—124no—
729C2×Dic3D3×D412yes—
730D12—68no—
731D12—124no—
732C4×D3—124no—
733C4×D3—124no—
734C4×D3—124no—
735C4×D3—124no—
736C4×D3—128no—
737C2×C32—42no—
738C2×C32C2×#12311yescharacteristic
739C2×C32#52511yescharacteristic
740C2×C32#53811yescharacteristic
741C2×C32D4211yescharacteristic
742C2×C32#54611yescharacteristic
743C2×C32#54611yescharacteristic
744C2×C32#55111yescharacteristic
745C3⋊D3—42no—
746C3×D3—24no—
747C3×D3—42no—
748C24—31no—
749C24—31no—
750C24—62no—
751C24—62no—
752C24—62no—
753C24—62no—
754C24—62no—
755C24—91no—
756C24—121no—
757C24—121no—
758C24C2×D3211yescharacteristic
759C2×D4—94no—
760C2×D4—182no—
761C2×D4—182no—
762C2×D4—182no—
763C2×D4—182no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—361no—
767C2×D4—361no—
768C22×C4—31no—
769C22×C4—31no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—182no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—361no—
784C22×C4—361no—
785C22×C4—361no—
786C22×C4C2×D3211yescharacteristic
787C22×C4C2×D3211yescharacteristic
788C4⋊C4—62no—
789C4⋊C4—182no—
790C4⋊C4—182no—
791C4⋊C4—361no—
792C4⋊C4—361no—
793C22⋊C4—22no—
794C22⋊C4—62no—
795C22⋊C4—62no—
796C22⋊C4—62no—
797C22⋊C4—62no—
798C22⋊C4—62no—
799C22⋊C4—94no—
800C22⋊C4—121no—
801C22⋊C4—121no—
802C22⋊C4—182no—
803C22⋊C4—182no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—361no—
809C42—182no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—34no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—1216no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3C2×#23511yescharacteristic
854C22×C3C2×D3×D411yescharacteristic
855C22×C3C2×D3×D411yescharacteristic
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C22×C3C2×#23711yescharacteristic
859C22×C3C2×#23711yescharacteristic
860C22×C3#100411yescharacteristic
861C22×C3#100411yescharacteristic
862C22×C3D3×#4111yescharacteristic
863C22×C3D3×#4111yescharacteristic
864C22×C3D3×#4111yescharacteristic
865C22×C3#100911yescharacteristic
866C22×C3#100911yescharacteristic
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—416no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—64no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—122no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—121no—
895C2×D3—121no—
896C2×D3—121no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3#88314yescomplemented
903C3×C4—42no—
904C3×C4—42no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—41no—
908C3×C4—41no—
909C3×C4—62no—
910C3×C4—121no—
911C3×C4—121no—
912C3×C4—121no—
913C3×C4—121no—
914C3×C4—121no—
915Dic3—22no—
916Dic3—41no—
917Dic3—41no—
918Dic3—41no—
919Dic3—41no—
920Dic3—41no—
921Dic3—62no—
922Dic3—62no—
923Dic3—62no—
924Dic3—62no—
925Dic3—122no—
926Dic3—122no—
927Dic3—122no—
928Dic3—121no—
929Dic3—121no—
930C32#241811yescharacteristic, complemented, Sylow
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—32no—
938C23—32no—
939C23—32no—
940C23—32no—
941C23—68no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—92no—
953C23—124no—
954C23—124no—
955C23—124no—
956C23—124no—
957C23—124no—
958C23—124no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23—181no—
963C23—181no—
964C23—181no—
965C23#381112yes—
966C23C22×D3211yescharacteristic
967D4—188no—
968D4—364no—
969D4—364no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—32no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—92no—
995C2×C4—92no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—364no—
1004C2×C4—364no—
1005C2×C4—364no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—42no—
1014C2×C3—42no—
1015C2×C3—64no—
1016C2×C3—82no—
1017C2×C3—122no—
1018C2×C3C2×#88311yescharacteristic
1019C2×C3#549011yescharacteristic
1020C2×C3#549511yescharacteristic
1021C2×C3#558611yescharacteristic
1022C2×C3#559011yescharacteristic
1023C2×C3#559111yescharacteristic
1024C2×C3#559311yescharacteristic
1025C2×C3#560911yescharacteristic
1026C2×C3D3×#12311yescharacteristic
1027C2×C3#565411yescharacteristic
1028C2×C3#565611yescharacteristic
1029C2×C3#567611yescharacteristic
1030C2×C3#570411yescharacteristic
1031C2×C3#570511yescharacteristic
1032D3—24no—
1033D3—42no—
1034D3—124no—
1035D3—122no—
1036D3—122no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—34no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—1216no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—121no—
1059C22—182no—
1060C22—182no—
1061C22—182no—
1062C22—361no—
1063C22—361no—
1064C22—361no—
1065C22—361no—
1066C22D3×#23511yescharacteristic
1067C22#6430711yescharacteristic
1068C22D32×D411yescharacteristic
1069C22D3×#23711yescharacteristic
1070C22D3×#23711yescharacteristic
1071C22#6431411yescharacteristic
1072C22C2×#381111yescharacteristic
1073C4—41no—
1074C4—41no—
1075C4—62no—
1076C4—121no—
1077C4—121no—
1078C4—121no—
1079C4—121no—
1080C4—121no—
1081C4—182no—
1082C4—182no—
1083C4—361no—
1084C3—21no—
1085C3#7382611yescharacteristic, complemented
1086C3#7766911yescharacteristic, complemented
1087C2—42no—
1088C2—64no—
1089C2—122no—
1090C2—362no—
1091C2#1059409311yescharacteristic
1092C2#1059412711yescharacteristic
1093C2D3×#88311yescharacteristic
1094C2#1059428111yescharacteristic
1095C2#1059507711yescharacteristic
1096C2#1059516011yescharacteristic
1097C2#1059529211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63977C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64092C2semidirect
3. C2×D3×#217C2semidirect
4. C2×#63881C2semidirect
5. C3×#4955C2semidirect
6. C3×#4952C2semidirect
7. #10591712C2semidirect
8. #10591703C2semidirect
9. #10591387C2semidirect
10. #10591379C2semidirect
11. #10591369C2semidirect
12. #10591364C2semidirect
13. #10591316C2semidirect
14. #10591303C2semidirect
15. #10591292C2semidirect
20. C22×C4×C3⋊D3C22semidirect
27. C2×#3752C22semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×#3750C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
41. C2×#3724C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×#3722C22semidirect
44. C2×#3722C22semidirect
49. C2×Dic32C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
74. #4955D3semidirect
75. #4952D3semidirect
129. #3757D4semidirect
215. C2×Dic3⋊C4C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
236. C3⋊#95C2×D3semidirect
504. C2×C3×D3#123semidirect
902. C2×D3#883semidirect
930. C32#2418semidirect
1085. C3#73826semidirect
1086. C3#77669semidirect

Maximal subgroups

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

subgroupindex
C2×#640922
C2×#639772
C2×D3×#2172
C2×#638812
C3×#49552
C3×#49522
#105917122
#105917032
#105913872
#105913792
#105913692
#105913642
#105913162
#105913032
#105912922
#776693
#738263