Finite Group Databasebeta

← #11802765

Subgroups — #11802765

Order 1152.

1439 conjugacy classes of subgroups.

The subgroup lattice has 967 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
2#10592368C211yesmaximal, characteristic, complemented
3C3×#4669C211yesmaximal, characteristic, complemented
4C3×#4666C211yesmaximal, characteristic, complemented
5#10591399C211yesmaximal, characteristic
6#10591399C211yesmaximal, characteristic
7#10591369C211yesmaximal, characteristic, complemented
8#10591366C211yesmaximal, characteristic, complemented
9#10591289C211yesmaximal, characteristic, complemented
10#10591286C211yesmaximal, characteristic, complemented
11#10591280C211yesmaximal, characteristic, complemented
12#10591279C211yesmaximal, characteristic, complemented
13C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
14#10591202C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#75825—31nomaximal
17#73567—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3750C2211yescharacteristic, complemented
25C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C3×C4×Dic3C2211yescharacteristic, complemented
33C2×C3×C4×Dic3C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C2×#3724C2211yescharacteristic, complemented
36C2×Dic3⋊Dic3C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45D3×(C2×D3)⋊C4C418yescomplemented
46C32×#95C2211yescharacteristic, complemented
47#63658C2211yescharacteristic, complemented
48C3×C3⋊#95C2211yescharacteristic, complemented
49C3×C3⋊#95C2211yescharacteristic, complemented
50#63579C2211yescharacteristic, complemented
51#63579C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54C22×(C2×D3)⋊C4—31no—
55C2×D3×C22⋊C4—31no—
56C3×#388—31no—
57C3×C4×C22⋊C4—31no—
58C4×#217—31no—
59#4990—31no—
60#4987—31no—
61#4955—31no—
62#4955—31no—
63#4955—31no—
64#4955—31no—
65#4951—31no—
66#4945—31no—
67#4944—31no—
68#4942—31no—
69#4942—31no—
70#4940—31no—
71#4940—31no—
72#4940—31no—
73#4940—31no—
74#4940—31no—
75C4×(C2×D3)⋊C4—31no—
76#4670—31no—
77#4669—31no—
78#4669—31no—
79#4669—31no—
80#4669—31no—
81#4669—61no—
82#4669D311yescharacteristic, complemented
83#4667—31no—
84#4666D311yescharacteristic, complemented
85C23×C3⋊D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×D32—22no—
89C22×D32—22no—
90C22×D32—41no—
91C22×D32—41no—
92C22×D32—41no—
93C22×D32—41no—
94C22×D32C2×C414yes—
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×C4×D3—41no—
108C2×C3×C4×D3—41no—
109C2×C3×C4×D3C2×C414yes—
110C2×D3×Dic3—41no—
111C2×D3×Dic3—41no—
112C2×D3×Dic3C2×C414yes—
113#3752—41no—
114#3752—41no—
115#3752C2×C414yes—
116#3750—41no—
117C4×C3⋊Dic3—41no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×(C2×D3)⋊C4—41no—
121C3×(C2×D3)⋊C4—41no—
122C3×(C2×D3)⋊C4C2×C414yes—
123C3×Dic3⋊C4—41no—
124C3×C4×Dic3—41no—
125C3×C4×Dic3—41no—
126C3×C4×Dic3—41no—
127#3724—41no—
128Dic3⋊Dic3—41no—
129#3722—41no—
130#3722—41no—
131#3722C2×C414yes—
132(C2×D3)⋊Dic3—22no—
133(C2×D3)⋊Dic3—22no—
134(C2×D3)⋊Dic3—41no—
135(C2×D3)⋊Dic3—41no—
136(C2×D3)⋊Dic3C2×C414yes—
137#2312—91noSylow
138C24×D3—31no—
139C24×D3—31no—
140C23×C3×C4—31no—
141C23×Dic3—31no—
142C22×C4×D3—31no—
143C22×C4×D3C2×D311yescharacteristic
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C42—31no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—38no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—61no—
177C2×(C2×D3)⋊C4—61no—
178C2×(C2×D3)⋊C4—61no—
179C2×(C2×D3)⋊C4C2×D311yescharacteristic
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×C4⋊Dic3—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—61no—
191C2×Dic3⋊C4C2×D311yescharacteristic, complemented
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—61no—
195C2×C4×Dic3C2×D311yescharacteristic, complemented
196C2×C4×Dic3C2×D311yescharacteristic, complemented
197C2×C4×Dic3C2×D311yescharacteristic, complemented
198D3×C22⋊C4—38no—
199C3×#95—21no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95C2×D311yescharacteristic, complemented
203C3×#95C2×D311yescharacteristic, complemented
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic, complemented
216C3⋊#95C2×D311yescharacteristic, complemented
217C23×C32C2411yescharacteristic
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3C22×C412yes—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3C22×C412yes—
236C22×C3×D3C22×C412yes—
237C22×C3×D3#4112yes—
238C22×C3×D3#4112yes—
239C2×D32—28no—
240C2×D32—44no—
241C2×D32—44no—
242C2×D32—44no—
243C2×D32—44no—
244C2×D32—44no—
245C2×D32—44no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C22×C412yes—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C22×C412yes—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C22×C412yes—
281C2×C3×Dic3C22×C412yes—
282C3×C4×D3—44no—
283D3×Dic3—44no—
284C22×C22⋊C4—91no—
285#388—31no—
286#388—91no—
287#388—91no—
288#388—91no—
289#388—91no—
290#388—91no—
291#388—91no—
292#388—91no—
293#380—91no—
294#380—91no—
295#379—91no—
296#379—91no—
297C4×C22⋊C4—31no—
298C4×C22⋊C4—91no—
299C24×C3—31no—
300C24×C3—31no—
301C23×D3—31no—
302C23×D3—31no—
303C23×D3—34no—
304C23×D3—34no—
305C23×D3—61no—
306C23×D3—62no—
307C23×D3—62no—
308C23×D3—62no—
309C23×D3—62no—
310C23×D3—121no—
311C23×D3—121no—
312C23×D3—121no—
313C23×D3—121no—
314C23×D3—121no—
315C23×D3—121no—
316C23×D3—121no—
317C23×D3—121no—
318C23×D3C22×D311yescharacteristic
319C23×D3C22×D311yescharacteristic
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—34no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—121no—
331C22×C3×C4—121no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—34no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—121no—
349C22×Dic3—121no—
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C2×C4×D3—34no—
357C2×C4×D3—41no—
358C2×C4×D3—41no—
359C2×C4×D3—121no—
360C2×C4×D3—121no—
361C2×C4×D3C4×D314yes—
362C3×C4⋊C4—121no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—62no—
366C3×C22⋊C4—121no—
367C3×C22⋊C4—121no—
368C3×C42—121no—
369C3×C42—121no—
370C3×C42—121no—
371#217—34no—
372#217—62no—
373#217—62no—
374#217—121no—
375#217—121no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—22no—
378(C2×D3)⋊C4—34no—
379(C2×D3)⋊C4—34no—
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—34no—
383(C2×D3)⋊C4—41no—
384(C2×D3)⋊C4—41no—
385(C2×D3)⋊C4—64no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4—121no—
390(C2×D3)⋊C4—121no—
391(C2×D3)⋊C4—121no—
392(C2×D3)⋊C4—121no—
393(C2×D3)⋊C4—121no—
394(C2×D3)⋊C4—121no—
395(C2×D3)⋊C4—121no—
396(C2×D3)⋊C4—122no—
397(C2×D3)⋊C4—122no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4C4×D314yes—
401C4⋊Dic3—121no—
402Dic3⋊C4—41no—
403Dic3⋊C4—121no—
404Dic3⋊C4—121no—
405Dic3⋊C4—121no—
406Dic3⋊C4—121no—
407Dic3⋊C4—121no—
408Dic3⋊C4—122no—
409C4×Dic3—41no—
410C4×Dic3—41no—
411C4×Dic3—41no—
412C4×Dic3—121no—
413C4×Dic3—121no—
414C4×Dic3—122no—
415C22×C32C23×C411yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C22×C32H(5,𝔽2)11yescharacteristic
419C22×C32H(5,𝔽2)11yescharacteristic
420C22×C32H(5,𝔽2)11yescharacteristic
421C22×C32H(5,𝔽2)11yescharacteristic
422C2×C3⋊D3—22no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3#11714yes—
443D32—416no—
444C32×C4—22no—
445C32×C4—41no—
446C32×C4—41no—
447C3⋊Dic3—22no—
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C25—91no—
457C23×C4—31no—
458C23×C4—91no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—31no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—98no—
469C2×C22⋊C4—91no—
470C2×C22⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C42—31no—
481C2×C42—31no—
482C2×C42—31no—
483C2×C42—91no—
484#95—31no—
485#95—31no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95D3211yescharacteristic, complemented
492C23×C3—21no—
493C23×C3—32no—
494C23×C3—32no—
495C23×C3—32no—
496C23×C3—32no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3C23×D311yescharacteristic
508C23×C3C23×D311yescharacteristic
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—32no—
520C22×D3—32no—
521C22×D3—62no—
522C22×D3—68no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—68no—
536C22×D3—121no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—121no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—124no—
543C22×D3—124no—
544C22×D3—124no—
545C22×D3—124no—
546C22×D3—124no—
547C22×D3—124no—
548C22×D3—124no—
549C22×D3—124no—
550C22×D3—124no—
551C22×D3—124no—
552C22×D3—124no—
553C22×D3—124no—
554C22×D3C2×C4×D312yes—
555C22×D3C2×C4×D312yes—
556C22×D3#23512yes—
557C22×D3#23512yes—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—22no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—124no—
602C2×C3×C4C2×C4×D312yes—
603C2×C3×C4C2×C4×D312yes—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—62no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—124no—
648C2×Dic3C2×C4×D312yes—
649C2×Dic3C2×C4×D312yes—
650C4×D3—44no—
651C4×D3—124no—
652C2×C32C2×#11711yescharacteristic
653C2×C32#51811yescharacteristic
654C2×C32#51811yescharacteristic
655C2×C32#53811yescharacteristic
656C2×C32#53811yescharacteristic
657C2×C32#53811yescharacteristic
658C2×C32#53811yescharacteristic
659C3⋊D3—42no—
660C3×D3—24no—
661C3×D3—42no—
662C24—31no—
663C24—31no—
664C24—94no—
665C24—91no—
666C24—182no—
667C24—182no—
668C24—361no—
669C24—361no—
670C24—361no—
671C24—361no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—34no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—94no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—121no—
684C22×C4—121no—
685C22×C4—361no—
686C22×C4—361no—
687C22×C4C2×D3211yescharacteristic
688C22×C4C2×D3211yescharacteristic
689C22×C4C2×D3211yescharacteristic
690C4⋊C4—121no—
691C4⋊C4—361no—
692C4⋊C4—361no—
693C4⋊C4—361no—
694C22⋊C4—34no—
695C22⋊C4—62no—
696C22⋊C4—62no—
697C22⋊C4—94no—
698C22⋊C4—94no—
699C22⋊C4—94no—
700C22⋊C4—121no—
701C22⋊C4—121no—
702C22⋊C4—182no—
703C22⋊C4—182no—
704C22⋊C4—361no—
705C22⋊C4—361no—
706C22⋊C4—361no—
707C22⋊C4—361no—
708C22⋊C4—361no—
709C22⋊C4—361no—
710C42—121no—
711C42—121no—
712C42—121no—
713C42—361no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—34no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3C22×C4×D311yescharacteristic
736C22×C3C22×C4×D311yescharacteristic
737C22×C3C2×#23511yescharacteristic
738C22×C3C2×#23511yescharacteristic
739C22×C3#100411yescharacteristic
740C22×C3#100411yescharacteristic
741C22×C3#100411yescharacteristic
742C22×C3#100411yescharacteristic
743C22×C3D3×#4111yescharacteristic
744C22×C3D3×#4111yescharacteristic
745C22×C3#100911yescharacteristic
746C22×C3#100911yescharacteristic
747C22×C3#100911yescharacteristic
748C22×C3#100911yescharacteristic
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—62no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—122no—
771C2×D3—1216no—
772C2×D3—1216no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3#87214yes—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—42no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—62no—
794C3×C4—62no—
795C3×C4—81no—
796C3×C4—81no—
797C3×C4—121no—
798C3×C4—121no—
799C3×C4—121no—
800C3×C4—121no—
801Dic3—22no—
802Dic3—22no—
803Dic3—41no—
804Dic3—41no—
805Dic3—41no—
806Dic3—41no—
807Dic3—62no—
808Dic3—62no—
809Dic3—122no—
810Dic3—122no—
811Dic3—122no—
812Dic3—121no—
813Dic3—121no—
814Dic3—121no—
815Dic3—121no—
816C32#231211yescharacteristic, complemented, Sylow
817C23—32no—
818C23—32no—
819C23—32no—
820C23—32no—
821C23—61no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—92no—
832C23—188no—
833C23—181no—
834C23—181no—
835C23—181no—
836C23—181no—
837C23—181no—
838C23—181no—
839C23—364no—
840C23—364no—
841C23—364no—
842C23—364no—
843C23—364no—
844C23—364no—
845C23C22×D3211yescharacteristic
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—92no—
873C2×C4—124no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—364no—
883C2×C4C4×D3212yes—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—64no—
892C2×C3—122no—
893C2×C3C2×#87211yescharacteristic
894C2×C3#548611yescharacteristic
895C2×C3D3×#11711yescharacteristic
896C2×C3#552111yescharacteristic
897C2×C3#554511yescharacteristic
898C2×C3#554511yescharacteristic
899C2×C3#556011yescharacteristic
900C2×C3#556011yescharacteristic
901C2×C3#556011yescharacteristic
902C2×C3#556011yescharacteristic
903C2×C3#561311yescharacteristic
904C2×C3#565711yescharacteristic
905C2×C3#567811yescharacteristic
906C2×C3#570411yescharacteristic
907D3—24no—
908D3—42no—
909D3—122no—
910D3—122no—
911D3—242no—
912C22—34no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—62no—
921C22—62no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—182no—
927C22—182no—
928C22—182no—
929C22—3616no—
930C22—361no—
931C22—361no—
932C22—361no—
933C22—361no—
934C22C2×C4×D3211yescharacteristic
935C22D3×#23511yescharacteristic
936C22D3×#23511yescharacteristic
937C22#6431311yescharacteristic
938C22#6431411yescharacteristic
939C22#6431411yescharacteristic
940C22#6432011yescharacteristic
941C4—22no—
942C4—41no—
943C4—41no—
944C4—62no—
945C4—62no—
946C4—121no—
947C4—121no—
948C4—121no—
949C4—121no—
950C4—182no—
951C4—361no—
952C4—361no—
953C3—21no—
954C3#7356711yescharacteristic, complemented
955C3#7582511yescharacteristic, complemented
956C2—64no—
957C2—122no—
958C2—362no—
959C2D3×#87211yescharacteristic
960C2#1059425411yescharacteristic
961C2#1059429711yescharacteristic
962C2#1059429811yescharacteristic
963C2#1059460411yescharacteristic
964C2#1059463811yescharacteristic
965C2#1059463911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenter#95D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592368C2semidirect
3. C3×#4669C2semidirect
4. C3×#4666C2semidirect
7. #10591369C2semidirect
8. #10591366C2semidirect
9. #10591289C2semidirect
10. #10591286C2semidirect
11. #10591280C2semidirect
12. #10591279C2semidirect
13. C4×(C2×D3)⋊Dic3C2semidirect
14. #10591202C2semidirect
15. #10591194C2semidirect
24. C2×#3750C22semidirect
25. C2×C4×C3⋊Dic3C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
32. C2×C3×C4×Dic3C22semidirect
33. C2×C3×C4×Dic3C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C2×#3724C22semidirect
36. C2×Dic3⋊Dic3C22semidirect
45. D3×(C2×D3)⋊C4C4semidirect
46. C32×#95C22semidirect
47. #63658C22semidirect
48. C3×C3⋊#95C22semidirect
49. C3×C3⋊#95C22semidirect
50. #63579C22semidirect
51. #63579C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
82. #4669D3semidirect
84. #4666D3semidirect
191. C2×Dic3⋊C4C2×D3semidirect
195. C2×C4×Dic3C2×D3semidirect
196. C2×C4×Dic3C2×D3semidirect
197. C2×C4×Dic3C2×D3semidirect
202. C3×#95C2×D3semidirect
203. C3×#95C2×D3semidirect
215. C3⋊#95C2×D3semidirect
216. C3⋊#95C2×D3semidirect
491. #95D32semidirect
816. C32#2312semidirect
954. C3#73567semidirect
955. C3#75825semidirect

Maximal subgroups

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

subgroupindex
C2×D3×(C2×D3)⋊C42
#105923682
C3×#46692
C3×#46662
#105913992
#105913692
#105913662
#105912892
#105912862
#105912802
#105912792
C4×(C2×D3)⋊Dic32
#105912022
#105911942
#758253
#735673