Finite Group Databasebeta

← #11872808

Subgroups — #11872808

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5625C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic
3#10592745C211yesmaximal, characteristic
4C3×#5045C211yesmaximal, characteristic, complemented
5#10591565C211yesmaximal, characteristic, complemented
6#10591565C211yesmaximal, characteristic, complemented
7#10591540C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10591183C211yesmaximal, characteristic
10#10591102C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590470C211yesmaximal, characteristic, complemented
13#10590468C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#83447—31nomaximal
17#81498—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic, complemented
23C3×#944C2211yescharacteristic, complemented
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#890—21no—
28C3×#890C2211yescharacteristic, complemented
29C3×#889—21no—
30C3×#887C2211yescharacteristic, complemented
31C3×#879—21no—
32C3×#879—21no—
33#63974—21no—
34#63974—21no—
35#63894—21no—
36#63894—21no—
37#63894C2211yescharacteristic
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63657C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#541—31no—
62#5625D311yescharacteristic, complemented
63#5521—31no—
64#5521—31no—
65C3×#485—31no—
66#5083—31no—
67#5083—31no—
68#5066—31no—
69#5066—31no—
70#5046—31no—
71#5046—31no—
72#5046—31no—
73#5046—61no—
74#5045—31no—
75#5045D311yescharacteristic, complemented
76#5026—31no—
77#5026—31no—
78C4×#215—31no—
79C4×#215—31no—
80#5000—31no—
81#4996—31no—
82#4891—31no—
83#4889—31no—
84#4871—31no—
85#4852—31no—
86#4818—31no—
87#4818—31no—
88#4817—31no—
89#4788—31no—
90#4731—31no—
91#4720—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#624—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×#624—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108#3755—22no—
109#3755—22no—
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#217—21no—
113C3×#217—21no—
114C3×#217D411yescharacteristic
115C3×#217D411yescharacteristic
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3D411yescharacteristic
119C3×C4⋊Dic3D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3717—22no—
140#3717—22no—
141#3123—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#126—61no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8C2×D311yescharacteristic
154C3×C22⋊Q8C2×D311yescharacteristic
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×#117—31no—
158C3×#117—31no—
159Q8×Dic3C2×D311yescharacteristic, complemented
160#944C2×D311yescharacteristic, complemented
161C2×#215—31no—
162C2×#215—31no—
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—61no—
168C2×#215—61no—
169#926C2×D311yescharacteristic
170#926C2×D311yescharacteristic
171#924C2×D311yescharacteristic
172C2×#204—31no—
173C2×#204—31no—
174#893—31no—
175#893—31no—
176#893—31no—
177#893—31no—
178#893—61no—
179#893—61no—
180#890—21no—
181#890C2×D311yescharacteristic, complemented
182#889—21no—
183#887C2×D311yescharacteristic, complemented
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#879—21no—
189#879—21no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—61no—
195C4×D12—61no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#835C2×D311yescharacteristic, complemented
204#835C2×D311yescharacteristic, complemented
205#830—31no—
206#830—31no—
207#830—61no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#815—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215#810—31no—
216#810—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#809—61no—
225#808—31no—
226#808—31no—
227#808C2×D311yescharacteristic, complemented
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic, complemented
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3—81no—
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C4⋊(C3⋊D3)—24no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4⋊(C3⋊D3)#4112yes—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×Dic6—21no—
263C3×Dic6—21no—
264#624—81no—
265#624—81no—
266#624—81no—
267#624—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
273#518—91no—
274#485—31no—
275#485—91no—
276#478—91no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C23×D3—61no—
288C23×D3—61no—
289C23×D3—121no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C22×D311yescharacteristic
294C22×C3×C4—21no—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C2×D12—31no—
298C2×D12—31no—
299C2×D12—31no—
300C2×D12—31no—
301C2×D12—61no—
302C2×D12—61no—
303C2×D12—62no—
304C2×D12—62no—
305C2×D12—62no—
306C2×D12—62no—
307C2×D12—61no—
308C2×D12—61no—
309C2×D12—122no—
310C2×D12—122no—
311C2×D12—121no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×Dic6C22×D311yescharacteristic
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—41no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42—61no—
353#217—21no—
354#217—21no—
355#217#6711yescharacteristic
356#217#6711yescharacteristic
357#215—62no—
358#215—62no—
359#215—62no—
360#215—62no—
361#215—62no—
362#215—62no—
363#215—122no—
364#215—122no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373C4⋊Dic3—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3#6711yescharacteristic
376C4⋊Dic3#6711yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3C22×D311yescharacteristic
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398#204—62no—
399#204—62no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—84no—
411C32×C4—21no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C22×D4—91no—
425C2×SD16—91no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×SD16—91no—
429C4⋊Q8—31no—
430#126—61no—
431#126—61no—
432#125—31no—
433#125—61no—
434#125—61no—
435C22⋊Q8—31no—
436C22⋊Q8D3211yescharacteristic
437C4×Q8—31no—
438C4×Q8—31no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—181no—
444C4×D4—181no—
445#117—31no—
446#117—31no—
447C2×C22⋊C4—181no—
448C2×C22⋊C4—181no—
449#107—31no—
450#107—91no—
451#106—31no—
452#106—91no—
453C4⋊C8—91no—
454C4⋊C8—91no—
455#103—31no—
456#103—31no—
457#103—91no—
458#103—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—31no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—91no—
467C23×C3—21no—
468C23×C3D3×D411yescharacteristic
469C23×C3C2×#6711yescharacteristic
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—121no—
477C22×D3—121no—
478C22×D3—124no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—242no—
484C22×D3—242no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3C2×#6711yescharacteristic
524C2×Dic3C2×#6711yescharacteristic
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527D12—32no—
528D12—32no—
529D12—32no—
530D12—32no—
531D12—62no—
532D12—62no—
533D12—64no—
534D12—64no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—124no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550Dic6—21no—
551Dic6—21no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C3⋊C8—121no—
562C2×C32—41no—
563C2×C32#52511yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—42no—
567C3⋊D3—42no—
568C24—181no—
569C2×Q8—31no—
570C2×Q8C2×D3211yescharacteristic
571C2×D4—91no—
572C2×D4—91no—
573C2×D4—182no—
574C2×D4—182no—
575C2×D4—181no—
576C22×C4—181no—
577C22×C4—181no—
578C22×C4—181no—
579C22×C4—181no—
580C22×C4C2×D3211yescharacteristic
581SD16—182no—
582SD16—182no—
583SD16—182no—
584SD16—182no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—91no—
589C4⋊C4—21no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—21no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C42—31no—
613C42—31no—
614C42—61no—
615C42—61no—
616C42—61no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×#6711yescharacteristic
629C2×D3—62no—
630C2×D3—62no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—122no—
634C2×D3—122no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—241no—
644C2×D3—241no—
645C2×D3—241no—
646C2×D3—241no—
647C2×D3—244no—
648C2×D3—244no—
649C2×D3—248no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681C32#312311yescharacteristic, complemented, Sylow
682C23—184no—
683C23—181no—
684C23—181no—
685C23—721no—
686C23—721no—
687C23D3×#6711yescharacteristic
688Q8—21no—
689Q8—21no—
690Q8—61no—
691Q8—61no—
692D4—92no—
693D4—92no—
694D4—184no—
695D4—181no—
696D4—181no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—721no—
710C2×C4—721no—
711C2×C4—721no—
712C2×C4—721no—
713C2×C4D3×#6711yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—61no—
716C8—61no—
717C8—181no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3#565611yescharacteristic
726C2×C3#577011yescharacteristic
727C2×C3#577811yescharacteristic
728C2×C3#582811yescharacteristic
729C2×C3#583711yescharacteristic
730C2×C3#583711yescharacteristic
731D3—122no—
732D3—122no—
733D3—122no—
734D3—122no—
735D3—242no—
736D3—242no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—182no—
741C22—182no—
742C22—361no—
743C22—361no—
744C22—361no—
745C22—361no—
746C22—724no—
747C22C2×D3×#6711yescharacteristic
748C4—21no—
749C4—41no—
750C4—41no—
751C4—61no—
752C4—61no—
753C4—61no—
754C4—61no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4#6431211yescharacteristic
760C4#6431211yescharacteristic
761C3—21no—
762C3#8149811yescharacteristic, complemented
763C3#8344711yescharacteristic, complemented
764C2—41no—
765C2—362no—
766C2—362no—
767C2#1059515911yescharacteristic
768C2#1059531911yescharacteristic
769C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22⋊Q8D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5625C2semidirect
4. C3×#5045C2semidirect
5. #10591565C2semidirect
6. #10591565C2semidirect
7. #10591540C2semidirect
8. #10591536C2semidirect
10. #10591102C2semidirect
11. #10591056C2semidirect
12. #10590470C2semidirect
13. #10590468C2semidirect
14. #10590458C2semidirect
15. #10590457C2semidirect
22. C3×Q8×Dic3C22semidirect
23. C3×#944C22semidirect
28. C3×#890C22semidirect
30. C3×#887C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5625D3semidirect
75. #5045D3semidirect
159. Q8×Dic3C2×D3semidirect
160. #944C2×D3semidirect
181. #890C2×D3semidirect
183. #887C2×D3semidirect
203. #835C2×D3semidirect
204. #835C2×D3semidirect
227. #808C2×D3semidirect
230. #807C2×D3semidirect
681. C32#3123semidirect
762. C3#81498semidirect
763. C3#83447semidirect

Maximal subgroups

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

subgroupindex
C3×#56252
#105949962
#105927452
C3×#50452
#105915652
#105915402
#105915362
#105911832
#105911022
#105910562
#105904702
#105904682
#105904582
#105904572
#834473
#814983