Finite Group Databasebeta

← #11889399

Subgroups — #11889399

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5513C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic
3C2×#63637C211yesmaximal, characteristic, complemented
4C3×#4971C211yesmaximal, characteristic, complemented
5#10591190C211yesmaximal, characteristic, complemented
6#10591188C211yesmaximal, characteristic, complemented
7#10591158C211yesmaximal, characteristic
8#10590604C211yesmaximal, characteristic, complemented
9#10590600C211yesmaximal, characteristic, complemented
10#10590587C211yesmaximal, characteristic, complemented
11#10590562C211yesmaximal, characteristic, complemented
12#10590561C211yesmaximal, characteristic, complemented
13#10590490C211yesmaximal, characteristic, complemented
14#10590480C211yesmaximal, characteristic, complemented
15#10590428C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#81451—31nomaximal
18C22×#634C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#929—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#926—21no—
25C3×#924C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#898—21no—
28C3×#897C2211yescharacteristic
29C3×#892C2211yescharacteristic
30C3×#890C2211yescharacteristic
31C3×#889—21no—
32C3×#887C2211yescharacteristic
33#63982—21no—
34#67⋊Dic3—21no—
35#63896—21no—
36#63866C2211yescharacteristic
37#63857C2211yescharacteristic
38#63844C2211yescharacteristic
39#63840—21no—
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#552—31no—
62#5632—31no—
63D4×Dic6—31no—
64#5513D311yescharacteristic
65C3×#483—31no—
66#5069—31no—
67#5063—31no—
68#5052—31no—
69#5051—31no—
70#5051—31no—
71#5050—31no—
72#5050—31no—
73#5031—31no—
74#5030—31no—
75#5011—31no—
76#5004—31no—
77#4996—31no—
78#4971D311yescharacteristic, complemented
79C2×#810—31no—
80C2×#810—31no—
81C2×#810—61no—
82#4868—31no—
83#4867—31no—
84#4857—31no—
85#4853—31no—
86#4809—31no—
87#4802—31no—
88#4797—31no—
89#4795—31no—
90#4739—31no—
91#4730—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634—41no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×D3×Dic3—21no—
106D3×Dic6—22no—
107D3×Dic6—41no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C2×C3⋊(C3⋊C8)—41no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#217D411yescharacteristic
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3719—22no—
141#3719—41no—
142#3718—41no—
143#3711—41no—
144#3312—91noSylow
145C2×D3×Q8—31no—
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160C3×#117—61no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164#944—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169D4×Dic3—61no—
170#929—21no—
171C4×#67C2×D311yescharacteristic
172#926—21no—
173#924—31no—
174#924C2×D311yescharacteristic
175#924C2×D311yescharacteristic
176C2×#208—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×Dic12—31no—
181C2×Dic12—31no—
182C2×ΓL(1,𝔽25)—31no—
183#898—21no—
184#897—31no—
185#897C2×D311yescharacteristic
186#896—61no—
187#892C2×D311yescharacteristic
188#890C2×D311yescharacteristic
189#889—21no—
190#888—61no—
191#888—61no—
192#887—31no—
193#887C2×D311yescharacteristic
194#67⋊C4—61no—
195#878—61no—
196#878—61no—
197#878—61no—
198#869—31no—
199C4×Dic6—31no—
200C3×#106—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#830—31no—
208#830C2×D311yescharacteristic
209(C2×D3)⋊C8—31no—
210#816—31no—
211#816—31no—
212#815—31no—
213Dic3⋊C8—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810—61no—
228#810—61no—
229#810—61no—
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#808C2×D311yescharacteristic
233#808C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—42no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—42no—
250#634—21no—
251#634—21no—
252#634—21no—
253#634—42no—
254#634#4112yes—
255C3×#67—22no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#627—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—91no—
277#491—91no—
278#485—91no—
279#483—31no—
280#479—91no—
281#470—91no—
282#467—91no—
283#462—91no—
284#451—91no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—31no—
291C2×C3×Q8—31no—
292C2×C3×D4—31no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—41no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C2×#67#6711yescharacteristic
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—121no—
305D3×Q8—62no—
306D3×Q8—121no—
307C2×C4×D3—61no—
308C2×C4×D3C22×D311yescharacteristic
309C2×Dic6—31no—
310C2×Dic6—31no—
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×Dic6—61no—
314C2×Dic6—61no—
315C2×Dic6—62no—
316C2×Dic6—62no—
317C2×Dic6—62no—
318C2×Dic6—64no—
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—121no—
324C2×Dic6—121no—
325C2×Dic6—121no—
326C2×Dic6—121no—
327C2×Dic6—122no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—31no—
357C3×C42—61no—
358C3×C42—61no—
359#217—21no—
360#217—21no—
361#217—61no—
362#217#6711yescharacteristic
363#216—62no—
364#216—121no—
365#216—121no—
366#216—121no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4#6711yescharacteristic
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393#208—121no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8—122no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—62no—
406Dic12—121no—
407ΓL(1,𝔽25)—121no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32#13712yes—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—22no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×Q8—91no—
430C22×Q8—91no—
431C2×Q16—91no—
432C2×Q16—91no—
433C2×Q16—91no—
434C2×M16—91no—
435C22×C8—91no—
436C4⋊Q8—91no—
437C4⋊Q8—181no—
438#126—61no—
439#125—31no—
440#125—61no—
441#123—61no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—181no—
452#117—31no—
453#117—61no—
454C2×C4⋊C4D3211yescharacteristic
455#107—91no—
456#106—31no—
457#106—31no—
458C4⋊C8—91no—
459#103—31no—
460#103—31no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469C22⋊C8—31no—
470C22⋊C8—91no—
471#97—91no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3D3×D411yescharacteristic
475C23×C3C2×#6711yescharacteristic
476C22×D3C2×#6711yescharacteristic
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×D4—62no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—82no—
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4C2×#6711yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—22no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—122no—
524C2×Dic3—122no—
525C2×Dic3—122no—
526C2×Dic3—124no—
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—122no—
533Dic6—21no—
534Dic6—21no—
535Dic6—21no—
536Dic6—21no—
537Dic6—32no—
538Dic6—32no—
539Dic6—62no—
540Dic6—61no—
541Dic6—61no—
542Dic6—62no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—121no—
548Dic6—121no—
549Dic6—122no—
550Dic6—122no—
551Dic6—122no—
552Dic6—122no—
553Dic6—124no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C3⋊C8—121no—
564C2×C32—22no—
565C2×C32#54611yescharacteristic
566C2×C32C2×#13711yescharacteristic
567C2×C32#57811yescharacteristic
568C3×D3—41no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—91no—
572C2×Q8—91no—
573C2×Q8—182no—
574C2×Q8—181no—
575C2×Q8—182no—
576C2×Q8—181no—
577C2×Q8—361no—
578C2×Q8—361no—
579C2×D4—31no—
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4C2×D3211yescharacteristic
585Q16—182no—
586Q16—361no—
587Q16—361no—
588M16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C2×C8—361no—
594C4⋊C4—21no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4C2×D3211yescharacteristic
609C4⋊C4C2×D3211yescharacteristic
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—181no—
617C42—31no—
618C42—61no—
619C42—61no—
620C42—181no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3#91512yes—
633C22×C3#95112yes—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C22×#6711yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4D3×#4111yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4#100911yescharacteristic
660C3×C4#100911yescharacteristic
661Dic3—21no—
662Dic3—21no—
663Dic3—21no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668Dic3—62no—
669Dic3—62no—
670Dic3—122no—
671Dic3—122no—
672Dic3—121no—
673Dic3—121no—
674C32#331211yescharacteristic, complemented, Sylow
675C23—31no—
676C23D3×#6711yescharacteristic
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—92no—
682Q8—181no—
683Q8—181no—
684Q8—181no—
685Q8—362no—
686Q8—362no—
687D4—62no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—42no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—362no—
705C2×C4—362no—
706C2×C4D3×#6711yescharacteristic
707C2×C4C22×D3211yescharacteristic
708C8—61no—
709C8—61no—
710C8—181no—
711C8—181no—
712C2×C3—24no—
713C2×C3—22no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—121no—
719C2×C3#565411yescharacteristic
720C2×C3C2×#91511yescharacteristic
721C2×C3#577911yescharacteristic
722C2×C3C2×#95111yescharacteristic
723C2×C3#582911yescharacteristic
724C2×C3#583811yescharacteristic
725D3—41no—
726C22—21no—
727C22—21no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22#6392912yes—
732C22C2×D3×#6711yescharacteristic
733C4—21no—
734C4—41no—
735C4—41no—
736C4—61no—
737C4—61no—
738C4—61no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—182no—
744C4—361no—
745C4#6430611yescharacteristic
746C4#6430811yescharacteristic
747C3—21no—
748C3#8145111yescharacteristic, complemented
749C3#8360311yescharacteristic, complemented
750C2—22no—
751C2—121no—
752C2#1059506811yescharacteristic
753C2C2×#6392911yescharacteristic
754C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63637C2semidirect
4. C3×#4971C2semidirect
5. #10591190C2semidirect
6. #10591188C2semidirect
8. #10590604C2semidirect
9. #10590600C2semidirect
10. #10590587C2semidirect
11. #10590562C2semidirect
12. #10590561C2semidirect
13. #10590490C2semidirect
14. #10590480C2semidirect
15. #10590428C2semidirect
78. #4971D3semidirect
674. C32#3312semidirect
748. C3#81451semidirect
749. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#55132
#105949152
C2×#636372
C3×#49712
#105911902
#105911882
#105911582
#105906042
#105906002
#105905872
#105905622
#105905612
#105904902
#105904802
#105904282
#836033
#814513