Finite Group Databasebeta

← #11872811

Subgroups — #11872811

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
1#10594996C211yesmaximal, characteristic
2#10594824C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic
4C3×#4723C211yesmaximal, characteristic, complemented
5C3×#4720C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic
7#10591134C211yesmaximal, characteristic, complemented
8#10590795C211yesmaximal, characteristic, complemented
9#10590792C211yesmaximal, characteristic, complemented
10#10590774C211yesmaximal, characteristic, complemented
11#10590773C211yesmaximal, characteristic, complemented
12#10590769C211yesmaximal, characteristic, complemented
13#10590760C211yesmaximal, characteristic, complemented
14#10590760C211yesmaximal, characteristic, complemented
15#10590758C211yesmaximal, characteristic, complemented
16#81498—31nomaximal
17#79387—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19#64133C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#924C2211yescharacteristic
25#63974—21no—
26#63974—21no—
27#63956—21no—
28#63956—21no—
29#63894—21no—
30#63894—21no—
31#63894C2211yescharacteristic
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35#63869C2211yescharacteristic, complemented
36#63866C2211yescharacteristic, complemented
37#63847—21no—
38#63846—21no—
39#63844C2211yescharacteristic, complemented
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#818C2211yescharacteristic, complemented
48C3×#817C2211yescharacteristic, complemented
49C3×#816C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5625—31no—
62#5521—31no—
63#5521—31no—
64#5518—31no—
65C3×#485—31no—
66C3×#433—31no—
67#5046—31no—
68#4996—31no—
69#4891—31no—
70#4889—31no—
71#4871—31no—
72#4852—31no—
73#4847—31no—
74#4847—31no—
75#4841—31no—
76#4841—31no—
77#4818—31no—
78#4818—31no—
79#4817—31no—
80#4788—31no—
81#4731—31no—
82#4731—31no—
83#4731—31no—
84#4731—61no—
85#4723—31no—
86#4723D311yescharacteristic, complemented
87#4720D311yescharacteristic, complemented
88#4710—31no—
89#4710—31no—
90C4×#204—31no—
91C4×#204—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#624—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×#624—21no—
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107#3757—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3744—22no—
111#3744—22no—
112C3×#217—21no—
113C3×#217—21no—
114C3×#217D411yescharacteristic
115C3×#217D411yescharacteristic
116C3×C4⋊Dic3D411yescharacteristic
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138Dic32—21no—
139#3717—22no—
140#3717—22no—
141#3123—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×C22⋊Q8—31no—
146C3×#117—31no—
147C3×#117—31no—
148Q8×Dic3—31no—
149#944—31no—
150C2×#215—31no—
151C2×#215—31no—
152#926C2×D311yescharacteristic
153#926C2×D311yescharacteristic
154#924—31no—
155#924—31no—
156#924—61no—
157#924C2×D311yescharacteristic
158C2×#204—31no—
159C2×#204—31no—
160C2×#204—31no—
161C2×#204—31no—
162C2×#204—31no—
163C2×#204—31no—
164C2×#204—61no—
165C2×#204—61no—
166#893—31no—
167#893—31no—
168#893—31no—
169#893—31no—
170#893—61no—
171#893—61no—
172#890—31no—
173#890—61no—
174#889—61no—
175#889—61no—
176#889—61no—
177#887—31no—
178D3×C22⋊C4—61no—
179D3×C22⋊C4—61no—
180D3×C22⋊C4—61no—
181D3×C22⋊C4—61no—
182#879—61no—
183#879—61no—
184#879—61no—
185#879—61no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—61no—
191C4×D12—61no—
192#870—31no—
193#869—31no—
194C4×Dic6—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×#97—31no—
207C3×C4×C8—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821—61no—
217#818—31no—
218#818C2×D311yescharacteristic, complemented
219#817—31no—
220#817C2×D311yescharacteristic, complemented
221#816—31no—
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224#816C2×D311yescharacteristic, complemented
225#815C2×D311yescharacteristic, complemented
226Dic3⋊C8C2×D311yescharacteristic, complemented
227Dic3⋊C8C2×D311yescharacteristic, complemented
228C8×Dic3C2×D311yescharacteristic, complemented
229#810—31no—
230#810—31no—
231#809—31no—
232#809—31no—
233#808—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3—81no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—24no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4⋊(C3⋊D3)#4112yes—
252#634—21no—
253#634—21no—
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—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
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—31no—
287C23×D3—61no—
288C23×D3—61no—
289C23×D3—121no—
290C2×C3×Q8—31no—
291C22×C3×C4—21no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C2×D12—31no—
295C2×D12—31no—
296C2×D12—31no—
297C2×D12—31no—
298C2×D12—61no—
299C2×D12—61no—
300C2×D12—62no—
301C2×D12—62no—
302C2×D12—62no—
303C2×D12—62no—
304C2×D12—61no—
305C2×D12—61no—
306C2×D12—122no—
307C2×D12—122no—
308C2×D12—121no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C2×Dic6C22×D311yescharacteristic
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8C22×D311yescharacteristic
326C2×C3×C8C22×D311yescharacteristic
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C22×D311yescharacteristic
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C22⋊C4—31no—
336C3×C22⋊C4—31no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—31no—
340C3×C42—31no—
341C3×C42—61no—
342#217—21no—
343#217—21no—
344#217—61no—
345#217—61no—
346#217—121no—
347#217D1211yescharacteristic
348#217D1211yescharacteristic
349#215—62no—
350#215—62no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3D1211yescharacteristic
367C4⋊Dic3D1211yescharacteristic
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—121no—
383C4×Dic3—21no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3C22×D311yescharacteristic
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392#204—62no—
393#204—62no—
394#204—62no—
395#204—62no—
396#204—62no—
397#204—62no—
398#204—122no—
399#204—122no—
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×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
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—91no—
430#126—181no—
431#126—181no—
432#125—91no—
433#125—181no—
434#125—181no—
435C22⋊Q8—31no—
436C22⋊Q8—91no—
437C4×Q8—91no—
438C4×Q8—91no—
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—31no—
454C4⋊C8—31no—
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⋊C8D3211yescharacteristic
465#97—31no—
466C4×C8—31no—
467C23×C3—21no—
468C23×C3C2×D1211yescharacteristic
469C23×C3D3×D411yescharacteristic
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—61no—
486C3×Q8—61no—
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—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4C2×D1211yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—121no—
516C2×Dic3—121no—
517C2×Dic3C2×D1211yescharacteristic
518C2×Dic3C2×D1211yescharacteristic
519C2×Dic3C2×D1211yescharacteristic
520C2×Dic3C2×D1211yescharacteristic
521D12—32no—
522D12—32no—
523D12—32no—
524D12—32no—
525D12—62no—
526D12—62no—
527D12—64no—
528D12—64no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12—121no—
535D12—124no—
536C4×D3—241no—
537C4×D3—241no—
538C4×D3—241no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544Dic6—21no—
545Dic6—21no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—121no—
551Dic6—121no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—41no—
563C2×C32#52511yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—42no—
567C3⋊D3—42no—
568C24—181no—
569C2×Q8—31no—
570C2×Q8—91no—
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×C8C2×D3211yescharacteristic
588C2×C8C2×D3211yescharacteristic
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C42—31no—
613C42—31no—
614C42—61no—
615C42—181no—
616C42—181no—
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×C3C22×D1211yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
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—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4D3×#4111yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680Dic3—241no—
681C32#312311yescharacteristic, complemented, Sylow
682C23—184no—
683C23—181no—
684C23—181no—
685C23—721no—
686C23—721no—
687C23D3×D1211yescharacteristic
688Q8—61no—
689Q8—61no—
690Q8—181no—
691Q8—181no—
692D4—92no—
693D4—92no—
694D4—184no—
695D4—181no—
696D4—181no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—721no—
710C2×C4—721no—
711C2×C4—721no—
712C2×C4—721no—
713C2×C4D3×D1211yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—21no—
716C8—21no—
717C8—61no—
718C8—61no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3#552411yescharacteristic
726C2×C3#565611yescharacteristic
727C2×C3#575111yescharacteristic
728C2×C3#575111yescharacteristic
729C2×C3#577011yescharacteristic
730C2×C3#577811yescharacteristic
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×D1211yescharacteristic
748C4—21no—
749C4—61no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—361no—
758C4—361no—
759C4#6431211yescharacteristic
760C4#6431211yescharacteristic
761C3—21no—
762C3#7938711yescharacteristic, complemented
763C3#8149811yescharacteristic, complemented
764C2—41no—
765C2—362no—
766C2—362no—
767C2#1059407911yescharacteristic
768C2#1059467911yescharacteristic
769C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22⋊C8D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594824C2semidirect
4. C3×#4723C2semidirect
5. C3×#4720C2semidirect
7. #10591134C2semidirect
8. #10590795C2semidirect
9. #10590792C2semidirect
10. #10590774C2semidirect
11. #10590773C2semidirect
12. #10590769C2semidirect
13. #10590760C2semidirect
14. #10590760C2semidirect
15. #10590758C2semidirect
35. #63869C22semidirect
36. #63866C22semidirect
39. #63844C22semidirect
40. Dic3×Dic6C22semidirect
47. C3×#818C22semidirect
48. C3×#817C22semidirect
49. C3×#816C22semidirect
50. C3×#816C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
86. #4723D3semidirect
87. #4720D3semidirect
218. #818C2×D3semidirect
220. #817C2×D3semidirect
223. #816C2×D3semidirect
224. #816C2×D3semidirect
225. #815C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
227. Dic3⋊C8C2×D3semidirect
228. C8×Dic3C2×D3semidirect
681. C32#3123semidirect
762. C3#79387semidirect
763. C3#81498semidirect

Maximal subgroups

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

subgroupindex
#105949962
#105948242
#105924302
C3×#47232
C3×#47202
#105911832
#105911342
#105907952
#105907922
#105907742
#105907732
#105907692
#105907602
#105907582
#814983
#793873