Finite Group Databasebeta

← #11870730

Subgroups — #11870730

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8×Dic3C211yesmaximal, characteristic, complemented
2#10594369C211yesmaximal, characteristic
3#10592487C211yesmaximal, characteristic, complemented
4C3×#4806C211yesmaximal, characteristic, complemented
5C3×#4791C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591571C211yesmaximal, characteristic, complemented
9#10590799C211yesmaximal, characteristic, complemented
10#10590775C211yesmaximal, characteristic, complemented
11#10590677C211yesmaximal, characteristic, complemented
12#10590656C211yesmaximal, characteristic, complemented
13#10590486C211yesmaximal, characteristic, complemented
14#10590483C211yesmaximal, characteristic, complemented
15#10590441C211yesmaximal, characteristic, complemented
16#80996—31nomaximal
17#80028—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3796—21no—
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#888C2211yescharacteristic
28#63911C2211yescharacteristic
29#63909C2211yescharacteristic
30#63907—21no—
31#63898C2211yescharacteristic
32D3×C4⋊Dic3—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34#63886—21no—
35#63881—21no—
36C4×D3×Dic3—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63843—21no—
39#63843C2211yescharacteristic
40Dic3×Dic6—21no—
41Dic3×Dic6C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63565C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61C2×Q8×Dic3—31no—
62#5725—31no—
63#5596—31no—
64C4×D3×Q8—31no—
65C3×#475—31no—
66C3×#448—31no—
67#5227—31no—
68#5163—31no—
69#5163—31no—
70Dic3×SD16—31no—
71Dic3×SD16—31no—
72#5094—31no—
73#5034—31no—
74#5027—31no—
75#4863—31no—
76#4863—31no—
77#4852—31no—
78#4852—31no—
79#4848—31no—
80#4833—31no—
81#4806—31no—
82#4806D311yescharacteristic, complemented
83#4791—31no—
84#4791D311yescharacteristic, complemented
85#4788—31no—
86#4788—31no—
87#4788—31no—
88#4788—31no—
89#4788—61no—
90#4735—31no—
91#4718—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111#3796—44no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#215—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—22no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3717—22no—
142#3103—91noSylow
143C22×C3×Q8—31no—
144C2×#239—61no—
145C2×D3×Q8C2×D311yescharacteristic
146C2×#237—61no—
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
149C3×C4⋊Q8—31no—
150C3×#121—31no—
151C3×C4×Q8—31no—
152#947—61no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—61no—
158Q8×Dic3—61no—
159Q8×Dic3—61no—
160Q8×Dic3C2×D311yescharacteristic
161C2×#215—31no—
162C2×#215—31no—
163C2×#215—31no—
164C2×#215—61no—
165C2×#215C2×D311yescharacteristic
166#940—31no—
167#939—61no—
168D4×Dic3—31no—
169#930—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—61no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—61no—
174C2×#204—31no—
175C2×#204C2×D311yescharacteristic
176#895—31no—
177#895—61no—
178#895C2×D311yescharacteristic
179#893—31no—
180#893—31no—
181#893—31no—
182#893—61no—
183#893—61no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186#888C2×D311yescharacteristic
187#887—31no—
188#887—61no—
189#885—61no—
190#67⋊C4—61no—
191#874—31no—
192C42×D3—31no—
193C42×D3—61no—
194C4×Dic6—31no—
195C4×Dic6—61no—
196C3×#106—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C2×D311yescharacteristic
204C3×C22⋊C8—31no—
205#835—31no—
206#835C2×D311yescharacteristic
207#832—31no—
208#832—31no—
209#830—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#817—31no—
218#817C2×D311yescharacteristic
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—61no—
226#810—31no—
227#810C2×D311yescharacteristic
228#809—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#808C2×D311yescharacteristic
235C4⋊(C3⋊C8)—31no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yescomplemented
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4×C3⋊D3—42no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—42no—
259C3×C4×D3—24no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×Dic6—24no—
263C3×Dic6—21no—
264C3×Dic6—42no—
265C3×Dic6#4112yescomplemented
266#626—42no—
267#626—42no—
268#626—42no—
269D3×Dic3—41no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272D3×Dic3SD1614yescomplemented
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#532—91no—
278C2×C4×Q8—91no—
279#481—91no—
280#481—91no—
281#475—31no—
282#475—91no—
283#460—91no—
284#460—91no—
285#448—31no—
286#448—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311#239—124no—
312D3×Q8—22no—
313D3×Q8—22no—
314#237—124no—
315C2×D12—21no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—121no—
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—21no—
333C2×Dic6—21no—
334C2×Dic6C22×D311yescharacteristic
335C3×SD16—62no—
336C3×SD16—62no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352#217—61no—
353#215—22no—
354#215—62no—
355#215—64no—
356#215—62no—
357#215—62no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—21no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—121no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381C4×Dic3—21no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402#204—22no—
403#204—62no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3C2×SD1612yes—
414C32×C4—22no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3C2×SD1612yes—
421C3×Dic3—21no—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3C2×SD1612yes—
427C2×#41—181no—
428C22×Q8—31no—
429C2×SD16—31no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×SD16—91no—
433C4⋊Q8—31no—
434#127—91no—
435#124—181no—
436#121—31no—
437#121—91no—
438#121—181no—
439C4×Q8—31no—
440C4×Q8—91no—
441C4×Q8—91no—
442C4×Q8—91no—
443C4×Q8—181no—
444C4×Q8—181no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—181no—
450C2×C42—91no—
451C2×C42—181no—
452#106—31no—
453#106—31no—
454#106—91no—
455#106—91no—
456C4⋊C8—31no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103D3211yescharacteristic
462#102—91no—
463#102—91no—
464#102—91no—
465#102—91no—
466C22⋊C8—31no—
467C22⋊C8—91no—
468C4×C8—91no—
469C4×C8—91no—
470C23×C3—31no—
471C23×C3—61no—
472C22×D3—21no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—121no—
476C22×D3D3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—64no—
483C3×Q8—61no—
484C3×Q8—122no—
485C3×Q8#23712yescomplemented
486C3×Q8#23912yescomplemented
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—122no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—64no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—122no—
509#67—122no—
510#67—122no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—34no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—122no—
526C2×Dic3—122no—
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530D12—21no—
531D12—21no—
532D12—42no—
533D12—62no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—121no—
539D12—122no—
540D12—122no—
541D12—122no—
542C4×D3—24no—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—34no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—121no—
550C4×D3—122no—
551C4×D3—242no—
552Dic6—24no—
553Dic6—21no—
554Dic6—42no—
555Dic6#23712yescomplemented
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—62no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C2×C32#52511yescharacteristic
567C2×C32C22×SD1611yescharacteristic
568C2×C32#57511yescharacteristic
569C3⋊D3—81no—
570C3×D3—22no—
571C3×D3—81no—
572#41—364no—
573C2×Q8—31no—
574C2×Q8—61no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8—62no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—91no—
582C2×D4—181no—
583C2×D4—181no—
584C2×D4—181no—
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592SD16—62no—
593SD16—62no—
594SD16—182no—
595SD16—182no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4C2×D3211yescharacteristic
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—61no—
616C42—91no—
617C42—91no—
618C42—91no—
619C42—181no—
620C42—181no—
621C42—181no—
622C22×C3—21no—
623C22×C3—32no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—122no—
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×D3D3×SD1612yes—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—42no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—62no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C2×#23711yescharacteristic
661C3×C4C2×#23711yescharacteristic
662C3×C4C2×#23911yescharacteristic
663C3×C4D3×#4111yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—22no—
667Dic3—32no—
668Dic3—32no—
669Dic3—41no—
670Dic3—41no—
671Dic3—62no—
672Dic3—61no—
673Dic3—61no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3D3×SD1612yes—
679C32#310311yescharacteristic, complemented, Sylow
680C23—31no—
681C23—61no—
682C23—181no—
683Q8—21no—
684Q8—32no—
685Q8—64no—
686Q8—61no—
687Q8—122no—
688Q8#379612yescomplemented
689D4—61no—
690D4—61no—
691D4—122no—
692D4—181no—
693D4—181no—
694D4—362no—
695D4—362no—
696D4—362no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—64no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—94no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—181no—
712C2×C4—362no—
713C2×C4—361no—
714C2×C4—362no—
715C2×C4—362no—
716C2×C4C22×D3211yescharacteristic
717C8—21no—
718C8—61no—
719C8—61no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—62no—
725C2×C3—241no—
726C2×C3#558611yescharacteristic
727C2×C3#562711yescharacteristic
728C2×C3C2×D3×SD1611yescharacteristic
729C2×C3C2×D3×SD1611yescharacteristic
730C2×C3#577711yescharacteristic
731C2×C3#577711yescharacteristic
732D3—22no—
733D3—81no—
734D3—242no—
735D3—241no—
736D3—241no—
737C22—32no—
738C22—61no—
739C22—61no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—361no—
744C22—361no—
745C22—361no—
746C22D32×D411yescharacteristic
747C4—22no—
748C4—32no—
749C4—41no—
750C4—61no—
751C4—62no—
752C4—61no—
753C4—92no—
754C4—121no—
755C4—121no—
756C4—181no—
757C4—361no—
758C4C2×#379611yescharacteristic
759C4D3×#23711yescharacteristic
760C3—21no—
761C3#8002811yescharacteristic, complemented
762C3#8099611yescharacteristic, complemented
763C2—62no—
764C2—241no—
765C2—721no—
766C2#1059405511yescharacteristic
767C2D32×SD1611yescharacteristic
768C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594369C2
hypercenter#103D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×Q8×Dic3C2semidirect
3. #10592487C2semidirect
4. C3×#4806C2semidirect
5. C3×#4791C2semidirect
6. #10591617C2semidirect
7. #10591584C2semidirect
8. #10591571C2semidirect
9. #10590799C2semidirect
10. #10590775C2semidirect
11. #10590677C2semidirect
12. #10590656C2semidirect
13. #10590486C2semidirect
14. #10590483C2semidirect
15. #10590441C2semidirect
82. #4806D3semidirect
84. #4791D3semidirect
240. C32×Q8#41semidirect
265. C3×Dic6#41semidirect
272. D3×Dic3SD16semidirect
485. C3×Q8#237semidirect
486. C3×Q8#239semidirect
555. Dic6#237semidirect
679. C32#3103semidirect
688. Q8#3796semidirect
761. C3#80028semidirect
762. C3#80996semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic32
#105943692
#105924872
C3×#48062
C3×#47912
#105916172
#105915842
#105915712
#105907992
#105907752
#105906772
#105906562
#105904862
#105904832
#105904412
#809963
#800283