Finite Group Databasebeta

← #11868667

Subgroups — #11868667

Order 1152.

975 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#624C211yesmaximal, characteristic
2#10594448C211yesmaximal, characteristic, complemented
3#10592469C211yesmaximal, characteristic
4C3×#4763C211yesmaximal, characteristic, complemented
5C3×#4759C211yesmaximal, characteristic, complemented
6#10591426C211yesmaximal, characteristic
7#10591409C211yesmaximal, characteristic, complemented
8#10591408C211yesmaximal, characteristic, complemented
9#10590774C211yesmaximal, characteristic, complemented
10#10590759C211yesmaximal, characteristic, complemented
11#10590688C211yesmaximal, characteristic, complemented
12#10590666C211yesmaximal, characteristic, complemented
13#10590582C211yesmaximal, characteristic, complemented
14#10590468C211yesmaximal, characteristic, complemented
15#10590464C211yesmaximal, characteristic, complemented
16#81166—31nomaximal
17#80965—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×#624—21no—
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×#890C2211yescharacteristic, complemented
25C3×#888C2211yescharacteristic, complemented
26#63974—21no—
27#63952—21no—
28#63952—21no—
29#63918C2211yescharacteristic, complemented
30#63900C2211yescharacteristic
31#63895—21no—
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34#63888—21no—
35C4×#624C2211yescharacteristic
36#63869C2211yescharacteristic, complemented
37#63849C2211yescharacteristic
38#63843—21no—
39#63838—21no—
40C2×#3712C2211yescharacteristic
41C32×#102C2211yescharacteristic
42#63659C2211yescharacteristic
43#63648C2211yescharacteristic
44#63636C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#818C2211yescharacteristic, complemented
48C3×#817C2211yescharacteristic, complemented
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5728—31no—
62#5688—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#478—31no—
66C3×#474—31no—
67#5087—31no—
68#5066—31no—
69#5009—31no—
70#5008—31no—
71#4891—31no—
72#4891—31no—
73#4890—31no—
74#4881—31no—
75#4881—31no—
76#4881—31no—
77#4870—31no—
78#4861—31no—
79#4847—31no—
80#4842—31no—
81#4837—31no—
82#4837—31no—
83#4770—31no—
84#4770—31no—
85#4770—31no—
86#4770—31no—
87#4770—61no—
88#4763—31no—
89#4763D311yescharacteristic, complemented
90#4761—31no—
91#4759D311yescharacteristic, complemented
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3Q814yescomplemented
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C2×C3×Dic6—21no—
102C2×#627—21no—
103C2×#624—21no—
104C2×#624—21no—
105C2×#624—21no—
106C2×#624—44no—
107C2×#624D411yescharacteristic
108C2×#624D411yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4×C3⋊Dic3—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115#3743—22no—
116C3×#217—21no—
117C3×#217—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136Dic32—21no—
137Dic32D411yescharacteristic
138Dic32D411yescharacteristic
139#3712—22no—
140#3077—91noSylow
141C2×D3×D4—31no—
142C2×D3×D4—31no—
143C2×D3×D4—61no—
144C22×C4×D3—61no—
145C22×C4×D3—61no—
146C3×C4⋊Q8—31no—
147C3×#125—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150#946—61no—
151Q8×Dic3—61no—
152D4×Dic3C2×D311yescharacteristic
153D4×Dic3C2×D311yescharacteristic
154C4×#67—61no—
155C4×#67—61no—
156C2×ΓL(1,𝔽25)—31no—
157C2×ΓL(1,𝔽25)—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×ΓL(1,𝔽25)—31no—
160C2×ΓL(1,𝔽25)—61no—
161#897—61no—
162#896—61no—
163#896—61no—
164#893—31no—
165#893—31no—
166#892—31no—
167#892—31no—
168#892—31no—
169#892—31no—
170#892—61no—
171D3×C4⋊C4—31no—
172D3×C4⋊C4—31no—
173#890—31no—
174#890C2×D311yescharacteristic, complemented
175#888—31no—
176#888C2×D311yescharacteristic, complemented
177#887—61no—
178#887—61no—
179#887—61no—
180#67⋊C4—61no—
181#67⋊C4—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—61no—
184C4×D12—31no—
185C4×D12—31no—
186C42×D3—31no—
187C42×D3—31no—
188#870—31no—
189#869—31no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#106—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#102—21no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102C2×D311yescharacteristic
200C3×#102C2×D311yescharacteristic
201#832—31no—
202#832—31no—
203#832—61no—
204#832C2×D311yescharacteristic
205#832C2×D311yescharacteristic
206#821—31no—
207#821—31no—
208#821—31no—
209#821—31no—
210#821—61no—
211#818C2×D311yescharacteristic, complemented
212#817—31no—
213#817—31no—
214#817C2×D311yescharacteristic, complemented
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8C2×D311yescharacteristic, complemented
218Dic3⋊C8C2×D311yescharacteristic, complemented
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic, complemented
231#807C2×D311yescharacteristic, complemented
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C23×C32—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—24no—
237C22×C3⋊D3—42no—
238C22×C3⋊D3—42no—
239C22×C3⋊D3C2×D411yescharacteristic
240C32×D4—21no—
241C32×D4C2×Q812yes—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244#638—24no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)C2×Q812yes—
249C4×C3⋊D3C2×Q812yes—
250C4×C3⋊D3#4112yes—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×Dic6—42no—
262#627—42no—
263#624—22no—
264#624—41no—
265#624—42no—
266#624—42no—
267#624—42no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#533—91no—
273C2×C4×D4—91no—
274#478—31no—
275#478—91no—
276#478—91no—
277#478—91no—
278#476—91no—
279#476—91no—
280#474—31no—
281#474—91no—
282#428—91no—
283#428—91no—
284#423—91no—
285#418—91no—
286#418—91no—
287C23×D3—61no—
288C23×D3—61no—
289C23×D3—121no—
290C2×C3×Q8—61no—
291C2×C3×D4—21no—
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C22×D311yescharacteristic
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C2×#67—61no—
298C2×#67—121no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301D3×D4—34no—
302D3×D4—34no—
303D3×D4—64no—
304D3×D4—62no—
305D3×D4—62no—
306D3×D4—122no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—61no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—124no—
324C2×C4×D3—124no—
325C2×Dic6—21no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C42—31no—
346C3×C42—31no—
347#217—21no—
348#217—21no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
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—121no—
358C4⋊Dic3—21no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3C22×D311yescharacteristic
365C4⋊Dic3C22×D311yescharacteristic
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368Dic3⋊C4—21no—
369Dic3⋊C4—21no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—121no—
385C4×Dic3C22×D311yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392ΓL(1,𝔽25)—62no—
393ΓL(1,𝔽25)—62no—
394ΓL(1,𝔽25)—62no—
395ΓL(1,𝔽25)—62no—
396ΓL(1,𝔽25)—122no—
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—48no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3C22⋊Q812yes—
408C32×C4—41no—
409C32×C4C22×Q811yescharacteristic
410C32×C4C2×#4111yescharacteristic
411C3⋊Dic3—41no—
412C3⋊Dic3C22⋊Q812yes—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3AGL(1,ℤ/8)12yes—
421C22×D4—91no—
422C23×C4—181no—
423C2×M16—91no—
424C2×M16—91no—
425C4⋊Q8—31no—
426C4⋊Q8—91no—
427#125—31no—
428#125—91no—
429C22⋊Q8—181no—
430C22⋊Q8—181no—
431C4×Q8—181no—
432C4×Q8—181no—
433C4×D4—31no—
434C4×D4—31no—
435C4×D4—91no—
436C4×D4—91no—
437C4×D4—181no—
438C4×D4—181no—
439#117—91no—
440#117—91no—
441C2×C4⋊C4—91no—
442C2×C22⋊C4—181no—
443C2×C42—91no—
444#107—31no—
445#107—31no—
446#107—31no—
447#107—91no—
448#106—31no—
449#106—91no—
450#106—91no—
451#106—91no—
452C4⋊C8—31no—
453C4⋊C8—31no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#102—31no—
457#102—31no—
458#102—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102D3211yescharacteristic
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—41no—
467C22×D3—31no—
468C22×D3—31no—
469C22×D3—61no—
470C22×D3—64no—
471C22×D3—64no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—124no—
475C22×D3—121no—
476C22×D3—122no—
477C22×D3—122no—
478C22×D3—122no—
479C22×D3—122no—
480C22×D3—242no—
481C22×D3—242no—
482C3×Q8—122no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—22no—
486C3×D4—41no—
487C3×D4D3×Q812yes—
488C3×D4D3×Q812yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—122no—
502C2×C3×C4—122no—
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505#67—64no—
506#67—64no—
507#67—124no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—42no—
515C2×Dic3—42no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3D3×D411yescharacteristic
521C2×Dic3D3×D411yescharacteristic
522C2×Dic3D3×D411yescharacteristic
523C2×Dic3D3×D411yescharacteristic
524D12—32no—
525D12—32no—
526D12—62no—
527D12—61no—
528D12—61no—
529D12—121no—
530C4×D3—32no—
531C4×D3—32no—
532C4×D3—32no—
533C4×D3—32no—
534C4×D3—62no—
535C4×D3—62no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—121no—
539C4×D3—121no—
540C4×D3—122no—
541C4×D3—122no—
542C4×D3—122no—
543C4×D3—122no—
544C4×D3—122no—
545C4×D3—122no—
546Dic6—42no—
547Dic6—122no—
548Dic6—122no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—41no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C2×C32—42no—
560C2×C32C2×C22⋊Q811yescharacteristic
561C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
562C2×C32#57511yescharacteristic
563C3⋊D3—22no—
564C3⋊D3—42no—
565C24—181no—
566C2×Q8—61no—
567C2×Q8—181no—
568C2×D4—94no—
569C2×D4—91no—
570C2×D4—182no—
571C2×D4—181no—
572C2×D4C2×D3211yescharacteristic
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—181no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—364no—
582M16—182no—
583M16—182no—
584C2×C8—31no—
585C2×C8—31no—
586C2×C8—91no—
587C2×C8C2×D3211yescharacteristic
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4C2×D3211yescharacteristic
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C42—31no—
608C42—31no—
609C42—91no—
610C42—91no—
611C42—181no—
612C42—181no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—21no—
616C22×C3—42no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3C2×D3×D411yescharacteristic
624C22×C3C2×D3×D411yescharacteristic
625C2×D3—32no—
626C2×D3—32no—
627C2×D3—62no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—121no—
635C2×D3—121no—
636C2×D3—122no—
637C2×D3—128no—
638C2×D3—128no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—248no—
644C2×D3—241no—
645C2×D3—241no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—32no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—81no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C2×D3×Q811yescharacteristic
660C3×C4C2×D3×Q811yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—32no—
667Dic3—32no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—62no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676Dic3#91112yes—
677C32#307711yescharacteristic, complemented, Sylow
678C23—21no—
679C23—91no—
680C23—184no—
681C23—181no—
682C23—362no—
683C23—362no—
684Q8—122no—
685Q8—362no—
686D4—21no—
687D4—92no—
688D4—184no—
689D4—181no—
690D4#379712yes—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—91no—
701C2×C4—92no—
702C2×C4—92no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—182no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4—361no—
709C2×C4—362no—
710C2×C4—362no—
711C2×C4C22×D3211yescharacteristic
712C8—21no—
713C8—61no—
714C8—61no—
715C8—181no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—42no—
721C2×C3—82no—
722C2×C3D3×C22⋊Q811yescharacteristic
723C2×C3D3×C22⋊Q811yescharacteristic
724C2×C3C2×#91111yescharacteristic
725C2×C3#576811yescharacteristic
726C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
727C2×C3#577711yescharacteristic
728D3—62no—
729D3—62no—
730D3—122no—
731D3—122no—
732D3—122no—
733D3—242no—
734C22—22no—
735C22—41no—
736C22—41no—
737C22—92no—
738C22—181no—
739C22—181no—
740C22—182no—
741C22—368no—
742C22—361no—
743C22—361no—
744C22D32×D411yescharacteristic
745C4—32no—
746C4—41no—
747C4—61no—
748C4—61no—
749C4—61no—
750C4—92no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—121no—
755C4—361no—
756C4C2×#379711yescharacteristic
757C4#6431211yescharacteristic
758C3—21no—
759C3#8096511yescharacteristic, complemented
760C3#8116611yescharacteristic, complemented
761C2—42no—
762C2—182no—
763C2—362no—
764C2#1059406711yescharacteristic
765C2D3×#91111yescharacteristic
766C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#102D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594448C2semidirect
4. C3×#4763C2semidirect
5. C3×#4759C2semidirect
7. #10591409C2semidirect
8. #10591408C2semidirect
9. #10590774C2semidirect
10. #10590759C2semidirect
11. #10590688C2semidirect
12. #10590666C2semidirect
13. #10590582C2semidirect
14. #10590468C2semidirect
15. #10590464C2semidirect
24. C3×#890C22semidirect
25. C3×#888C22semidirect
29. #63918C22semidirect
36. #63869C22semidirect
47. C3×#818C22semidirect
48. C3×#817C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
89. #4763D3semidirect
91. #4759D3semidirect
96. D4×C3⋊D3Q8semidirect
174. #890C2×D3semidirect
176. #888C2×D3semidirect
211. #818C2×D3semidirect
214. #817C2×D3semidirect
217. Dic3⋊C8C2×D3semidirect
218. Dic3⋊C8C2×D3semidirect
230. #807C2×D3semidirect
231. #807C2×D3semidirect
677. C32#3077semidirect
759. C3#80965semidirect
760. C3#81166semidirect

Maximal subgroups

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

subgroupindex
D4×#6242
#105944482
#105924692
C3×#47632
C3×#47592
#105914262
#105914092
#105914082
#105907742
#105907592
#105906882
#105906662
#105905822
#105904682
#105904642
#811663
#809653