Finite Group Databasebeta

← #11860489

Subgroups — #11860489

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic
3#10594361C211yesmaximal, characteristic, complemented
4C3⋊D3×#102C211yesmaximal, characteristic, complemented
5C3×#4758C211yesmaximal, characteristic, complemented
6C3×#4756C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8#10591430C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590792C211yesmaximal, characteristic, complemented
11#10590745C211yesmaximal, characteristic, complemented
12#10590700C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590583C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#79647—31nomaximal
17#79587—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×#887C2211yescharacteristic, complemented
28#63974—21no—
29C2×#3722—21no—
30#63952—21no—
31#63952—21no—
32#63937C418yescomplemented
33C4×#626—21no—
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36Dic3×D12C2211yescharacteristic, complemented
37#63881—21no—
38#63877—21no—
39D3×Dic3⋊C4—21no—
40#63874C2211yescharacteristic
41#63849C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63659C2211yescharacteristic
48#63648C2211yescharacteristic
49#63636C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×#911—31no—
64#5574—31no—
65#5546—31no—
66#5545—31no—
67#5545—31no—
68C3×C4×SD16—31no—
69C3×C4×D8—31no—
70#5164—31no—
71#5152—31no—
72#5026—31no—
73#5018—31no—
74#5014—31no—
75#5014—31no—
76#4889—31no—
77#4881—31no—
78#4869—31no—
79#4861—31no—
80#4804—31no—
81#4788—31no—
82#4772—31no—
83D3×#102—31no—
84D3×#102—31no—
85D3×#102—61no—
86#4758D311yescharacteristic, complemented
87#4756—31no—
88#4756D311yescharacteristic, complemented
89C4×D24—31no—
90C4×#204—31no—
91#4689—31no—
92#4689—31no—
93C23×C3⋊D3—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3C2×C414yescomplemented
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796C2×C414yescomplemented
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C8×C3⋊D3—22no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#214C2×C414yescomplemented
122C3×#213C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724D411yescharacteristic
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3717C2×C414yescomplemented
144#3714C2×C414yescomplemented
145#3712C2×C414yescomplemented
146#2946—91noSylow
147C2×#239—31no—
148C2×#237—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×C3×SD16—31no—
153C2×C3×D8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158Q8×Dic3—31no—
159C2×#215—31no—
160D4×Dic3—31no—
161D4×Dic3C2×D311yescharacteristic
162D4×Dic3C2×D311yescharacteristic
163C2×#214C2×D311yescharacteristic
164C2×#213—31no—
165C2×#213C2×D311yescharacteristic
166C4×#67—61no—
167C4×#67—61no—
168C4×#67—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×Dic3⋊C4—61no—
172#914—38no—
173#911—38no—
174C2×D24—31no—
175C2×#204—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180C2×D3×C8—61no—
181#893—31no—
182#893—31no—
183#893—61no—
184#893C2×D311yescharacteristic, complemented
185#892—31no—
186#892—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4—61no—
191#887C2×D311yescharacteristic, complemented
192#67⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195D3×C22⋊C4—61no—
196D3×C22⋊C4—61no—
197#877—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C4×D12—61no—
202#872—31no—
203#872—31no—
204#872—61no—
205C4×Dic6—31no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215#835—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—61no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic, complemented
224#818—31no—
225#817—31no—
226#816C2×D311yescharacteristic, complemented
227#815—31no—
228#815—31no—
229C8×Dic3C2×D311yescharacteristic, complemented
230C8×Dic3C2×D311yescharacteristic, complemented
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—61no—
236#808—31no—
237#808C2×D311yescharacteristic, complemented
238#807—31no—
239#807C2×D311yescharacteristic, complemented
240#803—31no—
241#803—31no—
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—24no—
245C22×C3⋊D3—81no—
246C22×C3⋊D3—81no—
247C22×C3⋊D3C2×D411yescharacteristic
248C22×C3×D3—21no—
249C32×D4—21no—
250C32×D4C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253#638—24no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)C22×C412yes—
258C4×C3⋊D3—81no—
259C4×C3⋊D3C22×C412yes—
260C4×C3⋊D3#4112yes—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12C22×C412yes—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6C22×C412yes—
275#626—24no—
276#624—81no—
277#624—81no—
278D3×Dic3—24no—
279D3×Dic3—81no—
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8C22×C412yes—
283C3×C3⋊C8C22×C412yes—
284C2×AGL(1,ℤ/8)—91no—
285#520—91no—
286#518—91no—
287#442—91no—
288#442—91no—
289#440—91no—
290#440—91no—
291C4×SD16—31no—
292C4×SD16—91no—
293C4×D8—31no—
294C4×D8—91no—
295#428—91no—
296#416—91no—
297C2×#102—91no—
298#405—91no—
299C23×D3—61no—
300C23×D3—61no—
301C23×D3—121no—
302C2×C3×Q8—31no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#239—34no—
319#239—62no—
320#237—34no—
321#237—62no—
322D3×D4—34no—
323D3×D4—34no—
324D3×D4—64no—
325D3×D4—62no—
326D3×D4—62no—
327D3×D4—122no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—121no—
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—34no—
348C3×D8—34no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—61no—
366#217—21no—
367#217—21no—
368#217—61no—
369#215—34no—
370#214C4×D314yescomplemented
371#213—34no—
372#213C4×D314yescomplemented
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400C4×Dic3—21no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—34no—
413#204—34no—
414ΓL(1,𝔽25)—34no—
415ΓL(1,𝔽25)—34no—
416D3×C8—62no—
417D3×C8—62no—
418D3×C8—122no—
419C22×C32—22no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—84no—
429C2×C3⋊D3C4×D412yes—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C32×C4—41no—
434C32×C4C23×C411yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—41no—
437C3⋊Dic3C4×D412yes—
438C3×Dic3—22no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C2×#41—91no—
446C22×D4—91no—
447AGL(1,ℤ/8)—98no—
448C2×SD16—31no—
449C2×SD16—91no—
450C2×D8—31no—
451C2×D8—91no—
452C2×M16—91no—
453C22×C8—91no—
454C4×Q8—31no—
455C4×Q8—91no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463C4×D4—181no—
464C4×D4—181no—
465C4×D4—181no—
466#117—91no—
467#117—91no—
468#117—181no—
469C2×C4⋊C4—91no—
470C2×C4⋊C4—181no—
471C2×C22⋊C4—181no—
472C2×C22⋊C4—181no—
473#107—31no—
474#107—91no—
475#106—31no—
476#106—91no—
477#103—31no—
478#103—91no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102D3211yescharacteristic
485#97—91no—
486#97—91no—
487C4×C8—31no—
488C4×C8—31no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—41no—
492C23×C3—61no—
493C22×D3—21no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C22×D3—64no—
498C22×D3—64no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—124no—
502C22×D3—121no—
503C22×D3—241no—
504C22×D3—241no—
505C22×D3—241no—
506C22×D3—241no—
507C22×D3—242no—
508C22×D3—242no—
509C3×Q8—32no—
510C3×Q8—61no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—22no—
514C3×D4—32no—
515C3×D4—41no—
516C3×D4—61no—
517C3×D4C2×C4×D312yes—
518C3×D4C2×C4×D312yes—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—241no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—64no—
536#67—64no—
537#67—64no—
538#67—124no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—61no—
545C2×Dic3—64no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—81no—
549C2×Dic3—81no—
550C2×Dic3—121no—
551C2×Dic3—241no—
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556D12—21no—
557D12—32no—
558D12—32no—
559D12—62no—
560D12—64no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12C2×C4×D312yes—
565C4×D3—32no—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—32no—
569C4×D3—62no—
570C4×D3—62no—
571C4×D3—64no—
572C4×D3—81no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578C4×D3—241no—
579C4×D3—241no—
580C4×D3—242no—
581Dic6—21no—
582Dic6C2×C4×D312yes—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—32no—
586C3×C8—32no—
587C3×C8—41no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—121no—
591C3⋊C8C2×C4×D312yes—
592C3⋊C8C2×C4×D312yes—
593C2×C32—42no—
594C2×C32C2×C4×D411yescharacteristic
595C2×C32#57611yescharacteristic
596C2×C32#57711yescharacteristic
597C3⋊D3—22no—
598C3⋊D3—42no—
599C3×D3—42no—
600C24—181no—
601#41—94no—
602#41—182no—
603C2×Q8—31no—
604C2×D4—31no—
605C2×D4—94no—
606C2×D4—91no—
607C2×D4—181no—
608C2×D4—182no—
609C2×D4—181no—
610C2×D4C2×D3211yescharacteristic
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—91no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620SD16—34no—
621SD16—94no—
622D8—34no—
623D8—94no—
624M16—94no—
625C2×C8—31no—
626C2×C8—31no—
627C2×C8—91no—
628C2×C8—182no—
629C2×C8C2×D3211yescharacteristic
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4C2×D3211yescharacteristic
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—91no—
643C22⋊C4—91no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—31no—
650C42—61no—
651C42—181no—
652C42—181no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—21no—
656C22×C3—42no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—62no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—22no—
669C2×D3—32no—
670C2×D3—32no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—122no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—244no—
690C2×D3—244no—
691C2×D3—248no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—62no—
701C3×C4—81no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4C22×C4×D311yescharacteristic
705C3×C4C22×C4×D311yescharacteristic
706C3×C4D3×#4111yescharacteristic
707C3×C4D3×#4111yescharacteristic
708Dic3—21no—
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—22no—
713Dic3—32no—
714Dic3—32no—
715Dic3—41no—
716Dic3—41no—
717Dic3—62no—
718Dic3—121no—
719Dic3—121no—
720Dic3—241no—
721C32#294611yescharacteristic, complemented, Sylow
722C23—21no—
723C23—61no—
724C23—91no—
725C23—184no—
726C23—181no—
727C23—721no—
728C23—721no—
729Q8—32no—
730Q8—61no—
731D4—21no—
732D4—32no—
733D4—61no—
734D4—92no—
735D4—184no—
736D4—184no—
737D4—181no—
738D4C4×D3212yes—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—91no—
748C2×C4—92no—
749C2×C4—92no—
750C2×C4—184no—
751C2×C4—181no—
752C2×C4—241no—
753C2×C4—241no—
754C2×C4—241no—
755C2×C4—721no—
756C2×C4—721no—
757C2×C4—721no—
758C2×C4—721no—
759C2×C4C22×D3211yescharacteristic
760C8—21no—
761C8—32no—
762C8—32no—
763C8—181no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—42no—
768C2×C3—42no—
769C2×C3—82no—
770C2×C3—122no—
771C2×C3C4×D3×D411yescharacteristic
772C2×C3C4×D3×D411yescharacteristic
773C2×C3#575711yescharacteristic
774C2×C3#576211yescharacteristic
775C2×C3#576911yescharacteristic
776C2×C3#577011yescharacteristic
777D3—42no—
778D3—64no—
779D3—62no—
780D3—62no—
781D3—122no—
782D3—122no—
783D3—242no—
784C22—22no—
785C22—41no—
786C22—41no—
787C22—62no—
788C22—92no—
789C22—121no—
790C22—121no—
791C22—181no—
792C22—181no—
793C22—182no—
794C22—361no—
795C22—361no—
796C22—724no—
797C22D32×D411yescharacteristic
798C4—41no—
799C4—61no—
800C4—61no—
801C4—61no—
802C4—61no—
803C4—62no—
804C4—92no—
805C4—121no—
806C4—121no—
807C4—361no—
808C4C2×C4×D3211yescharacteristic
809C4#6431211yescharacteristic
810C3—21no—
811C3#7958711yescharacteristic, complemented
812C3#7964711yescharacteristic, complemented
813C2—42no—
814C2—122no—
815C2—182no—
816C2—362no—
817C2#1059425511yescharacteristic
818C2#1059473411yescharacteristic
819C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63937C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595223C2semidirect
3. #10594361C2semidirect
4. C3⋊D3×#102C2semidirect
5. C3×#4758C2semidirect
6. C3×#4756C2semidirect
7. #10591440C2semidirect
8. #10591430C2semidirect
9. #10590956C2semidirect
10. #10590792C2semidirect
11. #10590745C2semidirect
12. #10590700C2semidirect
13. #10590589C2semidirect
14. #10590583C2semidirect
15. #10590457C2semidirect
26. C3×#893C22semidirect
27. C3×#887C22semidirect
32. #63937C4semidirect
36. Dic3×D12C22semidirect
42. Dic3×Dic6C22semidirect
50. C3×#821C22semidirect
51. C3×#816C22semidirect
52. C3×C8×Dic3C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63575C22semidirect
57. #63573C22semidirect
58. #63565C22semidirect
59. #63562C22semidirect
60. #63554C22semidirect
61. #63554C22semidirect
86. #4758D3semidirect
88. #4756D3semidirect
97. D4×C3⋊D3C2×C4semidirect
112. #3796C2×C4semidirect
121. C3×#214C2×C4semidirect
122. C3×#213C2×C4semidirect
143. #3717C2×C4semidirect
144. #3714C2×C4semidirect
145. #3712C2×C4semidirect
184. #893C2×D3semidirect
191. #887C2×D3semidirect
223. #821C2×D3semidirect
226. #816C2×D3semidirect
229. C8×Dic3C2×D3semidirect
230. C8×Dic3C2×D3semidirect
237. #808C2×D3semidirect
239. #807C2×D3semidirect
370. #214C4×D3semidirect
372. #213C4×D3semidirect
721. C32#2946semidirect
811. C3#79587semidirect
812. C3#79647semidirect

Maximal subgroups

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

subgroupindex
#105952232
C2×#639372
#105943612
C3⋊D3×#1022
C3×#47582
C3×#47562
#105914402
#105914302
#105909562
#105907922
#105907452
#105907002
#105905892
#105905832
#105904572
#796473
#795873