Finite Group Databasebeta

← #11860494

Subgroups — #11860494

Order 1152.

1072 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595215C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic
3#10594359C211yesmaximal, characteristic, complemented
4#10592456C211yesmaximal, characteristic, complemented
5C3×#4785C211yesmaximal, characteristic, complemented
6C3×D3×#102C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590747C211yesmaximal, characteristic, complemented
11#10590741C211yesmaximal, characteristic, complemented
12#10590693C211yesmaximal, characteristic, complemented
13#10590581C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#79866—31nomaximal
17#78726—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30D3×#217—21no—
31C2×(C2×D3)⋊Dic3—21no—
32#63932C418yescomplemented
33C4×#625—21no—
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36Dic3×D12C2211yescharacteristic
37#63879—21no—
38#63878—21no—
39D3×Dic3⋊C4—21no—
40#63855C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42#63841C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63643C2211yescharacteristic, complemented
48#63642C2211yescharacteristic, complemented
49#63634C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#808C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63574C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62#5798—31no—
63C2×#932—31no—
64C2×#911—31no—
65#5546—31no—
66#5545—31no—
67#5504—31no—
68C3×#442—31no—
69C2×C3×#102—31no—
70Dic3×D8—31no—
71#5113—31no—
72#5101—31no—
73C4×#214—31no—
74C4×#213—31no—
75#4964—31no—
76#4861—31no—
77#4852—31no—
78#4785—31no—
79#4785—31no—
80#4785D311yescharacteristic, complemented
81#4772—31no—
82D3×#102D311yescharacteristic, complemented
83#4758—31no—
84#4758—31no—
85#4757—31no—
86#4757—31no—
87#4757—31no—
88#4757—61no—
89#4756—31no—
90#4756—31no—
91#4710—31no—
92#4708—31no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4C2×C414yescomplemented
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795C2×C414yescomplemented
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3754C2×C414yescomplemented
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#213C2×C414yescomplemented
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—22no—
132#3724—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3716C2×C414yescomplemented
144#3713C2×C414yescomplemented
145#3711C2×C414yescomplemented
146#2946—91noSylow
147C22×C3×D4—31no—
148C2×#237—31no—
149C2×D3×D4C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×D8—31no—
152C22×C3×C8—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—31no—
156C2×#217—61no—
157C2×#217—61no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3C2×D311yescharacteristic
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—61no—
171#932—38no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213C2×D311yescharacteristic
175C4×#67—61no—
176C4×#67—61no—
177C4×#67—61no—
178C4×#67—61no—
179C2×(C2×D3)⋊C4—61no—
180#926—31no—
181#926—31no—
182C2×Dic3⋊C4—61no—
183C2×#208—31no—
184#911—38no—
185C2×#204—31no—
186C2×ΓL(1,𝔽25)—31no—
187C2×D3×C8C2×D311yescharacteristic
188#893—31no—
189#893—31no—
190#893C2×D311yescharacteristic, complemented
191#892—31no—
192#892—61no—
193D3×C4⋊C4—61no—
194D3×C4⋊C4C2×D311yescharacteristic
195#887—31no—
196#887—31no—
197#887—31no—
198#887—61no—
199#67⋊C4—61no—
200#67⋊C4—61no—
201D3×C22⋊C4—61no—
202#877—61no—
203C4×D12—31no—
204#872—31no—
205C4×Dic6—31no—
206C3×#106—31no—
207C3×#102—21no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×#97—31no—
215#832—31no—
216#832C2×D311yescharacteristic
217#821—31no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic, complemented
220#818—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#815—31no—
226#815—31no—
227#815—61no—
228#815C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808C2×D311yescharacteristic, complemented
237#807—31no—
238#807—31no—
239#807—31no—
240#807—61no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—81no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C32×D4—21no—
250C32×D4C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258#634—21no—
259#634C22×C412yes—
260C3×#67—24no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12C22×C412yes—
270C3×D12C22×C412yes—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×C4×D3C22×C412yes—
274C3×C4×D3#4112yes—
275#625—24no—
276D3×Dic3—24no—
277D3×Dic3—81no—
278D3×Dic3—81no—
279D3×Dic3—81no—
280C32×C8—21no—
281C3⋊(C3⋊C8)C22×C412yes—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C2×AGL(1,ℤ/8)—91no—
285#520—91no—
286#518—91no—
287#442—31no—
288#442—91no—
289#440—91no—
290#440—91no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×D8—91no—
294C4×D8—91no—
295#428—91no—
296#416—91no—
297C2×#102—31no—
298#405—91no—
299C24×C3—61no—
300C23×D3—21no—
301C2×C3×D4—21no—
302C2×C3×D4—34no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—121no—
324#237—34no—
325#237—62no—
326D3×D4—22no—
327D3×D4C4×D314yescomplemented
328#235—34no—
329#235—62no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C3×D8—34no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—62no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358#217—21no—
359#217—31no—
360#217—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—121no—
368#214—34no—
369#214—34no—
370#214—34no—
371#214—64no—
372#213—34no—
373#213—34no—
374#213C4×D314yescomplemented
375(C2×D3)⋊C4—21no—
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—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—121no—
407C4×Dic3C22×D311yescharacteristic
408#208—34no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—34no—
415ΓL(1,𝔽25)—34no—
416D3×C8—22no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—84no—
430C2×C3×D3C4×D412yes—
431C32×C4—41no—
432C32×C4C23×C411yescharacteristic
433C32×C4C2×#4111yescharacteristic
434C3⋊Dic3—22no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C4×D412yes—
443C2×#41—91no—
444C22×D4—31no—
445AGL(1,ℤ/8)—98no—
446C2×SD16—91no—
447C2×SD16—91no—
448C2×D8—31no—
449C2×D8—91no—
450C2×M16—91no—
451C22×C8—31no—
452C4×Q8—91no—
453C4×Q8—91no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4—181no—
464#117—91no—
465#117—91no—
466#117—181no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—181no—
469C2×C22⋊C4—181no—
470C2×C22⋊C4—181no—
471#107—91no—
472#107—91no—
473#106—31no—
474#106—91no—
475#103—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102D3211yescharacteristic
483#97—31no—
484#97—91no—
485C4×C8—91no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—64no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—241no—
495C23×C3—241no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—24no—
499C22×D3—81no—
500C22×D3—81no—
501C22×D3D3×D411yescharacteristic
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—22no—
505C3×D4—32no—
506C3×D4—32no—
507C3×D4—41no—
508C3×D4—64no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4C2×C4×D312yes—
512C3×D4C2×C4×D312yes—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530#67—64no—
531#67—64no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—64no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—81no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3—242no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557D12—21no—
558D12—21no—
559D12C2×C4×D312yes—
560D12C2×C4×D312yes—
561C4×D3—64no—
562C4×D3—81no—
563C4×D3—81no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3C2×C4×D312yes—
568C4×D3#23712yes—
569Dic6—32no—
570Dic6—32no—
571Dic6—62no—
572Dic6—61no—
573Dic6—61no—
574Dic6—121no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—32no—
578C3×C8—41no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—32no—
582C3⋊C8—32no—
583C3⋊C8—62no—
584C3⋊C8C2×C4×D312yes—
585C2×C32—42no—
586C2×C32C2×C4×D411yescharacteristic
587C2×C32#57611yescharacteristic
588C2×C32#57711yescharacteristic
589C3×D3—22no—
590C3×D3—42no—
591C3×D3—42no—
592C24—61no—
593#41—94no—
594#41—182no—
595C2×Q8—91no—
596C2×D4—34no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—181no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612SD16—94no—
613SD16—94no—
614D8—34no—
615D8—94no—
616M16—94no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—62no—
620C2×C8—91no—
621C2×C8C2×D3211yescharacteristic
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—91no—
642C42—181no—
643C42—181no—
644C42—181no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—244no—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C2×D3×D411yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—84no—
676C2×D3#67⋊C412yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—32no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C22×C4×D311yescharacteristic
688C3×C4C22×C4×D311yescharacteristic
689C3×C4C2×#23711yescharacteristic
690C3×C4D3×#4111yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—62no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—62no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3#67⋊C412yes—
708C32#294611yescharacteristic, complemented, Sylow
709C23—21no—
710C23—31no—
711C23—64no—
712C23—61no—
713C23—61no—
714C23—241no—
715C23—241no—
716Q8—92no—
717Q8—181no—
718D4—21no—
719D4—32no—
720D4—32no—
721D4—64no—
722D4—61no—
723D4—61no—
724D4—184no—
725D4C4×D3212yes—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—184no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—32no—
749C8—61no—
750C8—92no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—42no—
756C2×C3—62no—
757C2×C3—82no—
758C2×C3—122no—
759C2×C3—122no—
760C2×C3C2×#67⋊C411yescharacteristic
761C2×C3C4×D3×D411yescharacteristic
762C2×C3#575711yescharacteristic
763C2×C3#576211yescharacteristic
764C2×C3#577411yescharacteristic
765C2×C3#577511yescharacteristic
766D3—22no—
767D3—42no—
768D3—42no—
769C22—22no—
770C22—32no—
771C22—41no—
772C22—41no—
773C22—61no—
774C22—61no—
775C22—62no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—244no—
782C22D32×D411yescharacteristic
783C4—32no—
784C4—41no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—181no—
791C4—182no—
792C4—361no—
793C4C2×C4×D3211yescharacteristic
794C4D3×#23711yescharacteristic
795C3—21no—
796C3#7872611yescharacteristic, complemented
797C3#7986611yescharacteristic, complemented
798C2—42no—
799C2—62no—
800C2—122no—
801C2—122no—
802C2D3×#67⋊C411yescharacteristic
803C2#1059473211yescharacteristic
804C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63932C2
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. #10595215C2semidirect
3. #10594359C2semidirect
4. #10592456C2semidirect
5. C3×#4785C2semidirect
6. C3×D3×#102C2semidirect
7. #10591435C2semidirect
8. #10591401C2semidirect
9. #10590954C2semidirect
10. #10590747C2semidirect
11. #10590741C2semidirect
12. #10590693C2semidirect
13. #10590581C2semidirect
14. #10590460C2semidirect
15. #10590452C2semidirect
22. #64096C22semidirect
26. C3×#893C22semidirect
32. #63932C4semidirect
35. #63898C22semidirect
41. #63844C22semidirect
47. #63643C22semidirect
48. #63642C22semidirect
49. #63634C22semidirect
52. C3×#821C22semidirect
53. C3×#815C22semidirect
55. C3×#808C22semidirect
56. #63575C22semidirect
57. #63574C22semidirect
58. #63567C22semidirect
59. #63563C22semidirect
60. #63553C22semidirect
61. Dic3×C3⋊C8C22semidirect
80. #4785D3semidirect
82. D3×#102D3semidirect
100. C3×D3×D4C2×C4semidirect
112. #3795C2×C4semidirect
116. #3754C2×C4semidirect
123. C3×#213C2×C4semidirect
143. #3716C2×C4semidirect
144. #3713C2×C4semidirect
145. #3711C2×C4semidirect
190. #893C2×D3semidirect
219. #821C2×D3semidirect
228. #815C2×D3semidirect
236. #808C2×D3semidirect
327. D3×D4C4×D3semidirect
374. #213C4×D3semidirect
708. C32#2946semidirect
796. C3#78726semidirect
797. C3#79866semidirect

Maximal subgroups

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

subgroupindex
#105952152
C2×#639322
#105943592
#105924562
C3×#47852
C3×D3×#1022
#105914352
#105914012
#105909542
#105907472
#105907412
#105906932
#105905812
#105904602
#105904522
#798663
#787263