Finite Group Databasebeta

← #11860547

Subgroups — #11860547

Order 1152.

1071 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic
2#10594606C211yesmaximal, characteristic, complemented
3#10594361C211yesmaximal, characteristic, complemented
4#10592560C211yesmaximal, characteristic, complemented
5C3×#4869C211yesmaximal, characteristic, complemented
6C3×#4852C211yesmaximal, characteristic, complemented
7#10590910C211yesmaximal, characteristic, complemented
8#10590766C211yesmaximal, characteristic, complemented
9Dic3×D24C211yesmaximal, characteristic, complemented
10#10590611C211yesmaximal, characteristic, complemented
11#10590593C211yesmaximal, characteristic, complemented
12#10590475C211yesmaximal, characteristic, complemented
13#10590455C211yesmaximal, characteristic, complemented
14#10590454C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#79866—31nomaximal
17#79647—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic, complemented
28C3×#887C2211yescharacteristic, complemented
29D3×(C2×D3)⋊C4—21no—
30D3×(C2×D3)⋊C4—21no—
31C4×#626—21no—
32#63902—21no—
33C4×#625—21no—
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic, complemented
37#63881—21no—
38#63877—21no—
39D3×Dic3⋊C4—21no—
40#63874C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3710C2211yescharacteristic
45#63798C418yescomplemented
46C32×#106C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49#63634C2211yescharacteristic, complemented
50C3×#815C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×#911—31no—
64#5574—31no—
65#5546—31no—
66#5545—31no—
67#5545—31no—
68C3×#442—31no—
69C3×C4×SD16—31no—
70#5164—31no—
71Dic3×D8—31no—
72#5026—31no—
73C4×#214—31no—
74#5014—31no—
75C4×#213—31no—
76#4869D311yescharacteristic, complemented
77#4861—31no—
78#4861—31no—
79#4861—61no—
80#4852D311yescharacteristic, complemented
81#4804—31no—
82#4788—31no—
83#4785—31no—
84#4772—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4757—31no—
88#4756—31no—
89#4710—31no—
90#4708—31no—
91C4×D24—31no—
92#4689—31no—
93C22×D32—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802C2×C414yescomplemented
111#3796—22no—
112#3796C2×C414yescomplemented
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3743C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D24C2×C414yescomplemented
133C3×#204C2×C414yescomplemented
134#3724D411yescharacteristic
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137#3722D411yescharacteristic
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3715C2×C414yescomplemented
144#3713C2×C414yescomplemented
145#3710—22no—
146#2946—91noSylow
147C2×#239—31no—
148C2×#237—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×C3×SD16—31no—
152C2×C3×D8—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162C2×#214—31no—
163C2×#213—31no—
164C2×#213—31no—
165C4×#67—61no—
166C4×#67—61no—
167C4×#67—61no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×Dic3⋊C4—61no—
171#914—38no—
172#911—38no—
173C2×D24C2×D311yescharacteristic
174C2×#204C2×D311yescharacteristic
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—61no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#893—61no—
181#893C2×D311yescharacteristic
182#893C2×D311yescharacteristic
183#893C2×D311yescharacteristic, complemented
184#892—31no—
185#892—31no—
186#892—61no—
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×#106—21no—
207C3×#106C2×D311yescharacteristic, complemented
208C3×#106C2×D311yescharacteristic, complemented
209C3×#103—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#818—31no—
223#818—31no—
224#818—61no—
225#816—31no—
226#815—31no—
227#815C2×D311yescharacteristic, complemented
228C8×Dic3—31no—
229C8×Dic3C2×D311yescharacteristic, complemented
230#810C2×D311yescharacteristic, complemented
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#808—31no—
235#808—31no—
236#808—61no—
237#807—31no—
238#807—31no—
239#807—61no—
240#803—31no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C2×D32—24no—
247C2×D32—81no—
248C2×D32—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4×C3⋊D3—81no—
256C4×C3⋊D3C22×C412yes—
257C4×C3⋊D3#4112yes—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×D12C22×C412yes—
268C3×D12C22×C412yes—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6C22×C412yes—
274#626—24no—
275#625—24no—
276D3×Dic3—24no—
277D3×Dic3—81no—
278D3×Dic3—81no—
279D3×Dic3—81no—
280C32×C8C22×C412yes—
281C3⋊(C3⋊C8)C22×C412yes—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
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—31no—
292C4×SD16—91no—
293C4×D8—91no—
294C4×D8—91no—
295#428—91no—
296#416—91no—
297C2×#102—91no—
298#405—91no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×Q8—31no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—34no—
316#239—62no—
317#237—34no—
318#237—62no—
319D3×D4—34no—
320D3×D4—34no—
321D3×D4—62no—
322D3×D4—62no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—121no—
340C2×Dic6C22×D311yescharacteristic
341C3×SD16—34no—
342C3×D8—34no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#215—34no—
365#214—34no—
366#213—34no—
367#213—34no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397C4×Dic3—21no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D24C4×D314yescomplemented
411#204C4×D314yescomplemented
412ΓL(1,𝔽25)—34no—
413ΓL(1,𝔽25)—34no—
414ΓL(1,𝔽25)—64no—
415D3×C8—62no—
416D3×C8—62no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3C4×D412yes—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430D32—84no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C23×C411yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3⋊Dic3C4×D412yes—
438C3×Dic3—22no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C2×#41—91no—
444C22×D4—91no—
445AGL(1,ℤ/8)—98no—
446C2×SD16—31no—
447C2×SD16—91no—
448C2×D8—31no—
449C2×D8—91no—
450C2×M16—91no—
451C22×C8—91no—
452C4×Q8—31no—
453C4×Q8—91no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—31no—
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—91no—
468C2×C4⋊C4—181no—
469C2×C22⋊C4—181no—
470C2×C22⋊C4—181no—
471#107—91no—
472#107—91no—
473#106—91no—
474#106D3211yescharacteristic, complemented
475#103—31no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#97—31no—
484#97—91no—
485C4×C8—31no—
486C4×C8—91no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—61no—
496C22×D3—64no—
497C22×D3—64no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3—241no—
502C3×Q8—32no—
503C3×Q8—61no—
504C3×D4—32no—
505C3×D4—32no—
506C3×D4—32no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—241no—
523C2×C3×C4—241no—
524C2×C3×C4—241no—
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—64no—
528#67—64no—
529#67—64no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—64no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—21no—
550D12—21no—
551D12—64no—
552D12C2×C4×D312yes—
553D12C2×C4×D312yes—
554D12C2×C4×D312yes—
555C4×D3—32no—
556C4×D3—32no—
557C4×D3—32no—
558C4×D3—32no—
559C4×D3—62no—
560C4×D3—62no—
561C4×D3—64no—
562C4×D3—81no—
563C4×D3—81no—
564C4×D3—81no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—242no—
571Dic6—21no—
572Dic6C2×C4×D312yes—
573C3×C8—22no—
574C3×C8—61no—
575C3×C8—61no—
576C3×C8C2×C4×D312yes—
577C3×C8C2×C4×D312yes—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—32no—
581C3⋊C8—32no—
582C3⋊C8—62no—
583C2×C32C2×C4×D411yescharacteristic
584C2×C32#57611yescharacteristic
585C2×C32#57711yescharacteristic
586C3⋊D3—22no—
587C3×D3—42no—
588C3×D3—42no—
589C3×D3—42no—
590C24—181no—
591#41—94no—
592#41—182no—
593C2×Q8—31no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—94no—
598C2×D4—181no—
599C2×D4—182no—
600C2×D4—181no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610SD16—34no—
611SD16—94no—
612D8—34no—
613D8—94no—
614M16—94no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—182no—
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—31no—
640C42—61no—
641C42—181no—
642C42—181no—
643C22×C3—21no—
644C22×C3—62no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—32no—
659C2×D3—32no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—62no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—244no—
674C2×D3—244no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—62no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4C22×C4×D311yescharacteristic
689C3×C4C22×C4×D311yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4D3×#4111yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—22no—
697Dic3—32no—
698Dic3—32no—
699Dic3—62no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—241no—
705Dic3—241no—
706C32#294611yescharacteristic, complemented, Sylow
707C23—61no—
708C23—61no—
709C23—61no—
710C23—91no—
711C23—184no—
712C23—721no—
713C23—721no—
714Q8—32no—
715Q8—61no—
716D4—32no—
717D4—32no—
718D4—32no—
719D4—61no—
720D4—61no—
721D4—61no—
722D4—184no—
723D4—184no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—91no—
732C2×C4—92no—
733C2×C4—92no—
734C2×C4—184no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—241no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—92no—
748C8C4×D3212yes—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—122no—
753C2×C3—122no—
754C2×C3—122no—
755C2×C3C4×D3×D411yescharacteristic
756C2×C3C4×D3×D411yescharacteristic
757C2×C3#576211yescharacteristic
758C2×C3#576911yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3#577511yescharacteristic
761D3—42no—
762D3—42no—
763D3—42no—
764D3—62no—
765D3—62no—
766D3—122no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—92no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—181no—
778C22—181no—
779C22—724no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—41no—
783C4—62no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—61no—
788C4—92no—
789C4—361no—
790C4—361no—
791C4C2×C4×D3211yescharacteristic
792C4#6431911yescharacteristic
793C3—21no—
794C3#7964711yescharacteristic, complemented
795C3#7986611yescharacteristic, complemented
796C2—122no—
797C2—122no—
798C2—122no—
799C2—182no—
800C2#1059460511yescharacteristic
801C2#1059474911yescharacteristic
802C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63798C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594606C2semidirect
3. #10594361C2semidirect
4. #10592560C2semidirect
5. C3×#4869C2semidirect
6. C3×#4852C2semidirect
7. #10590910C2semidirect
8. #10590766C2semidirect
9. Dic3×D24C2semidirect
10. #10590611C2semidirect
11. #10590593C2semidirect
12. #10590475C2semidirect
13. #10590455C2semidirect
14. #10590454C2semidirect
15. #10590452C2semidirect
27. C3×#893C22semidirect
28. C3×#887C22semidirect
36. Dic3×D12C22semidirect
41. Dic3×Dic6C22semidirect
45. #63798C4semidirect
46. C32×#106C22semidirect
47. #63645C22semidirect
48. #63635C22semidirect
49. #63634C22semidirect
50. C3×#815C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
55. C3×#809C22semidirect
56. #63566C22semidirect
59. #63563C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
76. #4869D3semidirect
80. #4852D3semidirect
110. #3802C2×C4semidirect
112. #3796C2×C4semidirect
122. #3743C2×C4semidirect
132. C3×D24C2×C4semidirect
133. C3×#204C2×C4semidirect
143. #3715C2×C4semidirect
144. #3713C2×C4semidirect
183. #893C2×D3semidirect
191. #887C2×D3semidirect
207. C3×#106C2×D3semidirect
208. C3×#106C2×D3semidirect
227. #815C2×D3semidirect
229. C8×Dic3C2×D3semidirect
230. #810C2×D3semidirect
233. #809C2×D3semidirect
410. D24C4×D3semidirect
411. #204C4×D3semidirect
474. #106D32semidirect
706. C32#2946semidirect
794. C3#79647semidirect
795. C3#79866semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
#105946062
#105943612
#105925602
C3×#48692
C3×#48522
#105909102
#105907662
Dic3×D242
#105906112
#105905932
#105904752
#105904552
#105904542
#105904522
#798663
#796473