Finite Group Databasebeta

← #11860507

Subgroups — #11860507

Order 1152.

1077 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
1C2×#63798C211yesmaximal, characteristic
2#10593996C211yesmaximal, characteristic, complemented
3#10593889C211yesmaximal, characteristic, complemented
4#10592388C211yesmaximal, characteristic, complemented
5C3×C4×D24C211yesmaximal, characteristic, complemented
6C3×C4×#204C211yesmaximal, characteristic, complemented
7#10590956C211yesmaximal, characteristic, complemented
8#10590940C211yesmaximal, characteristic, complemented
9#10590781C211yesmaximal, characteristic, complemented
10#10590779C211yesmaximal, characteristic, complemented
11#10590742C211yesmaximal, characteristic, complemented
12#10590740C211yesmaximal, characteristic, complemented
13#10590688C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590344C211yesmaximal, characteristic, complemented
16#79647—31nomaximal
17#79587—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22#64081C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic, complemented
28C3×C4×Dic6C2211yescharacteristic, complemented
29D3×(C2×D3)⋊C4—21no—
30D3×(C2×D3)⋊C4—21no—
31#63904—21no—
32#63900C2211yescharacteristic
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36#63880—21no—
37#63879—21no—
38#63879—21no—
39#63877—21no—
40D3×Dic3⋊C4—21no—
41#63849C2211yescharacteristic
42#63843C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45#63798C418yescomplemented
46C32×C4×C8C2211yescharacteristic, complemented
47#63642C2211yescharacteristic, complemented
48C8×C3⋊Dic3C2211yescharacteristic, complemented
49#63630C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63574C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#63562C2211yescharacteristic, 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—
85#4758—31no—
86#4756—31no—
87#4756—31no—
88C4×D24D311yescharacteristic, complemented
89C4×#204D311yescharacteristic, complemented
90#4689—31no—
91#4689—31no—
92#4689—61no—
93C22×D32—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#625—21no—
104C2×#624—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
114C2×C32×C8C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752D411yescharacteristic
117#3752D411yescharacteristic
118#3750D411yescharacteristic
119#3750D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3743C2×C414yescomplemented
124C8×C3⋊D3—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×D24C2×C414yescomplemented
135C3×#204C2×C414yescomplemented
136#3724—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32—21no—
144#3715C2×C414yescomplemented
145#3713C2×C414yescomplemented
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—
180C2×D3×C8—61no—
181#893—31no—
182#893—31no—
183#893—31no—
184#893—61no—
185#892—31no—
186#892—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190#887—31no—
191#67⋊C4—61no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196#877—61no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200C4×D12C2×D311yescharacteristic, complemented
201#872—31no—
202#872—31no—
203#872—61no—
204#872—61no—
205C4×Dic6C2×D311yescharacteristic, complemented
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×C4×C8—21no—
213C3×C4×C8C2×D311yescharacteristic, complemented
214C3×C4×C8C2×D311yescharacteristic, complemented
215#835—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#821C2×D311yescharacteristic
220#821C2×D311yescharacteristic
221#821C2×D311yescharacteristic, complemented
222#818C2×D311yescharacteristic, complemented
223#817C2×D311yescharacteristic, complemented
224#816C2×D311yescharacteristic, complemented
225#815—31no—
226#815—31no—
227#815—61no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239#803—31no—
240#803—31no—
241#803—61no—
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×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4×C3⋊D3C22×C412yes—
256C4×C3⋊D3#4112yes—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12C22×C412yes—
266C3×D12C22×C412yes—
267C3×D12C22×C412yes—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273#626—24no—
274#625—24no—
275#624—81no—
276D3×Dic3—24no—
277D3×Dic3—81no—
278D3×Dic3—81no—
279D3×Dic3—81no—
280C32×C8—21no—
281C32×C8C22×C412yes—
282C3⋊(C3⋊C8)—21no—
283C3⋊(C3⋊C8)C22×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—
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×Dic6C22×D311yescharacteristic
340C3×SD16—34no—
341C3×D8—34no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—61no—
361#217—61no—
362#217—61no—
363#215—34no—
364#214—34no—
365#213—34no—
366#213—34no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—61no—
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—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—61no—
410D24C4×D314yescomplemented
411#204C4×D314yescomplemented
412ΓL(1,𝔽25)—34no—
413ΓL(1,𝔽25)—34no—
414ΓL(1,𝔽25)—64no—
415D3×C8—62no—
416D3×C8—62no—
417D3×C8—64no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3C4×D412yes—
422C2×C3×D3—22no—
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—41no—
430C2×C3×D3—41no—
431D32—84no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4C23×C411yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3C4×D412yes—
439C3×Dic3—22no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41—91no—
445C22×D4—91no—
446AGL(1,ℤ/8)—98no—
447C2×SD16—31no—
448C2×SD16—91no—
449C2×D8—31no—
450C2×D8—91no—
451C2×M16—91no—
452C22×C8—91no—
453C4×Q8—31no—
454C4×Q8—91no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4—181no—
464C4×D4—181no—
465#117—91no—
466#117—91no—
467#117—181no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—181no—
470C2×C22⋊C4—181no—
471C2×C22⋊C4—181no—
472#107—31no—
473#107—91no—
474#106—31no—
475#106—91no—
476#103—31no—
477#103—91no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#97—91no—
485#97—91no—
486C4×C8—91no—
487C4×C8D3211yescharacteristic, complemented
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C22×D3—64no—
498C22×D3—64no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3—241no—
503C3×Q8—32no—
504C3×Q8—61no—
505C3×D4—32no—
506C3×D4—32no—
507C3×D4—32no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—64no—
529#67—64no—
530#67—64no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—64no—
546C2×Dic3—241no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549D12—21no—
550D12—21no—
551D12—21no—
552D12—64no—
553D12C2×C4×D312yes—
554D12C2×C4×D312yes—
555D12C2×C4×D312yes—
556C4×D3—32no—
557C4×D3—32no—
558C4×D3—32no—
559C4×D3—32no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—64no—
563C4×D3—81no—
564C4×D3—81no—
565C4×D3—81no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571Dic6—21no—
572Dic6C2×C4×D312yes—
573C3×C8—22no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—22no—
577C3×C8C2×C4×D312yes—
578C3×C8C2×C4×D312yes—
579C3⋊C8—32no—
580C3⋊C8—32no—
581C3⋊C8—62no—
582C3⋊C8—62no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C2×C32C2×C4×D411yescharacteristic
586C2×C32#57611yescharacteristic
587C2×C32#57711yescharacteristic
588C3⋊D3—22no—
589C3×D3—42no—
590C3×D3—42no—
591C3×D3—42no—
592C24—181no—
593#41—94no—
594#41—182no—
595C2×Q8—31no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—94no—
600C2×D4—181no—
601C2×D4—182no—
602C2×D4—181no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612SD16—34no—
613SD16—94no—
614D8—34no—
615D8—94no—
616M16—94no—
617C2×C8—91no—
618C2×C8—91no—
619C2×C8—182no—
620C2×C8C2×D3211yescharacteristic
621C2×C8C2×D3211yescharacteristic
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—61no—
627C4⋊C4—91no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—61no—
641C42—91no—
642C42—181no—
643C42—181no—
644C42C2×D3211yescharacteristic
645C22×C3—21no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—62no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—32no—
661C2×D3—32no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—62no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—244no—
676C2×D3—244no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—62no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4C22×C4×D311yescharacteristic
691C3×C4C22×C4×D311yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4D3×#4111yescharacteristic
694Dic3—22no—
695Dic3—32no—
696Dic3—32no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—62no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—121no—
707Dic3—121no—
708C32#294611yescharacteristic, complemented, Sylow
709C23—61no—
710C23—61no—
711C23—61no—
712C23—91no—
713C23—184no—
714C23—721no—
715C23—721no—
716Q8—32no—
717Q8—61no—
718D4—32no—
719D4—32no—
720D4—32no—
721D4—61no—
722D4—61no—
723D4—61no—
724D4—184no—
725D4—184no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—91no—
732C2×C4—92no—
733C2×C4—92no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—184no—
737C2×C4—241no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4#380211yescharacteristic
745C2×C4#380211yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—92no—
749C8—181no—
750C8C4×D3212yes—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—122no—
755C2×C3—122no—
756C2×C3—122no—
757C2×C3C4×D3×D411yescharacteristic
758C2×C3C4×D3×D411yescharacteristic
759C2×C3#575711yescharacteristic
760C2×C3#576211yescharacteristic
761C2×C3#576911yescharacteristic
762C2×C3#577011yescharacteristic
763D3—42no—
764D3—42no—
765D3—42no—
766D3—62no—
767D3—62no—
768D3—122no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—92no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—181no—
780C22—181no—
781C22—724no—
782C22C2×#380211yescharacteristic
783C4—21no—
784C4—21no—
785C4—62no—
786C4—92no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—181no—
792C4—181no—
793C4C2×C4×D3211yescharacteristic
794C4#6430611yescharacteristic
795C3—21no—
796C3#7958711yescharacteristic, complemented
797C3#7964711yescharacteristic, complemented
798C2—122no—
799C2—122no—
800C2—122no—
801C2—182no—
802C2C4×#380211yescharacteristic
803C2#1059468611yescharacteristic
804C2#1059468711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63798C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593996C2semidirect
3. #10593889C2semidirect
4. #10592388C2semidirect
5. C3×C4×D24C2semidirect
6. C3×C4×#204C2semidirect
7. #10590956C2semidirect
8. #10590940C2semidirect
9. #10590781C2semidirect
10. #10590779C2semidirect
11. #10590742C2semidirect
12. #10590740C2semidirect
13. #10590688C2semidirect
14. #10590358C2semidirect
15. #10590344C2semidirect
27. C3×C4×D12C22semidirect
28. C3×C4×Dic6C22semidirect
35. #63898C22semidirect
42. #63843C22semidirect
45. #63798C4semidirect
46. C32×C4×C8C22semidirect
47. #63642C22semidirect
48. C8×C3⋊Dic3C22semidirect
49. #63630C22semidirect
52. C3×#821C22semidirect
53. C3×#818C22semidirect
54. C3×#817C22semidirect
55. C3×#816C22semidirect
56. #63576C22semidirect
57. #63574C22semidirect
58. #63565C22semidirect
61. #63562C22semidirect
88. C4×D24D3semidirect
89. C4×#204D3semidirect
110. #3802C2×C4semidirect
112. #3796C2×C4semidirect
123. #3743C2×C4semidirect
134. C3×D24C2×C4semidirect
135. C3×#204C2×C4semidirect
144. #3715C2×C4semidirect
145. #3713C2×C4semidirect
200. C4×D12C2×D3semidirect
205. C4×Dic6C2×D3semidirect
213. C3×C4×C8C2×D3semidirect
214. C3×C4×C8C2×D3semidirect
221. #821C2×D3semidirect
222. #818C2×D3semidirect
223. #817C2×D3semidirect
224. #816C2×D3semidirect
410. D24C4×D3semidirect
411. #204C4×D3semidirect
487. C4×C8D32semidirect
708. C32#2946semidirect
796. C3#79587semidirect
797. C3#79647semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
#105939962
#105938892
#105923882
C3×C4×D242
C3×C4×#2042
#105909562
#105909402
#105907812
#105907792
#105907422
#105907402
#105906882
#105903582
#105903442
#796473
#795873