Finite Group Databasebeta

← C4×#63811 #11860403

Subgroups — C4×#63811 #11860403

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63811C211yesmaximal, characteristic
2C4×#3797C211yesmaximal, characteristic, complemented
3C4×#3796C211yesmaximal, characteristic
4C4×#3743C211yesmaximal, characteristic, complemented
5C3×C4×Dic12C211yesmaximal, characteristic, complemented
6C3×C4×#204C211yesmaximal, characteristic, complemented
7#10590957C211yesmaximal, characteristic
8#10590819C211yesmaximal, characteristic, complemented
9#10590791C211yesmaximal, characteristic, complemented
10#10590779C211yesmaximal, characteristic, complemented
11#10590743C211yesmaximal, characteristic, complemented
12#10590691C211yesmaximal, characteristic, complemented
13#10590688C211yesmaximal, characteristic, complemented
14C4×#3718C211yesmaximal, characteristic, complemented
15C4×#3715C211yesmaximal, characteristic, complemented
16C4×#918—31nomaximal
17C4×#915—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C42×C3⋊D3C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C4×#627—21no—
30C4×#626—21no—
31#63900C2211yescharacteristic
32#63898C2211yescharacteristic
33#63883—21no—
34C4×#624—21no—
35#63881—21no—
36#63878—21no—
37C4×D3×Dic3—21no—
38#63849C2211yescharacteristic
39#63843C2211yescharacteristic
40#63843C2211yescharacteristic
41#63843C2211yescharacteristic
42#63838—21no—
43C2×#3718C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45#63811C418yesdirect product factor
46C32×C4×C8C2211yescharacteristic
47#63642C2211yescharacteristic
48#63642C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56#63576C2211yescharacteristic
57#63574C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#63562C2211yescharacteristic
62C2×#918—31no—
63C2×#915—31no—
64C4×#239—31no—
65C4×D3×Q8—31no—
66C4×D3×Q8—31no—
67C4×#237—31no—
68C3×C4×Q16—31no—
69C3×C4×SD16—31no—
70#5184—31no—
71#5164—31no—
72C4×#216—31no—
73C4×#216—31no—
74C4×#215—31no—
75C4×#214—31no—
76#4889—31no—
77#4881—31no—
78#4861—31no—
79#4853—31no—
80#4817—31no—
81#4803—31no—
82#4802—31no—
83#4802—31no—
84#4789—31no—
85#4789—31no—
86#4771—31no—
87#4757—31no—
88C4×Dic12D311yescharacteristic, complemented
89C4×#204D311yescharacteristic, complemented
90C4×ΓL(1,𝔽25)—31no—
91C4×ΓL(1,𝔽25)—31no—
92C4×ΓL(1,𝔽25)—61no—
93C2×C4×C3⋊D3D411yescharacteristic
94C2×C4×C3⋊D3D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#624—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107#3797—22no—
108#3797C2×C414yescomplemented
109#3796—22no—
110#3796C2×C414yes—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C42C2311yescharacteristic
114C4×C3⋊Dic3D411yescharacteristic
115C4×C3⋊Dic3D411yescharacteristic
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3743—22no—
120#3743C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×Dic12C2×C414yescomplemented
133C3×#204C2×C414yescomplemented
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144#3718C2×C414yescomplemented
145#3715C2×C414yescomplemented
146C4×#137—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×#237—31no—
151C2×C3×Q16—31no—
152C2×C3×SD16—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#215—31no—
163D4×Dic3—31no—
164C2×#214—31no—
165C4×#67—61no—
166C2×C4×Dic3—61no—
167#918—38no—
168#915—38no—
169C2×Dic12C2×D311yescharacteristic
170C2×#204C2×D311yescharacteristic
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—61no—
176C2×ΓL(1,𝔽25)—61no—
177#893—31no—
178#893—61no—
179#892—31no—
180#892—31no—
181#892—61no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—61no—
185D3×C4⋊C4—61no—
186#887—31no—
187#887—31no—
188#887—31no—
189#887—61no—
190#887—61no—
191#67⋊C4—61no—
192#877—61no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195C42×D3—31no—
196C42×D3—31no—
197C42×D3—61no—
198C42×D3—61no—
199C42×D3—61no—
200C42×D3—61no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C4×Dic6C2×D311yescharacteristic
204C4×Dic6C2×D311yescharacteristic
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×C4×C8—21no—
213C3×C4×C8C2×D311yescharacteristic
214C3×C4×C8C2×D311yescharacteristic
215#835—31no—
216#835—31no—
217#835—31no—
218#832—31no—
219#821C2×D311yescharacteristic
220#818C2×D311yescharacteristic
221#817C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—31no—
228#815—31no—
229#815—61no—
230#815—61no—
231#810—31no—
232#810—31no—
233#810—31no—
234#809—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8—61no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—22no—
251C4×C3⋊D3—41no—
252C4×C3⋊D3C22×C412yes—
253C4×C3⋊D3#4112yes—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C3×D12—21no—
262C3×D12C22×C412yes—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6C22×C412yes—
268C3×Dic6C22×C412yes—
269C3×Dic6C22×C412yes—
270#627—24no—
271#626—24no—
272#624—24no—
273#624—42no—
274D3×Dic3—24no—
275D3×Dic3—42no—
276C32×C8—21no—
277C32×C8C22×C412yes—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)C22×C412yes—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—91no—
286#440—91no—
287C4×Q16—31no—
288C4×Q16—91no—
289C4×SD16—31no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—91no—
294C4×M16—91no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303#239—34no—
304#239—62no—
305D3×Q8—34no—
306D3×Q8—34no—
307D3×Q8—62no—
308D3×Q8—62no—
309#237—34no—
310#237—62no—
311C2×D12—61no—
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×Q16—34no—
335C3×SD16—34no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—21no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—61no—
357#216—34no—
358#216—34no—
359#215—34no—
360#214—34no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380C4×Dic3—21no—
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406Dic12C4×D314yescomplemented
407#204C4×D314yescomplemented
408ΓL(1,𝔽25)—34no—
409ΓL(1,𝔽25)—34no—
410ΓL(1,𝔽25)—64no—
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)—62no—
413ΓL(1,𝔽25)—64no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3C4×D412yes—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C32×C4—21no—
422C32×C4#13712yescomplemented
423C32×C4C23×C411yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3C4×D412yes—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—22no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×Q8—91no—
437#137—98no—
438C2×Q16—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×M16—91no—
443C2×M16—91no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—181no—
451C4×Q8—181no—
452C4×D4—31no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456#117—91no—
457#117—181no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460C2×C42—91no—
461C2×C42—181no—
462C2×C42—181no—
463#107—31no—
464#107—91no—
465#106—31no—
466#106—91no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#97—91no—
476#97—91no—
477C4×C8—91no—
478C4×C8D3211yescharacteristic
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C3×Q8—32no—
485C3×Q8—32no—
486C3×Q8—32no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—32no—
491C3×D4—61no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—122no—
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—64no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—64no—
527C2×Dic3—122no—
528D12—21no—
529D12—64no—
530D12C2×C4×D312yes—
531C4×D3—32no—
532C4×D3—32no—
533C4×D3—32no—
534C4×D3—32no—
535C4×D3—42no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—64no—
539C4×D3—64no—
540C4×D3—64no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—122no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—121no—
547C4×D3—121no—
548C4×D3—122no—
549C4×D3—122no—
550Dic6—21no—
551Dic6—21no—
552Dic6—21no—
553Dic6—64no—
554Dic6—64no—
555Dic6C2×C4×D312yes—
556Dic6C2×C4×D312yes—
557Dic6C2×C4×D312yes—
558C3×C8—22no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—22no—
562C3×C8C2×C4×D312yes—
563C3×C8C2×C4×D312yes—
564C3⋊C8—32no—
565C3⋊C8—32no—
566C3⋊C8—62no—
567C3⋊C8—62no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C2×C32C2×C4×D411yescharacteristic
571C2×C32C2×#13711yescharacteristic
572C2×C32#57511yescharacteristic
573C3⋊D3—22no—
574C3×D3—42no—
575#41—94no—
576#41—182no—
577C2×Q8—31no—
578C2×Q8—31no—
579C2×Q8—31no—
580C2×Q8—94no—
581C2×Q8—181no—
582C2×Q8—182no—
583C2×D4—31no—
584C2×D4—181no—
585C22×C4—61no—
586C22×C4—91no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—181no—
593Q16—34no—
594Q16—94no—
595SD16—34no—
596SD16—94no—
597M16—94no—
598M16—182no—
599C2×C8—91no—
600C2×C8—91no—
601C2×C8C2×D3211yescharacteristic
602C2×C8C2×D3211yescharacteristic
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—61no—
618C42—61no—
619C42—61no—
620C42—91no—
621C42—91no—
622C42—91no—
623C42—181no—
624C42—181no—
625C42—181no—
626C42—181no—
627C42C2×D3211yescharacteristic
628C22×C3—21no—
629C22×C3—62no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—22no—
635C2×D3—32no—
636C2×D3—32no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—62no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—121no—
645C2×D3—121no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—22no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4#91512yescomplemented
660C3×C4#91812yescomplemented
661C3×C4C22×C4×D311yescharacteristic
662C3×C4C22×C4×D311yescharacteristic
663C3×C4D3×#4111yescharacteristic
664C3×C4D3×#4111yescharacteristic
665Dic3—22no—
666Dic3—22no—
667Dic3—22no—
668Dic3—32no—
669Dic3—32no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—62no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—121no—
680Dic3—121no—
681C32C4×#13711yescharacteristic, complemented, Sylow
682C23—61no—
683C23—91no—
684Q8—32no—
685Q8—32no—
686Q8—32no—
687Q8—61no—
688Q8—61no—
689Q8—61no—
690Q8—184no—
691D4—32no—
692D4—61no—
693D4—184no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—91no—
702C2×C4—92no—
703C2×C4—92no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—122no—
707C2×C4—184no—
708C2×C4—184no—
709C2×C4—182no—
710C2×C4—361no—
711C2×C4—362no—
712C2×C4—362no—
713C2×C4#380211yescharacteristic
714C2×C4#380211yescharacteristic
715C2×C4C22×D3211yescharacteristic
716C8—21no—
717C8—92no—
718C8—181no—
719C8C4×D3212yes—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—122no—
724C2×C3C4×D3×D411yescharacteristic
725C2×C3C4×D3×D411yescharacteristic
726C2×C3C2×#91511yescharacteristic
727C2×C3C2×#91811yescharacteristic
728C2×C3#576811yescharacteristic
729C2×C3#576811yescharacteristic
730D3—42no—
731D3—62no—
732D3—62no—
733D3—122no—
734C22—62no—
735C22—92no—
736C22—121no—
737C22—121no—
738C22—181no—
739C22—181no—
740C22C2×#380211yescharacteristic
741C4—21no—
742C4—62no—
743C4—62no—
744C4—62no—
745C4—92no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—181no—
751C4—181no—
752C4#6381112yesdirect product factor
753C4C2×C4×D3211yescharacteristic
754C4#6430611yescharacteristic
755C3—21no—
756C3C4×#91511yescharacteristic, complemented
757C3C4×#91811yescharacteristic, complemented
758C2—122no—
759C2—182no—
760C2C4×#380211yescharacteristic
761C2#1059468511yescharacteristic
762C2C2×#6381111yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×#3797C2semidirect
4. C4×#3743C2semidirect
5. C3×C4×Dic12C2semidirect
6. C3×C4×#204C2semidirect
8. #10590819C2semidirect
9. #10590791C2semidirect
10. #10590779C2semidirect
11. #10590743C2semidirect
12. #10590691C2semidirect
13. #10590688C2semidirect
14. C4×#3718C2semidirect
15. C4×#3715C2semidirect
45. #63811C4direct (N × H)
88. C4×Dic12D3semidirect
89. C4×#204D3semidirect
108. #3797C2×C4semidirect
120. #3743C2×C4semidirect
132. C3×Dic12C2×C4semidirect
133. C3×#204C2×C4semidirect
144. #3718C2×C4semidirect
145. #3715C2×C4semidirect
406. Dic12C4×D3semidirect
407. #204C4×D3semidirect
422. C32×C4#137semidirect
659. C3×C4#915semidirect
660. C3×C4#918semidirect
681. C32C4×#137semidirect
752. C4#63811direct (N × H)
756. C3C4×#915semidirect
757. C3C4×#918semidirect

Maximal subgroups

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

subgroupindex
C2×#638112
C4×#37972
C4×#37962
C4×#37432
C3×C4×Dic122
C3×C4×#2042
#105909572
#105908192
#105907912
#105907792
#105907432
#105906912
#105906882
C4×#37182
C4×#37152
C4×#9183
C4×#9153