Finite Group Databasebeta

← #11860447

Subgroups — #11860447

Order 1152.

1028 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63801C211yesmaximal, characteristic
2C4×#3799C211yesmaximal, characteristic
3C4×D3×Dic6C211yesmaximal, characteristic, complemented
4#10592409C211yesmaximal, characteristic, complemented
5C3×#4716C211yesmaximal, characteristic, complemented
6C3×#4707C211yesmaximal, characteristic, complemented
7#10590948C211yesmaximal, characteristic, complemented
8Dic3×Dic12C211yesmaximal, characteristic, complemented
9#10590793C211yesmaximal, characteristic, complemented
10#10590792C211yesmaximal, characteristic, complemented
11#10590758C211yesmaximal, characteristic, complemented
12#10590681C211yesmaximal, characteristic, complemented
13#10590671C211yesmaximal, characteristic
14#10590383C211yesmaximal, characteristic, complemented
15#10590362C211yesmaximal, characteristic, complemented
16#79829—31nomaximal
17C4×#909—31nomaximal
18C2×#3799C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C4×#627—21no—
30#63904—21no—
31C4×#626—21no—
32#63894C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34C4×#624—21no—
35D3×Dic3⋊C4—21no—
36C4×D3×Dic3—21no—
37#63844C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63837—21no—
42#63836—21no—
43C2×#3719C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45#63801C418yescomplemented
46C32×#97C2211yescharacteristic
47#63648C2211yescharacteristic
48#63645C2211yescharacteristic
49#63643C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#803C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#63564C2211yescharacteristic
62C2×#918—31no—
63C2×#909—31no—
64C4×#239—31no—
65C4×D3×Q8—31no—
66C4×#235—31no—
67C2×C4×Dic6—31no—
68C3×#441—31no—
69C3×C4×M16—31no—
70Dic3×Q16—31no—
71#5133—31no—
72#5121—31no—
73#5120—31no—
74#5030—31no—
75#5026—31no—
76#4861—31no—
77#4852—31no—
78#4803—31no—
79#4802—31no—
80#4790—31no—
81#4788—31no—
82#4716—31no—
83#4716D311yescharacteristic, complemented
84#4710—31no—
85#4710—31no—
86#4710—31no—
87#4710—61no—
88#4707D311yescharacteristic, complemented
89C4×Dic12—31no—
90C4×Dic12—31no—
91C4×#204—31no—
92C4×#204—31no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×C4×D3D411yescharacteristic
97C2×C3×C4×D3D411yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
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#3799—22no—
108#3799C2×C414yes—
109D3×Dic6—22no—
110D3×Dic6C2×C414yescomplemented
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119#3744C2×C414yescomplemented
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3D411yescharacteristic
127C3×C4×Dic3D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×Dic12C2×C414yescomplemented
132C3×ΓL(1,𝔽25)—22no—
133C3×ΓL(1,𝔽25)C2×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#3719C2×C414yescomplemented
145#3717C2×C414yescomplemented
146C4×#137—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×#235—31no—
150C22×Dic6—31no—
151C2×C3×Q16—31no—
152C2×C3×M16—31no—
153C2×C3×M16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C2×C3×C42—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160C2×#215—31no—
161C4×#67—61no—
162C4×#67—61no—
163#926—31no—
164C2×C4⋊Dic3—31no—
165C2×Dic3⋊C4—61no—
166C2×C4×Dic3—61no—
167#918—38no—
168#909—38no—
169C2×Dic12—31no—
170C2×Dic12C2×D311yescharacteristic
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—61no—
175C2×ΓL(1,𝔽25)C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)C2×D311yescharacteristic
177#893—31no—
178#893—61no—
179#892—31no—
180#892—61no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—61no—
183#887—31no—
184#887—61no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190#872—61no—
191C42×D3—61no—
192C42×D3—61no—
193C42×D3—61no—
194C42×D3C2×D311yescharacteristic
195C4×Dic6—31no—
196C4×Dic6—31no—
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C4×Dic6—61no—
204C4×Dic6C2×D311yescharacteristic
205C4×Dic6C2×D311yescharacteristic
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#97—21no—
210C3×#97—31no—
211C3×#97C2×D311yescharacteristic
212C3×#97C2×D311yescharacteristic
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#818—31no—
222#818—31no—
223#818—31no—
224#818—61no—
225#817—31no—
226#817C2×D311yescharacteristic
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—61no—
233#816C2×D311yescharacteristic
234#816C2×D311yescharacteristic
235C8×Dic3C2×D311yescharacteristic
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#809—31no—
239#808—31no—
240#807—31no—
241#803C2×D311yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)C22×C412yes—
252C4×C3⋊D3—42no—
253#634—21no—
254#634C22×C412yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—22no—
263C3×C4×D3—41no—
264C3×C4×D3C22×C412yes—
265C3×C4×D3#4112yes—
266C3×Dic6—21no—
267C3×Dic6—21no—
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⋊C8C22×C412yes—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—31no—
284#441—91no—
285#440—91no—
286#440—91no—
287C4×Q16—91no—
288C4×Q16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—91no—
294C4×M16—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C2×#67—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303#239—34no—
304#239—62no—
305D3×Q8—34no—
306D3×Q8—62no—
307#235—34no—
308#235—62no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—121no—
322C2×C4×D3D1211yescharacteristic
323C2×C4×D3D1211yescharacteristic
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—34no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×Q16—34no—
335C3×M16—34no—
336C3×M16—62no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42—31no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—61no—
358#216—34no—
359#215—34no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—121no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387C4×Dic3—21no—
388C4×Dic3—21no—
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—121no—
400C4×Dic3D1211yescharacteristic
401C4×Dic3D1211yescharacteristic
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—34no—
406Dic12C4×D314yescomplemented
407#204—34no—
408#204—34no—
409#204—34no—
410#204—64no—
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)C4×D314yescomplemented
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3C4×D412yes—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—22no—
425C3⋊Dic3—41no—
426C3⋊Dic3—41no—
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3C4×D412yes—
433C3×Dic3#13712yescomplemented
434C2×#41—91no—
435C22×Q8—91no—
436#137—98no—
437C2×Q16—31no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×M16—31no—
442C2×M16—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—181no—
459C2×C42—31no—
460C2×C42—181no—
461C2×C42—181no—
462#107—91no—
463#107—91no—
464#106—31no—
465#106—91no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—91no—
473#102—91no—
474#97—31no—
475#97D3211yescharacteristic
476C4×C8—31no—
477C4×C8—31no—
478C23×C3—31no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—121no—
482C22×D3C2×D1211yescharacteristic
483C3×Q8—32no—
484C3×Q8—32no—
485C3×Q8—61no—
486C3×Q8—61no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—31no—
495C2×C3×C4—62no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—121no—
501C2×C3×C4C2×D1211yescharacteristic
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—64no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—64no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—122no—
523C2×Dic3C2×D1211yescharacteristic
524C2×Dic3C2×D1211yescharacteristic
525C2×Dic3C2×D1211yescharacteristic
526D12—32no—
527D12—32no—
528D12—62no—
529D12—64no—
530D12—61no—
531D12—61no—
532D12—121no—
533C4×D3—22no—
534C4×D3—41no—
535C4×D3—64no—
536C4×D3—64no—
537C4×D3—64no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—122no—
541C4×D3—122no—
542C4×D3—122no—
543C4×D3—242no—
544C4×D3C2×C4×D312yes—
545C4×D3#23512yes—
546Dic6—21no—
547Dic6—21no—
548Dic6—32no—
549Dic6—32no—
550Dic6—62no—
551Dic6—64no—
552Dic6—61no—
553Dic6—61no—
554Dic6—64no—
555Dic6—121no—
556Dic6C2×C4×D312yes—
557Dic6C2×C4×D312yes—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—22no—
561C3×C8—32no—
562C3×C8—41no—
563C3×C8—61no—
564C3×C8C2×C4×D312yes—
565C3×C8C2×C4×D312yes—
566C3⋊C8—21no—
567C3⋊C8C2×C4×D312yes—
568C2×C32C2×C4×D411yescharacteristic
569C2×C32C2×#13711yescharacteristic
570C2×C32#57511yescharacteristic
571C3⋊D3—42no—
572C3×D3—22no—
573#41—94no—
574#41—182no—
575C2×Q8—31no—
576C2×Q8—31no—
577C2×Q8—94no—
578C2×Q8—91no—
579C2×Q8—181no—
580C2×Q8—182no—
581C2×D4—91no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591Q16—34no—
592Q16—94no—
593SD16—94no—
594SD16—94no—
595M16—34no—
596M16—62no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8C2×D3211yescharacteristic
600C2×C8C2×D3211yescharacteristic
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—31no—
617C42—31no—
618C42—61no—
619C42—61no—
620C42—181no—
621C42—181no—
622C42—181no—
623C42—181no—
624C42—181no—
625C42C2×D3211yescharacteristic
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3C22×D1211yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—122no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—241no—
642C2×D3—241no—
643C2×D3C4×D1212yes—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—61no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C22×C4×D311yescharacteristic
660C3×C4C22×C4×D311yescharacteristic
661C3×C4C2×#23511yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—21no—
664Dic3—22no—
665Dic3—22no—
666Dic3—41no—
667Dic3—41no—
668Dic3—62no—
669Dic3—62no—
670Dic3—122no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676Dic3—241no—
677Dic3C4×D1212yes—
678Dic3#90912yescomplemented
679C32C4×#13711yescharacteristic, complemented, Sylow
680C23—31no—
681C23—181no—
682Q8—32no—
683Q8—32no—
684Q8—61no—
685Q8—61no—
686Q8—92no—
687Q8—184no—
688Q8—181no—
689D4—92no—
690D4—184no—
691D4—181no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—31no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—121no—
703C2×C4—184no—
704C2×C4—184no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—362no—
709C2×C4—362no—
710C2×C4—362no—
711C2×C4D3×D1211yescharacteristic
712C2×C4D3×D1211yescharacteristic
713C2×C4C22×D3211yescharacteristic
714C8—21no—
715C8—32no—
716C8—61no—
717C8C4×D3212yes—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—62no—
722C2×C3C2×C4×D1211yescharacteristic
723C2×C3C4×D3×D411yescharacteristic
724C2×C3C2×#90911yescharacteristic
725C2×C3#574811yescharacteristic
726C2×C3D3×#13711yescharacteristic
727C2×C3#577711yescharacteristic
728D3—22no—
729D3—122no—
730D3—122no—
731D3—242no—
732C22—32no—
733C22—61no—
734C22—61no—
735C22—182no—
736C22—361no—
737C22—361no—
738C22C2×D3×D1211yescharacteristic
739C4—21no—
740C4—21no—
741C4—32no—
742C4—32no—
743C4—61no—
744C4—62no—
745C4—62no—
746C4—121no—
747C4—121no—
748C4—182no—
749C4—361no—
750C4—361no—
751C4C2×C4×D3211yescharacteristic
752C4D3×#23511yescharacteristic
753C3—21no—
754C3C4×#90911yescharacteristic, complemented
755C3#7982911yescharacteristic, complemented
756C2—62no—
757C2—362no—
758C2C4×D3×D1211yescharacteristic
759C2D3×#90911yescharacteristic
760C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. C4×D3×Dic6C2semidirect
4. #10592409C2semidirect
5. C3×#4716C2semidirect
6. C3×#4707C2semidirect
7. #10590948C2semidirect
8. Dic3×Dic12C2semidirect
9. #10590793C2semidirect
10. #10590792C2semidirect
11. #10590758C2semidirect
12. #10590681C2semidirect
14. #10590383C2semidirect
15. #10590362C2semidirect
45. #63801C4semidirect
83. #4716D3semidirect
88. #4707D3semidirect
110. D3×Dic6C2×C4semidirect
119. #3744C2×C4semidirect
131. C3×Dic12C2×C4semidirect
133. C3×ΓL(1,𝔽25)C2×C4semidirect
144. #3719C2×C4semidirect
145. #3717C2×C4semidirect
406. Dic12C4×D3semidirect
412. ΓL(1,𝔽25)C4×D3semidirect
433. C3×Dic3#137semidirect
678. Dic3#909semidirect
679. C32C4×#137semidirect
754. C3C4×#909semidirect
755. C3#79829semidirect

Maximal subgroups

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

subgroupindex
C2×#638012
C4×#37992
C4×D3×Dic62
#105924092
C3×#47162
C3×#47072
#105909482
Dic3×Dic122
#105907932
#105907922
#105907582
#105906812
#105906712
#105903832
#105903622
#798293
C4×#9093