Finite Group Databasebeta

← #11860393

Subgroups — #11860393

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
1D3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic
3#10594362C211yesmaximal, characteristic
4#10592516C211yesmaximal, characteristic, complemented
5C3×#4802C211yesmaximal, characteristic, complemented
6C3×#4790C211yesmaximal, characteristic, complemented
7#10591582C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590792C211yesmaximal, characteristic, complemented
10#10590791C211yesmaximal, characteristic, complemented
11#10590671C211yesmaximal, characteristic
12Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
13#10590484C211yesmaximal, characteristic, complemented
14#10590476C211yesmaximal, characteristic, complemented
15#10590436C211yesmaximal, characteristic, complemented
16C4×#918—31nomaximal
17#78946—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63948C418yescomplemented
29#63894C2211yescharacteristic
30D3×C4⋊Dic3—21no—
31D3×C4⋊Dic3C2211yescharacteristic
32C4×#624—21no—
33#63881—21no—
34#63880—21no—
35C4×D3×Dic3—21no—
36C4×D3×Dic3C2211yescharacteristic
37#63843—21no—
38#63843C2211yescharacteristic
39#63843C2211yescharacteristic
40Dic3×Dic6—21no—
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
43C2×#3718C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63648C2211yescharacteristic
48#63642C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63574C2211yescharacteristic
57#63573C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63555C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×Q8×Dic3—31no—
63C2×#942—31no—
64C2×#918—31no—
65C4×#239—31no—
66C4×D3×Q8—31no—
67#5522—31no—
68C3×C4×Q16—31no—
69C3×#419—31no—
70#5184—31no—
71#5133—31no—
72Dic3×M16—31no—
73C4×#216—31no—
74C4×#215—31no—
75#4995—31no—
76#4889—31no—
77#4881—31no—
78#4817—31no—
79#4817—31no—
80#4817—31no—
81#4817—61no—
82#4803—31no—
83#4802D311yescharacteristic, complemented
84#4790—31no—
85#4790D311yescharacteristic, complemented
86#4789—31no—
87#4789—31no—
88#4789—31no—
89#4788—31no—
90#4788—31no—
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C3×D3×Q8—22no—
97C3×D3×Q8C2×C414yescomplemented
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#624—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3D411yescharacteristic
108C2×D3×Dic3D411yescharacteristic
109#3799—22no—
110#3799C2×C414yes—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3755C2×C414yescomplemented
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#216C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—22no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3718C2×C414yescomplemented
144#3717C2×C414yescomplemented
145#3711C2×C414yescomplemented
146C4×#137—91noSylow
147C22×C3×Q8—31no—
148C2×#239—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×Q16—31no—
152C2×C3×M16—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×#117—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—61no—
162Q8×Dic3—61no—
163Q8×Dic3—61no—
164Q8×Dic3C2×D311yescharacteristic
165C2×#216—31no—
166C2×#216—31no—
167C2×#216C2×D311yescharacteristic
168#942—38no—
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—61no—
177C2×#208—31no—
178#918—38no—
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)C2×D311yescharacteristic
182#893—31no—
183#893—31no—
184#893—31no—
185#893—61no—
186#893—61no—
187#892—61no—
188#892C2×D311yescharacteristic
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191#887—31no—
192#887—31no—
193#887—61no—
194#887C2×D311yescharacteristic
195#67⋊C4—61no—
196#67⋊C4—61no—
197C4×D12—31no—
198C4×D12—61no—
199#872—61no—
200C42×D3—31no—
201C42×D3—61no—
202C42×D3—61no—
203C42×D3—61no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic
213C3×#103C2×D311yescharacteristic
214C3×C4×C8—31no—
215#835—31no—
216#835C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#817—31no—
222#816—31no—
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—31no—
228#815—31no—
229#815—61no—
230C8×Dic3—31no—
231C8×Dic3C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#809—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239#807—61no—
240#807C2×D311yescharacteristic
241C4×C3⋊C8—31no—
242C22×C3⋊D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)C22×C412yes—
254C4×C3⋊D3—42no—
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—24no—
263C3×C4×D3C22×C412yes—
264C3×C4×D3#4112yes—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—24no—
268C3×Dic6C22×C412yes—
269C3×Dic6C22×C412yes—
270#626—24no—
271#624—24no—
272#624—42no—
273D3×Dic3—22no—
274D3×Dic3—41no—
275D3×Dic3—42no—
276C32×C8—21no—
277C3⋊(C3⋊C8)C22×C412yes—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×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—91no—
290C4×SD16—91no—
291#428—91no—
292#419—31no—
293#417—91no—
294C4×M16—91no—
295C2×C3×Q8—21no—
296C2×C3×Q8—34no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—61no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309#239—34no—
310#239—62no—
311D3×Q8—22no—
312D3×Q8C4×D314yescomplemented
313#235—34no—
314#235—62no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—61no—
319C2×C4×D3—21no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
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×C4×D3—121no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×Q16—34no—
335C3×M16—62no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42—61no—
353#216—34no—
354#216—34no—
355#216C4×D314yescomplemented
356#215—34no—
357#215—34no—
358#215—34no—
359#215—64no—
360(C2×D3)⋊C4—21no—
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—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404#208—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—34no—
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)—34no—
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—22no—
421C32×C4—41no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
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—31no—
436#137—98no—
437C2×Q16—31no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×M16—31no—
442C2×M16—91no—
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—31no—
456#117—181no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—181no—
459C2×C42—91no—
460C2×C42—181no—
461C2×C42—181no—
462#107—31no—
463#107—91no—
464#106—91no—
465#106—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103D3211yescharacteristic
472#102—91no—
473#102—91no—
474#97—91no—
475#97—91no—
476C4×C8—31no—
477C4×C8—91no—
478C23×C3—31no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—121no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—22no—
486C3×Q8—32no—
487C3×Q8—32no—
488C3×Q8—41no—
489C3×Q8—64no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8C2×C4×D312yes—
493C3×Q8C2×C4×D312yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—64no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—64no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—61no—
538D12—61no—
539D12—121no—
540C4×D3—24no—
541C4×D3—64no—
542C4×D3—62no—
543C4×D3—64no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—121no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—242no—
551C4×D3C2×C4×D312yes—
552C4×D3#23712yes—
553Dic6—21no—
554Dic6—21no—
555Dic6—24no—
556Dic6C2×C4×D312yes—
557Dic6C2×C4×D312yes—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—32no—
561C3×C8—41no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—32no—
565C3⋊C8—32no—
566C3⋊C8—62no—
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—34no—
576C2×Q8—31no—
577C2×Q8—31no—
578C2×Q8—61no—
579C2×Q8—62no—
580C2×Q8C2×D3211yescharacteristic
581C2×D4—91no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591Q16—34no—
592Q16—94no—
593SD16—94no—
594SD16—94no—
595M16—62no—
596M16—94no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8C2×D3211yescharacteristic
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—61no—
617C42—61no—
618C42—61no—
619C42—91no—
620C42—91no—
621C42—91no—
622C42—181no—
623C42—181no—
624C42—181no—
625C42—181no—
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3C2×D3×D411yescharacteristic
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×D3#67⋊C412yes—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—32no—
649C3×C4—32no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—62no—
654C3×C4—61no—
655C3×C4—62no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C22×C4×D311yescharacteristic
660C3×C4C22×C4×D311yescharacteristic
661C3×C4C2×#23711yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—22no—
664Dic3—21no—
665Dic3—22no—
666Dic3—41no—
667Dic3—41no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—241no—
677Dic3#67⋊C412yes—
678Dic3#91812yescomplemented
679C32C4×#13711yescharacteristic, complemented, Sylow
680C23—31no—
681C23—181no—
682Q8—21no—
683Q8—32no—
684Q8—32no—
685Q8—64no—
686Q8—61no—
687Q8—61no—
688Q8C4×D3212yes—
689D4—92no—
690D4—184no—
691D4—181no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—31no—
699C2×C4—64no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—184no—
707C2×C4—182no—
708C2×C4—181no—
709C2×C4—362no—
710C2×C4—362no—
711C2×C4—361no—
712C2×C4—362no—
713C2×C4C22×D3211yescharacteristic
714C8—21no—
715C8—32no—
716C8—61no—
717C8—92no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—62no—
722C2×C3C2×#67⋊C411yescharacteristic
723C2×C3C4×D3×D411yescharacteristic
724C2×C3C2×#91811yescharacteristic
725C2×C3#576811yescharacteristic
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—
738C22D32×D411yescharacteristic
739C4—22no—
740C4—32no—
741C4—32no—
742C4—41no—
743C4—61no—
744C4—62no—
745C4—62no—
746C4—121no—
747C4—121no—
748C4—181no—
749C4—181no—
750C4—361no—
751C4C2×C4×D3211yescharacteristic
752C4D3×#23711yescharacteristic
753C3—21no—
754C3#7894611yescharacteristic, complemented
755C3C4×#91811yescharacteristic, complemented
756C2—62no—
757C2—362no—
758C2D3×#67⋊C411yescharacteristic
759C2#1059474611yescharacteristic
760C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×Q8×Dic3C2semidirect
4. #10592516C2semidirect
5. C3×#4802C2semidirect
6. C3×#4790C2semidirect
7. #10591582C2semidirect
8. #10591536C2semidirect
9. #10590792C2semidirect
10. #10590791C2semidirect
12. Dic3×ΓL(1,𝔽25)C2semidirect
13. #10590484C2semidirect
14. #10590476C2semidirect
15. #10590436C2semidirect
28. #63948C4semidirect
83. #4802D3semidirect
85. #4790D3semidirect
97. C3×D3×Q8C2×C4semidirect
113. #3755C2×C4semidirect
120. C3×#216C2×C4semidirect
143. #3718C2×C4semidirect
144. #3717C2×C4semidirect
145. #3711C2×C4semidirect
312. D3×Q8C4×D3semidirect
355. #216C4×D3semidirect
433. C3×Dic3#137semidirect
678. Dic3#918semidirect
679. C32C4×#137semidirect
754. C3#78946semidirect
755. C3C4×#918semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic32
C2×#639482
#105943622
#105925162
C3×#48022
C3×#47902
#105915822
#105915362
#105907922
#105907912
#105906712
Dic3×ΓL(1,𝔽25)2
#105904842
#105904762
#105904362
C4×#9183
#789463