Finite Group Databasebeta

← #11860387

Subgroups — #11860387

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic
3#10594358C211yesmaximal, characteristic
4#10592488C211yesmaximal, characteristic, complemented
5C3×#4802C211yesmaximal, characteristic, complemented
6C3×#4788C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10590793C211yesmaximal, characteristic, complemented
10#10590743C211yesmaximal, characteristic, complemented
11#10590670C211yesmaximal, characteristic
12Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
13#10590485C211yesmaximal, characteristic, complemented
14#10590475C211yesmaximal, characteristic, complemented
15#10590437C211yesmaximal, characteristic, complemented
16C4×#915—31nomaximal
17#78946—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64096C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63946C418yescomplemented
29#63902—21no—
30#63898C2211yescharacteristic
31D3×C4⋊Dic3—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33#63879—21no—
34#63877—21no—
35C4×D3×Dic3—21no—
36C4×D3×Dic3—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63844C2211yescharacteristic
39#63843—21no—
40#63843C2211yescharacteristic
41Dic3×Dic6—21no—
42Dic3×Dic6C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63643C2211yescharacteristic
48#63642C2211yescharacteristic
49#63635C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63576C2211yescharacteristic
57#63575C2211yescharacteristic
58#63567C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×Q8×Dic3—31no—
63C2×#942—31no—
64C2×#915—31no—
65C4×D3×Q8—31no—
66C4×#237—31no—
67#5522—31no—
68C3×C4×SD16—31no—
69C3×#419—31no—
70#5164—31no—
71#5133—31no—
72Dic3×M16—31no—
73C4×#216—31no—
74C4×#214—31no—
75#4995—31no—
76#4861—31no—
77#4853—31no—
78#4817—31no—
79#4817—31no—
80#4802D311yescharacteristic, complemented
81#4790—31no—
82#4790—31no—
83#4789—31no—
84#4789—31no—
85#4789—31no—
86#4789—61no—
87#4788—31no—
88#4788D311yescharacteristic, complemented
89#4771—31no—
90#4757—31no—
91C4×Dic12—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8C2×C414yescomplemented
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#625—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3D411yescharacteristic
108C2×D3×Dic3D411yescharacteristic
109#3795—22no—
110#3795C2×C414yes—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3756C2×C414yescomplemented
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#215C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—22no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3719C2×C414yescomplemented
144#3715C2×C414yescomplemented
145#3711C2×C414yescomplemented
146C4×#137—91noSylow
147C22×C3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×#237—31no—
150C2×#235—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C3×#117—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160Q8×Dic3—61no—
161Q8×Dic3—61no—
162Q8×Dic3—61no—
163Q8×Dic3C2×D311yescharacteristic
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—61no—
168#942—38no—
169C2×#215—31no—
170C2×#215C2×D311yescharacteristic
171D4×Dic3—31no—
172C2×#214—31no—
173C4×#67—61no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—61no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3—61no—
179C2×#208—31no—
180#915—38no—
181C2×Dic12—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)C2×D311yescharacteristic
184#893—31no—
185#893C2×D311yescharacteristic
186#892C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189#887—31no—
190#887—31no—
191#887—31no—
192#887—31no—
193#887—61no—
194#887—61no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#877—61no—
199#872—61no—
200C42×D3—31no—
201C42×D3—61no—
202C42×D3—61no—
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103C2×D311yescharacteristic
212C3×#103C2×D311yescharacteristic
213C3×#102—31no—
214C3×C4×C8—31no—
215#835C2×D311yescharacteristic
216#832—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219#818—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
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#810—31no—
233#810C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—61no—
237#808C2×D311yescharacteristic
238#807—31no—
239#807—31no—
240#807—31no—
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⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634C22×C412yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12C22×C412yes—
263C3×C4×D3—24no—
264C3×C4×D3—42no—
265C3×C4×D3C22×C412yes—
266C3×C4×D3#4112yes—
267C3×Dic6—21no—
268C3×Dic6—24no—
269C3×Dic6C22×C412yes—
270#625—24no—
271D3×Dic3—24no—
272D3×Dic3—22no—
273D3×Dic3—41no—
274D3×Dic3—42no—
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—91no—
288C4×Q16—91no—
289C4×SD16—31no—
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—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313D3×Q8—22no—
314D3×Q8C4×D314yescomplemented
315#237—34no—
316#237—62no—
317#235—34no—
318#235—62no—
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—21no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—34no—
334C3×M16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—61no—
351#217—61no—
352#216—34no—
353#216—34no—
354#216—34no—
355#216—64no—
356#215—34no—
357#215C4×D314yescomplemented
358#214—34no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362C4⋊Dic3—21no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—121no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
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—
400C4×Dic3—61no—
401C4×Dic3—121no—
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
410Dic12—34no—
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)—34no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3C4×D412yes—
420C32×C4—22no—
421C32×C4—41no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—22no—
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
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—91no—
438C2×Q16—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×M16—31no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—31no—
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—91no—
463#107—91no—
464#106—31no—
465#106—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103D3211yescharacteristic
472#102—31no—
473#102—91no—
474#97—91no—
475#97—91no—
476C4×C8—31no—
477C4×C8—91no—
478C23×C3—31no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3D3×D411yescharacteristic
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—64no—
488C3×Q8—61no—
489C3×Q8C2×C4×D312yes—
490C3×Q8C2×C4×D312yes—
491C3×D4—32no—
492C3×D4—61no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—64no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—64no—
513#67—64no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—64no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537D12—21no—
538D12C2×C4×D312yes—
539C4×D3—24no—
540C4×D3—42no—
541C4×D3—62no—
542C4×D3—64no—
543C4×D3—121no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3C2×C4×D312yes—
547C4×D3#23712yes—
548Dic6—21no—
549Dic6—24no—
550Dic6—32no—
551Dic6—32no—
552Dic6—62no—
553Dic6—61no—
554Dic6—61no—
555Dic6—121no—
556Dic6C2×C4×D312yes—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—32no—
560C3×C8—41no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—32no—
564C3⋊C8—32no—
565C3⋊C8—62no—
566C3⋊C8C2×C4×D312yes—
567C2×C32C2×C4×D411yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—42no—
572#41—94no—
573#41—182no—
574C2×Q8—34no—
575C2×Q8—31no—
576C2×Q8—61no—
577C2×Q8—62no—
578C2×Q8—91no—
579C2×Q8C2×D3211yescharacteristic
580C2×D4—31no—
581C2×D4—181no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590Q16—94no—
591Q16—94no—
592SD16—34no—
593SD16—94no—
594M16—62no—
595M16—94no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C42—31no—
615C42—61no—
616C42—61no—
617C42—91no—
618C42—91no—
619C42—91no—
620C42—181no—
621C42—181no—
622C42—181no—
623C42—181no—
624C42—181no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—62no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—22no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3#67⋊C412yes—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—32no—
645C3×C4—32no—
646C3×C4—42no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—61no—
650C3×C4—62no—
651C3×C4—81no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4C22×C4×D311yescharacteristic
655C3×C4C22×C4×D311yescharacteristic
656C3×C4C2×#23711yescharacteristic
657C3×C4D3×#4111yescharacteristic
658Dic3—22no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—62no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—62no—
668Dic3—122no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3#67⋊C412yes—
675Dic3#91512yescomplemented
676C32C4×#13711yescharacteristic, complemented, Sylow
677C23—31no—
678C23—61no—
679Q8—21no—
680Q8—32no—
681Q8—64no—
682Q8—61no—
683Q8—92no—
684Q8—181no—
685Q8C4×D3212yes—
686D4—32no—
687D4—61no—
688D4—184no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—31no—
696C2×C4—64no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—122no—
703C2×C4—182no—
704C2×C4—184no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—361no—
708C2×C4—362no—
709C2×C4—362no—
710C2×C4C22×D3211yescharacteristic
711C8—21no—
712C8—32no—
713C8—61no—
714C8—92no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—62no—
719C2×C3—122no—
720C2×C3C2×#67⋊C411yescharacteristic
721C2×C3C4×D3×D411yescharacteristic
722C2×C3C2×#91511yescharacteristic
723C2×C3#576811yescharacteristic
724C2×C3D3×#13711yescharacteristic
725C2×C3#577711yescharacteristic
726D3—22no—
727D3—42no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—62no—
732C22—121no—
733C22—121no—
734C22D32×D411yescharacteristic
735C4—22no—
736C4—32no—
737C4—32no—
738C4—41no—
739C4—61no—
740C4—62no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—181no—
745C4—182no—
746C4—361no—
747C4C2×C4×D3211yescharacteristic
748C4D3×#23711yescharacteristic
749C3—21no—
750C3#7894611yescharacteristic, complemented
751C3C4×#91511yescharacteristic, complemented
752C2—62no—
753C2—122no—
754C2D3×#67⋊C411yescharacteristic
755C2D3×#91511yescharacteristic
756C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
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. #10592488C2semidirect
5. C3×#4802C2semidirect
6. C3×#4788C2semidirect
7. #10591572C2semidirect
8. #10591537C2semidirect
9. #10590793C2semidirect
10. #10590743C2semidirect
12. Dic3×ΓL(1,𝔽25)C2semidirect
13. #10590485C2semidirect
14. #10590475C2semidirect
15. #10590437C2semidirect
28. #63946C4semidirect
80. #4802D3semidirect
88. #4788D3semidirect
96. C3×D3×Q8C2×C4semidirect
113. #3756C2×C4semidirect
121. C3×#215C2×C4semidirect
143. #3719C2×C4semidirect
144. #3715C2×C4semidirect
145. #3711C2×C4semidirect
314. D3×Q8C4×D3semidirect
357. #215C4×D3semidirect
433. C3×Dic3#137semidirect
675. Dic3#915semidirect
676. C32C4×#137semidirect
750. C3#78946semidirect
751. C3C4×#915semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic32
C2×#639462
#105943582
#105924882
C3×#48022
C3×#47882
#105915722
#105915372
#105907932
#105907432
#105906702
Dic3×ΓL(1,𝔽25)2
#105904852
#105904752
#105904372
C4×#9153
#789463