Finite Group Databasebeta

← #11860440

Subgroups — #11860440

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
1C3×C4×#239C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic
3C4×D3×Dic6C211yesmaximal, characteristic, complemented
4#10592729C211yesmaximal, characteristic, complemented
5C3×#5030C211yesmaximal, characteristic, complemented
6Dic3×#216C211yesmaximal, characteristic, complemented
7#10591550C211yesmaximal, characteristic
8#10591537C211yesmaximal, characteristic, complemented
9#10590600C211yesmaximal, characteristic, complemented
10#10590479C211yesmaximal, characteristic, complemented
11#10590475C211yesmaximal, characteristic, complemented
12#10590437C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590334C211yesmaximal, characteristic, complemented
16C4×#951—31nomaximal
17#79829—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#893—21no—
26C3×#893C2211yescharacteristic
27C3×#892—21no—
28C3×#892C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C42×D3—21no—
32C3×C42×D3C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63943C418yescomplemented
35C4×#627—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37D3×Dic3⋊C4—21no—
38C4×D3×Dic3—21no—
39#63844C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41#63837—21no—
42C2×#3716C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63662C2211yescharacteristic
47#63637C2211yescharacteristic
48#63635C2211yescharacteristic
49#63630C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63576C2211yescharacteristic
55#63575C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×C4×#41—31no—
63C2×#951—31no—
64C2×#918—31no—
65C4×#239D311yescharacteristic
66C4×D3×Q8—31no—
67C2×C4×Dic6—31no—
68C3×#441—31no—
69#5232—31no—
70Dic3×Q16—31no—
71#5030—31no—
72#5030—31no—
73#5030—61no—
74#5030D311yescharacteristic, complemented
75C4×#216—31no—
76C4×#216—31no—
77#5026—31no—
78#5018—31no—
79#5018—31no—
80C4×#214—31no—
81C4×#214—31no—
82#5004—31no—
83#4995—31no—
84C4×#208—31no—
85#4861—31no—
86#4852—31no—
87#4803—31no—
88#4802—31no—
89#4790—31no—
90#4788—31no—
91#4710—31no—
92#4707—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yes—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×Dic6—22no—
110D3×Dic6C2×C414yescomplemented
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C42—21no—
114C32×C42C2311yescharacteristic
115#3756C2×C414yescomplemented
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3716C2×C414yescomplemented
143#3715C2×C414yescomplemented
144#3711—22no—
145#3711C2×C414yescomplemented
146C4×#137—91noSylow
147C2×C3×#41—31no—
148C2×#239C2×D311yescharacteristic
149C2×D3×Q8—31no—
150C22×Dic6—31no—
151C2×C3×Q16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8C2×D311yescharacteristic
156C3×C4×Q8C2×D311yescharacteristic
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×C4×D4—61no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C42—31no—
164C2×C3×C42—61no—
165#951—38no—
166Q8×Dic3—31no—
167Q8×Dic3C2×D311yescharacteristic
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—61no—
171C2×#216C2×D311yescharacteristic
172C2×#215—31no—
173C2×#214—31no—
174C2×#214—31no—
175C2×C4⋊Dic3—31no—
176C2×Dic3⋊C4—61no—
177C2×C4×Dic3—61no—
178C2×#208—31no—
179C2×#208—31no—
180#918—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184#893—21no—
185#893C2×D311yescharacteristic
186#892—21no—
187#892C2×D311yescharacteristic
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190#887—31no—
191#887—61no—
192C4×D12—21no—
193C4×D12C2×D311yescharacteristic
194C42×D3—21no—
195C42×D3—61no—
196C42×D3C2×D311yescharacteristic
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C4×Dic6—61no—
204C4×Dic6—61no—
205C4×Dic6C2×D311yescharacteristic
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#832—31no—
217#821—31no—
218#818—31no—
219#816—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810C2×D311yescharacteristic
228#809—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#803—31no—
237#803—31no—
238#803—61no—
239#803C2×D311yescharacteristic
240C4×C3⋊C8—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×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
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—24no—
262C3×D12—21no—
263C3×D12C22×C412yes—
264C3×C4×D3—24no—
265C3×C4×D3—22no—
266C3×C4×D3—41no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273#627—24no—
274D3×Dic3—24no—
275D3×Dic3—42no—
276C3⋊(C3⋊C8)—21no—
277C3⋊(C3⋊C8)C22×C412yes—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×C412yes—
280C2×#137—91no—
281C4×#41—31no—
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—91no—
295C3×#41—34no—
296C3×#41—62no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311#239—22no—
312#239C4×D314yes—
313D3×Q8—34no—
314D3×Q8—62no—
315C2×D12—21no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3#6711yescharacteristic
323C2×C4×D3#6711yescharacteristic
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
333C3×Q16—34no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—31no—
353C3×C42—31no—
354C3×C42—31no—
355C3×C42—41no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359C3×C42C22×D311yescharacteristic
360C3×C42C22×D311yescharacteristic
361#216—34no—
362#216—34no—
363#216—64no—
364#216C4×D314yescomplemented
365#215—34no—
366#214—34no—
367#214—34no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
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—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—121no—
397C4×Dic3#6711yescharacteristic
398C4×Dic3#6711yescharacteristic
399C4×Dic3C22×D311yescharacteristic
400#208—34no—
401#208—62no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—34no—
411ΓL(1,𝔽25)—34no—
412ΓL(1,𝔽25)—62no—
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—21no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4C23×C411yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3⋊Dic3—22no—
427C3⋊Dic3—41no—
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3C4×D412yes—
433C3×Dic3#13712yescomplemented
434C2×#41—31no—
435C22×Q8—91no—
436#137—98no—
437C2×Q16—31no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×M16—91no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—181no—
449C4×Q8—181no—
450C4×Q8D3211yescharacteristic
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—61no—
455#117—31no—
456#117—61no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—181no—
459C2×C42—31no—
460C2×C42—61no—
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#97—91no—
476C4×C8—91no—
477C4×C8—91no—
478C23×C3—31no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3C2×#6711yescharacteristic
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—61no—
488C3×Q8C2×C4×D312yes—
489C3×Q8C2×C4×D312yes—
490C3×D4—32no—
491C3×D4—64no—
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—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—62no—
508C2×C3×C4—64no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—121no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—64no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535D12—24no—
536D12—21no—
537D12C2×C4×D312yes—
538C4×D3—24no—
539C4×D3—22no—
540C4×D3—41no—
541C4×D3—42no—
542C4×D3—42no—
543C4×D3—64no—
544C4×D3—122no—
545C4×D3C2×C4×D312yes—
546C4×D3#23512yes—
547Dic6—21no—
548Dic6—32no—
549Dic6—32no—
550Dic6—62no—
551Dic6—64no—
552Dic6—61no—
553Dic6—61no—
554Dic6—64no—
555Dic6—121no—
556Dic6C2×C4×D312yes—
557C3×C8—32no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—32no—
561C3⋊C8—32no—
562C3⋊C8—62no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8C2×C4×D312yes—
567C2×C32C2×C4×D411yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—42no—
572#41—34no—
573#41—62no—
574C2×Q8—31no—
575C2×Q8—94no—
576C2×Q8—91no—
577C2×Q8—181no—
578C2×Q8—182no—
579C2×Q8C2×D3211yescharacteristic
580C2×D4—31no—
581C2×D4—61no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589C22×C4—181no—
590Q16—34no—
591Q16—94no—
592SD16—94no—
593SD16—94no—
594M16—94no—
595M16—182no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8—91no—
600C4⋊C4—21no—
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⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C42—21no—
615C42—31no—
616C42—31no—
617C42—31no—
618C42—61no—
619C42—61no—
620C42—61no—
621C42—181no—
622C42—181no—
623C42—181no—
624C42C2×D3211yescharacteristic
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×C3C22×#6711yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—22no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3C4×#6712yes—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—32no—
649C3×C4—32no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—42no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—62no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C22×C4×D311yescharacteristic
661C3×C4C22×C4×D311yescharacteristic
662C3×C4C2×#23511yescharacteristic
663C3×C4D3×#4111yescharacteristic
664Dic3—22no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—62no—
669Dic3—62no—
670Dic3—122no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3C4×#6712yes—
675Dic3#95112yescomplemented
676C32C4×#13711yescharacteristic, complemented, Sylow
677C23—31no—
678C23—61no—
679Q8—21no—
680Q8—32no—
681Q8—61no—
682Q8—92no—
683Q8—184no—
684Q8—181no—
685Q8C4×D3212yes—
686D4—32no—
687D4—64no—
688D4—61no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—31no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—121no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—184no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4D3×#6711yescharacteristic
709C2×C4D3×#6711yescharacteristic
710C2×C4C22×D3211yescharacteristic
711C8—32no—
712C8—61no—
713C8—92no—
714C8—181no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—62no—
719C2×C3—122no—
720C2×C3C4×D3×D411yescharacteristic
721C2×C3D3×#13711yescharacteristic
722C2×C3#577711yescharacteristic
723C2×C3C2×C4×#6711yescharacteristic
724C2×C3#582211yescharacteristic
725C2×C3C2×#95111yescharacteristic
726D3—22no—
727D3—42no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—62no—
732C22—121no—
733C22—121no—
734C22C2×D3×#6711yescharacteristic
735C4—21no—
736C4—22no—
737C4—21no—
738C4—32no—
739C4—32no—
740C4—41no—
741C4—62no—
742C4—61no—
743C4—121no—
744C4—121no—
745C4—182no—
746C4—361no—
747C4C2×C4×D3211yescharacteristic
748C4D3×#23511yescharacteristic
749C3—21no—
750C3#7982911yescharacteristic, complemented
751C3C4×#95111yescharacteristic, complemented
752C2—62no—
753C2—122no—
754C2C4×D3×#6711yescharacteristic
755C2#1059531711yescharacteristic
756C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C4×D3×Dic6C2semidirect
4. #10592729C2semidirect
5. C3×#5030C2semidirect
6. Dic3×#216C2semidirect
8. #10591537C2semidirect
9. #10590600C2semidirect
10. #10590479C2semidirect
11. #10590475C2semidirect
12. #10590437C2semidirect
13. #10590360C2semidirect
14. #10590358C2semidirect
15. #10590334C2semidirect
34. #63943C4semidirect
74. #5030D3semidirect
110. D3×Dic6C2×C4semidirect
115. #3756C2×C4semidirect
121. C3×#216C2×C4semidirect
142. #3716C2×C4semidirect
143. #3715C2×C4semidirect
145. #3711C2×C4semidirect
364. #216C4×D3semidirect
433. C3×Dic3#137semidirect
675. Dic3#951semidirect
676. C32C4×#137semidirect
750. C3#79829semidirect
751. C3C4×#951semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C2×#639432
C4×D3×Dic62
#105927292
C3×#50302
Dic3×#2162
#105915502
#105915372
#105906002
#105904792
#105904752
#105904372
#105903602
#105903582
#105903342
C4×#9513
#798293