Finite Group Databasebeta

← #11860444

Subgroups — #11860444

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
1C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic
3C4×#3799C211yesmaximal, characteristic
4#10592725C211yesmaximal, characteristic, complemented
5C3×#5030C211yesmaximal, characteristic, complemented
6Dic3×#216C211yesmaximal, characteristic, complemented
7#10591557C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590609C211yesmaximal, characteristic
10#10590581C211yesmaximal, characteristic, complemented
11#10590476C211yesmaximal, characteristic, complemented
12#10590458C211yesmaximal, characteristic, complemented
13#10590381C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590334C211yesmaximal, characteristic, complemented
16C4×#942—31nomaximal
17#79829—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D3×C4⋊C4—21no—
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887—21no—
28C3×#887C2211yescharacteristic
29C3×C42×D3—21no—
30C3×C42×D3C2211yescharacteristic
31C3×C4×Dic6—21no—
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63948C418yescomplemented
35#63904—21no—
36C4×#626—21no—
37#63894C2211yescharacteristic
38C4×#624—21no—
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63836—21no—
42C2×#3718C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63662C2211yescharacteristic
47#63636C2211yescharacteristic
48#63634C2211yescharacteristic
49#63630C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×C3×C4×Q8—31no—
63C2×#942—31no—
64C2×#918—31no—
65C4×#239—31no—
66C4×D3×Q8D311yescharacteristic, complemented
67C4×#235—31no—
68C3×#441—31no—
69#5225—31no—
70Dic3×Q16—31no—
71#5030—31no—
72#5030—31no—
73#5030D311yescharacteristic, complemented
74C4×#216—31no—
75C4×#216—31no—
76#5026—31no—
77#5026—31no—
78#5026—31no—
79#5026—61no—
80C4×#215—31no—
81C4×#215—31no—
82#4966—31no—
83#4964—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×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×D3—21no—
100C2×C3×C4×D3D411yescharacteristic
101C2×C3×C4×D3D411yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109#3799—22no—
110#3799C2×C414yes—
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C42—21no—
114C32×C42C2311yescharacteristic
115#3755C2×C414yescomplemented
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#216C2×C414yescomplemented
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—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
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3718C2×C414yescomplemented
143#3717C2×C414yescomplemented
144#3711—22no—
145#3711C2×C414yescomplemented
146C4×#137—91noSylow
147C22×C3×Q8—31no—
148C2×#239—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×Q16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—61no—
158C3×C4×Q8—61no—
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×Q8C2×D311yescharacteristic
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—61no—
163C2×C3×C42—31no—
164C2×C3×C42—61no—
165Q8×Dic3—31no—
166Q8×Dic3C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216C2×D311yescharacteristic
170#942—38no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—61no—
175C4×#67—61no—
176C4×#67—61no—
177#926—31no—
178C2×#208—31no—
179C2×#208—31no—
180#918—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184#893—31no—
185#893—61no—
186#892—31no—
187#892—61no—
188D3×C4⋊C4—21no—
189D3×C4⋊C4C2×D311yescharacteristic
190#887—21no—
191#887C2×D311yescharacteristic
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—61no—
196C4×D12—61no—
197#872—61no—
198C42×D3—21no—
199C42×D3—61no—
200C42×D3—61no—
201C42×D3C2×D311yescharacteristic
202C4×Dic6—21no—
203C4×Dic6—31no—
204C4×Dic6C2×D311yescharacteristic
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—31no—
214#835—31no—
215#835—61no—
216#835C2×D311yescharacteristic
217#821—31no—
218#818—31no—
219#816—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810C2×D311yescharacteristic
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808C2×D311yescharacteristic
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
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—
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×D3—22no—
264C3×C4×D3—41no—
265C3×C4×D3—42no—
266C3×C4×D3C22×C412yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—24no—
271C3×Dic6C22×C412yes—
272C3×Dic6C22×C412yes—
273#626—24no—
274#624—24no—
275#624—42no—
276C3⋊(C3⋊C8)—21no—
277C3⋊(C3⋊C8)C22×C412yes—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×C412yes—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—31no—
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—
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—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—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—21no—
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—121no—
328C2×C4×D3#6711yescharacteristic
329C2×C4×D3#6711yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×Q16—34no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—21no—
353C3×C42—31no—
354C3×C42—31no—
355C3×C42—31no—
356C3×C42—41no—
357C3×C42—61no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—61no—
364#216—34no—
365#216—34no—
366#216C4×D314yescomplemented
367#215—34no—
368#215—34no—
369#215—34no—
370#215—64no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—121no—
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—61no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
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—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—21no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4C23×C411yescharacteristic
425C32×C4C2×#4111yescharacteristic
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—91no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—61no—
448C4×Q8—61no—
449C4×Q8—91no—
450C4×Q8D3211yescharacteristic
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—61no—
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—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—121no—
482C22×D3C2×#6711yescharacteristic
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—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—62no—
509C2×C3×C4—64no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—121no—
515C2×C3×C4—122no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—64no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—61no—
538D12—61no—
539D12—121no—
540C4×D3—24no—
541C4×D3—22no—
542C4×D3—41no—
543C4×D3—42no—
544C4×D3—64no—
545C4×D3—64no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—242no—
551C4×D3C2×C4×D312yes—
552C4×D3#23512yes—
553Dic6—21no—
554Dic6—21no—
555Dic6—24no—
556Dic6C2×C4×D312yes—
557Dic6C2×C4×D312yes—
558C3×C8—32no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—32no—
562C3⋊C8—32no—
563C3⋊C8—62no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—121no—
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—31no—
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591Q16—34no—
592Q16—94no—
593SD16—94no—
594SD16—94no—
595M16—94no—
596M16—182no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8—91no—
601C4⋊C4—21no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—91no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—21no—
616C42—31no—
617C42—31no—
618C42—31no—
619C42—61no—
620C42—61no—
621C42—61no—
622C42—61no—
623C42—181no—
624C42—181no—
625C42C2×D3211yescharacteristic
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C22×#6711yescharacteristic
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×#6712yes—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—62no—
661C3×C4—62no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C22×C4×D311yescharacteristic
666C3×C4C22×C4×D311yescharacteristic
667C3×C4C2×#23511yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—22no—
670Dic3—22no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—121no—
675Dic3—121no—
676Dic3—241no—
677Dic3C4×#6712yes—
678Dic3#94212yescomplemented
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—62no—
700C2×C4—64no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—121no—
706C2×C4—122no—
707C2×C4—184no—
708C2×C4—181no—
709C2×C4—362no—
710C2×C4—362no—
711C2×C4D3×#6711yescharacteristic
712C2×C4D3×#6711yescharacteristic
713C2×C4C22×D3211yescharacteristic
714C8—32no—
715C8—61no—
716C8—92no—
717C8—181no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—62no—
722C2×C3C4×D3×D411yescharacteristic
723C2×C3D3×#13711yescharacteristic
724C2×C3#577711yescharacteristic
725C2×C3C2×C4×#6711yescharacteristic
726C2×C3C2×#94211yescharacteristic
727C2×C3#582211yescharacteristic
728D3—22no—
729D3—122no—
730D3—122no—
731D3—242no—
732C22—32no—
733C22—61no—
734C22—61no—
735C22—182no—
736C22—361no—
737C22—361no—
738C22C2×D3×#6711yescharacteristic
739C4—21no—
740C4—22no—
741C4—21no—
742C4—32no—
743C4—32no—
744C4—41no—
745C4—61no—
746C4—62no—
747C4—62no—
748C4—121no—
749C4—121no—
750C4—361no—
751C4C2×C4×D3211yescharacteristic
752C4D3×#23511yescharacteristic
753C3—21no—
754C3#7982911yescharacteristic, complemented
755C3C4×#94211yescharacteristic, complemented
756C2—62no—
757C2—362no—
758C2C4×D3×#6711yescharacteristic
759C2D3×#94211yescharacteristic
760C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
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
1. C3×C4×D3×Q8C2semidirect
4. #10592725C2semidirect
5. C3×#5030C2semidirect
6. Dic3×#216C2semidirect
7. #10591557C2semidirect
8. #10591536C2semidirect
10. #10590581C2semidirect
11. #10590476C2semidirect
12. #10590458C2semidirect
13. #10590381C2semidirect
14. #10590362C2semidirect
15. #10590334C2semidirect
34. #63948C4semidirect
66. C4×D3×Q8D3semidirect
73. #5030D3semidirect
97. C3×D3×Q8C2×C4semidirect
115. #3755C2×C4semidirect
120. C3×#216C2×C4semidirect
142. #3718C2×C4semidirect
143. #3717C2×C4semidirect
145. #3711C2×C4semidirect
312. D3×Q8C4×D3semidirect
366. #216C4×D3semidirect
433. C3×Dic3#137semidirect
678. Dic3#942semidirect
679. C32C4×#137semidirect
754. C3#79829semidirect
755. C3C4×#942semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
C2×#639482
C4×#37992
#105927252
C3×#50302
Dic3×#2162
#105915572
#105915362
#105906092
#105905812
#105904762
#105904582
#105903812
#105903622
#105903342
C4×#9423
#798293