Finite Group Databasebeta

← #11860614

Subgroups — #11860614

Order 1152.

1000 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5572C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic
3#10593890C211yesmaximal, characteristic
4#10592725C211yesmaximal, characteristic, complemented
5C3×C4×#216C211yesmaximal, characteristic, complemented
6#10591576C211yesmaximal, characteristic, complemented
7D3×#835C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic
10#10590476C211yesmaximal, characteristic, complemented
11#10590457C211yesmaximal, characteristic, complemented
12#10590436C211yesmaximal, characteristic, complemented
13#10590381C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15#10590318C211yesmaximal, characteristic, complemented
16#82547—31nomaximal
17#79719—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#892—21no—
26C3×#892C2211yescharacteristic
27C3×#887—21no—
28C3×#887C2211yescharacteristic
29C3×#872—21no—
30C3×#872C2211yescharacteristic
31C3×C4×Dic6—21no—
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63948C418yescomplemented
35#63894C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63883—21no—
38#63881—21no—
39#63880—21no—
40Dic3×Dic6C2211yescharacteristic
41#63836—21no—
42C2×#3718C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63636C2211yescharacteristic
48#63634C2211yescharacteristic
49#63630C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×#519—31no—
63C2×#942—31no—
64C2×#918—31no—
65#5574—31no—
66#5572D311yescharacteristic, complemented
67#5523—31no—
68C3×C4×Q16—31no—
69C2×#835—31no—
70#5184—31no—
71#5030—31no—
72#5030—31no—
73#5030—31no—
74C4×#216—31no—
75C4×#216D311yescharacteristic, complemented
76#5026—31no—
77#5026—31no—
78#5026—31no—
79#5026—61no—
80C4×#215—31no—
81C4×#215—31no—
82#5002—31no—
83#4997—31no—
84#4995—31no—
85#4889—31no—
86#4881—31no—
87#4804—31no—
88D3×#103—31no—
89#4790—31no—
90#4788—31no—
91C4×#204—31no—
92#4689—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—
107#3799—22no—
108#3799C2×C414yes—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C42—21no—
112C32×C42C2311yescharacteristic
113#3755C2×C414yescomplemented
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216C2×C414yescomplemented
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3718C2×C414yescomplemented
143#3717C2×C414yescomplemented
144#3711C2×C414yescomplemented
145D3×C3⋊C8—22no—
146#2947—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
161C3×#117—31no—
162C3×#117—31no—
163C3×#117—61no—
164C3×#117—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—
175C2×C4⋊Dic3—31no—
176C2×#208—31no—
177C22×C3⋊C8—31no—
178#918—38no—
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#893—31no—
183#893—61no—
184#892—21no—
185#892—61no—
186#892C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4—61no—
190#887—21no—
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#67⋊C4—61no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12—61no—
199#872—21no—
200#872—61no—
201#872C2×D311yescharacteristic
202C4×Dic6—21no—
203C4×Dic6—31no—
204C4×Dic6C2×D311yescharacteristic
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×C4×C8—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#817—31no—
219#816—31no—
220#815—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#808—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic
236#803—31no—
237#803—31no—
238#803—31no—
239#803—61no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8C2×D311yescharacteristic
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—81no—
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—81no—
273D3×Dic3—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)C22×C412yes—
276C3×C3⋊C8—21no—
277C3×C3⋊C8C22×C412yes—
278C2×#137—91no—
279#520—91no—
280#519—31no—
281#441—91no—
282#441—91no—
283#440—91no—
284#440—91no—
285C4×Q16—31no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289#428—91no—
290#416—91no—
291C2×#103—91no—
292#405—91no—
293C2×C3×Q8—21no—
294C2×C3×Q8—34no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—61no—
298C2×C3×Q8—62no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—61no—
304C22×Dic3—61no—
305#239—34no—
306#239—62no—
307D3×Q8—22no—
308D3×Q8C4×D314yescomplemented
309#235—34no—
310#235—62no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12—61no—
315C2×C4×D3—21no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—121no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—21no—
326C2×Dic6C22×D311yescharacteristic
327C2×Dic6C22×D311yescharacteristic
328C3×Q16—34no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—41no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—61no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42—41no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#216—34no—
361#216—34no—
362#216C4×D314yescomplemented
363#215—34no—
364#215—34no—
365#215—34no—
366#215—64no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—121no—
373(C2×D3)⋊C4#6711yescharacteristic
374(C2×D3)⋊C4#6711yescharacteristic
375C4⋊Dic3—21no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4#6711yescharacteristic
389Dic3⋊C4#6711yescharacteristic
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398#208—34no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—62no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408#204—34no—
409ΓL(1,𝔽25)—34no—
410D3×C8—62no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C4×D412yes—
418C32×C4—22no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—41no—
425C3×Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C4×D412yes—
432C2×#41—91no—
433C22×Q8—31no—
434#137—98no—
435C2×Q16—31no—
436C2×Q16—91no—
437C2×SD16—91no—
438C2×SD16—91no—
439C2×M16—91no—
440C22×C8—91no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—61no—
446C4×Q8—61no—
447C4×Q8—91no—
448C4×Q8D3211yescharacteristic
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—31no—
454#117—31no—
455#117—61no—
456#117—61no—
457#117—181no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—31no—
461#107—91no—
462#106—91no—
463#106—91no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—91no—
471#102—91no—
472#97—91no—
473#97—91no—
474C4×C8—31no—
475C4×C8—91no—
476C23×C3—31no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—121no—
480C22×D3C2×#6711yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—22no—
484C3×Q8—32no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—64no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8C2×C4×D312yes—
491C3×Q8C2×C4×D312yes—
492C2×C3×C4—21no—
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—31no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—31no—
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×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C2×#6711yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—64no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—241no—
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529D12—32no—
530D12—32no—
531D12—62no—
532D12—64no—
533D12—61no—
534D12—61no—
535D12—121no—
536C4×D3—24no—
537C4×D3—64no—
538C4×D3—64no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—242no—
545C4×D3C2×C4×D312yes—
546C4×D3#23512yes—
547Dic6—21no—
548Dic6—21no—
549Dic6—24no—
550Dic6C2×C4×D312yes—
551Dic6C2×C4×D312yes—
552C3×C8—32no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—32no—
556C3⋊C8—32no—
557C3⋊C8—62no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C3⋊C8C2×C4×D312yes—
562C2×C32C2×C4×D411yescharacteristic
563C2×C32#57711yescharacteristic
564C2×C32#57811yescharacteristic
565C3⋊D3—42no—
566C3×D3—22no—
567#41—94no—
568#41—182no—
569C2×Q8—34no—
570C2×Q8—31no—
571C2×Q8—31no—
572C2×Q8—61no—
573C2×Q8—62no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—91no—
576C2×D4—181no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583Q16—34no—
584Q16—94no—
585SD16—94no—
586SD16—94no—
587M16—94no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—91no—
592C2×C8—182no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—21no—
612C42—31no—
613C42—61no—
614C42—61no—
615C42—61no—
616C42—61no—
617C42—61no—
618C42—181no—
619C42C2×D3211yescharacteristic
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×#6711yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—122no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—241no—
636C2×D3—241no—
637C2×D3C4×#6712yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—32no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C22×C4×D311yescharacteristic
660C3×C4C22×C4×D311yescharacteristic
661C3×C4C2×#23511yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—22no—
664Dic3—22no—
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—121no—
670Dic3—121no—
671Dic3—241no—
672Dic3C4×#6712yes—
673C32#294711yescharacteristic, complemented, Sylow
674C23—31no—
675C23—181no—
676Q8—21no—
677Q8—32no—
678Q8—32no—
679Q8—64no—
680Q8—61no—
681Q8—61no—
682Q8C4×D3212yes—
683D4—92no—
684D4—184no—
685D4—181no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—31no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—64no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—184no—
699C2×C4—181no—
700C2×C4—721no—
701C2×C4—721no—
702C2×C4—721no—
703C2×C4D3×#6711yescharacteristic
704C2×C4D3×#6711yescharacteristic
705C2×C4C22×D3211yescharacteristic
706C8—32no—
707C8—61no—
708C8—92no—
709C8—181no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—62no—
714C2×C3C4×D3×D411yescharacteristic
715C2×C3#576611yescharacteristic
716C2×C3#577011yescharacteristic
717C2×C3C2×C4×#6711yescharacteristic
718C2×C3#583711yescharacteristic
719C2×C3#583811yescharacteristic
720D3—22no—
721D3—122no—
722D3—122no—
723D3—242no—
724C22—32no—
725C22—61no—
726C22—61no—
727C22—182no—
728C22—361no—
729C22—361no—
730C22C2×D3×#6711yescharacteristic
731C4—21no—
732C4—22no—
733C4—21no—
734C4—32no—
735C4—41no—
736C4—61no—
737C4—62no—
738C4—62no—
739C4—61no—
740C4—121no—
741C4—121no—
742C4—361no—
743C4C2×C4×D3211yescharacteristic
744C4D3×#23511yescharacteristic
745C3—21no—
746C3#7971911yescharacteristic, complemented
747C3#8254711yescharacteristic, complemented
748C2—62no—
749C2—362no—
750C2C4×D3×#6711yescharacteristic
751C2#1059532711yescharacteristic
752C2#1059545711yescharacteristic
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
hypocenterC32#2947
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×#5572C2semidirect
4. #10592725C2semidirect
5. C3×C4×#216C2semidirect
6. #10591576C2semidirect
7. D3×#835C2semidirect
8. #10591536C2semidirect
10. #10590476C2semidirect
11. #10590457C2semidirect
12. #10590436C2semidirect
13. #10590381C2semidirect
14. C4×#3717C2semidirect
15. #10590318C2semidirect
34. #63948C4semidirect
66. #5572D3semidirect
75. C4×#216D3semidirect
97. C3×D3×Q8C2×C4semidirect
113. #3755C2×C4semidirect
118. C3×#216C2×C4semidirect
142. #3718C2×C4semidirect
143. #3717C2×C4semidirect
144. #3711C2×C4semidirect
308. D3×Q8C4×D3semidirect
362. #216C4×D3semidirect
673. C32#2947semidirect
746. C3#79719semidirect
747. C3#82547semidirect

Maximal subgroups

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

subgroupindex
C3×#55722
C2×#639482
#105938902
#105927252
C3×C4×#2162
#105915762
D3×#8352
#105915362
#105906102
#105904762
#105904572
#105904362
#105903812
C4×#37172
#105903182
#825473
#797193