Finite Group Databasebeta

← #11860616

Subgroups — #11860616

Order 1152.

995 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5572C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic
3#10593887C211yesmaximal, characteristic
4C4×#3756C211yesmaximal, characteristic, complemented
5C3×#5026C211yesmaximal, characteristic, complemented
6Dic3×#215C211yesmaximal, characteristic, complemented
7D3×#835C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic
10#10590481C211yesmaximal, characteristic, complemented
11#10590454C211yesmaximal, characteristic, complemented
12#10590436C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590319C211yesmaximal, characteristic, complemented
16#82547—31nomaximal
17#79776—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#892—21no—
26C3×#892C2211yescharacteristic
27C3×#887—21no—
28C3×#887C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×#872—21no—
31C3×#872C2211yescharacteristic
32C3×C4×Dic6—21no—
33C3×C4×Dic6C2211yescharacteristic
34#63946C418yescomplemented
35#63902—21no—
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63879—21no—
39#63878—21no—
40D3×Dic3⋊C4—21no—
41#63844C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63637C2211yescharacteristic
48#63634C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#807C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×#519—31no—
63C2×#942—31no—
64C2×#915—31no—
65#5572D311yescharacteristic, complemented
66#5546—31no—
67#5523—31no—
68C3×#440—31no—
69C2×#835—31no—
70Dic3×SD16—31no—
71#5030—31no—
72#5030—31no—
73C4×#216—31no—
74C4×#216—31no—
75C4×#216—31no—
76C4×#216—61no—
77#5026—31no—
78#5026D311yescharacteristic, complemented
79C4×#215—31no—
80C4×#215—31no—
81C4×#214—31no—
82#5002—31no—
83#4997—31no—
84#4995—31no—
85#4881—31no—
86#4873—31no—
87D3×#103—31no—
88#4789—31no—
89#4772—31no—
90#4757—31no—
91#4716—31no—
92#4708—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—
107#3795—22no—
108#3795C2×C414yes—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C42—21no—
112C32×C42C2311yescharacteristic
113#3756C2×C414yescomplemented
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#215C2×C414yescomplemented
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
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
138#3724—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3719C2×C414yescomplemented
143#3715C2×C414yescomplemented
144#3711C2×C414yescomplemented
145D3×C3⋊C8—22no—
146#2947—91noSylow
147C22×C3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×#237—31no—
150C2×#235—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—61no—
157C3×C4×Q8—61no—
158C3×C4×Q8C2×D311yescharacteristic
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—31no—
163C3×#117—61no—
164C3×#117—61no—
165Q8×Dic3C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—61no—
170#942—38no—
171C2×#215—31no—
172C2×#215C2×D311yescharacteristic
173D4×Dic3—31no—
174C2×#214—31no—
175C4×#67—61no—
176C2×C4⋊Dic3—31no—
177C2×Dic3⋊C4—61no—
178C2×#208—31no—
179C22×C3⋊C8—31no—
180#915—38no—
181C2×Dic12—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8—31no—
184#892—21no—
185#892—61no—
186#892C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189#887—21no—
190#887—31no—
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195#877—61no—
196C4×D12—31no—
197C4×D12C2×D311yescharacteristic
198#872—21no—
199#872C2×D311yescharacteristic
200C4×Dic6—21no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic
216#832—31no—
217#817—31no—
218#816—31no—
219#816—31no—
220#815—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#809—31no—
228#809C2×D311yescharacteristic
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#803C2×D311yescharacteristic
238C4×C3⋊C8—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8—61no—
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—21no—
262C3×D12C22×C412yes—
263C3×C4×D3—24no—
264C3×C4×D3—81no—
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—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—31no—
284#440—91no—
285C4×Q16—91no—
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—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309D3×Q8—22no—
310D3×Q8C4×D314yescomplemented
311#237—34no—
312#237—62no—
313#235—34no—
314#235—62no—
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3C22×D311yescharacteristic
322C2×Dic6—21no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×Dic6C22×D311yescharacteristic
327C3×SD16—34no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—41no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42—41no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42C22×D311yescharacteristic
357C3×C42C22×D311yescharacteristic
358#217—61no—
359#216—34no—
360#216—34no—
361#216—34no—
362#216—64no—
363#215—34no—
364#215C4×D314yescomplemented
365#214—34no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4#6711yescharacteristic
370(C2×D3)⋊C4#6711yescharacteristic
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—121no—
386Dic3⋊C4#6711yescharacteristic
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—121no—
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
408Dic12—34no—
409ΓL(1,𝔽25)—34no—
410D3×C8—62no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3C4×D412yes—
418C32×C4—21no—
419C32×C4—22no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—22no—
425C3⋊Dic3—41no—
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—91no—
436C2×Q16—91no—
437C2×SD16—31no—
438C2×SD16—91no—
439C2×M16—91no—
440C22×C8—91no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—61no—
445C4×Q8—61no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8D3211yescharacteristic
449C4×D4—31no—
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—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#97—31no—
473#97—91no—
474C4×C8—91no—
475C4×C8—91no—
476C23×C3—31no—
477C23×C3—61no—
478C22×D3—21no—
479C22×D3C2×#6711yescharacteristic
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—22no—
483C3×Q8—32no—
484C3×Q8—41no—
485C3×Q8—64no—
486C3×Q8—61no—
487C3×Q8C2×C4×D312yes—
488C3×Q8C2×C4×D312yes—
489C3×D4—32no—
490C3×D4—61no—
491C2×C3×C4—21no—
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—31no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—31no—
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—241no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—64no—
517#67—64no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—64no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—241no—
529C2×Dic3—241no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—21no—
534D12C2×C4×D312yes—
535C4×D3—24no—
536C4×D3—64no—
537C4×D3—81no—
538C4×D3—241no—
539C4×D3—241no—
540C4×D3C2×C4×D312yes—
541C4×D3#23512yes—
542Dic6—21no—
543Dic6—24no—
544Dic6—32no—
545Dic6—32no—
546Dic6—62no—
547Dic6—61no—
548Dic6—61no—
549Dic6—121no—
550Dic6C2×C4×D312yes—
551C3×C8—32no—
552C3×C8—61no—
553C3⋊C8—21no—
554C3⋊C8—32no—
555C3⋊C8—32no—
556C3⋊C8—62no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C3⋊C8C2×C4×D312yes—
561C2×C32C2×C4×D411yescharacteristic
562C2×C32#57711yescharacteristic
563C2×C32#57811yescharacteristic
564C3×D3—22no—
565C3×D3—42no—
566#41—94no—
567#41—182no—
568C2×Q8—34no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×Q8—62no—
572C2×Q8—91no—
573C2×Q8C2×D3211yescharacteristic
574C2×D4—31no—
575C2×D4—181no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582Q16—94no—
583Q16—94no—
584SD16—34no—
585SD16—94no—
586M16—94no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—91no—
590C2×C8—91no—
591C2×C8—182no—
592C4⋊C4—21no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4C2×D3211yescharacteristic
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C42—21no—
611C42—31no—
612C42—61no—
613C42—61no—
614C42—61no—
615C42—61no—
616C42—181no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—62no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3C2×D3×D411yescharacteristic
627C22×C3C22×#6711yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—22no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3C4×#6712yes—
634C3×C4—22no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—32no—
644C3×C4—41no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
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×#23511yescharacteristic
657C3×C4D3×#4111yescharacteristic
658Dic3—22no—
659Dic3—21no—
660Dic3—21no—
661Dic3—41no—
662Dic3—41no—
663Dic3—62no—
664Dic3—62no—
665Dic3—122no—
666Dic3—121no—
667Dic3—121no—
668Dic3—241no—
669Dic3C4×#6712yes—
670C32#294711yescharacteristic, complemented, Sylow
671C23—31no—
672C23—61no—
673Q8—21no—
674Q8—32no—
675Q8—64no—
676Q8—61no—
677Q8—92no—
678Q8—181no—
679Q8C4×D3212yes—
680D4—32no—
681D4—61no—
682D4—184no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—31no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—64no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—184no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—241no—
698C2×C4—721no—
699C2×C4—721no—
700C2×C4D3×#6711yescharacteristic
701C2×C4D3×#6711yescharacteristic
702C2×C4C22×D3211yescharacteristic
703C8—32no—
704C8—61no—
705C8—92no—
706C8—181no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—62no—
711C2×C3—122no—
712C2×C3C4×D3×D411yescharacteristic
713C2×C3#577511yescharacteristic
714C2×C3#577911yescharacteristic
715C2×C3C2×C4×#6711yescharacteristic
716C2×C3#583711yescharacteristic
717C2×C3#583811yescharacteristic
718D3—22no—
719D3—42no—
720C22—32no—
721C22—61no—
722C22—61no—
723C22—62no—
724C22—121no—
725C22—121no—
726C22C2×D3×#6711yescharacteristic
727C4—21no—
728C4—21no—
729C4—22no—
730C4—32no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—62no—
735C4—121no—
736C4—121no—
737C4—182no—
738C4—361no—
739C4C2×C4×D3211yescharacteristic
740C4D3×#23511yescharacteristic
741C3—21no—
742C3#7977611yescharacteristic, complemented
743C3#8254711yescharacteristic, complemented
744C2—62no—
745C2—122no—
746C2C4×D3×#6711yescharacteristic
747C2#1059532811yescharacteristic
748C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
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. C4×#3756C2semidirect
5. C3×#5026C2semidirect
6. Dic3×#215C2semidirect
7. D3×#835C2semidirect
8. #10591541C2semidirect
10. #10590481C2semidirect
11. #10590454C2semidirect
12. #10590436C2semidirect
13. #10590383C2semidirect
14. C4×#3715C2semidirect
15. #10590319C2semidirect
34. #63946C4semidirect
65. #5572D3semidirect
78. #5026D3semidirect
96. C3×D3×Q8C2×C4semidirect
113. #3756C2×C4semidirect
119. C3×#215C2×C4semidirect
142. #3719C2×C4semidirect
143. #3715C2×C4semidirect
144. #3711C2×C4semidirect
310. D3×Q8C4×D3semidirect
364. #215C4×D3semidirect
670. C32#2947semidirect
742. C3#79776semidirect
743. 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×#639462
#105938872
C4×#37562
C3×#50262
Dic3×#2152
D3×#8352
#105915412
#105906082
#105904812
#105904542
#105904362
#105903832
C4×#37152
#105903192
#825473
#797763