Finite Group Databasebeta

← #11866343

Subgroups — #11866343

Order 1152.

1036 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5572C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594000C211yesmaximal, characteristic
5#10592727C211yesmaximal, characteristic, complemented
6C3×#5027C211yesmaximal, characteristic, complemented
7#10591617C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10#10590592C211yesmaximal, characteristic, complemented
11#10590549C211yesmaximal, characteristic, complemented
12#10590532C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14#10590364C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#82551—31nomaximal
17#80385—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C2×#3756C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24#64084C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#892—21no—
29C3×#892C2211yescharacteristic
30C3×#887—21no—
31C3×#887C2211yescharacteristic, complemented
32C3×#874C2211yescharacteristic
33C3×#872—21no—
34C3×#872C2211yescharacteristic
35C3×C4×Dic6—21no—
36C3×C4×Dic6C2211yescharacteristic, complemented
37#63946—24no—
38D3×#215—24no—
39#63922—21no—
40#63922—21no—
41#63911C2211yescharacteristic
42#63886—21no—
43#63886—21no—
44#63860C2211yescharacteristic
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63637C2211yescharacteristic, complemented
52#63636C2211yescharacteristic
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic, complemented
63C3×#519—31no—
64C2×#942—31no—
65C22×#215—31no—
66C2×#915—31no—
67C2×D3×SD16—31no—
68#5715—31no—
69#5572D311yescharacteristic, complemented
70#5525—31no—
71C3×#460—31no—
72#5166—31no—
73#5163—31no—
74#5075—31no—
75#5028—31no—
76#5028—31no—
77#5028—31no—
78#5028—31no—
79#5028—31no—
80#5028—61no—
81#5027—31no—
82#5027—31no—
83#5027—31no—
84#5027D311yescharacteristic, complemented
85#5002—31no—
86#5001—31no—
87#4999—31no—
88#4845—31no—
89#4839—31no—
90#4772—31no—
91#4770—31no—
92#4767—31no—
93#4762—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×D3×Q8—22no—
99C3×D3×Q8D414yescomplemented
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×D3×Dic3—21no—
113D3×D12—22no—
114D3×D12—22no—
115#3795—22no—
116#3795—22no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121#3756—22no—
122#3755—22no—
123#3752—21no—
124#3752—21no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#215—22no—
128C3×#215—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3—21no—
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147#3719—22no—
148#3717—22no—
149#3715—22no—
150#3715—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3043—91noSylow
154C22×C3×Q8—31no—
155C2×D3×Q8C2×D311yescharacteristic
156C2×#237—31no—
157C2×D3×D4—31no—
158C2×#235—31no—
159C22×D12—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C3×#127—31no—
163C3×C4×Q8—21no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—31no—
167C3×C4×Q8—61no—
168C3×C4×Q8—61no—
169C3×C4×Q8C2×D311yescharacteristic, complemented
170C3×C4×Q8C2×D311yescharacteristic, complemented
171C3×#117—31no—
172C3×#117—31no—
173C3×#117—61no—
174C3×#117—61no—
175Q8×Dic3C2×D311yescharacteristic, complemented
176C2×#216—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—61no—
180#942—64no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—61no—
187C2×#215—64no—
188C2×#215C2×D311yescharacteristic
189C2×#215C2×D311yescharacteristic, complemented
190#940—31no—
191#939—61no—
192#939—61no—
193#937—61no—
194#937—61no—
195#936—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#208—31no—
199C22×C3⋊C8—31no—
200#915—64no—
201D3×SD16—64no—
202C2×Dic12—31no—
203C2×#204—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×D3×C8—31no—
206#895—61no—
207#895—61no—
208#892—21no—
209#892C2×D311yescharacteristic
210#887—21no—
211#887C2×D311yescharacteristic, complemented
212#882—61no—
213#882—61no—
214#875—31no—
215#875—31no—
216#875—31no—
217#875—61no—
218#874—31no—
219#874C2×D311yescharacteristic
220#872—21no—
221#872C2×D311yescharacteristic
222C4×Dic6—21no—
223C4×Dic6C2×D311yescharacteristic, complemented
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#832—31no—
228#832—31no—
229#821—31no—
230#816—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#810—61no—
237#809—31no—
238#809—31no—
239#809—31no—
240#809—31no—
241#809—31no—
242#809—61no—
243#809C2×D311yescharacteristic
244#809C2×D311yescharacteristic, complemented
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—42no—
256C2×D32—81no—
257C2×D32—81no—
258C32×Q8—21no—
259C32×Q8C2×D412yes—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268#634—21no—
269#634—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—81no—
280C3×D12—81no—
281C3×C4×D3—24no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—24no—
286C3×Dic6C2×D412yes—
287#626—42no—
288#626—81no—
289#626—81no—
290#625—42no—
291D3×Dic3—42no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—91no—
297C22×SD16—91no—
298#535—91no—
299#519—31no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—31no—
305#460—91no—
306#460—91no—
307#460—91no—
308#424—91no—
309#418—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—21no—
314C2×C3×Q8—34no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C22×Dic3—61no—
332D3×Q8—22no—
333D3×Q8D1214yescomplemented
334#237—62no—
335#237—62no—
336D3×D4—62no—
337D3×D4—62no—
338#235—62no—
339#235—62no—
340C2×D12—21no—
341C2×D12—21no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—61no—
345C2×D12—62no—
346C2×D12—62no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12C22×D311yescharacteristic
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×Dic6—21no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C3×SD16—62no—
361C3×SD16—62no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—41no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—61no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—31no—
383C3×C42—41no—
384C3×C42—61no—
385C3×C42—61no—
386C3×C42—61no—
387C3×C42—61no—
388C3×C42C22×D311yescharacteristic
389C3×C42C22×D311yescharacteristic
390#217—61no—
391#217—61no—
392#216—62no—
393#216—62no—
394#216—62no—
395#216—122no—
396#215—22no—
397#215—22no—
398#215—62no—
399#215—62no—
400#215—62no—
401#215—62no—
402#215—62no—
403#215—122no—
404#214—62no—
405#214—62no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4#6711yescharacteristic
416(C2×D3)⋊C4#6711yescharacteristic
417C4⋊Dic3—21no—
418C4⋊Dic3C22×D311yescharacteristic
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421Dic3⋊C4#6711yescharacteristic
422Dic3⋊C4#6711yescharacteristic
423C4×Dic3—21no—
424C4×Dic3—21no—
425C4×Dic3—21no—
426C4×Dic3—21no—
427C4×Dic3C22×D311yescharacteristic
428#208—62no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438Dic12—62no—
439#204—62no—
440ΓL(1,𝔽25)—62no—
441D3×C8—62no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—22no—
457C32×C4—21no—
458C32×C4—21no—
459C32×C4—41no—
460C32×C4C22×D411yescharacteristic
461C32×C4C2×#4111yescharacteristic
462C3⋊Dic3—41no—
463C3×Dic3—22no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—31no—
470C22×D4—91no—
471#137—184no—
472C2×Q16—91no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—184no—
481C2×M16—91no—
482C22×C8—91no—
483#127—31no—
484#127—91no—
485#124—91no—
486#124—91no—
487#121—181no—
488#121—181no—
489#120—181no—
490#120—181no—
491C4×Q8—31no—
492C4×Q8—31no—
493C4×Q8—31no—
494C4×Q8—61no—
495C4×Q8—61no—
496C4×Q8D3211yescharacteristic, complemented
497#117—31no—
498#117—31no—
499#117—61no—
500#117—61no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—91no—
506#103—91no—
507#102—31no—
508#102—31no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3C2×#6711yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—22no—
531C3×Q8—32no—
532C3×Q8—41no—
533C3×Q8—64no—
534C3×Q8—61no—
535C3×Q8C2×D1212yes—
536C3×Q8D3×D412yes—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—241no—
542C3×D4—241no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—31no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—64no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4D3×D411yescharacteristic
561C2×C3×C4D3×D411yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—122no—
567#67—122no—
568#67—122no—
569#67—241no—
570#67—241no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3C2×#6711yescharacteristic
578C2×Dic3C2×#6711yescharacteristic
579C2×Dic3C2×#6711yescharacteristic
580D12—21no—
581D12—21no—
582D12—21no—
583D12—21no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—81no—
589D12—81no—
590D12—121no—
591D12—121no—
592D12—122no—
593D12—241no—
594D12—241no—
595C4×D3—24no—
596C4×D3—122no—
597C4×D3C2×D1212yes—
598C4×D3#23512yes—
599Dic6—21no—
600Dic6—24no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
607Dic6C2×D1212yes—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—121no—
617C3⋊C8—121no—
618C2×C32C2×#12111yescharacteristic
619C2×C32#57711yescharacteristic
620C2×C32#57711yescharacteristic
621C3⋊D3—81no—
622C3×D3—22no—
623C3×D3—81no—
624C3×D3—81no—
625C24—181no—
626#41—182no—
627#41—182no—
628C2×Q8—34no—
629C2×Q8—31no—
630C2×Q8—61no—
631C2×Q8—62no—
632C2×Q8—91no—
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—91no—
639C2×D4—182no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—181no—
648Q16—182no—
649Q16—182no—
650SD16—62no—
651SD16—62no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655SD16—182no—
656M16—182no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—91no—
660C2×C8—91no—
661C2×C8—182no—
662C4⋊C4—21no—
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—61no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C42—21no—
678C42—31no—
679C42—61no—
680C42—61no—
681C42—61no—
682C42—61no—
683C42C2×D3211yescharacteristic
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C22×#6711yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3—244no—
714C2×D3—244no—
715C2×D3#93012yes—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—22no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—42no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—61no—
731C3×C4—61no—
732C3×C4—62no—
733C3×C4—81no—
734C3×C4—121no—
735C3×C4C22×D1211yescharacteristic
736C3×C4C2×#23511yescharacteristic
737C3×C4C2×D3×D411yescharacteristic
738C3×C4D3×#4111yescharacteristic
739Dic3—22no—
740Dic3—21no—
741Dic3—21no—
742Dic3—41no—
743Dic3—121no—
744Dic3—121no—
745Dic3—241no—
746Dic3#93012yes—
747C32#304311yescharacteristic, complemented, Sylow
748C23—31no—
749C23—61no—
750C23—61no—
751C23—181no—
752C23—362no—
753C23—721no—
754C23—721no—
755Q8—21no—
756Q8—32no—
757Q8—64no—
758Q8—61no—
759Q8—181no—
760Q8—181no—
761Q8D3×D1212yes—
762D4—61no—
763D4—61no—
764D4—61no—
765D4—61no—
766D4—181no—
767D4—181no—
768D4—241no—
769D4—241no—
770D4—362no—
771D4—362no—
772D4—721no—
773D4—721no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—31no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—64no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—181no—
785C2×C4—362no—
786C2×C4D3×#6711yescharacteristic
787C2×C4D3×#6711yescharacteristic
788C2×C4C22×D3211yescharacteristic
789C8—61no—
790C8—61no—
791C8—181no—
792C8—181no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—241no—
798C2×C3—241no—
799C2×C3D3×#12111yescharacteristic
800C2×C3#576211yescharacteristic
801C2×C3#577511yescharacteristic
802C2×C3C2×#93011yescharacteristic
803C2×C3#583711yescharacteristic
804C2×C3#583711yescharacteristic
805D3—22no—
806D3—81no—
807D3—81no—
808D3—241no—
809D3—241no—
810D3—481no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—724no—
824C22C2×D3×#6711yescharacteristic
825C4—21no—
826C4—21no—
827C4—22no—
828C4—32no—
829C4—41no—
830C4—61no—
831C4—61no—
832C4—62no—
833C4—121no—
834C4—361no—
835C4C2×D3×D1211yescharacteristic
836C4D3×#23511yescharacteristic
837C3—21no—
838C3#8038511yescharacteristic, complemented
839C3#8255111yescharacteristic, complemented
840C2—62no—
841C2—241no—
842C2—241no—
843C2—721no—
844C2D3×#93011yescharacteristic
845C2#1059531811yescharacteristic
846C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594000C2
hypercenterC4×Q8D32
hypocenterC32#3043
LCSG ▷ C2×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
2. C2×#63946C2semidirect
3. C2×D3×#215C2semidirect
5. #10592727C2semidirect
6. C3×#5027C2semidirect
7. #10591617C2semidirect
8. #10591604C2semidirect
9. #10590608C2semidirect
10. #10590592C2semidirect
11. #10590549C2semidirect
12. #10590532C2semidirect
13. #10590368C2semidirect
14. #10590364C2semidirect
15. #10590324C2semidirect
21. C32×C4×Q8C22semidirect
22. C2×#3756C22semidirect
25. C3×Q8×Dic3C22semidirect
27. C2×C3×#215C22semidirect
31. C3×#887C22semidirect
36. C3×C4×Dic6C22semidirect
45. C2×#3719C22semidirect
48. C2×#3715C22semidirect
51. #63637C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#809C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
62. #63562C22semidirect
69. #5572D3semidirect
84. #5027D3semidirect
99. C3×D3×Q8D4semidirect
169. C3×C4×Q8C2×D3semidirect
170. C3×C4×Q8C2×D3semidirect
175. Q8×Dic3C2×D3semidirect
189. C2×#215C2×D3semidirect
211. #887C2×D3semidirect
223. C4×Dic6C2×D3semidirect
244. #809C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
333. D3×Q8D12semidirect
496. C4×Q8D32semidirect
747. C32#3043semidirect
838. C3#80385semidirect
839. C3#82551semidirect

Maximal subgroups

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

subgroupindex
C3×#55722
C2×#639462
C2×D3×#2152
#105940002
#105927272
C3×#50272
#105916172
#105916042
#105906082
#105905922
#105905492
#105905322
#105903682
#105903642
#105903242
#825513
#803853