Finite Group Databasebeta

← #11866341

Subgroups — #11866341

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5572C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594001C211yesmaximal, characteristic
5#10592726C211yesmaximal, characteristic, complemented
6C3×#5028C211yesmaximal, characteristic, complemented
7#10591617C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590592C211yesmaximal, characteristic, complemented
11#10590549C211yesmaximal, characteristic, complemented
12#10590536C211yesmaximal, characteristic, complemented
13#10590367C211yesmaximal, characteristic, complemented
14#10590324C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#82551—31nomaximal
17#80600—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24#64083C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#892—21no—
29C3×#892C2211yescharacteristic
30C3×#887—21no—
31C3×#887C2211yescharacteristic, complemented
32C3×#875C2211yescharacteristic
33C3×#872—21no—
34C3×#872C2211yescharacteristic
35C3×C4×Dic6—21no—
36C3×C4×Dic6C2211yescharacteristic, complemented
37#63948—24no—
38D3×#215—24no—
39#63923—21no—
40#63923—21no—
41#63911C2211yescharacteristic
42#63910—21no—
43#63910—21no—
44#63864C2211yescharacteristic
45C2×#3718C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63636C2211yescharacteristic
52#63636C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63C3×#519—31no—
64C2×#942—31no—
65C22×#215—31no—
66C2×#918—31no—
67C2×D3×SD16—31no—
68#5674—31no—
69#5572D311yescharacteristic, complemented
70#5525—31no—
71C3×#464—31no—
72#5185—31no—
73#5163—31no—
74#5054—31no—
75#5028—31no—
76#5028—31no—
77#5028—31no—
78#5028D311yescharacteristic, complemented
79#5027—31no—
80#5027—31no—
81#5027—31no—
82#5027—31no—
83#5027—31no—
84#5027—61no—
85#5002—31no—
86#5001—31no—
87#4999—31no—
88#4848—31no—
89#4839—31no—
90#4804—31no—
91#4798—31no—
92#4770—31no—
93#4762—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C3×D3×Q8—22no—
101C3×D3×Q8D414yescomplemented
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113D3×D12—22no—
114D3×D12—22no—
115#3799—22no—
116#3799—22no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121#3755—22no—
122#3755—22no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#216—22no—
126C3×#215—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
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#3722—21no—
146#3722—21no—
147#3718—22no—
148#3717—22no—
149#3717—22no—
150#3715—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3043—91noSylow
154C22×C3×Q8—31no—
155C2×#239—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×#235—31no—
159C22×D12—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C3×#124—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—
175#947—31no—
176Q8×Dic3C2×D311yescharacteristic, complemented
177C2×#216—31no—
178C2×#216—31no—
179C2×#216C2×D311yescharacteristic, complemented
180#942—64no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—61no—
189C2×#215—61no—
190C2×#215—64no—
191C2×#215C2×D311yescharacteristic
192#940—31no—
193C2×#214—31no—
194C2×#208—31no—
195C22×C3⋊C8—31no—
196#918—64no—
197D3×SD16—64no—
198C2×#204—31no—
199C2×#204—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×D3×C8—31no—
202#895—61no—
203#895—61no—
204#892—21no—
205#892C2×D311yescharacteristic
206#887—21no—
207#887C2×D311yescharacteristic, complemented
208#884—61no—
209#884—61no—
210#882—61no—
211#882—61no—
212#882—61no—
213#882—61no—
214#875—31no—
215#875C2×D311yescharacteristic
216#874—31no—
217#874—31no—
218#874—31no—
219#874—61no—
220#872—21no—
221#872C2×D311yescharacteristic
222C4×Dic6—21no—
223C4×Dic6C2×D311yescharacteristic, complemented
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#832—31no—
229#821—31no—
230#821—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#810C2×D311yescharacteristic, complemented
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#809—31no—
240#809—31no—
241#809—31no—
242#809—61no—
243#809—61no—
244#809C2×D311yescharacteristic
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
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—81no—
270C4⋊(C3⋊D3)—81no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×C4×D3—24no—
280C3×C4×D3C2×D412yes—
281C3×C4×D3#4112yes—
282C3×Dic6—21no—
283C3×Dic6—24no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6C2×D412yes—
287#626—42no—
288#626—42no—
289#626—81no—
290#626—81no—
291#624—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—31no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—91no—
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—31no—
317C2×C3×Q8—61no—
318C2×C3×Q8—62no—
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×D4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328#239—62no—
329#239—62no—
330D3×Q8—22no—
331D3×Q8D1214yescomplemented
332D3×D4—62no—
333D3×D4—62no—
334#235—62no—
335#235—62no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—62no—
343C2×D12—62no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—121no—
353C2×D12—121no—
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—21no—
360C2×Dic6C22×D311yescharacteristic
361C2×Dic6C22×D311yescharacteristic
362C3×Q16—62no—
363C3×SD16—62no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—41no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—21no—
384C3×C42—21no—
385C3×C42—21no—
386C3×C42—31no—
387C3×C42—41no—
388C3×C42—61no—
389C3×C42—61no—
390C3×C42—61no—
391C3×C42—61no—
392C3×C42C22×D311yescharacteristic
393C3×C42C22×D311yescharacteristic
394#216—22no—
395#216—62no—
396#216—62no—
397#215—22no—
398#215—62no—
399#215—62no—
400#215—62no—
401#215—62no—
402#215—62no—
403#215—62no—
404#215—62no—
405#215—122no—
406#215—122no—
407#214—62no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
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
438#204—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—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—21no—
457C32×C4—22no—
458C32×C4—21no—
459C32×C4—41no—
460C32×C4C22×D411yescharacteristic
461C32×C4C2×#4111yescharacteristic
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—31no—
470C22×D4—91no—
471#137—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—184no—
481C2×M16—91no—
482C22×C8—91no—
483#127—91no—
484#127—91no—
485#124—31no—
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—31no—
506#103—91no—
507#102—31no—
508#102—91no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C22×D3—21no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C22×D3—121no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3C2×#6711yescharacteristic
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—22no—
532C3×Q8—32no—
533C3×Q8—41no—
534C3×Q8—64no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8C2×D1212yes—
539C3×Q8D3×D412yes—
540C3×D4—61no—
541C3×D4—61no—
542C2×C3×C4—21no—
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—31no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—64no—
557C2×C3×C4—61no—
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—241no—
569#67—241no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3C2×#6711yescharacteristic
574C2×Dic3C2×#6711yescharacteristic
575C2×Dic3C2×#6711yescharacteristic
576D12—21no—
577D12—21no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—61no—
582D12—61no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—121no—
587D12—121no—
588D12—121no—
589D12—121no—
590D12—122no—
591D12—122no—
592D12—241no—
593D12—241no—
594D12—241no—
595D12—241no—
596D12—242no—
597D12—242no—
598D12—241no—
599D12—241no—
600C4×D3—24no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3C2×D1212yes—
604C4×D3#23512yes—
605Dic6—21no—
606Dic6—24no—
607Dic6—21no—
608Dic6—21no—
609Dic6C2×D1212yes—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—121no—
619C3⋊C8—121no—
620C2×C32C2×#12111yescharacteristic
621C2×C32#57711yescharacteristic
622C2×C32#57711yescharacteristic
623C3⋊D3—81no—
624C3⋊D3—81no—
625C3×D3—22no—
626C3×D3—81no—
627C24—181no—
628#41—182no—
629#41—182no—
630C2×Q8—34no—
631C2×Q8—31no—
632C2×Q8—31no—
633C2×Q8—61no—
634C2×Q8—62no—
635C2×Q8C2×D3211yescharacteristic
636C2×D4—31no—
637C2×D4—91no—
638C2×D4—91no—
639C2×D4—182no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4—181no—
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—181no—
650Q16—62no—
651Q16—182no—
652SD16—62no—
653SD16—182no—
654SD16—182no—
655SD16—182no—
656SD16—182no—
657SD16—182no—
658M16—182no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—91no—
662C2×C8—91no—
663C2×C8—182no—
664C4⋊C4—21no—
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4C2×D3211yescharacteristic
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—21no—
680C42—31no—
681C42—61no—
682C42—61no—
683C42—61no—
684C42—61no—
685C42C2×D3211yescharacteristic
686C22×C3—21no—
687C22×C3—32no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C22×#6711yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—241no—
715C2×D3—241no—
716C2×D3—241no—
717C2×D3—241no—
718C2×D3—244no—
719C2×D3—244no—
720C2×D3#93012yes—
721C3×C4—22no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—22no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—22no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—32no—
731C3×C4—41no—
732C3×C4—42no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—62no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4C22×D1211yescharacteristic
742C3×C4C2×#23511yescharacteristic
743C3×C4C2×D3×D411yescharacteristic
744C3×C4D3×#4111yescharacteristic
745Dic3—22no—
746Dic3—21no—
747Dic3—21no—
748Dic3—41no—
749Dic3—41no—
750Dic3#93012yes—
751C32#304311yescharacteristic, complemented, Sylow
752C23—31no—
753C23—61no—
754C23—181no—
755C23—181no—
756C23—362no—
757C23—721no—
758C23—721no—
759Q8—21no—
760Q8—32no—
761Q8—64no—
762Q8—61no—
763Q8—61no—
764Q8—61no—
765Q8D3×D1212yes—
766D4—61no—
767D4—61no—
768D4—181no—
769D4—181no—
770D4—181no—
771D4—181no—
772D4—362no—
773D4—362no—
774D4—721no—
775D4—721no—
776D4—721no—
777D4—721no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—31no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—64no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—362no—
790C2×C4D3×#6711yescharacteristic
791C2×C4D3×#6711yescharacteristic
792C2×C4C22×D3211yescharacteristic
793C8—61no—
794C8—61no—
795C8—181no—
796C8—181no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—62no—
801C2×C3—241no—
802C2×C3D3×#12111yescharacteristic
803C2×C3#577011yescharacteristic
804C2×C3#577811yescharacteristic
805C2×C3C2×#93011yescharacteristic
806C2×C3#583711yescharacteristic
807C2×C3#583711yescharacteristic
808D3—22no—
809D3—81no—
810D3—241no—
811D3—241no—
812D3—241no—
813D3—241no—
814D3—481no—
815D3—481no—
816C22—32no—
817C22—61no—
818C22—61no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—361no—
823C22—361no—
824C22—361no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22—724no—
829C22C2×D3×#6711yescharacteristic
830C4—21no—
831C4—22no—
832C4—21no—
833C4—32no—
834C4—41no—
835C4—61no—
836C4—62no—
837C4—61no—
838C4—121no—
839C4—121no—
840C4C2×D3×D1211yescharacteristic
841C4D3×#23511yescharacteristic
842C3—21no—
843C3#8060011yescharacteristic, complemented
844C3#8255111yescharacteristic, complemented
845C2—62no—
846C2—241no—
847C2—721no—
848C2—721no—
849C2D3×#93011yescharacteristic
850C2#1059531911yescharacteristic
851C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594001C2
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×#63948C2semidirect
3. C2×D3×#215C2semidirect
5. #10592726C2semidirect
6. C3×#5028C2semidirect
7. #10591617C2semidirect
8. #10591607C2semidirect
9. #10590610C2semidirect
10. #10590592C2semidirect
11. #10590549C2semidirect
12. #10590536C2semidirect
13. #10590367C2semidirect
14. #10590324C2semidirect
15. #10590267C2semidirect
21. C32×C4×Q8C22semidirect
23. C2×#3755C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
31. C3×#887C22semidirect
36. C3×C4×Dic6C22semidirect
45. C2×#3718C22semidirect
47. C2×#3717C22semidirect
52. #63636C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#810C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
61. #63564C22semidirect
69. #5572D3semidirect
78. #5028D3semidirect
101. C3×D3×Q8D4semidirect
169. C3×C4×Q8C2×D3semidirect
170. C3×C4×Q8C2×D3semidirect
176. Q8×Dic3C2×D3semidirect
179. C2×#216C2×D3semidirect
207. #887C2×D3semidirect
223. C4×Dic6C2×D3semidirect
234. #810C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
331. D3×Q8D12semidirect
496. C4×Q8D32semidirect
751. C32#3043semidirect
843. C3#80600semidirect
844. 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×#639482
C2×D3×#2152
#105940012
#105927262
C3×#50282
#105916172
#105916072
#105906102
#105905922
#105905492
#105905362
#105903672
#105903242
#105902672
#825513
#806003