Finite Group Databasebeta

← #11884118

Subgroups — #11884118

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic, complemented
3#10595018C211yesmaximal, characteristic
4C22×#3717C211yesmaximal, characteristic, complemented
5#10592745C211yesmaximal, characteristic, complemented
6C3×#5051C211yesmaximal, characteristic, complemented
7#10591608C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10591185C211yesmaximal, characteristic, complemented
11#10591155C211yesmaximal, characteristic, complemented
12#10590616C211yesmaximal, characteristic, complemented
13#10590585C211yesmaximal, characteristic, complemented
14#10590536C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#80771—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C22×C3×Dic6C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×#896—21no—
32C3×#888—21no—
33C3×#887C2211yescharacteristic, complemented
34C3×#67⋊C4—21no—
35C3×#878—21no—
36#63981—21no—
37#63974—21no—
38#63948—24no—
39#63910—21no—
40#63909C2211yescharacteristic
41#63897—21no—
42#63894C2211yescharacteristic
43#63864C2211yescharacteristic
44C2×#3718C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3717—24no—
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52#63657C2211yescharacteristic
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64C2×#942—31no—
65C22×#215—31no—
66C2×#918—31no—
67C22×#204—31no—
68#5632D311yescharacteristic, complemented
69#5630—31no—
70#5550—31no—
71C3×#467—31no—
72#5228—31no—
73#5227—31no—
74#5190—31no—
75#5111—31no—
76#5086—31no—
77#5083—31no—
78#5051D311yescharacteristic, complemented
79#5050—31no—
80#5049—31no—
81#5047—31no—
82#5046—31no—
83#5046—31no—
84#5046—61no—
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4889—31no—
89#4886—31no—
90#4818—31no—
91#4808—31no—
92#4806—31no—
93#4798—31no—
94C23×C3⋊D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C3×D3×Q8—22no—
105C3×D3×Q8—41no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—22no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6—41no—
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#624—21no—
118C2×#624—21no—
119#3799—22no—
120#3799—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3755—22no—
125#3755—41no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×#216—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3718—22no—
150#3718—41no—
151#3717—22no—
152#3717—22no—
153#3717—22no—
154#3717D414yescomplemented
155#3711—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×D3×Q8C2×D311yescharacteristic, complemented
161C2×#235—31no—
162C22×D12—31no—
163C22×D12—31no—
164C22×D12—61no—
165C22×Dic6C2×D311yescharacteristic
166C2×C3×Q16—31no—
167C22×C3×C8—31no—
168C3×C4⋊Q8—31no—
169C3×C4⋊Q8—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—61no—
174C3×C22⋊Q8—61no—
175C3×C22⋊Q8C2×D311yescharacteristic
176C3×C22⋊Q8C2×D311yescharacteristic
177C3×C4×Q8—31no—
178C3×C4×D4—31no—
179C3×C4×D4—61no—
180#947—31no—
181#944C2×D311yescharacteristic, complemented
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216C2×D311yescharacteristic, complemented
187#942—64no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—61no—
197C2×#215—61no—
198C2×#215—64no—
199#937—61no—
200#930—31no—
201C4×#67C2×D311yescharacteristic
202#924C2×D311yescharacteristic
203C2×#208—31no—
204C22×C3⋊C8C2×D311yescharacteristic
205#918—64no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—64no—
211C2×ΓL(1,𝔽25)—31no—
212#897C2×D311yescharacteristic, complemented
213#896—21no—
214#895—31no—
215#895—61no—
216#894—61no—
217#894—61no—
218#893—31no—
219#888—21no—
220#887C2×D311yescharacteristic, complemented
221#884—61no—
222#882—61no—
223#67⋊C4—21no—
224D3×C22⋊C4—61no—
225D3×C22⋊C4—61no—
226#878—21no—
227#875—31no—
228C4×D12—31no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#103—31no—
232#835—31no—
233#835—31no—
234#835C2×D311yescharacteristic, complemented
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241Dic3⋊C8—31no—
242#810—31no—
243#810—31no—
244#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809—61no—
251#807C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)C2×D412yes—
274C3×#67—22no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#626—42no—
295#626—81no—
296#624—42no—
297#624—81no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—31no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—31no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—121no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8—121no—
329C2×C3×Q8—121no—
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×D4—31no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—61no—
340C2×#67—61no—
341C2×#67#6711yescharacteristic
342C22×Dic3—21no—
343#239—62no—
344#239—121no—
345D3×Q8—22no—
346D3×Q8—41no—
347#235—62no—
348#235—121no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—62no—
356C2×D12—62no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—122no—
362C2×D12—121no—
363C2×D12—121no—
364C2×D12—121no—
365C2×D12—122no—
366C2×C4×D3—21no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3C22×D311yescharacteristic
372C2×Dic6—22no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—41no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×Q16—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—62no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—41no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—41no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—31no—
404C3×C42—61no—
405#217—21no—
406#217#6711yescharacteristic
407#216—22no—
408#216—62no—
409#216—62no—
410#216—121no—
411#216—121no—
412#215—34no—
413#215—62no—
414#215—62no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—122no—
419#215—121no—
420#215—121no—
421#215—122no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4#6711yescharacteristic
432C4⋊Dic3—21no—
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—21no—
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4#6711yescharacteristic
439C4×Dic3—21no—
440C4×Dic3C22×D311yescharacteristic
441#208—62no—
442C2×C3⋊C8—22no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451#204—34no—
452#204—62no—
453#204—62no—
454#204—62no—
455ΓL(1,𝔽25)—62no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32#13712yescomplemented
459C22×C32C22×D411yescharacteristic
460C2×C3⋊D3—22no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—84no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3×Dic3—21no—
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—31no—
484C22×Q8—31no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—31no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—91no—
498C22×C8—31no—
499C4⋊Q8—31no—
500C4⋊Q8—61no—
501#124—91no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—61no—
506C22⋊Q8—61no—
507C22⋊Q8D3211yescharacteristic
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—31no—
512C4×D4—31no—
513C4×D4—61no—
514C4×D4—91no—
515C2×C22⋊C4—181no—
516#107—31no—
517C4⋊C8—91no—
518#103—31no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3D3×D411yescharacteristic
530C23×C3C2×#6711yescharacteristic
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—124no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—242no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3—242no—
546C22×D3C2×#6711yescharacteristic
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—32no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×Q8—122no—
560C3×Q8—122no—
561C3×D4—62no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—122no—
586C2×C3×C4—122no—
587C2×C3×C4D3×D411yescharacteristic
588C2×C3×C4C2×#6711yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—22no—
592#67—122no—
593#67—241no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—42no—
599C2×Dic3C2×#6711yescharacteristic
600C2×Dic3C2×#6711yescharacteristic
601C2×Dic3C2×#6711yescharacteristic
602D12—32no—
603D12—32no—
604D12—62no—
605D12—62no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—121no—
613D12—121no—
614D12—122no—
615D12—122no—
616D12—124no—
617D12—122no—
618D12—241no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—42no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—241no—
625C4×D3—241no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—42no—
632Dic6—42no—
633Dic6D3×D412yes—
634C3×C8—32no—
635C3×C8—61no—
636C3⋊C8—21no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C3⋊C8—121no—
643C3⋊C8D3×D412yes—
644C2×C32—22no—
645C2×C32D4211yescharacteristic
646C2×C32C2×#13711yescharacteristic
647C2×C32#57711yescharacteristic
648C3⋊D3—42no—
649C3⋊D3—81no—
650C3×D3—41no—
651C24—181no—
652#41—182no—
653#41—361no—
654C2×Q8—31no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—61no—
658C2×Q8—62no—
659C2×Q8—61no—
660C2×Q8—62no—
661C2×Q8—121no—
662C2×Q8—121no—
663C2×Q8C2×D3211yescharacteristic
664C2×D4—31no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—361no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4C2×D3211yescharacteristic
678Q16—62no—
679Q16—182no—
680Q16—361no—
681SD16—94no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685SD16—182no—
686SD16—361no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8—91no—
692C2×C8—91no—
693C4⋊C4—21no—
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4—61no—
701C4⋊C4C2×D3211yescharacteristic
702C22⋊C4—21no—
703C22⋊C4—31no—
704C22⋊C4—31no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C42—61no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—22no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3#91812yescomplemented
725C22×C3#94212yescomplemented
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C22×#6711yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—122no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—122no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—241no—
749C2×D3—244no—
750C2×D3—244no—
751C2×D3—248no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—62no—
765C3×C4—81no—
766C3×C4—81no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4C2×D3×D411yescharacteristic
771C3×C4C2×D3×D411yescharacteristic
772C3×C4#100411yescharacteristic
773C3×C4#100911yescharacteristic
774Dic3—22no—
775Dic3—21no—
776Dic3—21no—
777Dic3—21no—
778Dic3—41no—
779Dic3—41no—
780Dic3—41no—
781C32#326611yescharacteristic, complemented, Sylow
782C23—31no—
783C23—181no—
784C23—181no—
785C23—362no—
786C23—362no—
787C23—721no—
788C23D3×#6711yescharacteristic
789Q8—21no—
790Q8—21no—
791Q8—32no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796Q8—61no—
797Q8—122no—
798Q8—122no—
799D4—62no—
800D4—92no—
801D4—181no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—721no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—362no—
823C2×C4—721no—
824C2×C4D3×#6711yescharacteristic
825C2×C4C22×D3211yescharacteristic
826C8—32no—
827C8—61no—
828C8—181no—
829C8—181no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3—121no—
837C2×C3#560911yescharacteristic
838C2×C3C2×#91811yescharacteristic
839C2×C3#577011yescharacteristic
840C2×C3D4×#6711yescharacteristic
841C2×C3C2×#94211yescharacteristic
842C2×C3#583711yescharacteristic
843D3—41no—
844D3—122no—
845D3—122no—
846D3—242no—
847D3—242no—
848D3—241no—
849D3—241no—
850C22—21no—
851C22—21no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—182no—
856C22—361no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—724no—
862C22#6394812yescomplemented
863C22C2×D3×#6711yescharacteristic
864C4—21no—
865C4—41no—
866C4—41no—
867C4—61no—
868C4—61no—
869C4—61no—
870C4—62no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4D32×D411yescharacteristic
875C4#6431411yescharacteristic
876C3—21no—
877C3#8077111yescharacteristic, complemented
878C3#8355911yescharacteristic, complemented
879C2—22no—
880C2—121no—
881C2—362no—
882C2—721no—
883C2#1059529111yescharacteristic
884C2C2×#6394811yescharacteristic
885C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC22⋊Q8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5632C2semidirect
2. C2×#63948C2semidirect
4. C22×#3717C2semidirect
5. #10592745C2semidirect
6. C3×#5051C2semidirect
7. #10591608C2semidirect
8. #10591584C2semidirect
9. #10591565C2semidirect
10. #10591185C2semidirect
11. #10591155C2semidirect
12. #10590616C2semidirect
13. #10590585C2semidirect
14. #10590536C2semidirect
15. #10590457C2semidirect
19. C2×C3×D3×Q8C22semidirect
25. C3×#944C22semidirect
26. C2×C3×#216C22semidirect
30. C3×#897C22semidirect
33. C3×#887C22semidirect
44. C2×#3718C22semidirect
45. C2×#3718C22semidirect
51. C2×#3711C22semidirect
55. C3×#835C22semidirect
56. C3×#810C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
68. #5632D3semidirect
78. #5051D3semidirect
154. #3717D4semidirect
160. C2×D3×Q8C2×D3semidirect
181. #944C2×D3semidirect
186. C2×#216C2×D3semidirect
212. #897C2×D3semidirect
220. #887C2×D3semidirect
234. #835C2×D3semidirect
244. #810C2×D3semidirect
251. #807C2×D3semidirect
458. C22×C32#137semidirect
724. C22×C3#918semidirect
725. C22×C3#942semidirect
781. C32#3266semidirect
862. C22#63948semidirect
877. C3#80771semidirect
878. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
C2×#639482
#105950182
C22×#37172
#105927452
C3×#50512
#105916082
#105915842
#105915652
#105911852
#105911552
#105906162
#105905852
#105905362
#105904572
#835593
#807713