Finite Group Databasebeta

← #11884152

Subgroups — #11884152

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594003C211yesmaximal, characteristic
5#10592785C211yesmaximal, characteristic, complemented
6C3×#5083C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591596C211yesmaximal, characteristic, complemented
10#10591595C211yesmaximal, characteristic, complemented
11#10591589C211yesmaximal, characteristic, complemented
12#10591584C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#80444—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic
26C2×#3755C2211yescharacteristic
27#64084C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C3×#946C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#896—21no—
33C3×#896—21no—
34C3×#893—21no—
35C3×#888—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic, complemented
39#63946—24no—
40D3×#215—24no—
41#63922—21no—
42D3×(C2×D3)⋊C4—21no—
43#63909C2211yescharacteristic
44#63906—21no—
45#63890—21no—
46#63857C2211yescharacteristic
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63630C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64C2×#942—31no—
65C22×#215—31no—
66C2×#915—31no—
67C2×D3×SD16—31no—
68#5727D311yescharacteristic, complemented
69#5554—31no—
70#5550—31no—
71C3×#461—31no—
72#5228—31no—
73#5227—31no—
74#5173—31no—
75#5169—31no—
76#5086—31no—
77#5086—31no—
78#5086—61no—
79#5083D311yescharacteristic, complemented
80#5051—31no—
81#5049—31no—
82#5047—31no—
83#5046—31no—
84#5028—31no—
85#5026—31no—
86#5018—31no—
87#5011—31no—
88#4845—31no—
89#4836—31no—
90#4813—31no—
91#4812—31no—
92#4809—31no—
93#4806—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C3×D3×Q8—41no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3795—22no—
120#3795—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3756—22no—
125#3756—41no—
126#3755—22no—
127#3755—41no—
128#3752—21no—
129#3752—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#215—22no—
133C3×#215—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×C4×Dic3—21no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148Dic3⋊Dic3—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151#3719—22no—
152#3717—22no—
153#3715D414yescomplemented
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C2×D3×Q8C2×D311yescharacteristic
160C2×D3×Q8C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—21no—
168C3×C4⋊Q8—61no—
169C3×C4⋊Q8C2×D311yescharacteristic, complemented
170C3×C4⋊Q8C2×D311yescharacteristic, complemented
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—61no—
174C3×C22⋊Q8—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C3×C4×D4—61no—
179#946C2×D311yescharacteristic
180#946C2×D311yescharacteristic, complemented
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—61no—
187C2×#216—61no—
188#942—64no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—61no—
196C2×#215—61no—
197C2×#215—64no—
198C2×#215C2×D311yescharacteristic
199C2×#215C2×D311yescharacteristic
200#937—61no—
201C2×#214—31no—
202#930—31no—
203#930—61no—
204C2×(C2×D3)⋊C4—61no—
205#924—31no—
206C2×#208—31no—
207C22×C3⋊C8—31no—
208#915—64no—
209D3×SD16—64no—
210C2×Dic12—31no—
211C2×#204—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×D3×C8—31no—
214#897—31no—
215#896—21no—
216#896—21no—
217#895—31no—
218#894—61no—
219#893—21no—
220#888—21no—
221#886—61no—
222#884—61no—
223#882—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226#875—31no—
227#875—61no—
228C4×D12C2×D311yescharacteristic
229C4×D12C2×D311yescharacteristic
230C4×Dic6C2×D311yescharacteristic, complemented
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#103—31no—
234#835—31no—
235#835C2×D311yescharacteristic, complemented
236#835C2×D311yescharacteristic, complemented
237#832—31no—
238#830—31no—
239#830—31no—
240#821—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243#816—31no—
244#810—31no—
245#810—31no—
246#809—31no—
247#809—31no—
248#807—31no—
249#807—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273#634—21no—
274#634—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—22no—
281C3×D12—21no—
282C3×D12C2×D412yes—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×C4×D3—81no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#626—42no—
295#626—81no—
296#625—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—31no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—31no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8—61no—
323C2×C3×Q8—61no—
324C2×C3×Q8—62no—
325C2×C3×Q8—62no—
326C2×C3×Q8—121no—
327C2×C3×Q8—121no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C22×Dic3—61no—
344D3×Q8—22no—
345D3×Q8—22no—
346D3×Q8—41no—
347D3×Q8—41no—
348#237—62no—
349#237—121no—
350D3×D4—62no—
351D3×D4—121no—
352#235—62no—
353#235—121no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12—62no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—121no—
361C2×D12#6711yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—61no—
367C2×C4×D3C22×D311yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—61no—
374C2×Dic6C22×D311yescharacteristic
375C3×SD16—62no—
376C3×SD16—62no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—41no—
387C3×C4⋊C4—41no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—21no—
397C3×C42—61no—
398C3×C42C22×D311yescharacteristic
399C3×C42C22×D311yescharacteristic
400#217—61no—
401#216—62no—
402#216—62no—
403#216—62no—
404#216—122no—
405#216—121no—
406#216—121no—
407#216—122no—
408#215—22no—
409#215—22no—
410#215—34no—
411#215—62no—
412#215—62no—
413#215—62no—
414#215—122no—
415#215—121no—
416#215—121no—
417#215—122no—
418#214—34no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—61no—
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—121no—
430(C2×D3)⋊C4—121no—
431(C2×D3)⋊C4#6711yescharacteristic
432(C2×D3)⋊C4#6711yescharacteristic
433C4⋊Dic3—61no—
434C4⋊Dic3#6711yescharacteristic
435C4⋊Dic3C22×D311yescharacteristic
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4—61no—
441C4×Dic3—21no—
442#208—62no—
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⋊C8—62no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—62no—
453#204—62no—
454ΓL(1,𝔽25)—62no—
455D3×C8—62no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—21no—
471C32×C4—21no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—41no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—22no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—31no—
484C22×Q8—31no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—91no—
498C22×C8—91no—
499C4⋊Q8—61no—
500C4⋊Q8D3211yescharacteristic, complemented
501#124—91no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—61no—
506C22⋊Q8—61no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—31no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—61no—
515C2×C22⋊C4—181no—
516#107—91no—
517C4⋊C8—31no—
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—31no—
528C23×C3—31no—
529C23×C3—61no—
530C22×D3—21no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—121no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—241no—
539C22×D3—241no—
540C22×D3C2×#6711yescharacteristic
541C22×D3C2×#6711yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—32no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—122no—
557C3×Q8—122no—
558C3×D4—32no—
559C3×D4—62no—
560C3×D4—61no—
561C2×C3×C4—21no—
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—31no—
569C2×C3×C4—31no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4—122no—
581C2×C3×C4—241no—
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4C2×#6711yescharacteristic
585C2×C3×C4C2×#6711yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588#67—122no—
589#67—122no—
590#67—122no—
591#67—241no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—121no—
598C2×Dic3—122no—
599C2×Dic3C2×#6711yescharacteristic
600C2×Dic3C2×#6711yescharacteristic
601D12—22no—
602D12—21no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—121no—
609D12—122no—
610D12—241no—
611D12D3×D412yes—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—21no—
616C4×D3—42no—
617C4×D3—42no—
618C4×D3—81no—
619C4×D3—122no—
620Dic6—21no—
621Dic6—42no—
622Dic6—42no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—121no—
628Dic6—121no—
629Dic6D3×D412yes—
630C3×C8—61no—
631C3×C8—61no—
632C3⋊C8—21no—
633C3⋊C8—21no—
634C3⋊C8—32no—
635C3⋊C8—32no—
636C3⋊C8—62no—
637C3⋊C8—62no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C2×C32D4211yescharacteristic
641C2×C32C2×#13711yescharacteristic
642C2×C32#57711yescharacteristic
643C3⋊D3—81no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—41no—
647C24—181no—
648#41—182no—
649#41—361no—
650C2×Q8—31no—
651C2×Q8—61no—
652C2×Q8—61no—
653C2×Q8—62no—
654C2×Q8—62no—
655C2×Q8—91no—
656C2×Q8—121no—
657C2×Q8—121no—
658C2×Q8C2×D3211yescharacteristic
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—91no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—361no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—181no—
674Q16—182no—
675Q16—182no—
676Q16—361no—
677SD16—62no—
678SD16—62no—
679SD16—94no—
680SD16—182no—
681SD16—182no—
682SD16—361no—
683M16—182no—
684C2×C8—31no—
685C2×C8—31no—
686C2×C8—91no—
687C2×C8—91no—
688C2×C8—182no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—181no—
698C22⋊C4—31no—
699C22⋊C4—31no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—61no—
708C42C2×D3211yescharacteristic
709C22×C3—21no—
710C22×C3—32no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—62no—
716C22×C3—61no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3C2×D3×D411yescharacteristic
720C22×C3C22×#6711yescharacteristic
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—241no—
736C2×D3—241no—
737C2×D3—241no—
738C2×D3—244no—
739C2×D3—244no—
740C2×D3#94212yescomplemented
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—62no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4C2×D3×D411yescharacteristic
761C3×C4C2×D3×D411yescharacteristic
762C3×C4#100411yescharacteristic
763C3×C4#100911yescharacteristic
764Dic3—22no—
765Dic3—21no—
766Dic3—21no—
767Dic3—41no—
768Dic3—41no—
769Dic3—121no—
770Dic3—121no—
771Dic3—241no—
772C32#326611yescharacteristic, complemented, Sylow
773C23—31no—
774C23—31no—
775C23—61no—
776C23—181no—
777C23—362no—
778C23—362no—
779C23—721no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—32no—
785Q8—61no—
786Q8—122no—
787Q8—122no—
788Q8—181no—
789Q8—181no—
790D4—32no—
791D4—62no—
792D4—61no—
793D4—181no—
794D4—181no—
795D4—362no—
796D4—362no—
797D4—721no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—122no—
810C2×C4—122no—
811C2×C4—181no—
812C2×C4—241no—
813C2×C4—362no—
814C2×C4D3×#6711yescharacteristic
815C2×C4D3×#6711yescharacteristic
816C2×C4C22×D3211yescharacteristic
817C8—61no—
818C8—61no—
819C8—92no—
820C8—181no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—62no—
825C2×C3—121no—
826C2×C3—122no—
827C2×C3#560911yescharacteristic
828C2×C3#576211yescharacteristic
829C2×C3D3×#13711yescharacteristic
830C2×C3D4×#6711yescharacteristic
831C2×C3C2×#94211yescharacteristic
832C2×C3#583711yescharacteristic
833D3—22no—
834D3—42no—
835D3—41no—
836D3—241no—
837D3—241no—
838D3—481no—
839C22—32no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—62no—
844C22—61no—
845C22—61no—
846C22—121no—
847C22—121no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—724no—
852C22C2×D3×#6711yescharacteristic
853C4—21no—
854C4—21no—
855C4—41no—
856C4—41no—
857C4—61no—
858C4—61no—
859C4—62no—
860C4—121no—
861C4—121no—
862C4—361no—
863C4D32×D411yescharacteristic
864C4#6431411yescharacteristic
865C3—21no—
866C3#8044411yescharacteristic, complemented
867C3#8355911yescharacteristic, complemented
868C2—62no—
869C2—121no—
870C2—122no—
871C2—721no—
872C2#1059528811yescharacteristic
873C2D3×#94211yescharacteristic
874C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594003C2
hypercenterC4⋊Q8D32
hypocenterC32#3266
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×#5727C2semidirect
2. C2×#63946C2semidirect
3. C2×D3×#215C2semidirect
5. #10592785C2semidirect
6. C3×#5083C2semidirect
7. #10591655C2semidirect
8. #10591651C2semidirect
9. #10591596C2semidirect
10. #10591595C2semidirect
11. #10591589C2semidirect
12. #10591584C2semidirect
13. #10590368C2semidirect
14. #10590358C2semidirect
15. #10590330C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C32×C4⋊Q8C22semidirect
23. C2×#3756C22semidirect
24. C2×#3756C22semidirect
29. C3×#946C22semidirect
38. C3×C4×Dic6C22semidirect
47. C2×#3719C22semidirect
50. C2×#3711C22semidirect
52. #63630C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. #63576C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5727D3semidirect
79. #5083D3semidirect
153. #3715D4semidirect
160. C2×D3×Q8C2×D3semidirect
169. C3×C4⋊Q8C2×D3semidirect
170. C3×C4⋊Q8C2×D3semidirect
180. #946C2×D3semidirect
230. C4×Dic6C2×D3semidirect
235. #835C2×D3semidirect
236. #835C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
468. C2×C3×D3#137semidirect
500. C4⋊Q8D32semidirect
740. C2×D3#942semidirect
772. C32#3266semidirect
866. C3#80444semidirect
867. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C2×#639462
C2×D3×#2152
#105940032
#105927852
C3×#50832
#105916552
#105916512
#105915962
#105915952
#105915892
#105915842
#105903682
#105903582
#105903302
#835593
#804443