Finite Group Databasebeta

← #11884132

Subgroups — #11884132

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic
2C2×#63929C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10593904C211yesmaximal, characteristic, complemented
5#10592717C211yesmaximal, characteristic, complemented
6C3×#5019C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591458C211yesmaximal, characteristic, complemented
9#10590604C211yesmaximal, characteristic, complemented
10#10590603C211yesmaximal, characteristic, complemented
11#10590518C211yesmaximal, characteristic, complemented
12#10590515C211yesmaximal, characteristic, complemented
13#10590378C211yesmaximal, characteristic, complemented
14#10590376C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83506—31nomaximal
17#80444—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×#930—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#886—21no—
32C3×#882—21no—
33C3×#875C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#869C2211yescharacteristic, complemented
36#63929—24no—
37D3×#214—24no—
38#63919—21no—
39#63899—21no—
40#63899—21no—
41#63898—21no—
42#63856C2211yescharacteristic
43#63856C2211yescharacteristic, complemented
44C2×#3719C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63659C2211yescharacteristic
53#63637C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#951—31no—
65C22×#214—31no—
66C2×#915—31no—
67C2×D3×SD16—31no—
68#5727—31no—
69#5554D311yescharacteristic
70D4×Dic6—31no—
71C3×#461—31no—
72#5239—31no—
73#5218—31no—
74#5173—31no—
75#5169—31no—
76#5086—31no—
77#5060—31no—
78#5054—31no—
79#5051—31no—
80#5050—31no—
81#5042—31no—
82#5040—31no—
83#5019D311yescharacteristic, complemented
84#5018—31no—
85#5018—31no—
86#5018—61no—
87#5011—31no—
88#4845—31no—
89#4836—31no—
90#4813—31no—
91#4812—31no—
92#4809—31no—
93#4806—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237—41no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12D411yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#627—21no—
114C2×#627—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×Dic6—22no—
118D3×Dic6—22no—
119D3×Dic6—41no—
120D3×Dic6—41no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3754D414yescomplemented
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C4×C3⋊Dic3—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#214—22no—
131C3×#214—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3D411yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724—21no—
145#3724—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3718—22no—
150#3718—41no—
151#3716—22no—
152#3715—22no—
153#3715—41no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×#237C2×D311yescharacteristic
162C2×D3×D4C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×C22⋊Q8—31no—
171C3×#121—31no—
172C3×#121—61no—
173C3×#120—61no—
174C3×C4×D4—21no—
175C3×C4×D4—31no—
176C3×C4×D4C2×D311yescharacteristic
177C3×C4×D4C2×D311yescharacteristic
178C2×C3×C22⋊C4—61no—
179#951—64no—
180#946—31no—
181#946—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#215—31no—
188C2×#215—31no—
189D4×Dic3—61no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—61no—
196C2×#214—64no—
197C2×#214C2×D311yescharacteristic
198C2×#214C2×D311yescharacteristic
199#930—21no—
200C2×(C2×D3)⋊C4—21no—
201#924—31no—
202#924—31no—
203C2×#208—31no—
204C22×C3⋊C8—31no—
205#915—64no—
206D3×SD16—64no—
207C2×Dic12—31no—
208C2×#204—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211#897C2×D311yescharacteristic
212#896—61no—
213#896—61no—
214#895C2×D311yescharacteristic
215#893—61no—
216#888—61no—
217#888—61no—
218#886—21no—
219#882—21no—
220#878—61no—
221#878—61no—
222#875C2×D311yescharacteristic
223C4×D12C2×D311yescharacteristic
224#869C2×D311yescharacteristic, complemented
225C4×Dic6—31no—
226C4×Dic6—31no—
227C4×Dic6—61no—
228C3×C4⋊C8—31no—
229C3×#103—31no—
230C3×#103—31no—
231#835—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#830—31no—
237#830—31no—
238#821—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241#816—31no—
242#810—31no—
243#810—31no—
244#810—61no—
245#810C2×D311yescharacteristic, complemented
246#810C2×D311yescharacteristic, complemented
247#807—31no—
248#807—31no—
249#807—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×D4—21no—
262C32×D4C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—81no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270#634—21no—
271#634C2×D412yes—
272C3×#67—42no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—22no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—81no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#627—42no—
295#627—42no—
296D3×Dic3—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—91no—
305#546—31no—
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—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×D4—21no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—62no—
330C2×C3×D4—61no—
331C2×C3×D4—121no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—41no—
339C22×C3×C4—61no—
340C2×#67—21no—
341C2×#67—21no—
342C22×Dic3—21no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345D3×Q8—62no—
346D3×Q8—62no—
347D3×Q8—121no—
348D3×Q8—121no—
349#237—22no—
350#237—41no—
351D3×D4—22no—
352D3×D4—41no—
353C2×D12—21no—
354C2×D12#6711yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3C22×D311yescharacteristic
359C2×C4×D3C22×D311yescharacteristic
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—61no—
363C2×Dic6—62no—
364C2×Dic6—62no—
365C2×Dic6—61no—
366C2×Dic6—61no—
367C2×Dic6—61no—
368C2×Dic6—61no—
369C2×Dic6—121no—
370C2×Dic6—121no—
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—62no—
375C3×SD16—62no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—41no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—21no—
395C3×C42C22×D311yescharacteristic
396C3×C42C22×D311yescharacteristic
397#217—61no—
398#217—61no—
399#216—62no—
400#216—62no—
401#216—62no—
402#216—121no—
403#216—121no—
404#215—62no—
405#215—121no—
406#214—22no—
407#214—22no—
408#214—34no—
409#214—34no—
410#214—64no—
411#214—62no—
412#214—62no—
413#214—121no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4#6711yescharacteristic
421(C2×D3)⋊C4#6711yescharacteristic
422C4⋊Dic3—21no—
423C4⋊Dic3—21no—
424C4⋊Dic3—21no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3#6711yescharacteristic
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—121no—
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3—121no—
439#208—62no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—62no—
450#204—62no—
451ΓL(1,𝔽25)—62no—
452D3×C8—62no—
453C22×C32—22no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32C22×D411yescharacteristic
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—84no—
466C2×C3×D3#13712yescomplemented
467C32×C4—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3⋊Dic3—22no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C22×Q8—91no—
481C22×Q8—91no—
482C22×D4—31no—
483#137—184no—
484C2×Q16—91no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×SD16—31no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—184no—
494C2×M16—91no—
495C22×C8—91no—
496C4⋊Q8—31no—
497C4⋊Q8—181no—
498#124—31no—
499#123—61no—
500C22⋊Q8—31no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503C22⋊Q8—181no—
504C22⋊Q8—181no—
505#121—31no—
506#121—61no—
507#120—61no—
508C4×Q8—91no—
509C4×D4—31no—
510C4×D4—181no—
511C4×D4D3211yescharacteristic
512C2×C22⋊C4—61no—
513#107—91no—
514C4⋊C8—31no—
515#103—31no—
516#103—31no—
517#103—91no—
518#103—91no—
519#102—91no—
520#102—91no—
521C22⋊C8—91no—
522C22⋊C8—91no—
523#97—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—41no—
529C23×C3—61no—
530C23×C3—122no—
531C23×C3—122no—
532C23×C3—241no—
533C22×D3—21no—
534C22×D3—42no—
535C22×D3—42no—
536C22×D3—81no—
537C22×D3C2×#6711yescharacteristic
538C22×D3C2×#6711yescharacteristic
539C3×Q8—61no—
540C3×Q8—61no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—22no—
548C3×D4—41no—
549C3×D4—62no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4—122no—
553C3×D4—122no—
554C3×D4—241no—
555C3×D4D3×D412yes—
556C3×D4D3×D412yes—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—81no—
573C2×C3×C4—81no—
574C2×C3×C4—82no—
575C2×C3×C4—122no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C2×#6711yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—42no—
583#67—42no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—42no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3—122no—
596C2×Dic3C2×#6711yescharacteristic
597C2×Dic3C2×#6711yescharacteristic
598D12—22no—
599D12—21no—
600D12—21no—
601D12—81no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—122no—
607C4×D3—122no—
608Dic6—21no—
609Dic6—21no—
610Dic6—21no—
611Dic6—21no—
612Dic6—21no—
613Dic6—21no—
614Dic6—32no—
615Dic6—32no—
616Dic6—62no—
617Dic6—61no—
618Dic6—61no—
619Dic6—121no—
620Dic6—122no—
621Dic6—122no—
622Dic6—122no—
623Dic6—122no—
624C3×C8—61no—
625C3×C8—61no—
626C3⋊C8—21no—
627C3⋊C8—21no—
628C3⋊C8—32no—
629C3⋊C8—32no—
630C3⋊C8—62no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—121no—
634C2×C32—42no—
635C2×C32D4211yescharacteristic
636C2×C32C2×#13711yescharacteristic
637C2×C32#57711yescharacteristic
638C3×D3—22no—
639C3×D3—41no—
640C3×D3—81no—
641C24—61no—
642#41—62no—
643#41—121no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—31no—
647C2×Q8—91no—
648C2×Q8—181no—
649C2×Q8—181no—
650C2×Q8—182no—
651C2×Q8—182no—
652C2×Q8—361no—
653C2×Q8—361no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—61no—
660C2×D4—121no—
661C2×D4C2×D3211yescharacteristic
662C22×C4—21no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—61no—
666C22×C4—181no—
667C22×C4—181no—
668Q16—182no—
669Q16—182no—
670Q16—361no—
671SD16—62no—
672SD16—62no—
673SD16—94no—
674SD16—182no—
675SD16—182no—
676SD16—361no—
677M16—182no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—91no—
681C2×C8—91no—
682C2×C8—182no—
683C4⋊C4—31no—
684C4⋊C4—61no—
685C4⋊C4—61no—
686C4⋊C4—61no—
687C4⋊C4—91no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C4⋊C4C2×D3211yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—31no—
694C22⋊C4—31no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C42—181no—
702C42C2×D3211yescharacteristic
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—42no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C22×#6711yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—84no—
734C2×D3#95112yescomplemented
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—81no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4—121no—
751C3×C4C2×D3×D411yescharacteristic
752C3×C4C2×D3×D411yescharacteristic
753C3×C4#100411yescharacteristic
754C3×C4#100911yescharacteristic
755Dic3—21no—
756Dic3—21no—
757Dic3—41no—
758Dic3—41no—
759Dic3—41no—
760Dic3—62no—
761Dic3—62no—
762Dic3—122no—
763Dic3—121no—
764Dic3—121no—
765Dic3—241no—
766C32#326611yescharacteristic, complemented, Sylow
767C23—21no—
768C23—31no—
769C23—31no—
770C23—61no—
771C23—122no—
772C23—122no—
773C23—241no—
774Q8—61no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—92no—
781Q8—181no—
782Q8—362no—
783Q8—362no—
784D4—21no—
785D4—62no—
786D4—61no—
787D4—61no—
788D4—122no—
789D4—122no—
790D4—241no—
791D4#380212yes—
792C2×C4—21no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—81no—
803C2×C4—122no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—362no—
807C2×C4—362no—
808C2×C4D3×#6711yescharacteristic
809C2×C4D3×#6711yescharacteristic
810C2×C4C22×D3211yescharacteristic
811C8—61no—
812C8—61no—
813C8—92no—
814C8—181no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—42no—
819C2×C3—42no—
820C2×C3—62no—
821C2×C3—82no—
822C2×C3—121no—
823C2×C3—241no—
824C2×C3#560911yescharacteristic
825C2×C3#576211yescharacteristic
826C2×C3D3×#13711yescharacteristic
827C2×C3D4×#6711yescharacteristic
828C2×C3C2×#95111yescharacteristic
829C2×C3#583611yescharacteristic
830D3—22no—
831D3—41no—
832D3—81no—
833C22—22no—
834C22—32no—
835C22—41no—
836C22—41no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—244no—
846C22C2×D3×#6711yescharacteristic
847C4—21no—
848C4—21no—
849C4—41no—
850C4—61no—
851C4—61no—
852C4—121no—
853C4—121no—
854C4—121no—
855C4—182no—
856C4—361no—
857C4C2×#380211yescharacteristic
858C4#6430711yescharacteristic
859C3—21no—
860C3#8044411yescharacteristic, complemented
861C3#8350611yescharacteristic, complemented
862C2—42no—
863C2—62no—
864C2—121no—
865C2—241no—
866C2#1059506911yescharacteristic
867C2#1059510511yescharacteristic
868C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5554C2
hypercenterC4×D4D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63929C2semidirect
3. C2×D3×#214C2semidirect
4. #10593904C2semidirect
5. #10592717C2semidirect
6. C3×#5019C2semidirect
7. #10591461C2semidirect
8. #10591458C2semidirect
9. #10590604C2semidirect
10. #10590603C2semidirect
11. #10590518C2semidirect
12. #10590515C2semidirect
13. #10590378C2semidirect
14. #10590376C2semidirect
15. #10590330C2semidirect
21. C2×D3×Dic6C22semidirect
24. C4×#634C22semidirect
35. C3×#869C22semidirect
43. #63856C22semidirect
44. C2×#3719C22semidirect
45. C2×#3718C22semidirect
46. C2×#3718C22semidirect
50. C2×#3711C22semidirect
53. #63637C22semidirect
54. #63634C22semidirect
55. #63630C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #5019D3semidirect
124. #3754D4semidirect
224. #869C2×D3semidirect
245. #810C2×D3semidirect
246. #810C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
466. C2×C3×D3#137semidirect
734. C2×D3#951semidirect
766. C32#3266semidirect
860. C3#80444semidirect
861. C3#83506semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
C2×#639292
C2×D3×#2142
#105939042
#105927172
C3×#50192
#105914612
#105914582
#105906042
#105906032
#105905182
#105905152
#105903782
#105903762
#105903302
#835063
#804443