Finite Group Databasebeta

← #11884315

Subgroups — #11884315

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic, complemented
3#10594834C211yesmaximal, characteristic, complemented
4C2×#63808C211yesmaximal, characteristic, complemented
5C3×#5137C211yesmaximal, characteristic, complemented
6C3×#5127C211yesmaximal, characteristic, complemented
7#10591184C211yesmaximal, characteristic, complemented
8#10591183C211yesmaximal, characteristic, complemented
9#10590970C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590830C211yesmaximal, characteristic, complemented
13#10590770C211yesmaximal, characteristic, complemented
14#10590768C211yesmaximal, characteristic, complemented
15#10590760C211yesmaximal, characteristic, complemented
16#80921—31nomaximal
17#79496—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×C32×M16C2211yescharacteristic
23#64117—24no—
24C2×#3745C2211yescharacteristic
25C2×#3745C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27C2×#3744C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C2×C3×Dic12C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63981—21no—
34#63975—21no—
35#63974—21no—
36#63958—21no—
37#63910—21no—
38#63909C2211yescharacteristic
39#63897—21no—
40#63894C2211yescharacteristic
41#63894C2211yescharacteristic, complemented
42#63883—21no—
43#63866C2211yescharacteristic, complemented
44#63864C2211yescharacteristic
45#63857C2211yescharacteristic, complemented
46#63853—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic, complemented
51#63808—24no—
52C3×#830C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63564C2211yescharacteristic
62#63564C2211yescharacteristic, complemented
63C2×#919—31no—
64C2×#908—31no—
65C2×#908—31no—
66C2×#908—61no—
67C2×#904—31no—
68#5631—31no—
69#5630—31no—
70#5551—31no—
71#5550—31no—
72C3×#470—31no—
73C3×#435—31no—
74#5190—31no—
75#5137D311yescharacteristic, complemented
76#5127D311yescharacteristic, complemented
77#5114—31no—
78#5047—31no—
79#5046—31no—
80#4869—31no—
81#4864—31no—
82#4844—31no—
83#4841—31no—
84#4819—31no—
85#4818—31no—
86#4810—31no—
87#4808—31no—
88#4734—31no—
89#4733—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4711—31no—
94C23×C3⋊D3—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97#3828—22no—
98#3828—41no—
99C2×C4⋊(C3⋊D3)—22no—
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)—41no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×#624—21no—
116C2×#624—21no—
117C2×#624—21no—
118#3799—22no—
119#3799—22no—
120#3799—41no—
121#3799—41no—
122C32×M16—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125#3745—22no—
126#3745D414yescomplemented
127#3744—22no—
128#3744—22no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217D411yescharacteristic
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—22no—
142C3×D3×C8—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3717—22no—
154#3717—22no—
155#3717—41no—
156#3267—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#235—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—61no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C2×C3×Q16—31no—
168C2×C3×M16—21no—
169C2×C3×M16C2×D311yescharacteristic
170C2×C3×M16C2×D311yescharacteristic
171C22×C3×C8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×C4×D4—31no—
175#947—31no—
176#944—31no—
177C2×#216—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181#938—61no—
182#937—61no—
183#930—31no—
184C4×#67C2×D311yescharacteristic
185#924—31no—
186#924C2×D311yescharacteristic
187#924C2×D311yescharacteristic
188#919—64no—
189#908—64no—
190#908—64no—
191#908—68no—
192C2×Dic12—31no—
193C2×Dic12C2×D311yescharacteristic, complemented
194#904—64no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—31no—
198C2×D24—31no—
199C2×D24—61no—
200C2×D24—61no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—61no—
209C2×#204—61no—
210C2×D3×C8C2×D311yescharacteristic, complemented
211#897—31no—
212#895—31no—
213#895—61no—
214#894—61no—
215#894—61no—
216#894—61no—
217#893—31no—
218#893—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4—61no—
221#884—61no—
222#884—61no—
223#883—61no—
224#883—61no—
225#883—61no—
226#882—61no—
227D3×C22⋊C4—61no—
228D3×C22⋊C4—61no—
229#875—31no—
230C4×D12—31no—
231C4×D12—31no—
232#869—31no—
233C3×#106—31no—
234C3×C4⋊C8—31no—
235C3×#103—31no—
236C3×#103—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#830C2×D311yescharacteristic
241#821—31no—
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8C2×D311yescharacteristic, complemented
245#817C2×D311yescharacteristic, complemented
246#816—31no—
247#816C2×D311yescharacteristic, complemented
248#816C2×D311yescharacteristic, complemented
249#815C2×D311yescharacteristic, complemented
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#810—31no—
252#809—31no—
253#809—31no—
254#809—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—42no—
277#634—21no—
278#634—21no—
279C3×#67—41no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#626—42no—
294#626—42no—
295#626—81no—
296#624—42no—
297#624—42no—
298#624—42no—
299#624—81no—
300C32×C8—21no—
301C32×C8C2×D412yes—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—91no—
305C2×#135—91no—
306#547—91no—
307#546—91no—
308#497—91no—
309#470—31no—
310#465—91no—
311#463—91no—
312#461—91no—
313#452—91no—
314#452—91no—
315#450—91no—
316#449—91no—
317#442—91no—
318#435—31no—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3—121no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—121no—
335C2×#67D1211yescharacteristic
336#239—62no—
337#239—62no—
338#239—121no—
339#239—121no—
340#235—62no—
341#235—62no—
342#235—62no—
343#235—62no—
344#235—64no—
345#235—121no—
346#235—121no—
347#235—121no—
348#235—121no—
349#235—122no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—62no—
360C2×D12—62no—
361C2×D12—64no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—121no—
368C2×D12—121no—
369C2×D12—121no—
370C2×D12—122no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—121no—
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×Q16—62no—
389C3×M16—24no—
390C3×M16—22no—
391C3×M16—22no—
392C2×C3×C8—21no—
393C2×C3×C8—21no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—62no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4—61no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411#217—21no—
412#217—21no—
413#217—61no—
414#217D1211yescharacteristic
415#216—121no—
416#215—62no—
417#215—62no—
418#215—121no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
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—61no—
430(C2×D3)⋊C4D1211yescharacteristic
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4D1211yescharacteristic
442C4×Dic3C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444C2×C3⋊C8C22×D311yescharacteristic
445Dic12—22no—
446Dic12—121no—
447D24—34no—
448D24—34no—
449D24—64no—
450D24—62no—
451D24—62no—
452D24—64no—
453#204—62no—
454#204—62no—
455#204—64no—
456#204—64no—
457#204—62no—
458#204—62no—
459#204—62no—
460#204—62no—
461#204—121no—
462D3×C8—22no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—84no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—21no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—91no—
492C2×#41—91no—
493C2×#41—91no—
494C22×D4—91no—
495AGL(1,ℤ/8)—184no—
496#135—184no—
497C2×Q16—31no—
498C2×Q16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—91no—
505C2×D8—91no—
506C2×M16D3211yescharacteristic
507C22×C8—31no—
508C4⋊Q8—91no—
509#124—91no—
510#123—181no—
511#123—181no—
512#123—181no—
513C22⋊Q8—31no—
514C22⋊Q8—31no—
515C22⋊Q8—91no—
516#121—91no—
517#121—181no—
518#121—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—91no—
522C4×D4—91no—
523C2×C4⋊C4—181no—
524C2×C22⋊C4—181no—
525#106—31no—
526C4⋊C8—31no—
527#103—31no—
528#103—31no—
529#103—91no—
530#102—91no—
531#102—91no—
532#102—91no—
533C22⋊C8—31no—
534C22⋊C8—31no—
535#97—31no—
536C23×C3—21no—
537C23×C3—31no—
538C23×C3C2×D1211yescharacteristic
539C23×C3D3×D411yescharacteristic
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—124no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—242no—
555C22×D3—241no—
556C22×D3—241no—
557C22×D3—242no—
558C22×D3C2×D1211yescharacteristic
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—121no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
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—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4C2×D1211yescharacteristic
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—41no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—124no—
591#67—241no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3C2×D1211yescharacteristic
600C2×Dic3C2×D1211yescharacteristic
601C2×Dic3C2×D1211yescharacteristic
602D12—32no—
603D12—32no—
604D12—32no—
605D12—32no—
606D12—62no—
607D12—62no—
608D12—62no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—121no—
618D12—121no—
619D12—121no—
620D12—122no—
621D12—122no—
622D12—124no—
623D12—122no—
624D12—122no—
625D12—241no—
626C4×D3—21no—
627C4×D3—21no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3—122no—
631C4×D3—122no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—124no—
637C4×D3—241no—
638C4×D3—241no—
639Dic6—21no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6—62no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649C3×C8—22no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—22no—
653C3×C8—61no—
654C3×C8—61no—
655C3×C8D3×D412yes—
656C3×C8D3×D412yes—
657C3⋊C8—21no—
658C3⋊C8—21no—
659C2×C32—41no—
660C2×C32D4211yescharacteristic
661C2×C32#57511yescharacteristic
662C2×C32#57711yescharacteristic
663C3⋊D3—42no—
664C3⋊D3—42no—
665C3⋊D3—81no—
666C3×D3—41no—
667C24—181no—
668#41—182no—
669#41—182no—
670#41—182no—
671#41—361no—
672#41—361no—
673#41—361no—
674C2×Q8—31no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×D4—31no—
678C2×D4—91no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—361no—
688C22×C4—31no—
689C22×C4—181no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4—181no—
693C22×C4—181no—
694C22×C4C2×D3211yescharacteristic
695Q16—62no—
696Q16—361no—
697SD16—182no—
698SD16—182no—
699SD16—182no—
700SD16—182no—
701SD16—361no—
702D8—94no—
703D8—182no—
704M16—22no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—62no—
708C2×C8C2×D3211yescharacteristic
709C2×C8C2×D3211yescharacteristic
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—31no—
713C4⋊C4—61no—
714C4⋊C4—61no—
715C4⋊C4—181no—
716C4⋊C4—181no—
717C4⋊C4—181no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3C22×D1211yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—122no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—244no—
775C2×D3—244no—
776C2×D3—248no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—121no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100911yescharacteristic
792C3×C4#100911yescharacteristic
793Dic3—21no—
794Dic3—21no—
795Dic3—21no—
796Dic3—41no—
797Dic3—41no—
798Dic3—41no—
799Dic3—41no—
800Dic3—122no—
801Dic3—121no—
802Dic3—121no—
803C32#326711yescharacteristic, complemented, Sylow
804C23—31no—
805C23—181no—
806C23—181no—
807C23—181no—
808C23—362no—
809C23—362no—
810C23—721no—
811C23D3×D1211yescharacteristic
812Q8—61no—
813Q8—61no—
814Q8—61no—
815Q8—61no—
816Q8—181no—
817Q8—181no—
818D4—92no—
819D4—92no—
820D4—121no—
821D4—181no—
822D4—181no—
823D4—181no—
824D4—181no—
825D4—362no—
826D4—362no—
827D4—362no—
828D4—362no—
829D4—721no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—181no—
842C2×C4—362no—
843C2×C4—362no—
844C2×C4—362no—
845C2×C4—362no—
846C2×C4—721no—
847C2×C4D3×D1211yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C8—21no—
850C8—61no—
851C8—61no—
852C8#381112yes—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—41no—
858C2×C3—41no—
859C2×C3—121no—
860C2×C3D4×D1211yescharacteristic
861C2×C3#560911yescharacteristic
862C2×C3#574811yescharacteristic
863C2×C3#575111yescharacteristic
864C2×C3#577711yescharacteristic
865C2×C3#577811yescharacteristic
866D3—41no—
867D3—122no—
868D3—122no—
869D3—122no—
870D3—122no—
871D3—242no—
872D3—242no—
873D3—242no—
874D3—241no—
875D3—241no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—61no—
880C22—61no—
881C22—61no—
882C22—182no—
883C22—182no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22—361no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—724no—
892C22C2×D3×D1211yescharacteristic
893C4—21no—
894C4—61no—
895C4—61no—
896C4—61no—
897C4—121no—
898C4—121no—
899C4—121no—
900C4—121no—
901C4—361no—
902C4#6430811yescharacteristic
903C4C2×#381111yescharacteristic
904C3—21no—
905C3#7949611yescharacteristic, complemented
906C3#8092111yescharacteristic, complemented
907C2—41no—
908C2—121no—
909C2—362no—
910C2—362no—
911C2—721no—
912C2#1059471111yescharacteristic
913C2#1059471511yescharacteristic
914C2#1059507411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64117C2semidirect
2. #10595018C2semidirect
3. #10594834C2semidirect
4. C2×#63808C2semidirect
5. C3×#5137C2semidirect
6. C3×#5127C2semidirect
7. #10591184C2semidirect
8. #10591183C2semidirect
9. #10590970C2semidirect
10. #10590967C2semidirect
11. #10590899C2semidirect
12. #10590830C2semidirect
13. #10590770C2semidirect
14. #10590768C2semidirect
15. #10590760C2semidirect
21. C2×#3799C22semidirect
31. C2×C3×Dic12C22semidirect
32. C2×C3×D3×C8C22semidirect
41. #63894C22semidirect
43. #63866C22semidirect
45. #63857C22semidirect
47. C2×#3719C22semidirect
50. C2×#3717C22semidirect
53. C3×(C2×D3)⋊C8C22semidirect
54. C3×#817C22semidirect
55. C3×#816C22semidirect
56. C3×#816C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63567C22semidirect
62. #63564C22semidirect
75. #5137D3semidirect
76. #5127D3semidirect
126. #3745D4semidirect
193. C2×Dic12C2×D3semidirect
210. C2×D3×C8C2×D3semidirect
244. (C2×D3)⋊C8C2×D3semidirect
245. #817C2×D3semidirect
247. #816C2×D3semidirect
248. #816C2×D3semidirect
249. #815C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
803. C32#3267semidirect
905. C3#79496semidirect
906. C3#80921semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105950182
#105948342
C2×#638082
C3×#51372
C3×#51272
#105911842
#105911832
#105909702
#105909672
#105908992
#105908302
#105907702
#105907682
#105907602
#809213
#794963