Finite Group Databasebeta

← #11864352

Subgroups — #11864352

Order 1152.

1580 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic
2C3×#5628C211yesmaximal, characteristic, complemented
3C2×#63946C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic, complemented
5#10592746C211yesmaximal, characteristic, complemented
6C3×#5046C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591184C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11#10591145C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590608C211yesmaximal, characteristic, complemented
14#10590596C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#83404—31nomaximal
17#80148—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C2×D3×#67—21no—
23C2×D3×#67—21no—
24#64307—24no—
25#64307—24no—
26C2×#3802—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3796—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C32×C22⋊Q8C2211yescharacteristic, complemented
33C2×#3756C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C3×#924C2211yescharacteristic, complemented
39C3×#897C2211yescharacteristic, complemented
40C3×#894—21no—
41C3×#892C2211yescharacteristic, complemented
42C3×#888—21no—
43C3×#885—21no—
44C3×#883—21no—
45#63946—24no—
46D3×#215—24no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C3×#536—31no—
68C2×#942—31no—
69C22×#215—31no—
70C2×#915—31no—
71C2×D3×SD16—31no—
72#5628D311yescharacteristic, complemented
73C3×#450—31no—
74#5234—31no—
75#5218—31no—
76#5173—31no—
77#5169—31no—
78#5047—31no—
79#5047—31no—
80#5047—31no—
81#5047—31no—
82#5047—31no—
83#5047—61no—
84#5046—31no—
85#5046—31no—
86#5046—31no—
87#5046D311yescharacteristic, complemented
88#5002—31no—
89#5001—31no—
90#4783—31no—
91#4776—31no—
92#4772—31no—
93#4770—31no—
94#4733—31no—
95#4727—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67D411yescharacteristic
108C2×C3×#67D411yescharacteristic
109C3×D3×Q8—22no—
110C3×D3×Q8—22no—
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12—21no—
114C2×C3×D12—22no—
115C2×C3×D12—22no—
116C2×C3×D12D411yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6—21no—
123C2×C3×Dic6D411yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125D3×#67—28no—
126D3×#67—28no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#625—21no—
130C2×#625—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133#3802—28no—
134D3×D12—22no—
135D3×D12—22no—
136D3×D12—22no—
137D3×D12D414yes—
138#3796—28no—
139#3795—22no—
140#3795—22no—
141#3795—22no—
142#3795D414yes—
143C32×C4⋊C4—21no—
144C32×C4⋊C4C2311yescharacteristic
145C32×C22⋊C4—21no—
146#3756—22no—
147#3755—22no—
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150C3×#217—21no—
151C3×#215—22no—
152C3×#215—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C3×Dic3⋊C4—21no—
160C3×C4×Dic3—21no—
161C2×C3×C3⋊C8C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163#3719—22no—
164#3717—22no—
165#3715—22no—
166#3715—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3009—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C22×#67—61no—
175#1009—64no—
176#1009—64no—
177C2×#239—61no—
178C2×D3×Q8C2×D311yescharacteristic, complemented
179#1004—64no—
180#1004—64no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C2×#235C2×D311yescharacteristic
196C22×D12—31no—
197C22×D12—31no—
198C22×D12C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C3×C4⋊Q8—61no—
202C3×#124—61no—
203C3×#123—61no—
204C3×#123—61no—
205C3×C22⋊Q8—21no—
206C3×C22⋊Q8—31no—
207C3×C22⋊Q8—31no—
208C3×C22⋊Q8—31no—
209C3×C22⋊Q8C2×D311yescharacteristic, complemented
210C3×C22⋊Q8C2×D311yescharacteristic, complemented
211C3×#117—31no—
212#946C2×D311yescharacteristic, complemented
213C2×#216—31no—
214C2×#216—31no—
215C2×#216—31no—
216C2×#216—61no—
217#942—64no—
218C2×#215—31no—
219C2×#215—31no—
220C2×#215—31no—
221C2×#215—31no—
222C2×#215—31no—
223C2×#215—61no—
224C2×#215—64no—
225C2×#215C2×D311yescharacteristic, complemented
226C2×#215C2×D311yescharacteristic, complemented
227C2×#214—31no—
228C2×#214—31no—
229#924C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C22×C3⋊C8—31no—
232#915—64no—
233D3×SD16—64no—
234C2×Dic12—31no—
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8—31no—
238#897C2×D311yescharacteristic, complemented
239#894—21no—
240#892C2×D311yescharacteristic, complemented
241#888—21no—
242#885—21no—
243#883—21no—
244C3×#102—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#832—31no—
248#832—31no—
249#830—31no—
250#830—31no—
251#830—31no—
252#830—31no—
253#830—61no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258#816—31no—
259#810—31no—
260#810—31no—
261#810—31no—
262#810—61no—
263#809—31no—
264#809—31no—
265#809—31no—
266#809—31no—
267#809—31no—
268#809—61no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—24no—
276C22×C3×D3—81no—
277C22×C3×D3—81no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C32×Q8—21no—
287C32×Q8—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4C2×D411yescharacteristic
293C2×C32×C4C2411yescharacteristic
294#638—24no—
295C2×C3⋊Dic3—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)C2×D412yes—
298C4×C3⋊D3—24no—
299#634—21no—
300#634C2×D412yes—
301C3×#67—22no—
302C3×#67—22no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—24no—
308C3×D12—22no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12C2×D412yes—
312C3×D12C2×D412yes—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—42no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318C3×Dic6—22no—
319C3×Dic6—21no—
320C3×Dic6—21no—
321C3×Dic6—42no—
322#626—24no—
323#626—24no—
324#625—24no—
325#625—24no—
326D3×Dic3—24no—
327D3×Dic3—24no—
328C3⋊(C3⋊C8)—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C2×H(5,𝔽2)—91no—
333C2×#137—91no—
334C22×SD16—91no—
335#536—31no—
336#452—91no—
337#452—91no—
338#452—91no—
339#452—91no—
340#450—31no—
341#450—91no—
342#450—91no—
343#450—91no—
344#418—91no—
345#416—91no—
346#408—91no—
347C24×C3—61no—
348C23×D3—21no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8—31no—
358C2×C3×Q8—61no—
359C2×C3×Q8—62no—
360C2×C3×Q8—62no—
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—62no—
369C2×C3×D4—62no—
370C2×C3×D4—61no—
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—61no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—68no—
378C2×#67—68no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—121no—
388C2×#67#6711yescharacteristic
389C2×#67#6711yescharacteristic
390C22×Dic3—61no—
391C22×Dic3—61no—
392#239—68no—
393D3×Q8—22no—
394D3×Q8—22no—
395#237—34no—
396#237—68no—
397#237—62no—
398#237—62no—
399#237—62no—
400D3×D4—34no—
401D3×D4—62no—
402D3×D4—62no—
403D3×D4—68no—
404D3×D4—68no—
405D3×D4—68no—
406D3×D4—68no—
407D3×D4—62no—
408#235—22no—
409#235—22no—
410#235—34no—
411#235—62no—
412#235—62no—
413#235—62no—
414#235—62no—
415#235—62no—
416#235—62no—
417#235—62no—
418#235—122no—
419#235—122no—
420C2×D12—21no—
421C2×D12—22no—
422C2×D12—22no—
423C2×D12—31no—
424C2×D12—31no—
425C2×D12—34no—
426C2×D12—61no—
427C2×D12—62no—
428C2×D12—62no—
429C2×D12—61no—
430C2×D12—61no—
431C2×D12—62no—
432C2×D12#6711yescharacteristic
433C2×D12C22×D311yescharacteristic
434C2×D12C22×D311yescharacteristic
435C2×C4×D3—21no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—121no—
441C2×C4×D3C22×D311yescharacteristic
442C2×C4×D3C22×D311yescharacteristic
443C2×Dic6—21no—
444C2×Dic6—31no—
445C2×Dic6—31no—
446C2×Dic6—61no—
447C2×Dic6#6711yescharacteristic
448C2×Dic6C22×D311yescharacteristic
449C3×SD16—62no—
450C3×SD16—62no—
451C2×C3×C8—31no—
452C2×C3×C8—31no—
453C3×C4⋊C4—21no—
454C3×C4⋊C4—21no—
455C3×C4⋊C4—21no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—41no—
458C3×C4⋊C4—61no—
459C3×C4⋊C4—61no—
460C3×C4⋊C4—61no—
461C3×C4⋊C4C22×D311yescharacteristic
462C3×C4⋊C4C22×D311yescharacteristic
463C3×C22⋊C4—21no—
464C3×C22⋊C4—21no—
465C3×C22⋊C4—41no—
466C3×C22⋊C4—61no—
467C3×C22⋊C4—61no—
468C3×C22⋊C4—61no—
469C3×C22⋊C4—61no—
470C3×C42—61no—
471#217—21no—
472#216—62no—
473#216—62no—
474#216—62no—
475#216—122no—
476#215—22no—
477#215—22no—
478#215—62no—
479#215—62no—
480#215—62no—
481#215—62no—
482#215—62no—
483#215—122no—
484#214—62no—
485#214—62no—
486(C2×D3)⋊C4—21no—
487(C2×D3)⋊C4—21no—
488(C2×D3)⋊C4—21no—
489C4⋊Dic3—21no—
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—21no—
492Dic3⋊C4—21no—
493C4×Dic3—21no—
494#208—62no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—62no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504Dic12—62no—
505#204—62no—
506ΓL(1,𝔽25)—62no—
507D3×C8—62no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—22no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—84no—
527C2×C3×D3#12012yes—
528D32—84no—
529D32—84no—
530C32×C4—21no—
531C32×C4—41no—
532C32×C4—41no—
533C32×C4C22×D411yescharacteristic
534C32×C4C22×D411yescharacteristic
535C3⋊Dic3—22no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C3×Dic3#12012yes—
540H(5,𝔽2)—184no—
541H(5,𝔽2)—184no—
542C2×#41—31no—
543C2×#41—91no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—181no—
547C22×Q8—31no—
548C22×D4—31no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—181no—
552C22×D4—181no—
553C22×D4—181no—
554#137—184no—
555C2×Q16—91no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×SD16—91no—
562C2×SD16—91no—
563C2×SD16—184no—
564C2×M16—91no—
565C22×C8—91no—
566C4⋊Q8—61no—
567#124—61no—
568#123—61no—
569#123—61no—
570C22⋊Q8—31no—
571C22⋊Q8—31no—
572C22⋊Q8—31no—
573C22⋊Q8D3211yescharacteristic, complemented
574#117—31no—
575#103—91no—
576#103—91no—
577#102—31no—
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582#102—91no—
583C22⋊C8—31no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C22⋊C8—91no—
587C23×C3—21no—
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—64no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—241no—
594C23×C3—241no—
595C23×C3D3×D411yescharacteristic
596C23×C3C2×#6711yescharacteristic
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—24no—
600C22×D3—64no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—64no—
606C22×D3—81no—
607C22×D3—81no—
608C22×D3—121no—
609C22×D3—241no—
610C22×D3—241no—
611C22×D3—241no—
612C22×D3—241no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3C2×#6711yescharacteristic
618C22×D3C2×#6711yescharacteristic
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—21no—
623C3×Q8—41no—
624C3×Q8—41no—
625C3×Q8—62no—
626C3×Q8—61no—
627C3×Q8—61no—
628C3×Q8—122no—
629C3×D4—32no—
630C3×D4—32no—
631C3×D4—62no—
632C3×D4—64no—
633C3×D4—62no—
634C3×D4—62no—
635C3×D4—61no—
636C3×D4—61no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—31no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—31no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—122no—
660C2×C3×C4D3×D411yescharacteristic
661C2×C3×C4C2×#6711yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664#67—22no—
665#67—22no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—64no—
671#67—64no—
672#67—64no—
673#67—64no—
674#67—124no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—64no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—64no—
681C2×Dic3—121no—
682C2×Dic3C2×#6711yescharacteristic
683C2×Dic3C2×#6711yescharacteristic
684D12—24no—
685D12—22no—
686D12—21no—
687D12—21no—
688D12—32no—
689D12—32no—
690D12—62no—
691D12—64no—
692D12—64no—
693D12—61no—
694D12—61no—
695D12—121no—
696D12D3×D412yes—
697D12D3×D412yes—
698C4×D3—21no—
699C4×D3—21no—
700C4×D3—42no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—124no—
706C4×D3D3×D412yes—
707C4×D3D3×D412yes—
708Dic6—22no—
709Dic6—21no—
710Dic6—21no—
711Dic6—32no—
712Dic6—32no—
713Dic6—42no—
714Dic6—62no—
715Dic6—61no—
716Dic6—61no—
717Dic6—121no—
718C3×C8—61no—
719C3×C8—61no—
720C3⋊C8—21no—
721C3⋊C8—21no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—121no—
727C3⋊C8—121no—
728C2×C32—41no—
729C2×C32C2×#12011yescharacteristic
730C2×C32#57711yescharacteristic
731C2×C32#57711yescharacteristic
732C3⋊D3—42no—
733C3×D3—22no—
734C3×D3—41no—
735C3×D3—42no—
736C3×D3—42no—
737C24—61no—
738C24—181no—
739C24—181no—
740#41—62no—
741#41—62no—
742#41—94no—
743#41—182no—
744#41—182no—
745#41—182no—
746#41—182no—
747#41—182no—
748#41—188no—
749C2×Q8—31no—
750C2×Q8—31no—
751C2×Q8—61no—
752C2×Q8—62no—
753C2×Q8—62no—
754C2×Q8—91no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—31no—
759C2×D4—31no—
760C2×D4—31no—
761C2×D4—62no—
762C2×D4—62no—
763C2×D4—61no—
764C2×D4—94no—
765C2×D4—91no—
766C2×D4—182no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—182no—
770C2×D4—182no—
771C2×D4—188no—
772C2×D4—188no—
773C2×D4—188no—
774C2×D4—181no—
775C2×D4—181no—
776C2×D4—181no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—61no—
780C22×C4—181no—
781C22×C4—181no—
782C22×C4—181no—
783C22×C4C2×D3211yescharacteristic
784Q16—182no—
785Q16—182no—
786SD16—62no—
787SD16—62no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792M16—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—91no—
796C2×C8—91no—
797C2×C8—182no—
798C4⋊C4—21no—
799C4⋊C4—31no—
800C4⋊C4—61no—
801C4⋊C4—61no—
802C4⋊C4—61no—
803C4⋊C4C2×D3211yescharacteristic
804C22⋊C4—21no—
805C22⋊C4—61no—
806C22⋊C4—61no—
807C22⋊C4—61no—
808C22⋊C4—61no—
809C42—61no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—32no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—61no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—244no—
833C22×C3C2×D3×D411yescharacteristic
834C22×C3C22×#6711yescharacteristic
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—21no—
839C2×D3—21no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—84no—
849C2×D3—122no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—244no—
857C2×D3—244no—
858C2×D3—244no—
859C2×D3—244no—
860C2×D3#93712yes—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—32no—
866C3×C4—41no—
867C3×C4—41no—
868C3×C4—41no—
869C3×C4—41no—
870C3×C4—41no—
871C3×C4—61no—
872C3×C4—81no—
873C3×C4—81no—
874C3×C4—121no—
875C3×C4—121no—
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C2×D3×D411yescharacteristic
879C3×C4C2×D3×D411yescharacteristic
880Dic3—21no—
881Dic3—41no—
882Dic3—41no—
883Dic3—62no—
884Dic3—62no—
885Dic3—122no—
886Dic3#93712yes—
887C32#300911yescharacteristic, complemented, Sylow
888C23—31no—
889C23—31no—
890C23—64no—
891C23—61no—
892C23—61no—
893C23—184no—
894C23—184no—
895C23—181no—
896C23—241no—
897C23—241no—
898C23—721no—
899C23—721no—
900C23—721no—
901C23—721no—
902C23D3×#6711yescharacteristic
903Q8—21no—
904Q8—21no—
905Q8—62no—
906Q8—61no—
907Q8—61no—
908Q8—92no—
909Q8—122no—
910Q8—181no—
911D4—32no—
912D4—32no—
913D4—62no—
914D4—64no—
915D4—62no—
916D4—62no—
917D4—61no—
918D4—61no—
919D4—92no—
920D4—184no—
921D4—184no—
922D4—184no—
923D4—184no—
924D4—184no—
925D4—181no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—31no—
931C2×C4—32no—
932C2×C4—32no—
933C2×C4—31no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—122no—
939C2×C4—184no—
940C2×C4—184no—
941C2×C4—184no—
942C2×C4—181no—
943C2×C4D3×#6711yescharacteristic
944C2×C4C22×D3211yescharacteristic
945C8—61no—
946C8—61no—
947C8—181no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—41no—
953C2×C3—41no—
954C2×C3—62no—
955C2×C3—81no—
956C2×C3—121no—
957C2×C3—122no—
958C2×C3—122no—
959C2×C3D3×#12011yescharacteristic
960C2×C3#576211yescharacteristic
961C2×C3#577511yescharacteristic
962C2×C3C2×#93711yescharacteristic
963C2×C3#583711yescharacteristic
964C2×C3#583711yescharacteristic
965D3—22no—
966D3—42no—
967D3—42no—
968D3—41no—
969D3—122no—
970D3—122no—
971D3—242no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—32no—
976C22—61no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—62no—
981C22—62no—
982C22—61no—
983C22—121no—
984C22—121no—
985C22—121no—
986C22—121no—
987C22—182no—
988C22—244no—
989C22—361no—
990C22—361no—
991C22—724no—
992C22—724no—
993C22C2×D3×#6711yescharacteristic
994C4—21no—
995C4—32no—
996C4—41no—
997C4—41no—
998C4—61no—
999C4—121no—
1000C4—121no—
1001C4—182no—
1002C4D32×D411yescharacteristic
1003C4D32×D411yescharacteristic
1004C3—21no—
1005C3#8014811yescharacteristic, complemented
1006C3#8340411yescharacteristic, complemented
1007C2—41no—
1008C2—62no—
1009C2—121no—
1010C2—122no—
1011C2—122no—
1012C2—362no—
1013C2D3×#93711yescharacteristic
1014C2#1059531811yescharacteristic
1015C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#64307C2
hypercenterC22⋊Q8D32
hypocenterC32#3009
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
2. C3×#5628C2semidirect
3. C2×#63946C2semidirect
4. C2×D3×#215C2semidirect
5. #10592746C2semidirect
6. C3×#5046C2semidirect
7. #10591655C2semidirect
8. #10591651C2semidirect
9. #10591184C2semidirect
10. #10591169C2semidirect
11. #10591145C2semidirect
12. #10590614C2semidirect
13. #10590608C2semidirect
14. #10590596C2semidirect
15. #10590592C2semidirect
19. C2×C3×D3×Q8C22semidirect
32. C32×C22⋊Q8C22semidirect
33. C2×#3756C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C3×#924C22semidirect
39. C3×#897C22semidirect
41. C3×#892C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3715C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63657C22semidirect
54. #63637C22semidirect
55. #63636C22semidirect
56. C3×#830C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
72. #5628D3semidirect
87. #5046D3semidirect
178. C2×D3×Q8C2×D3semidirect
209. C3×C22⋊Q8C2×D3semidirect
210. C3×C22⋊Q8C2×D3semidirect
212. #946C2×D3semidirect
225. C2×#215C2×D3semidirect
226. C2×#215C2×D3semidirect
229. #924C2×D3semidirect
238. #897C2×D3semidirect
240. #892C2×D3semidirect
254. #830C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
573. C22⋊Q8D32semidirect
887. C32#3009semidirect
1005. C3#80148semidirect
1006. C3#83404semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C3×#56282
C2×#639462
C2×D3×#2152
#105927462
C3×#50462
#105916552
#105916512
#105911842
#105911692
#105911452
#105906142
#105906082
#105905962
#105905922
#834043
#801483