Finite Group Databasebeta

← #11864229

Subgroups — #11864229

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 997 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C3×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#63948C211yesmaximal, characteristic, complemented
4C2×#63946C211yesmaximal, characteristic, complemented
5#10592746C211yesmaximal, characteristic, complemented
6C3×#5047C211yesmaximal, characteristic, complemented
7#10591653C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591184C211yesmaximal, characteristic, complemented
10#10591170C211yesmaximal, characteristic, complemented
11#10591154C211yesmaximal, characteristic, complemented
12#10590609C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590604C211yesmaximal, characteristic, complemented
15#10590596C211yesmaximal, characteristic, complemented
16#82735—31nomaximal
17#80228—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C2×D3×#67—21no—
23C2×#3804—21no—
24D3×#235—24no—
25D3×#235—24no—
26C2×D3×D12C2211yescharacteristic
27C2×C4×D32—21no—
28C2×#3799C2211yescharacteristic
29C2×#3798—21no—
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C32×C22⋊Q8C2211yescharacteristic, complemented
33C2×#3756C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C3×#924C2211yescharacteristic, complemented
39C3×#897C2211yescharacteristic
40C3×#896—21no—
41C3×D3×C4⋊C4—21no—
42C3×D3×C4⋊C4C2211yescharacteristic, complemented
43C3×D3×C22⋊C4—21no—
44C3×#878—21no—
45#63948—24no—
46#63946—24no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3718C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C2×D3×#41—31no—
66C22×#235—31no—
67C2×C3×C22⋊Q8—31no—
68C2×#942—31no—
69C2×#942—31no—
70C2×#918—31no—
71C2×#915—31no—
72D3×C22⋊Q8D311yescharacteristic, complemented
73C3×#452—31no—
74#5239—31no—
75#5207—31no—
76#5186—31no—
77#5169—31no—
78#5050—31no—
79#5050—31no—
80#5047—31no—
81#5047—31no—
82#5047—31no—
83#5047—31no—
84#5047—61no—
85#5047D311yescharacteristic, complemented
86#5046—31no—
87#5046—31no—
88#4966—31no—
89#4966—31no—
90#4809—31no—
91#4803—31no—
92#4776—31no—
93#4771—31no—
94#4733—31no—
95#4726—31no—
96C23×C3×D3D411yescharacteristic
97C22×D32—21no—
98C2×C32×Q8C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101#3828—22no—
102#3828—22no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C22×C3×Dic3D411yescharacteristic
108C3×D3×Q8—22no—
109C3×D3×Q8—22no—
110C3×#235—22no—
111C3×#235—22no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3D411yescharacteristic
119C2×C3×C4×D3D411yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6—21no—
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125D3×#67—28no—
126C2×#627—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#625—21no—
130C2×#624—21no—
131#3804—28no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134D3×D12—22no—
135D3×D12—22no—
136C4×D32—28no—
137#3799—22no—
138#3799D414yes—
139#3798—28no—
140#3795—22no—
141#3795D414yes—
142D3×Dic6—22no—
143D3×Dic6—22no—
144C32×C4⋊C4—21no—
145C32×C4⋊C4C2311yescharacteristic
146C32×C22⋊C4—21no—
147#3756—22no—
148#3755—22no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C3×#217—21no—
152C3×#216—22no—
153C3×#215—22no—
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×Dic3⋊C4—21no—
161C2×C3×C3⋊C8C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163#3719—22no—
164#3718—22no—
165#3717—22no—
166#3715—22no—
167#3711—22no—
168#3711—22no—
169#3007—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172C23×C3×C4—31no—
173C22×#67—61no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×D3×Q8—31no—
178C2×D3×Q8C2×D311yescharacteristic, complemented
179C2×#237—31no—
180C2×#237—61no—
181C2×D3×D4—31no—
182C2×D3×D4—61no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—31no—
186C2×#235—31no—
187C2×#235—61no—
188C2×#235—61no—
189C2×#235—64no—
190C2×#235—64no—
191C2×#235—61no—
192C2×#235—61no—
193C2×#235C2×D311yescharacteristic
194C22×D12—31no—
195C22×C4×D3—61no—
196C22×C4×D3—61no—
197C22×C4×D3C2×D311yescharacteristic
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C3×C22⋊Q8—21no—
202C3×C22⋊Q8—31no—
203C3×C22⋊Q8—31no—
204C3×C22⋊Q8—31no—
205C3×C22⋊Q8—61no—
206C3×C22⋊Q8—61no—
207C3×C22⋊Q8C2×D311yescharacteristic, complemented
208C3×C22⋊Q8C2×D311yescharacteristic, complemented
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—61no—
211C2×C3×C22⋊C4—61no—
212#946C2×D311yescharacteristic
213C2×#216—31no—
214C2×#216—31no—
215C2×#216—31no—
216C2×#216—31no—
217C2×#216—31no—
218C2×#216—61no—
219C2×#216C2×D311yescharacteristic, complemented
220#942—64no—
221#942—64no—
222C2×#215—31no—
223C2×#215—31no—
224C2×#215—31no—
225C2×#215—31no—
226C2×#215—61no—
227C2×#215C2×D311yescharacteristic, complemented
228C2×#214—31no—
229#924C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C2×#208—31no—
232#918—64no—
233#915—64no—
234C2×Dic12—31no—
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×ΓL(1,𝔽25)—31no—
238#897C2×D311yescharacteristic
239#896—21no—
240D3×C4⋊C4—21no—
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242D3×C22⋊C4—21no—
243#878—21no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—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—31no—
263#810—61no—
264#810C2×D311yescharacteristic, complemented
265#809—31no—
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—41no—
277C22×C3×D3C2×D411yescharacteristic
278C22×C3×D3C2×D411yescharacteristic
279C2×D32—24no—
280C2×D32—42no—
281C2×D32—42no—
282C32×Q8—21no—
283C32×Q8—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4C2×D411yescharacteristic
289C2×C32×C4C2411yescharacteristic
290#638—24no—
291C2×C3⋊Dic3—21no—
292C4⋊(C3⋊D3)—21no—
293C4⋊(C3⋊D3)C2×D412yes—
294C4×C3⋊D3—24no—
295#634—21no—
296#634C2×D412yes—
297C3×#67—24no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3C2×D411yescharacteristic
303C2×C3×Dic3C2×D411yescharacteristic
304C3×D12—21no—
305C3×D12C2×D412yes—
306C3×C4×D3—24no—
307C3×C4×D3—22no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×C4×D3—22no—
311C3×C4×D3—42no—
312C3×C4×D3—42no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6—21no—
318C3×Dic6—42no—
319C3×Dic6C2×D412yes—
320#627—24no—
321#626—24no—
322#626—24no—
323#625—24no—
324#624—24no—
325D3×Dic3—24no—
326D3×Dic3—24no—
327C3⋊(C3⋊C8)—21no—
328C3⋊(C3⋊C8)—21no—
329C3×C3⋊C8—21no—
330C3×C3⋊C8—21no—
331C22×#41—91no—
332C2×#137—91no—
333C2×#137—91no—
334C2×C22⋊Q8—31no—
335#452—31no—
336#452—91no—
337#452—91no—
338#452—91no—
339#451—91no—
340#451—91no—
341#450—91no—
342#450—91no—
343#417—91no—
344#417—91no—
345#407—91no—
346C24×C3—31no—
347C23×D3—61no—
348C23×D3—61no—
349C23×D3#6711yescharacteristic
350C3×#41—62no—
351C3×#41—62no—
352C2×C3×Q8—21no—
353C2×C3×Q8—31no—
354C2×C3×Q8—31no—
355C2×C3×Q8—61no—
356C2×C3×Q8—62no—
357C2×C3×Q8—62no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—31no—
361C2×C3×D4—61no—
362C22×C3×C4—21no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—62no—
369C22×C3×C4—62no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C2×#67—21no—
376C2×#67—61no—
377C2×#67—68no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—121no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3#6711yescharacteristic
387#239—34no—
388#239—62no—
389D3×Q8—22no—
390D3×Q8—22no—
391D3×Q8—62no—
392D3×Q8—62no—
393#237—34no—
394#237—68no—
395#237—62no—
396D3×D4—62no—
397D3×D4—62no—
398D3×D4—68no—
399#235—22no—
400#235—22no—
401#235—34no—
402#235—34no—
403#235—62no—
404#235—62no—
405#235—62no—
406#235—68no—
407#235—68no—
408#235—62no—
409#235—62no—
410#235—62no—
411#235—68no—
412#235—122no—
413#235—122no—
414C2×D12—31no—
415C2×D12—31no—
416C2×D12—61no—
417C2×D12—62no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—62no—
421C2×D12C22×D311yescharacteristic
422C2×C4×D3—21no—
423C2×C4×D3—22no—
424C2×C4×D3—22no—
425C2×C4×D3—21no—
426C2×C4×D3—21no—
427C2×C4×D3—68no—
428C2×C4×D3—68no—
429C2×C4×D3—61no—
430C2×C4×D3—61no—
431C2×C4×D3—61no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—121no—
436C2×C4×D3#6711yescharacteristic
437C2×C4×D3#6711yescharacteristic
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D311yescharacteristic
440C2×Dic6—21no—
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—61no—
444C2×Dic6—62no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6—62no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×SD16—62no—
452C2×C3×C8—31no—
453C2×C3×C8—31no—
454C3×C4⋊C4—21no—
455C3×C4⋊C4—21no—
456C3×C4⋊C4—21no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—41no—
459C3×C4⋊C4—61no—
460C3×C4⋊C4—61no—
461C3×C4⋊C4—61no—
462C3×C4⋊C4—61no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C22⋊C4—21no—
466C3×C22⋊C4—21no—
467C3×C22⋊C4—41no—
468C3×C22⋊C4—61no—
469C3×C22⋊C4—61no—
470C3×C22⋊C4—61no—
471#217—21no—
472#216—22no—
473#216—62no—
474#216—62no—
475#216—62no—
476#216—62no—
477#216—62no—
478#216—122no—
479#215—22no—
480#215—62no—
481#215—62no—
482#215—62no—
483#215—62no—
484#215—122no—
485#214—62no—
486(C2×D3)⋊C4—21no—
487(C2×D3)⋊C4—21no—
488C4⋊Dic3—21no—
489C4⋊Dic3C22×D311yescharacteristic
490Dic3⋊C4—21no—
491Dic3⋊C4—21no—
492Dic3⋊C4—21no—
493#208—62no—
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⋊C8C22×D311yescharacteristic
502C2×C3⋊C8C22×D311yescharacteristic
503Dic12—62no—
504#204—62no—
505ΓL(1,𝔽25)—62no—
506ΓL(1,𝔽25)—62no—
507C22×C32—21no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32C22×D411yescharacteristic
511C2×C3⋊D3—22no—
512C2×C3⋊D3—41no—
513C2×C3⋊D3—41no—
514C2×C3×D3—21no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—44no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3#12012yes—
523C2×C3×D3#13712yescomplemented
524D32—48no—
525C32×C4—21no—
526C32×C4—41no—
527C32×C4—41no—
528C32×C4C22×D411yescharacteristic
529C32×C4C22×D411yescharacteristic
530C3⋊Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—21no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3#12012yes—
536C2×#41—31no—
537C2×#41—91no—
538C2×#41—91no—
539C2×#41—91no—
540C2×#41—181no—
541C2×#41—181no—
542C2×#41—184no—
543C2×#41—184no—
544C22×Q8—31no—
545C22×Q8—91no—
546C22×D4—91no—
547C22×D4—181no—
548C23×C4—31no—
549C23×C4—181no—
550#137—184no—
551#137—184no—
552C2×Q16—31no—
553C2×Q16—91no—
554C2×Q16—91no—
555C2×Q16—91no—
556C2×SD16—31no—
557C2×SD16—91no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×M16—91no—
561C2×M16—91no—
562C22⋊Q8—31no—
563C22⋊Q8—31no—
564C22⋊Q8—31no—
565C22⋊Q8—61no—
566C22⋊Q8—61no—
567C22⋊Q8D3211yescharacteristic, complemented
568C2×C4⋊C4—31no—
569C2×C4⋊C4—61no—
570C2×C22⋊C4—61no—
571#103—31no—
572#103—91no—
573#103—91no—
574#103—91no—
575#102—31no—
576#102—91no—
577#102—91no—
578#102—91no—
579C22⋊C8—31no—
580C22⋊C8—91no—
581C22⋊C8—91no—
582C22⋊C8—91no—
583C23×C3—21no—
584C23×C3—31no—
585C23×C3—31no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—61no—
589C23×C3—121no—
590C23×C3D3×D411yescharacteristic
591C23×C3C2×#6711yescharacteristic
592C22×D3—21no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—41no—
596C22×D3—64no—
597C22×D3—64no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—121no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3—122no—
604C22×D3—122no—
605C22×D3C2×#6711yescharacteristic
606C22×D3C2×#6711yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—21no—
610C3×Q8—21no—
611C3×Q8—32no—
612C3×Q8—41no—
613C3×Q8—41no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×Q8—122no—
618C3×D4—32no—
619C3×D4—64no—
620C3×D4—61no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—31no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—62no—
640C2×C3×C4—62no—
641C2×C3×C4—64no—
642C2×C3×C4—62no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—122no—
649C2×C3×C4—122no—
650C2×C3×C4D3×D411yescharacteristic
651C2×C3×C4C2×#6711yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654#67—24no—
655#67—64no—
656#67—64no—
657#67—64no—
658#67—64no—
659#67—64no—
660#67—64no—
661#67—124no—
662C2×Dic3—21no—
663C2×Dic3—22no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—64no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—64no—
670C2×Dic3—121no—
671C2×Dic3C2×#6711yescharacteristic
672C2×Dic3C2×#6711yescharacteristic
673D12—21no—
674D12—32no—
675D12—32no—
676D12—62no—
677D12—64no—
678D12—64no—
679D12—61no—
680D12—61no—
681D12—121no—
682D12D3×D412yes—
683C4×D3—24no—
684C4×D3—22no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—22no—
688C4×D3—42no—
689C4×D3—42no—
690C4×D3—64no—
691C4×D3—64no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—124no—
697C4×D3D3×D412yes—
698C4×D3D3×D412yes—
699Dic6—21no—
700Dic6—21no—
701Dic6—21no—
702Dic6—32no—
703Dic6—32no—
704Dic6—42no—
705Dic6—62no—
706Dic6—64no—
707Dic6—64no—
708Dic6—61no—
709Dic6—61no—
710Dic6—121no—
711Dic6D3×D412yes—
712C3×C8—61no—
713C3×C8—61no—
714C3⋊C8—21no—
715C3⋊C8—21no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—121no—
721C3⋊C8—121no—
722C2×C32—41no—
723C2×C32C2×#12011yescharacteristic
724C2×C32C2×#13711yescharacteristic
725C2×C32#57511yescharacteristic
726C3⋊D3—42no—
727C3×D3—22no—
728C3×D3—22no—
729C3×D3—42no—
730C24—31no—
731C24—181no—
732#41—62no—
733#41—62no—
734#41—94no—
735#41—94no—
736#41—182no—
737#41—182no—
738#41—182no—
739#41—182no—
740#41—188no—
741#41—188no—
742C2×Q8—31no—
743C2×Q8—31no—
744C2×Q8—61no—
745C2×Q8—62no—
746C2×Q8—62no—
747C2×Q8—91no—
748C2×Q8—181no—
749C2×Q8—182no—
750C2×Q8—182no—
751C2×Q8C2×D3211yescharacteristic
752C2×D4—31no—
753C2×D4—61no—
754C2×D4—91no—
755C2×D4—181no—
756C2×D4—182no—
757C2×D4—182no—
758C2×D4—181no—
759C2×D4—188no—
760C2×D4—181no—
761C2×D4—181no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—62no—
768C22×C4—62no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4—188no—
775C22×C4—181no—
776C22×C4—181no—
777C22×C4C2×D3211yescharacteristic
778Q16—62no—
779Q16—182no—
780Q16—182no—
781Q16—182no—
782SD16—62no—
783SD16—182no—
784SD16—182no—
785SD16—182no—
786M16—182no—
787M16—182no—
788C2×C8—31no—
789C2×C8—31no—
790C2×C8—91no—
791C2×C8—91no—
792C4⋊C4—21no—
793C4⋊C4—31no—
794C4⋊C4—61no—
795C4⋊C4—61no—
796C4⋊C4—61no—
797C4⋊C4—61no—
798C4⋊C4C2×D3211yescharacteristic
799C22⋊C4—21no—
800C22⋊C4—61no—
801C22⋊C4—61no—
802C22⋊C4—61no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—32no—
811C22×C3—32no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—62no—
820C22×C3—124no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C22×#6711yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—22no—
830C2×D3—44no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—122no—
836C2×D3—128no—
837C2×D3—128no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—241no—
843C2×D3—241no—
844C2×D3#93712yes—
845C2×D3#94212yescomplemented
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—32no—
851C3×C4—41no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—41no—
855C3×C4—41no—
856C3×C4—62no—
857C3×C4—61no—
858C3×C4—81no—
859C3×C4—81no—
860C3×C4—121no—
861C3×C4—121no—
862C3×C4C2×D3×D411yescharacteristic
863C3×C4C2×D3×D411yescharacteristic
864C3×C4C2×D3×D411yescharacteristic
865C3×C4C2×D3×D411yescharacteristic
866Dic3—21no—
867Dic3—22no—
868Dic3—41no—
869Dic3—41no—
870Dic3—62no—
871Dic3—62no—
872Dic3—122no—
873Dic3#93712yes—
874C32#300711yescharacteristic, complemented, Sylow
875C23—31no—
876C23—31no—
877C23—62no—
878C23—62no—
879C23—61no—
880C23—121no—
881C23—184no—
882C23—181no—
883C23—362no—
884C23—362no—
885C23D3×#6711yescharacteristic
886Q8—21no—
887Q8—21no—
888Q8—32no—
889Q8—61no—
890Q8—61no—
891Q8—61no—
892Q8—92no—
893Q8—122no—
894Q8—184no—
895Q8—181no—
896D4—32no—
897D4—64no—
898D4—61no—
899D4—92no—
900D4—184no—
901D4—184no—
902D4—184no—
903D4—184no—
904D4—181no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—31no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—31no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—64no—
916C2×C4—62no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—122no—
923C2×C4—122no—
924C2×C4—184no—
925C2×C4—184no—
926C2×C4—184no—
927C2×C4—184no—
928C2×C4—181no—
929C2×C4D3×#6711yescharacteristic
930C2×C4C22×D3211yescharacteristic
931C8—61no—
932C8—61no—
933C8—181no—
934C8—181no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—41no—
939C2×C3—41no—
940C2×C3—62no—
941C2×C3—62no—
942C2×C3—81no—
943C2×C3—122no—
944C2×C3D3×#12011yescharacteristic
945C2×C3#576811yescharacteristic
946C2×C3D3×#13711yescharacteristic
947C2×C3C2×#93711yescharacteristic
948C2×C3C2×#94211yescharacteristic
949C2×C3#582211yescharacteristic
950D3—22no—
951D3—22no—
952D3—42no—
953D3—122no—
954D3—122no—
955D3—242no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—32no—
960C22—32no—
961C22—61no—
962C22—61no—
963C22—61no—
964C22—61no—
965C22—62no—
966C22—124no—
967C22—121no—
968C22—121no—
969C22—182no—
970C22—368no—
971C22—361no—
972C22—361no—
973C22C2×D3×#6711yescharacteristic
974C4—21no—
975C4—32no—
976C4—41no—
977C4—41no—
978C4—61no—
979C4—62no—
980C4—121no—
981C4—121no—
982C4—182no—
983C4D32×D411yescharacteristic
984C4D32×D411yescharacteristic
985C3—21no—
986C3#8022811yescharacteristic, complemented
987C3#8273511yescharacteristic, complemented
988C2—41no—
989C2—62no—
990C2—62no—
991C2—122no—
992C2—362no—
993C2D3×#93711yescharacteristic
994C2D3×#94211yescharacteristic
995C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
hypercenterC22⋊Q8D32
hypocenterC32#3007
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×D3×C22⋊Q8C2semidirect
3. C2×#63948C2semidirect
4. C2×#63946C2semidirect
5. #10592746C2semidirect
6. C3×#5047C2semidirect
7. #10591653C2semidirect
8. #10591651C2semidirect
9. #10591184C2semidirect
10. #10591170C2semidirect
11. #10591154C2semidirect
12. #10590609C2semidirect
13. #10590607C2semidirect
14. #10590604C2semidirect
15. #10590596C2semidirect
19. C2×C3×D3×Q8C22semidirect
32. C32×C22⋊Q8C22semidirect
33. C2×#3756C22semidirect
34. C2×#3755C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C3×#924C22semidirect
42. C3×D3×C4⋊C4C22semidirect
47. C2×#3719C22semidirect
48. C2×#3718C22semidirect
49. C2×#3717C22semidirect
50. C2×#3715C22semidirect
51. C2×#3711C22semidirect
52. C2×#3711C22semidirect
53. #63657C22semidirect
54. #63637C22semidirect
55. #63636C22semidirect
56. C3×#830C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
72. D3×C22⋊Q8D3semidirect
85. #5047D3semidirect
178. C2×D3×Q8C2×D3semidirect
207. C3×C22⋊Q8C2×D3semidirect
208. C3×C22⋊Q8C2×D3semidirect
219. C2×#216C2×D3semidirect
227. C2×#215C2×D3semidirect
229. #924C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
254. #830C2×D3semidirect
264. #810C2×D3semidirect
270. #809C2×D3semidirect
523. C2×C3×D3#137semidirect
567. C22⋊Q8D32semidirect
845. C2×D3#942semidirect
874. C32#3007semidirect
986. C3#80228semidirect
987. C3#82735semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C3×D3×C22⋊Q82
C2×#639482
C2×#639462
#105927462
C3×#50472
#105916532
#105916512
#105911842
#105911702
#105911542
#105906092
#105906072
#105906042
#105905962
#827353
#802283