Finite Group Databasebeta

← #11864224

Subgroups — #11864224

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1007 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic
2C2×#64127C211yesmaximal, characteristic, complemented
3#10595429C211yesmaximal, characteristic, complemented
4C2×#63951C211yesmaximal, characteristic, complemented
5C3×#5187C211yesmaximal, characteristic, complemented
6C3×#5186C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591599C211yesmaximal, characteristic, complemented
10#10591595C211yesmaximal, characteristic, complemented
11#10591554C211yesmaximal, characteristic, complemented
12#10590970C211yesmaximal, characteristic, complemented
13#10590957C211yesmaximal, characteristic, complemented
14#10590946C211yesmaximal, characteristic, complemented
15#10590937C211yesmaximal, characteristic, complemented
16#80228—31nomaximal
17#80184—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22D3×#239—24no—
23D3×#239—24no—
24C2×D3×D12—21no—
25C2×D3×D12C2211yescharacteristic
26C2×C4×D32—21no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799—21no—
29C2×#3799C2211yescharacteristic
30C2×#3796—21no—
31C2×#3796C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33C2×#3756C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35#64127—24no—
36C2×#3744C2211yescharacteristic, complemented
37C2×#3743C2211yescharacteristic, complemented
38C3×#946C2211yescharacteristic
39C3×#946C2211yescharacteristic, complemented
40C2×C3×#216C2211yescharacteristic, complemented
41C2×C3×#215C2211yescharacteristic, complemented
42#63951—24no—
43#63921—21no—
44#63900C2211yescharacteristic, complemented
45#63896—21no—
46#63896—21no—
47#63883—21no—
48#63857C2211yescharacteristic
49#63857C2211yescharacteristic, complemented
50C2×#3719C2211yescharacteristic, complemented
51C2×#3716C2211yescharacteristic, complemented
52C2×#3712C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#918—31no—
68C2×#918—31no—
69C2×#918—31no—
70C2×#918—61no—
71C2×#915—31no—
72D3×C22⋊Q8—31no—
73D3×C22⋊Q8—31no—
74C3×#452—31no—
75C3×#451—31no—
76#5239—31no—
77#5228—31no—
78#5187—31no—
79#5187D311yescharacteristic, complemented
80#5186D311yescharacteristic, complemented
81#5169—31no—
82#5047—31no—
83#5046—31no—
84#4809—31no—
85#4808—31no—
86#4808—31no—
87#4803—31no—
88#4803—31no—
89#4803—31no—
90#4776—31no—
91#4771—31no—
92#4733—31no—
93#4731—31no—
94#4726—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832D414yes—
102Q8×C3⋊D3—22no—
103Q8×C3⋊D3—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×#634—21no—
110C2×#634C2311yescharacteristic
111C3×#239—22no—
112C3×#239—22no—
113C3×D3×Q8—22no—
114C3×D3×Q8—22no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#624—21no—
127C2×#624—21no—
128C2×#624D411yescharacteristic
129C2×D3×Dic3—21no—
130C2×D3×Dic3D411yescharacteristic
131C2×D3×Dic3D411yescharacteristic
132D3×D12—28no—
133D3×D12—22no—
134D3×D12—22no—
135C4×D32—28no—
136C4×D32—22no—
137C4×D32—22no—
138#3799—28no—
139#3799—22no—
140#3799—22no—
141#3796—28no—
142#3796—22no—
143#3796D414yes—
144C32×Q16—22no—
145C2×C32×C8C2311yescharacteristic
146#3756—22no—
147#3755—22no—
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149#3744—22no—
150#3743—22no—
151C3×#216—22no—
152C3×#215—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2311yescharacteristic
157C3×Dic3⋊C4—21no—
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161#3724—21no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166#3719—22no—
167#3716—22no—
168#3712—22no—
169#3007—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172D3×#41—64no—
173D3×#41—64no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—61no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—64no—
182C2×#239—64no—
183C2×#239C2×D311yescharacteristic
184C2×D3×Q8—31no—
185C2×D3×Q8—31no—
186C2×D3×Q8—61no—
187C2×D3×Q8C2×D311yescharacteristic
188C2×#237—31no—
189C2×#237—61no—
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×#235—31no—
193C2×#235—61no—
194C22×D12—31no—
195C22×D12—61no—
196C22×C4×D3—31no—
197C22×C4×D3—31no—
198C22×C4×D3—61no—
199C22×C4×D3—61no—
200C2×C3×Q16—21no—
201C2×C3×Q16—31no—
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×Q16C2×D311yescharacteristic, complemented
204C2×C3×SD16—31no—
205C3×C22⋊Q8—31no—
206C3×C22⋊Q8—31no—
207#946C2×D311yescharacteristic
208#946C2×D311yescharacteristic, complemented
209C2×#216—31no—
210C2×#216—31no—
211C2×#216—31no—
212C2×#216—61no—
213C2×#216C2×D311yescharacteristic, complemented
214C2×#215—31no—
215C2×#215—31no—
216C2×#215—61no—
217C2×#215C2×D311yescharacteristic, complemented
218C2×#214—31no—
219#924—31no—
220#924—31no—
221#918—64no—
222#918—64no—
223#918—64no—
224#918—68no—
225#915—64no—
226C2×Dic12—31no—
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×#204—61no—
231C2×ΓL(1,𝔽25)—31no—
232C2×ΓL(1,𝔽25)—31no—
233C2×ΓL(1,𝔽25)—31no—
234C2×ΓL(1,𝔽25)—31no—
235C2×ΓL(1,𝔽25)—61no—
236#897—31no—
237#897—31no—
238#896—61no—
239#896—61no—
240D3×C4⋊C4—31no—
241D3×C4⋊C4—31no—
242D3×C4⋊C4—61no—
243D3×C4⋊C4—61no—
244D3×C22⋊C4—61no—
245D3×C22⋊C4—61no—
246#878—61no—
247#878—61no—
248C3×#103—31no—
249C3×#103—31no—
250C3×#103—31no—
251C3×#102—31no—
252C3×C22⋊C8—31no—
253C3×C22⋊C8—31no—
254#835—31no—
255#835C2×D311yescharacteristic, complemented
256#835C2×D311yescharacteristic, complemented
257#832—31no—
258#830—31no—
259#830—31no—
260#821—31no—
261#821—31no—
262#821C2×D311yescharacteristic, complemented
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8C2×D311yescharacteristic
266(C2×D3)⋊C8C2×D311yescharacteristic, complemented
267#816C2×D311yescharacteristic, complemented
268#810—31no—
269#809—31no—
270#809—31no—
271#809—31no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—22no—
279C2×D32—22no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8—21no—
285C32×Q8—21no—
286C32×Q8C2×D412yes—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2411yescharacteristic
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3C2×D411yescharacteristic
292C4⋊(C3⋊D3)—24no—
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)C2×D412yes—
295C4×C3⋊D3—24no—
296C4×C3⋊D3—42no—
297C4×C3⋊D3C2×D412yes—
298C4×C3⋊D3C2×D412yes—
299#634—21no—
300#634—21no—
301#634—42no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—24no—
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×C4×D3—24no—
311C3×C4×D3—24no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×Dic6—24no—
317C3×Dic6—21no—
318C3×Dic6C2×D412yes—
319#626—24no—
320#626—24no—
321#626—24no—
322#624—24no—
323#624—22no—
324#624—42no—
325D3×Dic3—22no—
326D3×Dic3—24no—
327D3×Dic3—22no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—91no—
334C2×#137—91no—
335C2×C22⋊Q8—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#451—31no—
341#451—91no—
342#450—91no—
343#450—91no—
344#417—91no—
345#417—91no—
346#407—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—21no—
354C2×C3×Q8—21no—
355C2×C3×Q8—31no—
356C2×C3×Q8—61no—
357C2×C3×Q8—62no—
358C2×C3×Q8—62no—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×D4—31no—
364C2×C3×D4—61no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—61no—
375#239—22no—
376#239—22no—
377#239—34no—
378#239—34no—
379#239—34no—
380#239—64no—
381#239—62no—
382#239—62no—
383#239—68no—
384#239—62no—
385#239—62no—
386#239—62no—
387#239—68no—
388#239—122no—
389D3×Q8—22no—
390D3×Q8—22no—
391D3×Q8—62no—
392D3×Q8—62no—
393D3×Q8—62no—
394D3×Q8—62no—
395D3×Q8—64no—
396D3×Q8—122no—
397#237—34no—
398#237—62no—
399#237—68no—
400D3×D4—62no—
401D3×D4—62no—
402D3×D4—68no—
403#235—62no—
404#235—68no—
405#235—62no—
406C2×D12—21no—
407C2×D12—31no—
408C2×D12—31no—
409C2×D12—61no—
410C2×D12—62no—
411C2×D12—68no—
412C2×D12—61no—
413C2×D12—61no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—62no—
418C2×D12—121no—
419C2×D12C22×D311yescharacteristic
420C2×C4×D3—21no—
421C2×C4×D3—21no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—61no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—62no—
432C2×C4×D3—62no—
433C2×C4×D3—68no—
434C2×C4×D3—68no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—121no—
445C2×C4×D3—121no—
446C2×C4×D3C22×D311yescharacteristic
447C2×C4×D3C22×D311yescharacteristic
448C2×Dic6—21no—
449C2×Dic6—31no—
450C2×Dic6—31no—
451C2×Dic6—61no—
452C2×Dic6—61no—
453C2×Dic6—61no—
454C2×Dic6—121no—
455C2×Dic6C22×D311yescharacteristic
456C3×Q16—24no—
457C3×Q16—22no—
458C3×Q16—22no—
459C3×Q16—62no—
460C3×SD16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—31no—
463C2×C3×C8—31no—
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—31no—
467C3×C4⋊C4—31no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4—61no—
470C3×C22⋊C4—61no—
471C3×C22⋊C4—61no—
472#217—61no—
473#217—61no—
474#216—22no—
475#216—62no—
476#216—64no—
477#216—62no—
478#216—62no—
479#215—22no—
480#215—62no—
481#215—62no—
482#215—64no—
483#214—62no—
484(C2×D3)⋊C4—21no—
485(C2×D3)⋊C4—21no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488C4⋊Dic3—61no—
489C4⋊Dic3—61no—
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—21no—
493Dic3⋊C4—21no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—61no—
497Dic3⋊C4—61no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8C22×D311yescharacteristic
502C2×C3⋊C8C22×D311yescharacteristic
503Dic12—62no—
504#204—62no—
505#204—62no—
506#204—64no—
507#204—62no—
508ΓL(1,𝔽25)—62no—
509ΓL(1,𝔽25)—62no—
510ΓL(1,𝔽25)—62no—
511ΓL(1,𝔽25)—62no—
512ΓL(1,𝔽25)—64no—
513C22×C32C22×D411yescharacteristic
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3#12012yes—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—22no—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3#13712yescomplemented
529D32—44no—
530D32—48no—
531C32×C4—22no—
532C32×C4—41no—
533C32×C4C22×D411yescharacteristic
534C32×C4C22×D411yescharacteristic
535C3⋊Dic3—41no—
536C3⋊Dic3#12012yes—
537C3×Dic3—21no—
538C3×Dic3—21no—
539C3×Dic3—22no—
540C3×Dic3—41no—
541C3×Dic3—41no—
542C2×#41—31no—
543C2×#41—91no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—181no—
547C2×#41—181no—
548C2×#41—184no—
549C2×#41—184no—
550C22×Q8—31no—
551C22×Q8—91no—
552C22×D4—91no—
553C22×D4—181no—
554C23×C4—91no—
555C23×C4—181no—
556#137—184no—
557#137—184no—
558C2×Q16—31no—
559C2×Q16—91no—
560C2×Q16—91no—
561C2×Q16D3211yescharacteristic, complemented
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×M16—91no—
567C2×M16—91no—
568C22⋊Q8—31no—
569C22⋊Q8—31no—
570C22⋊Q8—91no—
571C22⋊Q8—91no—
572C22⋊Q8—181no—
573C22⋊Q8—181no—
574C2×C4⋊C4—91no—
575C2×C4⋊C4—181no—
576C2×C22⋊C4—181no—
577#103—31no—
578#103—31no—
579#103—31no—
580#103—91no—
581#102—31no—
582#102—91no—
583#102—91no—
584#102—91no—
585C22⋊C8—31no—
586C22⋊C8—31no—
587C22⋊C8—91no—
588C22⋊C8—91no—
589C23×C3—31no—
590C23×C3—31no—
591C23×C3—61no—
592C22×D3—21no—
593C22×D3—31no—
594C22×D3—31no—
595C22×D3—61no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—62no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3D3×D411yescharacteristic
612C22×D3D3×D411yescharacteristic
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—22no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—21no—
619C3×Q8—21no—
620C3×Q8—22no—
621C3×Q8—32no—
622C3×Q8—41no—
623C3×Q8—41no—
624C3×Q8—64no—
625C3×Q8—61no—
626C3×Q8D3×D412yes—
627C3×Q8D3×D412yes—
628C3×D4—32no—
629C3×D4—64no—
630C3×D4—61no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—64no—
641C2×C3×C4—64no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651#67—64no—
652#67—64no—
653#67—64no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—61no—
660C2×Dic3—62no—
661C2×Dic3—64no—
662C2×Dic3—62no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—121no—
666C2×Dic3D3×D411yescharacteristic
667C2×Dic3D3×D411yescharacteristic
668D12—24no—
669D12—21no—
670D12—32no—
671D12—32no—
672D12—62no—
673D12—64no—
674D12—64no—
675D12—64no—
676D12—64no—
677D12—64no—
678D12—61no—
679D12—61no—
680D12—121no—
681D12—124no—
682D12D3×D412yes—
683C4×D3—24no—
684C4×D3—24no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—32no—
690C4×D3—32no—
691C4×D3—32no—
692C4×D3—32no—
693C4×D3—62no—
694C4×D3—62no—
695C4×D3—62no—
696C4×D3—62no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—62no—
702C4×D3—62no—
703C4×D3—64no—
704C4×D3—124no—
705C4×D3—122no—
706C4×D3—122no—
707C4×D3—122no—
708C4×D3—122no—
709C4×D3—124no—
710Dic6—24no—
711Dic6—21no—
712Dic6—62no—
713Dic6—61no—
714Dic6—61no—
715Dic6—61no—
716Dic6—61no—
717Dic6—121no—
718Dic6—122no—
719Dic6—122no—
720Dic6—124no—
721Dic6D3×D412yes—
722C3×C8—22no—
723C3×C8—21no—
724C3×C8—21no—
725C3×C8—61no—
726C3×C8—61no—
727C3⋊C8—21no—
728C3⋊C8—21no—
729C3⋊C8—62no—
730C3⋊C8—61no—
731C3⋊C8—61no—
732C2×C32C2×#12011yescharacteristic
733C2×C32C2×#13711yescharacteristic
734C2×C32#57511yescharacteristic
735C3⋊D3—22no—
736C3⋊D3—42no—
737C3×D3—22no—
738C3×D3—41no—
739C3×D3—42no—
740C24—91no—
741C24—181no—
742#41—62no—
743#41—62no—
744#41—94no—
745#41—94no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—182no—
750#41—182no—
751#41—188no—
752C2×Q8—31no—
753C2×Q8—61no—
754C2×Q8—62no—
755C2×Q8—62no—
756C2×Q8—91no—
757C2×Q8—181no—
758C2×Q8—182no—
759C2×Q8—182no—
760C2×Q8C2×D3211yescharacteristic
761C2×Q8C2×D3211yescharacteristic
762C2×D4—31no—
763C2×D4—61no—
764C2×D4—91no—
765C2×D4—181no—
766C2×D4—181no—
767C2×D4—182no—
768C2×D4—182no—
769C2×D4—188no—
770C2×D4—181no—
771C2×D4—181no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—91no—
780C22×C4—181no—
781C22×C4—181no—
782C22×C4—181no—
783C22×C4—182no—
784C22×C4—182no—
785C22×C4—188no—
786C22×C4—181no—
787C22×C4—181no—
788Q16—22no—
789Q16—62no—
790Q16—182no—
791Q16—182no—
792SD16—62no—
793SD16—182no—
794SD16—182no—
795SD16—182no—
796M16—182no—
797M16—182no—
798C2×C8—31no—
799C2×C8—31no—
800C2×C8—91no—
801C2×C8C2×D3211yescharacteristic
802C4⋊C4—31no—
803C4⋊C4—31no—
804C4⋊C4—61no—
805C4⋊C4—61no—
806C4⋊C4—181no—
807C4⋊C4—181no—
808C4⋊C4—181no—
809C22⋊C4—61no—
810C22⋊C4—61no—
811C22⋊C4—181no—
812C22⋊C4—181no—
813C22×C3—21no—
814C22×C3—32no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—62no—
820C22×C3—61no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—22no—
831C2×D3—32no—
832C2×D3—32no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—62no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—61no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—122no—
845C2×D3—124no—
846C2×D3—128no—
847C2×D3—124no—
848C2×D3—128no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—241no—
854C2×D3—241no—
855C2×D3#91812yescomplemented
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4—62no—
867C3×C4—121no—
868C3×C4—121no—
869C3×C4C2×D3×D411yescharacteristic
870C3×C4C2×D3×D411yescharacteristic
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873Dic3—21no—
874Dic3—22no—
875Dic3—21no—
876Dic3—32no—
877Dic3—32no—
878Dic3—41no—
879Dic3—41no—
880Dic3—62no—
881Dic3—122no—
882Dic3—121no—
883Dic3—121no—
884C32#300711yescharacteristic, complemented, Sylow
885C23—31no—
886C23—31no—
887C23—61no—
888C23—91no—
889C23—182no—
890C23—182no—
891C23—184no—
892C23—181no—
893C23—362no—
894C23—361no—
895C23—362no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—32no—
900Q8—64no—
901Q8—61no—
902Q8—181no—
903Q8—181no—
904Q8—362no—
905Q8#381112yes—
906D4—32no—
907D4—64no—
908D4—61no—
909D4—92no—
910D4—184no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—181no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—64no—
920C2×C4—64no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—91no—
929C2×C4—92no—
930C2×C4—92no—
931C2×C4—184no—
932C2×C4—182no—
933C2×C4—184no—
934C2×C4—182no—
935C2×C4—182no—
936C2×C4—184no—
937C2×C4—181no—
938C2×C4—362no—
939C2×C4—362no—
940C2×C4C22×D3211yescharacteristic
941C8—21no—
942C8—61no—
943C8—61no—
944C8—181no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—62no—
949C2×C3—121no—
950C2×C3—122no—
951C2×C3D3×#12011yescharacteristic
952C2×C3D3×#12011yescharacteristic
953C2×C3C2×#91811yescharacteristic
954C2×C3#576811yescharacteristic
955C2×C3D3×#13711yescharacteristic
956C2×C3#577711yescharacteristic
957D3—22no—
958D3—41no—
959D3—42no—
960D3—62no—
961D3—62no—
962D3—122no—
963D3—122no—
964D3—122no—
965D3—242no—
966C22—32no—
967C22—61no—
968C22—61no—
969C22—61no—
970C22—61no—
971C22—62no—
972C22—61no—
973C22—92no—
974C22—121no—
975C22—121no—
976C22—181no—
977C22—181no—
978C22—182no—
979C22—364no—
980C22—368no—
981C22—361no—
982C22—361no—
983C22D32×D411yescharacteristic
984C4—22no—
985C4—41no—
986C4—61no—
987C4—61no—
988C4—62no—
989C4—92no—
990C4—121no—
991C4—121no—
992C4—361no—
993C4D32×D411yescharacteristic
994C4C2×#381111yescharacteristic
995C3—21no—
996C3#8018411yescharacteristic, complemented
997C3#8022811yescharacteristic, complemented
998C2—62no—
999C2—121no—
1000C2—122no—
1001C2—182no—
1002C2—362no—
1003C2D3×#91811yescharacteristic
1004C2#1059476311yescharacteristic
1005C2#1059527811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×D3×#239C2
hypercenterC2×Q16D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#64127C2semidirect
3. #10595429C2semidirect
4. C2×#63951C2semidirect
5. C3×#5187C2semidirect
6. C3×#5186C2semidirect
7. #10591657C2semidirect
8. #10591651C2semidirect
9. #10591599C2semidirect
10. #10591595C2semidirect
11. #10591554C2semidirect
12. #10590970C2semidirect
13. #10590957C2semidirect
14. #10590946C2semidirect
15. #10590937C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
32. C2×C32×Q16C22semidirect
33. C2×#3756C22semidirect
34. C2×#3755C22semidirect
36. C2×#3744C22semidirect
37. C2×#3743C22semidirect
39. C3×#946C22semidirect
40. C2×C3×#216C22semidirect
41. C2×C3×#215C22semidirect
44. #63900C22semidirect
49. #63857C22semidirect
50. C2×#3719C22semidirect
51. C2×#3716C22semidirect
52. C2×#3712C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #5187D3semidirect
80. #5186D3semidirect
202. C2×C3×Q16C2×D3semidirect
203. C2×C3×Q16C2×D3semidirect
208. #946C2×D3semidirect
213. C2×#216C2×D3semidirect
217. C2×#215C2×D3semidirect
255. #835C2×D3semidirect
256. #835C2×D3semidirect
262. #821C2×D3semidirect
266. (C2×D3)⋊C8C2×D3semidirect
267. #816C2×D3semidirect
528. C2×C3×D3#137semidirect
561. C2×Q16D32semidirect
855. C2×D3#918semidirect
884. C32#3007semidirect
996. C3#80184semidirect
997. C3#80228semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#641272
#105954292
C2×#639512
C3×#51872
C3×#51862
#105916572
#105916512
#105915992
#105915952
#105915542
#105909702
#105909572
#105909462
#105909372
#802283
#801843