Finite Group Databasebeta

← #11864194

Subgroups — #11864194

Order 1152.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic
2C2×C3×#915C211yesmaximal, characteristic, complemented
3D3×#946C211yesmaximal, characteristic, complemented
4C2×#63948C211yesmaximal, characteristic, complemented
5#10592868C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591654C211yesmaximal, characteristic, complemented
9#10591467C211yesmaximal, characteristic, complemented
10#10591461C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12#10590966C211yesmaximal, characteristic, complemented
13#10590950C211yesmaximal, characteristic, complemented
14#10590936C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#83981—31nomaximal
17#80228—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic
22C2×#3811—21no—
23C22×#624—21no—
24C2×#3804—21no—
25C2×#3804—21no—
26#64312—24no—
27#64312—24no—
28C2×C4×D32C2211yescharacteristic
29C2×#3799C2211yescharacteristic
30C2×#3799C2211yescharacteristic
31C2×#3797C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#216C2211yescharacteristic, complemented
38C2×C3×#214C2211yescharacteristic, complemented
39C3×#915—24no—
40C2×C3×Dic12C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42#63948—24no—
43D3×(C2×D3)⋊C4—21no—
44D3×C4⋊Dic3C2211yescharacteristic, complemented
45#63888—21no—
46#63887—21no—
47D3×Dic3⋊C4—21no—
48#63871C2211yescharacteristic
49#63856C2211yescharacteristic, complemented
50C2×#3718C2211yescharacteristic, complemented
51C2×#3717C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×C3×#137—31no—
68C2×#946—31no—
69C2×#942—31no—
70C2×#918—31no—
71C2×#915D311yescharacteristic, complemented
72D3×C22⋊Q8—31no—
73C3×#452—31no—
74#5239—31no—
75#5232—31no—
76#5187—31no—
77#5187—31no—
78#5186—31no—
79#5186—31no—
80#5186—31no—
81#5173—31no—
82#5173D311yescharacteristic, complemented
83#5169—31no—
84#5169—31no—
85#5169—31no—
86#5169—61no—
87#5133—31no—
88#5126—31no—
89#5047—31no—
90#4809—31no—
91#4803—31no—
92#4776—31no—
93#4771—31no—
94#4733—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3—22no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×D3×Q8—22no—
110C3×D3×Q8—22no—
111C3×#237—22no—
112C3×#237—22no—
113C3×#237—22no—
114C3×#237D414yes—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122#3811—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#624—28no—
127C2×#624—21no—
128C2×#624—21no—
129C2×#624—21no—
130C2×#624D411yescharacteristic
131#3804—28no—
132#3804—28no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3D411yescharacteristic
135C2×D3×Dic3D411yescharacteristic
136C4×D32—22no—
137C4×D32—22no—
138#3799—22no—
139#3799—22no—
140#3799—22no—
141#3799D414yes—
142#3797—22no—
143#3797—22no—
144C32×SD16—22no—
145C2×C32×C8C2311yescharacteristic
146#3755—22no—
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C3×#216—22no—
152C3×#216—22no—
153C3×#214—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×Dic12—22no—
160C3×ΓL(1,𝔽25)—22no—
161#3724—21no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3718—22no—
167#3717—22no—
168#3711—22no—
169#3007—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×Q8—31no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8C2×D311yescharacteristic, complemented
182C2×#237—61no—
183C2×#237—61no—
184C2×#237C2×D311yescharacteristic
185C2×#237C2×D311yescharacteristic
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C3×#137—64no—
200C2×C3×Q16—31no—
201C2×C3×Q16—31no—
202C2×C3×Q16—31no—
203C2×C3×SD16—21no—
204C2×C3×SD16—31no—
205C2×C3×SD16C2×D311yescharacteristic, complemented
206C2×C3×SD16C2×D311yescharacteristic, complemented
207C2×C3×M16—31no—
208C3×C22⋊Q8—31no—
209#946—31no—
210#946—31no—
211#946—31no—
212#946—31no—
213#946—61no—
214#946—61no—
215#946—61no—
216#946C2×D311yescharacteristic, complemented
217C2×#216—31no—
218C2×#216—31no—
219C2×#216C2×D311yescharacteristic, complemented
220C2×#216C2×D311yescharacteristic, complemented
221#942—64no—
222C2×#215—31no—
223C2×#215—31no—
224C2×#215—31no—
225C2×#215—61no—
226C2×#214C2×D311yescharacteristic, complemented
227C2×(C2×D3)⋊C4—61no—
228C2×C4⋊Dic3—31no—
229#924—31no—
230C2×Dic3⋊C4—61no—
231C2×#208—31no—
232#918—64no—
233#915—24no—
234C2×Dic12C2×D311yescharacteristic, complemented
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
238#897—31no—
239#896—61no—
240D3×C4⋊C4—31no—
241D3×C4⋊C4—61no—
242D3×C22⋊C4—61no—
243#878—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—31no—
250#832—31no—
251#832—31no—
252#832—61no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256#821—31no—
257#821—31no—
258#821—61no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—61no—
265(C2×D3)⋊C8C2×D311yescharacteristic, complemented
266#816—31no—
267#816—31no—
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#809—31no—
271C23×C32—21no—
272C22×C3⋊D3—24no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3—42no—
275C22×C3⋊D3—42no—
276C22×C3⋊D3C2×D411yescharacteristic
277C22×C3×D3C2×D411yescharacteristic
278C22×C3×D3C2×D411yescharacteristic
279C2×D32—22no—
280C2×D32—22no—
281C2×D32—41no—
282C32×Q8—21no—
283C32×Q8—21no—
284C32×D4—21no—
285C32×D4C2×D412yes—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288#638—24no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3C2×D411yescharacteristic
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)C2×D412yes—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—21no—
295C3×#67—24no—
296C3×#67—24no—
297C2×C3×Dic3—24no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×C4×D3—21no—
306C3×C4×D3—21no—
307C3×C4×D3—42no—
308C3×C4×D3C2×D412yes—
309C3×C4×D3C2×D412yes—
310C3×Dic6—21no—
311C3×Dic6—21no—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6—42no—
315C3×Dic6C2×D412yes—
316C3×Dic6C2×D412yes—
317#627—24no—
318#626—24no—
319#626—24no—
320#624—24no—
321#624—24no—
322#624—24no—
323#624—22no—
324D3×Dic3—22no—
325D3×Dic3—22no—
326D3×Dic3—42no—
327C32×C8—21no—
328C3⋊(C3⋊C8)—21no—
329C3×C3⋊C8—21no—
330C3×C3⋊C8—21no—
331C22×#41—91no—
332C2×#137—31no—
333C2×#137—91no—
334C2×C22⋊Q8—91no—
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—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3—121no—
351C3×#41—34no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8—31no—
358C2×C3×Q8—31no—
359C2×C3×Q8—61no—
360C2×C3×Q8—62no—
361C2×C3×Q8—62no—
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×D4—21no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D311yescharacteristic
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—121no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386#239—34no—
387#239—62no—
388#239—62no—
389#239—62no—
390D3×Q8—22no—
391D3×Q8—22no—
392D3×Q8—62no—
393D3×Q8—62no—
394D3×Q8—62no—
395D3×Q8—62no—
396#237—22no—
397#237—22no—
398#237—22no—
399#237—68no—
400#237—68no—
401#237#6714yes—
402D3×D4—62no—
403D3×D4—62no—
404D3×D4—68no—
405D3×D4—68no—
406D3×D4—62no—
407D3×D4—62no—
408D3×D4—122no—
409D3×D4—122no—
410#235—34no—
411#235—62no—
412#235—62no—
413#235—68no—
414#235—68no—
415#235—62no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—61no—
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—61no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—68no—
436C2×C4×D3—68no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—61no—
442C2×C4×D3C22×D311yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×Dic6—21no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6C22×D311yescharacteristic
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×Q16—62no—
452C3×Q16—62no—
453C3×SD16—22no—
454C3×SD16—22no—
455C3×SD16—42no—
456C3×SD16—62no—
457C3×M16—62no—
458C2×C3×C8—21no—
459C2×C3×C8—31no—
460C2×C3×C8—31no—
461C2×C3×C8C22×D311yescharacteristic
462C2×C3×C8C22×D311yescharacteristic
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C22⋊C4—61no—
466#217—61no—
467#216—22no—
468#216—22no—
469#216—62no—
470#216—62no—
471#215—62no—
472#215—62no—
473#215—62no—
474#215—122no—
475#214—22no—
476(C2×D3)⋊C4—21no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—121no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—61no—
488C4⋊Dic3C22×D311yescharacteristic
489Dic3⋊C4—21no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—121no—
497#208—62no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8C22×D311yescharacteristic
502C2×C3⋊C8C22×D311yescharacteristic
503Dic12—22no—
504#204—62no—
505ΓL(1,𝔽25)—22no—
506ΓL(1,𝔽25)—62no—
507C22×C32—22no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32C22×D411yescharacteristic
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—48no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3#13712yescomplemented
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3#12012yes—
524D32—44no—
525C32×C4—41no—
526C32×C4C22×D411yescharacteristic
527C32×C4C22×D411yescharacteristic
528C3⋊Dic3—21no—
529C3⋊Dic3—41no—
530C3×Dic3—21no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3#12012yes—
536C2×#41—31no—
537C2×#41—31no—
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—91no—
549C23×C4—181no—
550#137—64no—
551#137—184no—
552C2×Q16—31no—
553C2×Q16—31no—
554C2×Q16—31no—
555C2×Q16—91no—
556C2×SD16—31no—
557C2×SD16—91no—
558C2×SD16—91no—
559C2×SD16D3211yescharacteristic, complemented
560C2×M16—31no—
561C2×M16—91no—
562C22⋊Q8—31no—
563C22⋊Q8—91no—
564C22⋊Q8—91no—
565C22⋊Q8—91no—
566C22⋊Q8—181no—
567C22⋊Q8—181no—
568C2×C4⋊C4—91no—
569C2×C4⋊C4—181no—
570C2×C22⋊C4—181no—
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—21no—
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—41no—
588C22×D3—31no—
589C22×D3—31no—
590C22×D3—61no—
591C22×D3—62no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—64no—
595C22×D3—64no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—62no—
599C22×D3—121no—
600C22×D3—124no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—122no—
604C22×D3—122no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—242no—
608C22×D3—242no—
609C22×D3D3×D411yescharacteristic
610C22×D3D3×D411yescharacteristic
611C3×Q8—21no—
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—32no—
616C3×Q8—32no—
617C3×Q8—41no—
618C3×Q8—41no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8—61no—
623C3×Q8—122no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—22no—
627C3×D4—41no—
628C3×D4—64no—
629C3×D4—64no—
630C3×D4D3×D412yes—
631C3×D4C2×#6712yes—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—31no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—31no—
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—122no—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651#67—24no—
652#67—24no—
653#67—64no—
654#67—64no—
655#67—64no—
656#67—64no—
657#67—124no—
658C2×Dic3—24no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—24no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—61no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—121no—
672C2×Dic3—122no—
673C2×Dic3D3×D411yescharacteristic
674C2×Dic3D3×D411yescharacteristic
675D12—32no—
676D12—32no—
677D12—62no—
678D12—64no—
679D12—64no—
680D12—61no—
681D12—61no—
682D12—121no—
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—42no—
686C4×D3—62no—
687C4×D3—64no—
688C4×D3—64no—
689C4×D3—64no—
690C4×D3—64no—
691C4×D3—64no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—61no—
695C4×D3—61no—
696C4×D3—61no—
697C4×D3—61no—
698C4×D3—62no—
699C4×D3—64no—
700C4×D3—121no—
701C4×D3—121no—
702C4×D3—122no—
703C4×D3D3×D412yes—
704C4×D3C2×#6712yes—
705Dic6—21no—
706Dic6—21no—
707Dic6—21no—
708Dic6—21no—
709Dic6—42no—
710Dic6—64no—
711Dic6—64no—
712Dic6D3×D412yes—
713Dic6C2×#6712yes—
714C3×C8—21no—
715C3×C8—21no—
716C3×C8—41no—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—121no—
724C2×C32—42no—
725C2×C32C2×#12011yescharacteristic
726C2×C32C2×#13711yescharacteristic
727C2×C32#57511yescharacteristic
728C3⋊D3—22no—
729C3⋊D3—42no—
730C3×D3—22no—
731C3×D3—41no—
732C24—91no—
733C24—181no—
734#41—34no—
735#41—62no—
736#41—62no—
737#41—62no—
738#41—94no—
739#41—182no—
740#41—188no—
741#41—188no—
742#41—182no—
743#41—182no—
744C2×Q8—31no—
745C2×Q8—31no—
746C2×Q8—31no—
747C2×Q8—61no—
748C2×Q8—62no—
749C2×Q8—62no—
750C2×Q8—181no—
751C2×Q8—182no—
752C2×Q8—182no—
753C2×Q8C2×D3211yescharacteristic
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—91no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—182no—
761C2×D4—188no—
762C2×D4—182no—
763C2×D4C2×D3211yescharacteristic
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—182no—
774C22×C4—182no—
775C22×C4—181no—
776C22×C4—181no—
777C22×C4—181no—
778C22×C4—188no—
779C22×C4—181no—
780Q16—62no—
781Q16—62no—
782Q16—62no—
783Q16—182no—
784SD16—22no—
785SD16—62no—
786SD16—182no—
787SD16—182no—
788M16—62no—
789M16—182no—
790C2×C8—31no—
791C2×C8—31no—
792C2×C8—91no—
793C2×C8C2×D3211yescharacteristic
794C4⋊C4—31no—
795C4⋊C4—61no—
796C4⋊C4—91no—
797C4⋊C4—181no—
798C4⋊C4—181no—
799C4⋊C4—181no—
800C4⋊C4—181no—
801C22⋊C4—61no—
802C22⋊C4—181no—
803C22⋊C4—181no—
804C22⋊C4—181no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—21no—
808C22×C3—32no—
809C22×C3—42no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3C2×D3×D411yescharacteristic
822C22×C3C2×D3×D411yescharacteristic
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—32no—
829C2×D3—32no—
830C2×D3—62no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—122no—
840C2×D3—124no—
841C2×D3—124no—
842C2×D3—128no—
843C2×D3—128no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—248no—
849C2×D3—241no—
850C2×D3—241no—
851C2×D3#93712yes—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—32no—
855C3×C4—41no—
856C3×C4—41no—
857C3×C4—62no—
858C3×C4—61no—
859C3×C4—62no—
860C3×C4—81no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4C2×D3×D411yescharacteristic
864C3×C4C2×D3×D411yescharacteristic
865C3×C4C2×D3×D411yescharacteristic
866C3×C4C22×#6711yescharacteristic
867Dic3—22no—
868Dic3—22no—
869Dic3—21no—
870Dic3—41no—
871Dic3—41no—
872Dic3—61no—
873Dic3—61no—
874Dic3—121no—
875Dic3—121no—
876Dic3—121no—
877Dic3—241no—
878Dic3#93712yes—
879C32#300711yescharacteristic, complemented, Sylow
880C23—21no—
881C23—31no—
882C23—31no—
883C23—91no—
884C23—184no—
885C23—182no—
886C23—182no—
887C23—181no—
888C23—362no—
889C23—362no—
890C23—361no—
891Q8—21no—
892Q8—21no—
893Q8—32no—
894Q8—32no—
895Q8—61no—
896Q8—61no—
897Q8—61no—
898Q8—61no—
899Q8—122no—
900Q8—184no—
901D4—21no—
902D4—64no—
903D4—64no—
904D4—92no—
905D4—184no—
906D4—184no—
907D4—184no—
908D4—181no—
909D4D3×#6712yes—
910C2×C4—21no—
911C2×C4—31no—
912C2×C4—32no—
913C2×C4—32no—
914C2×C4—31no—
915C2×C4—64no—
916C2×C4—64no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—91no—
924C2×C4—122no—
925C2×C4—182no—
926C2×C4—184no—
927C2×C4—182no—
928C2×C4—184no—
929C2×C4—184no—
930C2×C4—182no—
931C2×C4—181no—
932C2×C4—181no—
933C2×C4—181no—
934C2×C4—362no—
935C2×C4C22×D3211yescharacteristic
936C8—21no—
937C8—61no—
938C8—61no—
939C8—181no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—62no—
946C2×C3—82no—
947C2×C3—121no—
948C2×C3D3×#12011yescharacteristic
949C2×C3#576811yescharacteristic
950C2×C3D3×#13711yescharacteristic
951C2×C3D3×#13711yescharacteristic
952C2×C3#577711yescharacteristic
953C2×C3C2×#93711yescharacteristic
954D3—22no—
955D3—41no—
956D3—62no—
957D3—62no—
958D3—122no—
959D3—122no—
960D3—122no—
961D3—242no—
962C22—22no—
963C22—32no—
964C22—41no—
965C22—41no—
966C22—61no—
967C22—61no—
968C22—61no—
969C22—61no—
970C22—61no—
971C22—92no—
972C22—181no—
973C22—181no—
974C22—182no—
975C22—368no—
976C22—364no—
977C22—361no—
978C22—361no—
979C22D32×D411yescharacteristic
980C4—32no—
981C4—41no—
982C4—61no—
983C4—62no—
984C4—62no—
985C4—121no—
986C4—121no—
987C4—181no—
988C4—361no—
989C4D32×D411yescharacteristic
990C4C2×D3×#6711yescharacteristic
991C3—21no—
992C3#8022811yescharacteristic, complemented
993C3#8398111yescharacteristic, complemented
994C2—42no—
995C2—62no—
996C2—121no—
997C2—182no—
998C2—362no—
999C2#1059474211yescharacteristic
1000C2#1059474611yescharacteristic
1001C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×#64312C2
hypercenterC2×SD16D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#915C2semidirect
3. D3×#946C2semidirect
4. C2×#63948C2semidirect
5. #10592868C2semidirect
6. C3×#5173C2semidirect
7. #10591657C2semidirect
8. #10591654C2semidirect
9. #10591467C2semidirect
10. #10591461C2semidirect
11. #10591414C2semidirect
12. #10590966C2semidirect
13. #10590950C2semidirect
14. #10590936C2semidirect
15. #10590671C2semidirect
19. C2×C3×D3×Q8C22semidirect
32. C2×C32×SD16C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#216C22semidirect
38. C2×C3×#214C22semidirect
40. C2×C3×Dic12C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
44. D3×C4⋊Dic3C22semidirect
49. #63856C22semidirect
50. C2×#3718C22semidirect
51. C2×#3717C22semidirect
52. C2×#3711C22semidirect
53. #63659C22semidirect
54. #63648C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×#915D3semidirect
82. #5173D3semidirect
181. C2×D3×Q8C2×D3semidirect
205. C2×C3×SD16C2×D3semidirect
206. C2×C3×SD16C2×D3semidirect
216. #946C2×D3semidirect
219. C2×#216C2×D3semidirect
220. C2×#216C2×D3semidirect
226. C2×#214C2×D3semidirect
234. C2×Dic12C2×D3semidirect
237. C2×ΓL(1,𝔽25)C2×D3semidirect
253. #832C2×D3semidirect
265. (C2×D3)⋊C8C2×D3semidirect
268. #816C2×D3semidirect
517. C2×C3⋊D3#137semidirect
559. C2×SD16D32semidirect
879. C32#3007semidirect
992. C3#80228semidirect
993. C3#83981semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×C3×#9152
D3×#9462
C2×#639482
#105928682
C3×#51732
#105916572
#105916542
#105914672
#105914612
#105914142
#105909662
#105909502
#105909362
#105906712
#839813
#802283