Finite Group Databasebeta

← #11864223

Subgroups — #11864223

Order 1152.

1582 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic
2C2×C3×#918C211yesmaximal, characteristic, complemented
3D3×#946C211yesmaximal, characteristic, complemented
4C2×#63946C211yesmaximal, characteristic, complemented
5#10592885C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591652C211yesmaximal, characteristic, complemented
9#10591603C211yesmaximal, characteristic, complemented
10#10591597C211yesmaximal, characteristic, complemented
11#10591550C211yesmaximal, characteristic, complemented
12#10590960C211yesmaximal, characteristic, complemented
13#10590943C211yesmaximal, characteristic, complemented
14#10590936C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#83981—31nomaximal
17#80228—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic, complemented
22#64319—24no—
23#64319—24no—
24C2×#3802—21no—
25C2×#3802C2211yescharacteristic
26C2×C4×D32—21no—
27C2×C4×D32C2211yescharacteristic
28C2×#3795—21no—
29C2×#3795—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic
34C2×#3756C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#215C2211yescharacteristic, complemented
39C3×#918—24no—
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42#63946—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×#3719C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63647C2211yescharacteristic
55#63643C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, 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×#918D311yescharacteristic, complemented
71C2×#915—31no—
72D3×C22⋊Q8—31no—
73C3×#452—31no—
74#5239—31no—
75#5232—31no—
76#5187—31no—
77#5187D311yescharacteristic, complemented
78#5186—31no—
79#5186—31no—
80#5186—31no—
81#5186—61no—
82#5173—31no—
83#5173—31no—
84#5169—31no—
85#5169—31no—
86#5169—31no—
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—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100Q8×C3⋊D3—22no—
101Q8×C3⋊D3—22no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×#634C2311yescharacteristic
106C3×#239—22no—
107C3×#239—22no—
108C3×#239—22no—
109C3×#239D414yes—
110C3×D3×Q8—22no—
111C3×D3×Q8—22no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
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×#625—21no—
124C2×#625—21no—
125C2×#625—21no—
126C2×#624D411yescharacteristic
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3D411yescharacteristic
131C2×D3×Dic3D411yescharacteristic
132#3802—28no—
133#3802—22no—
134#3802—22no—
135C4×D32—28no—
136C4×D32—22no—
137C4×D32—22no—
138#3795—28no—
139#3795—28no—
140#3795—22no—
141#3795—22no—
142#3795—22no—
143#3795D414yes—
144C32×Q16—22no—
145C2×C32×C8C2311yescharacteristic
146#3756—22no—
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C3×#216—22no—
152C3×#215—22no—
153C3×#215—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×ΓL(1,𝔽25)—22no—
161#3724—21no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3719—22no—
167#3715—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×#239C2×D311yescharacteristic
178C2×#239C2×D311yescharacteristic
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—61no—
182C2×D3×Q8C2×D311yescharacteristic, complemented
183C2×#237—31no—
184C2×#237—31no—
185C2×#237—61no—
186C2×#237—61no—
187C2×D3×D4—31no—
188C2×D3×D4—31no—
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—21no—
201C2×C3×Q16—31no—
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×Q16C2×D311yescharacteristic, complemented
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16—31no—
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×#216—31no—
220C2×#216—61no—
221C2×#216C2×D311yescharacteristic, complemented
222#942—64no—
223C2×#215—31no—
224C2×#215C2×D311yescharacteristic, complemented
225C2×#215C2×D311yescharacteristic, complemented
226C2×#214—31no—
227C2×(C2×D3)⋊C4—61no—
228C2×C4⋊Dic3—31no—
229#924—31no—
230C2×Dic3⋊C4—61no—
231C2×#208—31no—
232#918—24no—
233#915—64no—
234C2×Dic12—31no—
235C2×#204C2×D311yescharacteristic, complemented
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—61no—
250#835C2×D311yescharacteristic, complemented
251#832—31no—
252#832—31no—
253#832—31no—
254#830—31no—
255#821—31no—
256#821—31no—
257#821C2×D311yescharacteristic, complemented
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—61no—
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#816—31no—
267#816—31no—
268#816—61no—
269#810—31no—
270#809—31no—
271C22×C3⋊D3C2×D411yescharacteristic
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3C2×D411yescharacteristic
275C22×C3×D3C2×D411yescharacteristic
276C2×D32—24no—
277C2×D32—22no—
278C2×D32—22no—
279C2×D32—41no—
280C2×D32—42no—
281C2×D32—42no—
282C32×Q8—21no—
283C32×Q8—21no—
284C32×Q8—21no—
285C32×Q8C2×D412yes—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4C2411yescharacteristic
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3C2×D411yescharacteristic
292C4×C3⋊D3—24no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—21no—
295#634—24no—
296#634—21no—
297#634C2×D412yes—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C2×D411yescharacteristic
301C2×C3×Dic3C2×D411yescharacteristic
302C3×D12—24no—
303C3×D12—24no—
304C3×D12—21no—
305C3×D12—21no—
306C3×D12C2×D412yes—
307C3×D12C2×D412yes—
308C3×C4×D3—24no—
309C3×C4×D3—21no—
310C3×C4×D3—21no—
311C3×C4×D3—24no—
312C3×C4×D3—42no—
313C3×C4×D3C2×D412yes—
314C3×C4×D3C2×D412yes—
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6—42no—
318#625—24no—
319#625—24no—
320#625—24no—
321#624—22no—
322D3×Dic3—24no—
323D3×Dic3—22no—
324D3×Dic3—22no—
325D3×Dic3—24no—
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—
350C3×#41—34no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—62no—
354C2×C3×Q8—21no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8—61no—
358C2×C3×Q8—62no—
359C2×C3×Q8—62no—
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384#239—22no—
385#239—22no—
386#239—22no—
387#239#6714yes—
388D3×Q8—22no—
389D3×Q8—22no—
390D3×Q8—62no—
391D3×Q8—62no—
392D3×Q8—62no—
393D3×Q8—62no—
394D3×Q8—122no—
395D3×Q8—122no—
396#237—34no—
397#237—62no—
398#237—62no—
399#237—68no—
400#237—68no—
401#237—62no—
402D3×D4—62no—
403D3×D4—62no—
404D3×D4—68no—
405D3×D4—68no—
406D3×D4—62no—
407D3×D4—62no—
408#235—34no—
409#235—62no—
410#235—62no—
411#235—68no—
412#235—68no—
413#235—62no—
414C2×D12—21no—
415C2×D12—21no—
416C2×D12C22×D311yescharacteristic
417C2×D12C22×D311yescharacteristic
418C2×C4×D3—21no—
419C2×C4×D3—21no—
420C2×C4×D3—21no—
421C2×C4×D3—31no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—61no—
428C2×C4×D3—62no—
429C2×C4×D3—62no—
430C2×C4×D3—68no—
431C2×C4×D3—68no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—62no—
437C2×C4×D3—62no—
438C2×C4×D3—61no—
439C2×C4×D3—121no—
440C2×C4×D3C22×D311yescharacteristic
441C2×C4×D3C22×D311yescharacteristic
442C2×Dic6—21no—
443C2×Dic6—31no—
444C2×Dic6—31no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6—121no—
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—22no—
451C3×Q16—22no—
452C3×Q16—42no—
453C3×Q16—62no—
454C3×SD16—62no—
455C3×SD16—62no—
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—62no—
469#216—62no—
470#216—62no—
471#216—122no—
472#215—22no—
473#215—22no—
474#215—62no—
475#214—62no—
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—62no—
504#204—22no—
505ΓL(1,𝔽25)—22no—
506ΓL(1,𝔽25)—62no—
507C22×C32C22×D411yescharacteristic
508C2×C3⋊D3—21no—
509C2×C3⋊D3—21no—
510C2×C3⋊D3#13712yescomplemented
511C2×C3×D3—21no—
512C2×C3×D3—21no—
513C2×C3×D3—21no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3#12012yes—
523D32—44no—
524D32—48no—
525C32×C4—22no—
526C32×C4—41no—
527C32×C4C22×D411yescharacteristic
528C32×C4C22×D411yescharacteristic
529C3⋊Dic3—21no—
530C3⋊Dic3—22no—
531C3⋊Dic3—41no—
532C3×Dic3—21no—
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—91no—
554C2×Q16—91no—
555C2×Q16D3211yescharacteristic, complemented
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—91no—
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—31no—
584C23×C3—31no—
585C23×C3—61no—
586C23×C3—61no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—31no—
590C22×D3—31no—
591C22×D3—61no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—64no—
596C22×D3—64no—
597C22×D3—62no—
598C22×D3—121no—
599C22×D3—121no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3—122no—
604C22×D3D3×D411yescharacteristic
605C22×D3D3×D411yescharacteristic
606C3×Q8—21no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—21no—
610C3×Q8—21no—
611C3×Q8—21no—
612C3×Q8—22no—
613C3×Q8—41no—
614C3×Q8—41no—
615C3×Q8—41no—
616C3×Q8—61no—
617C3×Q8—61no—
618C3×Q8—122no—
619C3×Q8D3×D412yes—
620C3×Q8C2×#6712yes—
621C3×D4—32no—
622C3×D4—32no—
623C3×D4—64no—
624C3×D4—64no—
625C3×D4—61no—
626C3×D4—61no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—31no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—31no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—122no—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—64no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—64no—
652#67—64no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—61no—
658C2×Dic3—62no—
659C2×Dic3—64no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—64no—
663C2×Dic3—62no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—122no—
669C2×Dic3D3×D411yescharacteristic
670C2×Dic3D3×D411yescharacteristic
671D12—24no—
672D12—24no—
673D12—21no—
674D12—21no—
675D12D3×D412yes—
676D12C2×#6712yes—
677C4×D3—24no—
678C4×D3—21no—
679C4×D3—21no—
680C4×D3—24no—
681C4×D3—42no—
682C4×D3—62no—
683C4×D3—64no—
684C4×D3—64no—
685C4×D3—62no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—62no—
689C4×D3—61no—
690C4×D3—61no—
691C4×D3—61no—
692C4×D3—61no—
693C4×D3—62no—
694C4×D3—121no—
695C4×D3—121no—
696C4×D3—124no—
697C4×D3—122no—
698C4×D3D3×D412yes—
699C4×D3C2×#6712yes—
700Dic6—21no—
701Dic6—21no—
702Dic6—32no—
703Dic6—32no—
704Dic6—42no—
705Dic6—62no—
706Dic6—64no—
707Dic6—64no—
708Dic6—61no—
709Dic6—61no—
710Dic6—121no—
711Dic6—124no—
712C3×C8—21no—
713C3×C8—21no—
714C3×C8—41no—
715C3×C8—61no—
716C3×C8—61no—
717C3⋊C8—21no—
718C3⋊C8—21no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—121no—
722C2×C32C2×#12011yescharacteristic
723C2×C32C2×#13711yescharacteristic
724C2×C32#57511yescharacteristic
725C3⋊D3—22no—
726C3×D3—22no—
727C3×D3—41no—
728C3×D3—42no—
729C3×D3—42no—
730C24—91no—
731C24—181no—
732#41—34no—
733#41—62no—
734#41—62no—
735#41—62no—
736#41—94no—
737#41—182no—
738#41—182no—
739#41—182no—
740#41—188no—
741#41—188no—
742C2×Q8—31no—
743C2×Q8—61no—
744C2×Q8—62no—
745C2×Q8—62no—
746C2×Q8—91no—
747C2×Q8—181no—
748C2×Q8—182no—
749C2×Q8—182no—
750C2×Q8C2×D3211yescharacteristic
751C2×Q8C2×D3211yescharacteristic
752C2×D4—31no—
753C2×D4—31no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—181no—
757C2×D4—182no—
758C2×D4—182no—
759C2×D4—188no—
760C2×D4—181no—
761C2×D4—181no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—181no—
772C22×C4—182no—
773C22×C4—182no—
774C22×C4—181no—
775C22×C4—181no—
776C22×C4—188no—
777C22×C4—181no—
778Q16—22no—
779Q16—62no—
780Q16—182no—
781Q16—182no—
782SD16—62no—
783SD16—62no—
784SD16—62no—
785SD16—182no—
786M16—62no—
787M16—182no—
788C2×C8—31no—
789C2×C8—31no—
790C2×C8—91no—
791C2×C8C2×D3211yescharacteristic
792C4⋊C4—31no—
793C4⋊C4—61no—
794C4⋊C4—91no—
795C4⋊C4—181no—
796C4⋊C4—181no—
797C4⋊C4—181no—
798C4⋊C4—181no—
799C22⋊C4—61no—
800C22⋊C4—181no—
801C22⋊C4—181no—
802C22⋊C4—181no—
803C22×C3—21no—
804C22×C3—32no—
805C22×C3—61no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—62no—
810C22×C3—61no—
811C22×C3—62no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3C2×D3×D411yescharacteristic
817C22×C3C2×D3×D411yescharacteristic
818C2×D3—21no—
819C2×D3—21no—
820C2×D3—21no—
821C2×D3—21no—
822C2×D3—22no—
823C2×D3—21no—
824C2×D3—22no—
825C2×D3—32no—
826C2×D3—32no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—62no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—124no—
839C2×D3—124no—
840C2×D3—128no—
841C2×D3—128no—
842C2×D3#93712yes—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—32no—
848C3×C4—42no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—61no—
852C3×C4—81no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4C2×D3×D411yescharacteristic
856C3×C4C2×D3×D411yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858C3×C4C22×#6711yescharacteristic
859Dic3—21no—
860Dic3—41no—
861Dic3—41no—
862Dic3—62no—
863Dic3—61no—
864Dic3—62no—
865Dic3—61no—
866Dic3—122no—
867Dic3—121no—
868Dic3—121no—
869Dic3—121no—
870Dic3—241no—
871Dic3#93712yes—
872C32#300711yescharacteristic, complemented, Sylow
873C23—31no—
874C23—31no—
875C23—61no—
876C23—61no—
877C23—91no—
878C23—182no—
879C23—182no—
880C23—184no—
881C23—361no—
882C23—362no—
883C23—362no—
884Q8—21no—
885Q8—21no—
886Q8—21no—
887Q8—61no—
888Q8—61no—
889Q8—92no—
890Q8—122no—
891Q8—184no—
892Q8—181no—
893Q8D3×#6712yes—
894D4—32no—
895D4—32no—
896D4—64no—
897D4—64no—
898D4—61no—
899D4—61no—
900D4—184no—
901D4—184no—
902D4—184no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—31no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—31no—
909C2×C4—64no—
910C2×C4—64no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—91no—
916C2×C4—122no—
917C2×C4—184no—
918C2×C4—182no—
919C2×C4—182no—
920C2×C4—184no—
921C2×C4—182no—
922C2×C4—184no—
923C2×C4—181no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—362no—
928C2×C4C22×D3211yescharacteristic
929C8—21no—
930C8—61no—
931C8—61no—
932C8—181no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—62no—
937C2×C3—121no—
938C2×C3—122no—
939C2×C3—122no—
940C2×C3D3×#12011yescharacteristic
941C2×C3#576811yescharacteristic
942C2×C3D3×#13711yescharacteristic
943C2×C3D3×#13711yescharacteristic
944C2×C3#577711yescharacteristic
945C2×C3C2×#93711yescharacteristic
946D3—22no—
947D3—42no—
948D3—41no—
949D3—42no—
950D3—62no—
951D3—62no—
952D3—122no—
953C22—32no—
954C22—61no—
955C22—61no—
956C22—61no—
957C22—61no—
958C22—62no—
959C22—62no—
960C22—61no—
961C22—92no—
962C22—121no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—181no—
967C22—181no—
968C22—364no—
969C22—368no—
970C22D32×D411yescharacteristic
971C4—22no—
972C4—32no—
973C4—41no—
974C4—61no—
975C4—121no—
976C4—121no—
977C4—181no—
978C4—182no—
979C4—361no—
980C4D32×D411yescharacteristic
981C4C2×D3×#6711yescharacteristic
982C3—21no—
983C3#8022811yescharacteristic, complemented
984C3#8398111yescharacteristic, complemented
985C2—62no—
986C2—121no—
987C2—122no—
988C2—122no—
989C2—182no—
990C2#1059476011yescharacteristic
991C2#1059476311yescharacteristic
992C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#64319C2
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×C3×#918C2semidirect
3. D3×#946C2semidirect
4. C2×#63946C2semidirect
5. #10592885C2semidirect
6. C3×#5187C2semidirect
7. #10591655C2semidirect
8. #10591652C2semidirect
9. #10591603C2semidirect
10. #10591597C2semidirect
11. #10591550C2semidirect
12. #10590960C2semidirect
13. #10590943C2semidirect
14. #10590936C2semidirect
15. #10590670C2semidirect
21. C2×C3×D3×Q8C22semidirect
32. C2×C32×Q16C22semidirect
34. C2×#3756C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
40. C2×C3×#204C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
44. D3×C4⋊Dic3C22semidirect
49. #63856C22semidirect
50. C2×#3719C22semidirect
51. C2×#3715C22semidirect
52. C2×#3711C22semidirect
53. #63662C22semidirect
55. #63643C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63567C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×#918D3semidirect
77. #5187D3semidirect
182. C2×D3×Q8C2×D3semidirect
202. C2×C3×Q16C2×D3semidirect
203. C2×C3×Q16C2×D3semidirect
216. #946C2×D3semidirect
221. C2×#216C2×D3semidirect
224. C2×#215C2×D3semidirect
225. C2×#215C2×D3semidirect
235. C2×#204C2×D3semidirect
237. C2×ΓL(1,𝔽25)C2×D3semidirect
250. #835C2×D3semidirect
257. #821C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
510. C2×C3⋊D3#137semidirect
555. C2×Q16D32semidirect
872. C32#3007semidirect
983. C3#80228semidirect
984. C3#83981semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×C3×#9182
D3×#9462
C2×#639462
#105928852
C3×#51872
#105916552
#105916522
#105916032
#105915972
#105915502
#105909602
#105909432
#105909362
#105906702
#839813
#802283