Finite Group Databasebeta

← #11864233

Subgroups — #11864233

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
2D3×#924C211yesmaximal, characteristic, complemented
3C2×#63801C211yesmaximal, characteristic, complemented
4C2×#63800C211yesmaximal, characteristic, complemented
5#10592432C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×#4726C211yesmaximal, characteristic, complemented
8#10591184C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10590952C211yesmaximal, characteristic, complemented
11#10590949C211yesmaximal, characteristic, complemented
12#10590946C211yesmaximal, characteristic, complemented
13#10590942C211yesmaximal, characteristic, complemented
14#10590671C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#80228—31nomaximal
17#78640—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3804—21no—
23D3×#235—24no—
24D3×#235—24no—
25C2×D3×D12C2211yescharacteristic
26C2×C4×D32—21no—
27C2×#3799C2211yescharacteristic
28C2×#3798—21no—
29C2×#3795C2211yescharacteristic
30C2×D3×Dic6C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic, complemented
32#64133C2211yescharacteristic, complemented
33C2×#3746C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
40D3×#217—21no—
41#63964—21no—
42D3×C4⋊Dic3C2211yescharacteristic, complemented
43D3×Dic3⋊C4—21no—
44#63857C2211yescharacteristic
45#63856C2211yescharacteristic
46#63851—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic, complemented
51#63801—24no—
52#63800—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×(C2×D3)⋊C8C2211yescharacteristic
60C3×#816C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63#63564C2211yescharacteristic, complemented
64#63563C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#235—31no—
67C2×#924—31no—
68C2×#918—31no—
69C2×#915—31no—
70C2×#909—31no—
71C2×#909—31no—
72D3×C22⋊Q8—31no—
73C3×#452—31no—
74C3×#407—31no—
75#5239—31no—
76#5186—31no—
77#5169—31no—
78#5133—31no—
79#5133—31no—
80#5047—31no—
81#4809—31no—
82#4803—31no—
83#4776—31no—
84#4771—31no—
85#4739—31no—
86#4739—31no—
87#4733—31no—
88#4733—31no—
89#4733—31no—
90#4733—31no—
91#4733—61no—
92#4733D311yescharacteristic, complemented
93#4731—31no—
94#4731—31no—
95#4726D311yescharacteristic, complemented
96C23×C3×D3D411yescharacteristic
97C22×D32—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100#3828—22no—
101#3828—22no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×#634C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C22×C3×Dic3D411yescharacteristic
108C3×#235—22no—
109C3×#235—22no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3D411yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120D3×#67—28no—
121C2×#627—21no—
122C2×#627—21no—
123C2×#626—21no—
124C2×#626—21no—
125C2×#625—21no—
126C2×#624—21no—
127#3804—28no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132D3×D12—22no—
133D3×D12—22no—
134C4×D32—28no—
135#3799—22no—
136#3799D414yes—
137#3798—28no—
138#3795—22no—
139#3795D414yes—
140D3×Dic6—22no—
141D3×Dic6—22no—
142D3×Dic6—22no—
143D3×Dic6—22no—
144C2×C32×C8C2311yescharacteristic
145C2×C32×C8C2311yescharacteristic
146#3757—21no—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148#3750—21no—
149#3746—22no—
150#3744—22no—
151C3×#217—21no—
152C3×C4⋊Dic3C2311yescharacteristic
153C3×Dic3⋊C4—21no—
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156C3×Dic12—22no—
157C3×#204—22no—
158C3×ΓL(1,𝔽25)—22no—
159C3×ΓL(1,𝔽25)—22no—
160#3724—21no—
161Dic3⋊Dic3—21no—
162Dic3⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165#3719—22no—
166#3719—22no—
167#3717—22no—
168#3716—22no—
169#3007—91noSylow
170C2×C3×#41—31no—
171C23×C3×C4—31no—
172C22×#67—61no—
173D3×#41—64no—
174D3×#41—64no—
175C2×#239—31no—
176C2×D3×Q8—31no—
177C2×D3×Q8—31no—
178C2×#237—31no—
179C2×#237—61no—
180C2×D3×D4—31no—
181C2×D3×D4—61no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—31no—
186C2×#235—61no—
187C2×#235—61no—
188C2×#235—64no—
189C2×#235—64no—
190C2×#235—61no—
191C2×#235—61no—
192C2×#235C2×D311yescharacteristic
193C22×D12—31no—
194C22×C4×D3—61no—
195C22×C4×D3—61no—
196C22×C4×D3C2×D311yescharacteristic
197C22×Dic6—31no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C2×C3×M16—31no—
203C3×C22⋊Q8—31no—
204C2×#217—61no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#215—31no—
209C2×#214—31no—
210C2×C4⋊Dic3—31no—
211#924—31no—
212#924—31no—
213#924—31no—
214#924—31no—
215#924—61no—
216#924—61no—
217#924—61no—
218#924C2×D311yescharacteristic, complemented
219C2×Dic3⋊C4—61no—
220#918—64no—
221#915—64no—
222#909—64no—
223#909—64no—
224C2×Dic12—31no—
225C2×Dic12—31no—
226C2×Dic12—31no—
227C2×Dic12—31no—
228C2×Dic12—61no—
229C2×Dic12C2×D311yescharacteristic, complemented
230C2×#204—31no—
231C2×#204—31no—
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—61no—
235C2×#204C2×D311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
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—21no—
247C3×C22⋊C8—31no—
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250C3×C22⋊C8C2×D311yescharacteristic, complemented
251C3×C22⋊C8C2×D311yescharacteristic, complemented
252#835—31no—
253#832—31no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—61no—
260#821C2×D311yescharacteristic, complemented
261(C2×D3)⋊C8C2×D311yescharacteristic
262(C2×D3)⋊C8C2×D311yescharacteristic
263#816—31no—
264#816—31no—
265#816—31no—
266#816—31no—
267#816—61no—
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#809—31no—
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—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4C2×D411yescharacteristic
285C2×C32×C4C2411yescharacteristic
286#638—24no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)C2×D412yes—
292C4×C3⋊D3—24no—
293#634—21no—
294#634—21no—
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×D3C2×D412yes—
312C3×C4×D3C2×D412yes—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317#627—24no—
318#627—42no—
319#626—24no—
320#626—24no—
321#625—24no—
322#624—24no—
323D3×Dic3—24no—
324D3×Dic3—24no—
325D3×Dic3—42no—
326D3×Dic3—42no—
327C32×C8—21no—
328C32×C8—21no—
329C3×C3⋊C8—21no—
330C3×C3⋊C8—21no—
331C22×#41—91no—
332C2×#137—91no—
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—31no—
346C24×C3—31no—
347C23×D3—61no—
348C23×D3—61no—
349C23×D3D1211yescharacteristic
350C3×#41—62no—
351C3×#41—62no—
352C2×C3×Q8—31no—
353C2×C3×Q8—31no—
354C2×C3×D4—31no—
355C2×C3×D4—61no—
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—61no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C2×#67—21no—
368C2×#67—61no—
369C2×#67—68no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—121no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3D1211yescharacteristic
381#239—34no—
382#239—62no—
383D3×Q8—62no—
384D3×Q8—62no—
385D3×Q8—62no—
386D3×Q8—62no—
387#237—34no—
388#237—68no—
389#237—62no—
390D3×D4—62no—
391D3×D4—62no—
392D3×D4—68no—
393#235—22no—
394#235—22no—
395#235—34no—
396#235—34no—
397#235—62no—
398#235—62no—
399#235—62no—
400#235—68no—
401#235—68no—
402#235—62no—
403#235—62no—
404#235—62no—
405#235—68no—
406#235—122no—
407#235—122no—
408C2×D12—31no—
409C2×D12—31no—
410C2×D12—61no—
411C2×D12—62no—
412C2×D12—61no—
413C2×D12—61no—
414C2×D12—62no—
415C2×D12C22×D311yescharacteristic
416C2×C4×D3—21no—
417C2×C4×D3—22no—
418C2×C4×D3—22no—
419C2×C4×D3—68no—
420C2×C4×D3—68no—
421C2×C4×D3—61no—
422C2×C4×D3—61no—
423C2×C4×D3—61no—
424C2×C4×D3—61no—
425C2×C4×D3—61no—
426C2×C4×D3—61no—
427C2×C4×D3—61no—
428C2×C4×D3—61no—
429C2×C4×D3—121no—
430C2×C4×D3D1211yescharacteristic
431C2×C4×D3D1211yescharacteristic
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D311yescharacteristic
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C2×Dic6—61no—
439C2×Dic6—61no—
440C2×Dic6—62no—
441C2×Dic6—62no—
442C2×Dic6—62no—
443C2×Dic6—61no—
444C2×Dic6—61no—
445C2×Dic6—62no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×SD16—62no—
452C3×M16—62no—
453C3×M16—62no—
454C2×C3×C8—21no—
455C2×C3×C8—21no—
456C2×C3×C8—31no—
457C2×C3×C8—31no—
458C2×C3×C8C22×D311yescharacteristic
459C2×C3×C8C22×D311yescharacteristic
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C3×C4⋊C4—31no—
463C3×C4⋊C4—61no—
464C3×C22⋊C4—61no—
465#217—21no—
466#217—61no—
467#217—61no—
468#217—61no—
469#217—61no—
470#217—121no—
471#216—62no—
472#216—62no—
473#215—62no—
474#214—62no—
475(C2×D3)⋊C4—61no—
476(C2×D3)⋊C4—61no—
477C4⋊Dic3—31no—
478C4⋊Dic3—31no—
479C4⋊Dic3—61no—
480C4⋊Dic3—61no—
481C4⋊Dic3—61no—
482C4⋊Dic3C22×D311yescharacteristic
483Dic3⋊C4—21no—
484Dic3⋊C4—61no—
485Dic3⋊C4—61no—
486Dic3⋊C4—61no—
487Dic3⋊C4—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490Dic3⋊C4—121no—
491C2×C3⋊C8C22×D311yescharacteristic
492C2×C3⋊C8C22×D311yescharacteristic
493Dic12—22no—
494Dic12—62no—
495Dic12—62no—
496Dic12—62no—
497Dic12—62no—
498Dic12—122no—
499#204—22no—
500#204—62no—
501#204—62no—
502#204—62no—
503#204—62no—
504#204—122no—
505ΓL(1,𝔽25)—22no—
506ΓL(1,𝔽25)—22no—
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×C4C22×D411yescharacteristic
527C32×C4C22×D411yescharacteristic
528C3⋊Dic3—22no—
529C3⋊Dic3—41no—
530C3⋊Dic3—41no—
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—91no—
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—31no—
561C2×M16—31no—
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—31no—
581C22⋊C8—31no—
582C22⋊C8D3211yescharacteristic, complemented
583C23×C3—21no—
584C23×C3—31no—
585C23×C3—31no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—61no—
589C23×C3—121no—
590C23×C3C2×D1211yescharacteristic
591C23×C3D3×D411yescharacteristic
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×D1211yescharacteristic
606C22×D3C2×D1211yescharacteristic
607C3×Q8—32no—
608C3×Q8—61no—
609C3×Q8—61no—
610C3×Q8—61no—
611C3×D4—32no—
612C3×D4—64no—
613C3×D4—61no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—31no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—31no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—64no—
629C2×C3×C4—62no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4C2×D1211yescharacteristic
636C2×C3×C4D3×D411yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638C2×C3×C4C23×D311yescharacteristic
639#67—24no—
640#67—64no—
641#67—64no—
642#67—64no—
643#67—64no—
644#67—64no—
645#67—64no—
646#67—124no—
647C2×Dic3—21no—
648C2×Dic3—22no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—64no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—64no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—122no—
663C2×Dic3—122no—
664C2×Dic3C2×D1211yescharacteristic
665C2×Dic3C2×D1211yescharacteristic
666D12—21no—
667D12—32no—
668D12—32no—
669D12—62no—
670D12—64no—
671D12—64no—
672D12—61no—
673D12—61no—
674D12—121no—
675D12D3×D412yes—
676C4×D3—24no—
677C4×D3—22no—
678C4×D3—21no—
679C4×D3—21no—
680C4×D3—22no—
681C4×D3—64no—
682C4×D3—64no—
683C4×D3—64no—
684C4×D3—64no—
685C4×D3—64no—
686C4×D3—64no—
687C4×D3—124no—
688C4×D3—122no—
689C4×D3—122no—
690C4×D3D3×D412yes—
691C4×D3D3×D412yes—
692Dic6—21no—
693Dic6—21no—
694Dic6—21no—
695Dic6—32no—
696Dic6—32no—
697Dic6—62no—
698Dic6—64no—
699Dic6—64no—
700Dic6—61no—
701Dic6—61no—
702Dic6—61no—
703Dic6—61no—
704Dic6—61no—
705Dic6—61no—
706Dic6—121no—
707Dic6—121no—
708Dic6—121no—
709Dic6—122no—
710Dic6—122no—
711Dic6D3×D412yes—
712C3×C8—21no—
713C3×C8—21no—
714C3×C8—21no—
715C3×C8—21no—
716C3×C8—41no—
717C3×C8—41no—
718C3×C8—61no—
719C3×C8—61no—
720C3⋊C8—21no—
721C3⋊C8—21no—
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—91no—
745C2×Q8—91no—
746C2×Q8—181no—
747C2×Q8—181no—
748C2×Q8—182no—
749C2×Q8—182no—
750C2×Q8—182no—
751C2×Q8—182no—
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—181no—
771C22×C4—181no—
772C22×C4—188no—
773C22×C4—181no—
774C22×C4—181no—
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—62no—
787M16—62no—
788C2×C8—31no—
789C2×C8—31no—
790C2×C8C2×D3211yescharacteristic
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—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×C3C22×D1211yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
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#88212yes—
845C2×D3#90912yescomplemented
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—32no—
851C3×C4—41no—
852C3×C4—62no—
853C3×C4—61no—
854C3×C4—121no—
855C3×C4—121no—
856C3×C4C2×D3×D411yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858C3×C4C2×D3×D411yescharacteristic
859C3×C4C2×D3×D411yescharacteristic
860Dic3—21no—
861Dic3—22no—
862Dic3—41no—
863Dic3—41no—
864Dic3—62no—
865Dic3—62no—
866Dic3—122no—
867Dic3—121no—
868Dic3—121no—
869Dic3—121no—
870Dic3—121no—
871Dic3—241no—
872Dic3—241no—
873Dic3#88212yes—
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×D1211yescharacteristic
886Q8—32no—
887Q8—61no—
888Q8—61no—
889Q8—61no—
890Q8—92no—
891Q8—184no—
892Q8—181no—
893Q8—181no—
894Q8—181no—
895Q8—362no—
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—31no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—31no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—64no—
914C2×C4—62no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—184no—
921C2×C4—184no—
922C2×C4—184no—
923C2×C4—184no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—362no—
928C2×C4—362no—
929C2×C4D3×D1211yescharacteristic
930C2×C4C22×D3211yescharacteristic
931C8—21no—
932C8—21no—
933C8—61no—
934C8—61no—
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×C3C2×#88211yescharacteristic
945C2×C3D3×#12011yescharacteristic
946C2×C3C2×#90911yescharacteristic
947C2×C3#574811yescharacteristic
948C2×C3#576811yescharacteristic
949C2×C3D3×#13711yescharacteristic
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×D1211yescharacteristic
974C4—21no—
975C4—32no—
976C4—61no—
977C4—62no—
978C4—121no—
979C4—121no—
980C4—182no—
981C4—361no—
982C4—361no—
983C4D32×D411yescharacteristic
984C4D32×D411yescharacteristic
985C3—21no—
986C3#7864011yescharacteristic, complemented
987C3#8022811yescharacteristic, complemented
988C2—41no—
989C2—62no—
990C2—62no—
991C2—122no—
992C2—362no—
993C2D3×#88211yescharacteristic
994C2#1059467611yescharacteristic
995C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
hypercenterC22⋊C8D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. D3×#924C2semidirect
3. C2×#63801C2semidirect
4. C2×#63800C2semidirect
5. #10592432C2semidirect
6. C3×#4733C2semidirect
7. C3×#4726C2semidirect
8. #10591184C2semidirect
9. #10591173C2semidirect
10. #10590952C2semidirect
11. #10590949C2semidirect
12. #10590946C2semidirect
13. #10590942C2semidirect
14. #10590671C2semidirect
15. #10590670C2semidirect
31. C2×D3×Dic6C22semidirect
32. #64133C22semidirect
33. C2×#3746C22semidirect
34. C2×#3744C22semidirect
35. C3×#924C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
42. D3×C4⋊Dic3C22semidirect
47. C2×#3719C22semidirect
48. C2×#3719C22semidirect
49. C2×#3717C22semidirect
50. C2×#3716C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. #63643C22semidirect
56. C3×#830C22semidirect
57. C3×#821C22semidirect
60. C3×#816C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
63. #63564C22semidirect
64. #63563C22semidirect
92. #4733D3semidirect
95. #4726D3semidirect
218. #924C2×D3semidirect
229. C2×Dic12C2×D3semidirect
235. C2×#204C2×D3semidirect
236. C2×ΓL(1,𝔽25)C2×D3semidirect
237. C2×ΓL(1,𝔽25)C2×D3semidirect
250. C3×C22⋊C8C2×D3semidirect
251. C3×C22⋊C8C2×D3semidirect
254. #830C2×D3semidirect
260. #821C2×D3semidirect
268. #816C2×D3semidirect
523. C2×C3×D3#137semidirect
582. C22⋊C8D32semidirect
845. C2×D3#909semidirect
874. C32#3007semidirect
986. C3#78640semidirect
987. C3#80228semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
D3×#9242
C2×#638012
C2×#638002
#105924322
C3×#47332
C3×#47262
#105911842
#105911732
#105909522
#105909492
#105909462
#105909422
#105906712
#105906702
#802283
#786403