Finite Group Databasebeta

← #11864198

Subgroups — #11864198

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 995 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic
2C2×#63931C211yesmaximal, characteristic, complemented
3C2×#63811C211yesmaximal, characteristic, complemented
4#10594631C211yesmaximal, characteristic, complemented
5#10592470C211yesmaximal, characteristic, complemented
6C3×#4783C211yesmaximal, characteristic, complemented
7C3×#4776C211yesmaximal, characteristic, complemented
8#10591461C211yesmaximal, characteristic, complemented
9#10591458C211yesmaximal, characteristic, complemented
10#10590960C211yesmaximal, characteristic, complemented
11#10590949C211yesmaximal, characteristic, complemented
12#10590937C211yesmaximal, characteristic, complemented
13#10590614C211yesmaximal, characteristic, complemented
14#10590612C211yesmaximal, characteristic, complemented
15#10590604C211yesmaximal, characteristic, complemented
16#80228—31nomaximal
17#80147—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237—24no—
27C2×C4×D32C2211yescharacteristic
28C2×#3797C2211yescharacteristic, complemented
29C2×#3796C2211yescharacteristic
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×#3743C2211yescharacteristic, complemented
33C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic
39C3×#897C2211yescharacteristic, complemented
40#63931—24no—
41#63921—21no—
42#63900—21no—
43#63899—21no—
44#63899—21no—
45#63856C2211yescharacteristic
46#63856C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52#63811—24no—
53C32×#102C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×#918—31no—
68C2×#915—31no—
69C2×#915—31no—
70C2×#915—31no—
71D3×C22⋊Q8—31no—
72D3×C22⋊Q8—31no—
73C3×#452—31no—
74C3×#450—31no—
75#5239—31no—
76#5218—31no—
77#5186—31no—
78#5173—31no—
79#5173—31no—
80#5169—31no—
81#5050—31no—
82#5047—31no—
83#4809—31no—
84#4803—31no—
85#4783—31no—
86#4783D311yescharacteristic, complemented
87#4776D311yescharacteristic, complemented
88#4771—31no—
89#4771—31no—
90#4771—31no—
91#4771—61no—
92#4739—31no—
93#4733—31no—
94#4726—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100C22×C3⋊Dic3—21no—
101#3830—22no—
102#3830D414yes—
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—22no—
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119D3×#67—28no—
120C2×#627—21no—
121C2×#627—21no—
122C2×#626—21no—
123C2×#625—21no—
124C2×#624—21no—
125C2×#624D411yescharacteristic
126#3805—28no—
127#3804—28no—
128C2×D3×Dic3—28no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134C4×D32—22no—
135C4×D32—22no—
136#3797—22no—
137#3797—22no—
138#3796—22no—
139#3796D414yes—
140#3795—22no—
141#3795—22no—
142D3×Dic6—22no—
143D3×Dic6—22no—
144C2×C32×C8C2311yescharacteristic
145C32×C4⋊C4C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147#3750—21no—
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149#3743—22no—
150C3×#214—22no—
151C3×#214—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C3×Dic12—22no—
159C3×#204—22no—
160#3724—21no—
161#3724—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3719—22no—
165#3719—22no—
166#3718—22no—
167#3715—22no—
168#3712—22no—
169#3007—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C23×Dic3—61no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×D3×Q8—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×#237—61no—
186C2×#237—61no—
187C2×#237—64no—
188C2×#237—64no—
189C2×#237—61no—
190C2×#237C2×D311yescharacteristic
191C2×D3×D4—61no—
192C2×D3×D4C2×D311yescharacteristic
193C2×#235—31no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×SD16—31no—
202C2×C3×SD16—31no—
203C3×C22⋊Q8—31no—
204C3×C22⋊Q8—31no—
205#946—31no—
206#946—31no—
207C2×#216—31no—
208C2×#216—31no—
209C2×#216—31no—
210C2×#216—31no—
211C2×#215—31no—
212C2×#214—31no—
213C2×#214C2×D311yescharacteristic, complemented
214C2×#214C2×D311yescharacteristic, complemented
215#924—31no—
216#924—31no—
217#918—64no—
218#915—64no—
219#915—64no—
220#915—64no—
221C2×Dic12—31no—
222C2×Dic12—31no—
223C2×Dic12C2×D311yescharacteristic, complemented
224C2×#204C2×D311yescharacteristic, complemented
225C2×ΓL(1,𝔽25)—31no—
226C2×ΓL(1,𝔽25)—31no—
227C2×ΓL(1,𝔽25)—31no—
228C2×ΓL(1,𝔽25)—31no—
229C2×ΓL(1,𝔽25)—61no—
230#897C2×D311yescharacteristic
231#897C2×D311yescharacteristic, complemented
232#896—61no—
233#896—61no—
234D3×C4⋊C4—31no—
235D3×C4⋊C4—31no—
236D3×C4⋊C4—61no—
237D3×C4⋊C4—61no—
238D3×C4⋊C4—61no—
239D3×C22⋊C4—61no—
240D3×C22⋊C4—61no—
241#878—61no—
242#878—61no—
243C3×#103—31no—
244C3×#102—21no—
245C3×#102—31no—
246C3×#102C2×D311yescharacteristic, complemented
247C3×#102C2×D311yescharacteristic, complemented
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250#835—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—61no—
255#830—31no—
256#830—31no—
257#821—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8C2×D311yescharacteristic
261(C2×D3)⋊C8C2×D311yescharacteristic, complemented
262#816—31no—
263#816—31no—
264#816—31no—
265#816—61no—
266#810—31no—
267#810—31no—
268#810—61no—
269#810C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—24no—
274C22×C3×D3—21no—
275C22×C3×D3—42no—
276C22×C3×D3—42no—
277C22×C3×D3C2×D411yescharacteristic
278C22×C3×D3C2×D411yescharacteristic
279C2×D32—22no—
280C2×D32—22no—
281C2×D32—41no—
282C32×D4—21no—
283C32×D4C2×D412yes—
284C2×C32×C4—21no—
285C2×C32×C4C2411yescharacteristic
286#638—24no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—24no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3C2×D411yescharacteristic
291C4×C3⋊D3—42no—
292C4×C3⋊D3C2×D412yes—
293C4×C3⋊D3C2×D412yes—
294#634—21no—
295#634C2×D412yes—
296C3×#67—24no—
297C3×#67—24no—
298C2×C3×Dic3—24no—
299C2×C3×Dic3—21no—
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—21no—
307C3×C4×D3—21no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×Dic6—21no—
311C3×Dic6—21no—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6C2×D412yes—
316#627—24no—
317#627—42no—
318#626—24no—
319#625—24no—
320#624—22no—
321#624—42no—
322D3×Dic3—24no—
323D3×Dic3—24no—
324D3×Dic3—24no—
325D3×Dic3—22no—
326D3×Dic3—22no—
327C32×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—91no—
335#452—31no—
336#452—91no—
337#452—91no—
338#452—91no—
339#451—91no—
340#451—91no—
341#450—31no—
342#450—91no—
343#417—91no—
344#417—91no—
345#407—91no—
346C24×C3—61no—
347C23×D3—21no—
348C23×D3—31no—
349C23×D3—31no—
350C3×#41—62no—
351C3×#41—62no—
352C2×C3×Q8—31no—
353C2×C3×Q8—31no—
354C2×C3×Q8—31no—
355C2×C3×D4—21no—
356C2×C3×D4—31no—
357C2×C3×D4—61no—
358C2×C3×D4—62no—
359C2×C3×D4—61no—
360C2×C3×D4—62no—
361C2×C3×D4C22×D311yescharacteristic
362C2×C3×D4C22×D311yescharacteristic
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—61no—
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—61no—
369C2×#67—68no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—121no—
375C22×Dic3—21no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—68no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—121no—
385#239—34no—
386#239—62no—
387D3×Q8—62no—
388D3×Q8—62no—
389D3×Q8—62no—
390D3×Q8—62no—
391D3×Q8—62no—
392D3×Q8—62no—
393#237—22no—
394#237—22no—
395#237—34no—
396#237—34no—
397#237—34no—
398#237—64no—
399#237—62no—
400#237—62no—
401#237—62no—
402#237—62no—
403#237—62no—
404#237—68no—
405#237—68no—
406#237—68no—
407#237—122no—
408D3×D4—22no—
409D3×D4—22no—
410D3×D4—68no—
411#235—62no—
412#235—68no—
413#235—62no—
414C2×D12—61no—
415C2×D12C22×D311yescharacteristic
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—61no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—62no—
426C2×C4×D3—62no—
427C2×C4×D3—61no—
428C2×C4×D3—61no—
429C2×C4×D3—68no—
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×D3C22×D311yescharacteristic
437C2×C4×D3C22×D311yescharacteristic
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6—61no—
441C2×Dic6—62no—
442C2×Dic6—61no—
443C2×Dic6—61no—
444C2×Dic6—62no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6C22×D311yescharacteristic
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×SD16—62no—
452C3×SD16—62no—
453C3×SD16—62no—
454C2×C3×C8—21no—
455C2×C3×C8—31no—
456C2×C3×C8—31no—
457C2×C3×C8C22×D311yescharacteristic
458C2×C3×C8C22×D311yescharacteristic
459C3×C4⋊C4—21no—
460C3×C4⋊C4—61no—
461C3×C4⋊C4—61no—
462C3×C4⋊C4C22×D311yescharacteristic
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C22⋊C4—61no—
465C3×C22⋊C4—61no—
466#217—61no—
467#217—61no—
468#216—62no—
469#216—62no—
470#216—62no—
471#216—62no—
472#215—62no—
473#214—22no—
474#214—22no—
475#214—62no—
476(C2×D3)⋊C4—21no—
477(C2×D3)⋊C4—21no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480C4⋊Dic3—21no—
481C4⋊Dic3—21no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—61no—
485Dic3⋊C4—61no—
486Dic3⋊C4—61no—
487Dic3⋊C4—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490Dic3⋊C4—61no—
491Dic3⋊C4—121no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—61no—
495C2×C3⋊C8C22×D311yescharacteristic
496C2×C3⋊C8C22×D311yescharacteristic
497Dic12—22no—
498Dic12—62no—
499Dic12—62no—
500#204—22no—
501ΓL(1,𝔽25)—62no—
502ΓL(1,𝔽25)—62no—
503ΓL(1,𝔽25)—62no—
504ΓL(1,𝔽25)—62no—
505ΓL(1,𝔽25)—122no—
506C22×C32—22no—
507C22×C32—41no—
508C22×C32—41no—
509C22×C32C22×D411yescharacteristic
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3#12012yes—
513C2×C3×D3—21no—
514C2×C3×D3—21no—
515C2×C3×D3—22no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—48no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3#13712yescomplemented
523D32—44no—
524C32×C4—41no—
525C32×C4C22×D411yescharacteristic
526C32×C4C22×D411yescharacteristic
527C3⋊Dic3—22no—
528C3⋊Dic3—41no—
529C3⋊Dic3#12012yes—
530C3×Dic3—21no—
531C3×Dic3—22no—
532C3×Dic3—21no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C2×#41—31no—
536C2×#41—91no—
537C2×#41—91no—
538C2×#41—91no—
539C2×#41—181no—
540C2×#41—181no—
541C2×#41—184no—
542C2×#41—184no—
543C22×Q8—91no—
544C22×Q8—91no—
545C22×D4—31no—
546C22×D4—181no—
547C23×C4—91no—
548C23×C4—181no—
549#137—184no—
550#137—184no—
551C2×Q16—31no—
552C2×Q16—91no—
553C2×Q16—91no—
554C2×Q16—91no—
555C2×SD16—31no—
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×M16—91no—
560C2×M16—91no—
561C22⋊Q8—31no—
562C22⋊Q8—31no—
563C22⋊Q8—91no—
564C22⋊Q8—91no—
565C22⋊Q8—181no—
566C22⋊Q8—181no—
567C2×C4⋊C4—91no—
568C2×C4⋊C4—181no—
569C2×C22⋊C4—181no—
570#103—31no—
571#103—91no—
572#103—91no—
573#103—91no—
574#102—31no—
575#102—91no—
576#102—91no—
577#102D3211yescharacteristic, complemented
578C22⋊C8—31no—
579C22⋊C8—31no—
580C22⋊C8—91no—
581C22⋊C8—91no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—31no—
585C23×C3—31no—
586C23×C3—41no—
587C23×C3—64no—
588C23×C3—61no—
589C23×C3—122no—
590C23×C3—122no—
591C22×D3—24no—
592C22×D3—21no—
593C22×D3—31no—
594C22×D3—31no—
595C22×D3—42no—
596C22×D3—42no—
597C22×D3—61no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3D3×D411yescharacteristic
605C22×D3D3×D411yescharacteristic
606C3×Q8—32no—
607C3×Q8—61no—
608C3×Q8—61no—
609C3×Q8—61no—
610C3×Q8—61no—
611C3×Q8—61no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—22no—
615C3×D4—32no—
616C3×D4—41no—
617C3×D4—64no—
618C3×D4—64no—
619C3×D4—61no—
620C3×D4D3×D412yes—
621C3×D4D3×D412yes—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—41no—
628C2×C3×C4—64no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638#67—24no—
639#67—24no—
640#67—64no—
641#67—64no—
642#67—64no—
643#67—64no—
644#67—64no—
645#67—124no—
646C2×Dic3—24no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—61no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—64no—
656C2×Dic3—64no—
657C2×Dic3—64no—
658C2×Dic3—64no—
659C2×Dic3—64no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—124no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3D3×D411yescharacteristic
668C2×Dic3D3×D411yescharacteristic
669D12—21no—
670D12—64no—
671D12D3×D412yes—
672C4×D3—21no—
673C4×D3—21no—
674C4×D3—21no—
675C4×D3—21no—
676C4×D3—32no—
677C4×D3—32no—
678C4×D3—32no—
679C4×D3—32no—
680C4×D3—62no—
681C4×D3—62no—
682C4×D3—62no—
683C4×D3—62no—
684C4×D3—62no—
685C4×D3—62no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—64no—
689C4×D3—122no—
690C4×D3—122no—
691C4×D3—122no—
692C4×D3—122no—
693C4×D3—242no—
694Dic6—21no—
695Dic6—21no—
696Dic6—21no—
697Dic6—21no—
698Dic6—21no—
699Dic6—32no—
700Dic6—32no—
701Dic6—62no—
702Dic6—64no—
703Dic6—64no—
704Dic6—61no—
705Dic6—61no—
706Dic6—121no—
707Dic6—122no—
708Dic6—122no—
709Dic6D3×D412yes—
710C3×C8—21no—
711C3×C8—21no—
712C3×C8—41no—
713C3×C8—61no—
714C3×C8—61no—
715C3⋊C8—21no—
716C3⋊C8—21no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—121no—
720C2×C32—42no—
721C2×C32C2×#12011yescharacteristic
722C2×C32C2×#13711yescharacteristic
723C2×C32#57511yescharacteristic
724C3⋊D3—22no—
725C3×D3—22no—
726C3×D3—41no—
727C3×D3—42no—
728C24—61no—
729C24—91no—
730#41—62no—
731#41—62no—
732#41—94no—
733#41—94no—
734#41—182no—
735#41—182no—
736#41—188no—
737#41—182no—
738#41—182no—
739#41—188no—
740C2×Q8—31no—
741C2×Q8—31no—
742C2×Q8—31no—
743C2×Q8—91no—
744C2×Q8—181no—
745C2×Q8—181no—
746C2×Q8—182no—
747C2×Q8—182no—
748C2×Q8—182no—
749C2×Q8—182no—
750C2×D4—31no—
751C2×D4—61no—
752C2×D4—62no—
753C2×D4—61no—
754C2×D4—62no—
755C2×D4—181no—
756C2×D4—188no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4C2×D3211yescharacteristic
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—61no—
763C22×C4—91no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—181no—
768C22×C4—181no—
769C22×C4—182no—
770C22×C4—182no—
771C22×C4—181no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4—188no—
775C22×C4—181no—
776Q16—62no—
777Q16—182no—
778Q16—182no—
779Q16—182no—
780SD16—62no—
781SD16—62no—
782SD16—62no—
783SD16—182no—
784M16—182no—
785M16—182no—
786C2×C8—31no—
787C2×C8—31no—
788C2×C8—91no—
789C2×C8C2×D3211yescharacteristic
790C4⋊C4—61no—
791C4⋊C4—61no—
792C4⋊C4—91no—
793C4⋊C4—181no—
794C4⋊C4—181no—
795C4⋊C4—181no—
796C4⋊C4C2×D3211yescharacteristic
797C22⋊C4—61no—
798C22⋊C4—61no—
799C22⋊C4—181no—
800C22⋊C4—181no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—32no—
805C22×C3—42no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—62no—
815C22×C3—61no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—128no—
819C22×C3—121no—
820C22×C3—121no—
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—22no—
829C2×D3—32no—
830C2×D3—32no—
831C2×D3—48no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—62no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—124no—
842C2×D3—124no—
843C2×D3#91512yescomplemented
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—61no—
849C3×C4—62no—
850C3×C4—61no—
851C3×C4—81no—
852C3×C4—121no—
853C3×C4—121no—
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C2×D3×D411yescharacteristic
856C3×C4C2×D3×D411yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858Dic3—22no—
859Dic3—21no—
860Dic3—21no—
861Dic3—32no—
862Dic3—32no—
863Dic3—41no—
864Dic3—41no—
865Dic3—62no—
866Dic3—62no—
867Dic3—62no—
868Dic3—122no—
869Dic3—121no—
870Dic3—121no—
871Dic3—241no—
872C32#300711yescharacteristic, complemented, Sylow
873C23—21no—
874C23—31no—
875C23—31no—
876C23—64no—
877C23—61no—
878C23—91no—
879C23—122no—
880C23—122no—
881C23—182no—
882C23—182no—
883C23—361no—
884Q8—32no—
885Q8—61no—
886Q8—61no—
887Q8—61no—
888Q8—61no—
889Q8—61no—
890Q8—92no—
891Q8—184no—
892Q8—181no—
893Q8—362no—
894D4—21no—
895D4—32no—
896D4—64no—
897D4—64no—
898D4—61no—
899D4—184no—
900D4—184no—
901D4—184no—
902D4#380212yes—
903C2×C4—21no—
904C2×C4—31no—
905C2×C4—31no—
906C2×C4—64no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—91no—
915C2×C4—92no—
916C2×C4—92no—
917C2×C4—182no—
918C2×C4—182no—
919C2×C4—182no—
920C2×C4—184no—
921C2×C4—184no—
922C2×C4—184no—
923C2×C4—184no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—362no—
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—42no—
937C2×C3—42no—
938C2×C3—62no—
939C2×C3—82no—
940C2×C3—121no—
941C2×C3—122no—
942C2×C3D3×#12011yescharacteristic
943C2×C3D3×#12011yescharacteristic
944C2×C3C2×#91511yescharacteristic
945C2×C3#576811yescharacteristic
946C2×C3#577311yescharacteristic
947C2×C3D3×#13711yescharacteristic
948D3—22no—
949D3—42no—
950D3—41no—
951D3—62no—
952D3—62no—
953D3—122no—
954C22—22no—
955C22—32no—
956C22—41no—
957C22—41no—
958C22—61no—
959C22—61no—
960C22—61no—
961C22—61no—
962C22—61no—
963C22—62no—
964C22—92no—
965C22—128no—
966C22—121no—
967C22—121no—
968C22—181no—
969C22—181no—
970C22—364no—
971C22D32×D411yescharacteristic
972C4—41no—
973C4—61no—
974C4—61no—
975C4—62no—
976C4—92no—
977C4—121no—
978C4—121no—
979C4—182no—
980C4—361no—
981C4C2×#380211yescharacteristic
982C4D32×D411yescharacteristic
983C3—21no—
984C3#8014711yescharacteristic, complemented
985C3#8022811yescharacteristic, complemented
986C2—42no—
987C2—62no—
988C2—121no—
989C2—122no—
990C2—182no—
991C2#1059425811yescharacteristic
992C2#1059472911yescharacteristic
993C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
hypercenter#102D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#63931C2semidirect
3. C2×#63811C2semidirect
4. #10594631C2semidirect
5. #10592470C2semidirect
6. C3×#4783C2semidirect
7. C3×#4776C2semidirect
8. #10591461C2semidirect
9. #10591458C2semidirect
10. #10590960C2semidirect
11. #10590949C2semidirect
12. #10590937C2semidirect
13. #10590614C2semidirect
14. #10590612C2semidirect
15. #10590604C2semidirect
28. C2×#3797C22semidirect
32. C2×#3743C22semidirect
33. C4⋊C4×C3⋊D3C22semidirect
34. C2×C3×#214C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×#204C22semidirect
39. C3×#897C22semidirect
46. #63856C22semidirect
47. C2×#3719C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
50. C2×#3715C22semidirect
51. C2×#3712C22semidirect
53. C32×#102C22semidirect
54. #63659C22semidirect
55. #63643C22semidirect
56. #63637C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
86. #4783D3semidirect
87. #4776D3semidirect
213. C2×#214C2×D3semidirect
214. C2×#214C2×D3semidirect
223. C2×Dic12C2×D3semidirect
224. C2×#204C2×D3semidirect
231. #897C2×D3semidirect
246. C3×#102C2×D3semidirect
247. C3×#102C2×D3semidirect
261. (C2×D3)⋊C8C2×D3semidirect
269. #810C2×D3semidirect
270. #809C2×D3semidirect
522. C2×C3×D3#137semidirect
577. #102D32semidirect
843. C2×D3#915semidirect
872. C32#3007semidirect
984. C3#80147semidirect
985. C3#80228semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#639312
C2×#638112
#105946312
#105924702
C3×#47832
C3×#47762
#105914612
#105914582
#105909602
#105909492
#105909372
#105906142
#105906122
#105906042
#802283
#801473