Finite Group Databasebeta

← #11904923

Subgroups — #11904923

Order 1152.

2993 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5494C212yesmaximal, complemented
3#10595527C212yesmaximal, complemented
4#10595508C212yesmaximal, complemented
5#10595084C211yesmaximal, characteristic, complemented
6#10595058C212yesmaximal, complemented
7#10595016C212yesmaximal, complemented
8#10594981C211yesmaximal, characteristic, complemented
9#10594922C212yesmaximal, complemented
10#10594285C214yesmaximal, complemented
11#10594279C214yesmaximal, complemented
12#10594228C214yesmaximal, complemented
13#10594153C214yesmaximal, complemented
14#86414—32nomaximal
15C24×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic, complemented
17C22×C4×C3⋊D3C2211yescharacteristic, complemented
18C2×#3811C2212yes—
19C2×#3811C2212yescomplemented
20C2×#3811C2212yescomplemented
21C2×#3798C2212yescomplemented
22C2×#3796C2212yescomplemented
23C2×C32×C22⋊C4C2211yescharacteristic, complemented
24C2×#3757C2211yescharacteristic, complemented
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C22⋊C4×C3⋊D3C2214yescomplemented
28C22⋊C4×C3⋊D3C2214yescomplemented
29C3×#953C2214yescomplemented
30C3×#930C2212yescomplemented
31C3×C4×#67C2214yescomplemented
32C3×#924C2212yescomplemented
33C3×#885C2214yescomplemented
34C3×#884C2214yescomplemented
35C3×#883C2214yescomplemented
36C3×#879C2214yescomplemented
37#63982C2212yescomplemented
38#63981C2214yes—
39#63981C2214yes—
40#63981C2214yescomplemented
41#63980C2212yescomplemented
42#63974C2212yes—
43#63974C2212yescomplemented
44#63974C2212yescomplemented
45#67⋊Dic3C2214yescomplemented
46#63970C2214yescomplemented
47#63969C2214yescomplemented
48#63959C2214yescomplemented
49#63956C2214yescomplemented
50#63922C2214yescomplemented
51D3×(C2×D3)⋊C4C2214yescomplemented
52#63916C2212yescomplemented
53#63912C2212yescomplemented
54#63904C2214yescomplemented
55C4×#626C2214yescomplemented
56#63895C2214yescomplemented
57#63888C2214yescomplemented
58#63881C2214yescomplemented
59#63880C2214yescomplemented
60#63874C2212yescomplemented
61#63871C2212yescomplemented
62#63865C2212yescomplemented
63#63854C2214yescomplemented
64#63853C2214yescomplemented
65#63853C2214yescomplemented
66#63849C2212yescomplemented
67#63836C2214yescomplemented
68C3×#538—32no—
69#5705—34no—
70#5705—34no—
71#5679—34no—
72#5676—34no—
73#5659—34no—
74#5654—34no—
75#5634—32no—
76#5627—32no—
77#5612—34no—
78#5610—34no—
79#5606—32no—
80#5605—32no—
81#5593—34no—
82D3×#120—34no—
83#5547—34no—
84#5545—34no—
85#5494D312yescomplemented
86C2×D3×C22⋊C4—32no—
87C2×D3×C22⋊C4—61no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3—24no—
90C23×C3⋊D3—42no—
91C23×C3⋊D3—42no—
92C23×C3⋊D3C2311yescharacteristic
93C23×C3⋊D3C2312yes—
94C23×C3⋊D3C2312yes—
95C23×C3⋊D3C2311yescharacteristic
96C22×D32C2312yes—
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4×C3⋊D3—42no—
102C2×C4×C3⋊D3—42no—
103C2×C4×C3⋊D3C2312yes—
104C2×C4×C3⋊D3C2312yes—
105C2×C4×C3⋊D3C2312yes—
106C2×C4×C3⋊D3C2312yes—
107C2×C3×#67C2314yes—
108C2×C3×#67C2314yes—
109C2×C3×#67C2314yes—
110C2×C3×D12C2312yescomplemented
111C2×C3×C4×D3C2314yescomplemented
112C2×C3×Dic6C2312yescomplemented
113#3811—28no—
114#3811—44no—
115#3811—44no—
116C2×#627C2312yescomplemented
117C2×#626C2314yes—
118C2×#626C2314yes—
119C2×#626C2314yes—
120C2×#625C2312yescomplemented
121C2×#624C2312yes—
122C2×#624C2312yes—
123C2×#624C2312yes—
124C2×D3×Dic3C2314yescomplemented
125#3798—44no—
126#3796—44no—
127C32×C22⋊C4C2314yes—
128#3757C2314yes—
129#3752C2314yes—
130#3752C2314yes—
131C3×#217C2314yes—
132C3×#217C2314yes—
133C3×#217C2314yes—
134C3×(C2×D3)⋊C4C2314yescomplemented
135C3×(C2×D3)⋊C4C2314yescomplemented
136C3×C4⋊Dic3C2312yescomplemented
137C3×C4⋊Dic3C2312yescomplemented
138C3×Dic3⋊C4C2314yescomplemented
139C3×Dic3⋊C4C2314yescomplemented
140C3×C4×Dic3C2314yescomplemented
141#3724C2312yescomplemented
142#3724C2312yescomplemented
143Dic3⋊Dic3C2314yescomplemented
144Dic3⋊Dic3C2314yescomplemented
145#3722C2314yes—
146#3722C2314yes—
147#3722C2314yes—
148(C2×D3)⋊Dic3C2314yescomplemented
149(C2×D3)⋊Dic3C2314yescomplemented
150Dic32C2314yescomplemented
151#3490—91noSylow
152C24×D3—32no—
153C24×D3—61no—
154C2×#239—32no—
155C2×#237—32no—
156C2×D3×D4—34no—
157C2×D3×D4—34no—
158C2×D3×D4—34no—
159C2×#235—34no—
160C22×C4×D3—32no—
161C22×C4×D3—32no—
162C22×C4×D3—61no—
163C22×C4×D3—61no—
164C3×#126—34no—
165C3×#124—34no—
166C3×#123—34no—
167C3×C22⋊Q8—32no—
168C3×#121—32no—
169C3×#121—34no—
170C3×#120—34no—
171C3×C4×D4—34no—
172C2×C3×C22⋊C4—21no—
173C2×C3×C22⋊C4C2×D312yescomplemented
174#953C2×D314yescomplemented
175C2×#217—32no—
176C2×#217—61no—
177#946—32no—
178#946—34no—
179#939—34no—
180#939—34no—
181#938—34no—
182#938—32no—
183#937—34no—
184#937—34no—
185#937—34no—
186#937—34no—
187#936—34no—
188#935—34no—
189D4×Dic3—34no—
190#930C2×D312yescomplemented
191C4×#67—34no—
192C4×#67—34no—
193C4×#67C2×D314yescomplemented
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4—32no—
196C2×(C2×D3)⋊C4—34no—
197C2×(C2×D3)⋊C4—61no—
198C2×(C2×D3)⋊C4—61no—
199#924C2×D312yescomplemented
200#897—32no—
201#897—34no—
202#896—34no—
203#896—34no—
204#896—34no—
205#895—32no—
206#894—34no—
207#894—34no—
208#894—34no—
209#893—34no—
210#893—34no—
211#892—32no—
212#892—32no—
213#892—34no—
214#885—34no—
215#885C2×D314yescomplemented
216#884—34no—
217#884C2×D314yescomplemented
218#883—34no—
219#883—34no—
220#883—34no—
221#883—34no—
222#883C2×D314yescomplemented
223#882—34no—
224#882—34no—
225#882—34no—
226#882—34no—
227#67⋊C4—34no—
228#67⋊C4—34no—
229#67⋊C4—34no—
230D3×C22⋊C4—34no—
231D3×C22⋊C4—34no—
232D3×C22⋊C4—34no—
233D3×C22⋊C4—34no—
234D3×C22⋊C4—34no—
235D3×C22⋊C4—34no—
236D3×C22⋊C4—34no—
237D3×C22⋊C4—34no—
238D3×C22⋊C4—64no—
239D3×C22⋊C4—64no—
240#879—34no—
241#879—34no—
242#879C2×D314yescomplemented
243#878—34no—
244C4×D12—34no—
245C4×D12—34no—
246#872—34no—
247#872—34no—
248C23×C32—22no—
249C23×C32—41no—
250C23×C32—41no—
251C23×C32C2412yes—
252C23×C32C2411yescharacteristic
253C22×C3⋊D3—22no—
254C22×C3⋊D3—22no—
255C22×C3⋊D3—22no—
256C22×C3⋊D3—24no—
257C22×C3⋊D3—24no—
258C22×C3⋊D3—24no—
259C22×C3⋊D3—24no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—41no—
263C22×C3⋊D3—41no—
264C22×C3⋊D3—416no—
265C22×C3⋊D3#4114yescomplemented
266C22×C3⋊D3C2412yes—
267C22×C3⋊D3C2411yescharacteristic
268C22×C3⋊D3C2411yescharacteristic
269C22×C3×D3C2414yes—
270C2×D32—24no—
271C2×D32—42no—
272C2×D32—42no—
273C2×C32×C4—41no—
274C2×C32×C4—41no—
275C2×C32×C4C2412yes—
276C2×C32×C4C2412yes—
277C2×C3⋊Dic3—41no—
278C2×C3⋊Dic3—41no—
279C2×C3⋊Dic3C2412yes—
280C2×C3⋊Dic3C2412yes—
281C4×C3⋊D3—24no—
282C4×C3⋊D3—24no—
283C4×C3⋊D3—42no—
284C4×C3⋊D3—42no—
285C3×#67—28no—
286C3×#67—44no—
287C3×#67—44no—
288C2×C3×Dic3C2414yes—
289C2×C3×Dic3C2414yes—
290C2×C3×Dic3C2414yes—
291C3×D12—42no—
292C3×C4×D3—44no—
293C3×Dic6—42no—
294#627—42no—
295#626—28no—
296#626—28no—
297#626—28no—
298#625—42no—
299#624—24no—
300#624—42no—
301#624—42no—
302D3×Dic3—44no—
303#551—94no—
304#551—94no—
305#546—94no—
306#546—94no—
307#543—91no—
308#538—32no—
309#538—92no—
310#534—91no—
311#525—92no—
312#525—92no—
313C2×#120—92no—
314#518—92no—
315C22×C22⋊C4—91no—
316C24×C3—21no—
317C24×C3C22×D312yes—
318C23×D3—32no—
319C23×D3—32no—
320C23×D3—34no—
321C23×D3—34no—
322C23×D3—34no—
323C23×D3—61no—
324C23×D3—62no—
325C23×D3—62no—
326C23×D3—61no—
327C23×D3—68no—
328C23×D3—68no—
329C23×D3—124no—
330C23×D3—124no—
331C23×D3—124no—
332C23×D3—124no—
333C2×C3×Q8—32no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—32no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—34no—
341C22×C3×C4C22×D312yes—
342C22×C3×C4C22×D312yes—
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—34no—
346C2×#67—34no—
347C2×#67C22×D314yes—
348C2×#67C22×D314yes—
349C2×#67C22×D314yes—
350C22×Dic3—32no—
351C22×Dic3—32no—
352C22×Dic3—34no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355#239—124no—
356#237—124no—
357D3×D4—616no—
358D3×D4—128no—
359D3×D4—128no—
360#235—128no—
361C2×D12—34no—
362C2×D12—34no—
363C2×D12—34no—
364C2×D12C22×D312yescomplemented
365C2×C4×D3—34no—
366C2×C4×D3—32no—
367C2×C4×D3—32no—
368C2×C4×D3—34no—
369C2×C4×D3—34no—
370C2×C4×D3—34no—
371C2×C4×D3—32no—
372C2×C4×D3—32no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—124no—
380C2×C4×D3—124no—
381C2×C4×D3—124no—
382C2×C4×D3—124no—
383C2×C4×D3C22×D314yescomplemented
384C2×Dic6—34no—
385C2×Dic6C22×D312yescomplemented
386C3×C4⋊C4—34no—
387C3×C4⋊C4—32no—
388C3×C4⋊C4—32no—
389C3×C4⋊C4—34no—
390C3×C22⋊C4—24no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4C22×D314yes—
397C3×C22⋊C4C22×D314yes—
398C3×C42—34no—
399#217—34no—
400#217—34no—
401#217—34no—
402#217—34no—
403#217—64no—
404#217C22×D314yes—
405#217C22×D314yes—
406#217C22×D314yes—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—64no—
420(C2×D3)⋊C4—64no—
421(C2×D3)⋊C4C22×D314yescomplemented
422(C2×D3)⋊C4C22×D314yescomplemented
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3C22×D312yescomplemented
426C4⋊Dic3C22×D312yescomplemented
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4C22×D314yescomplemented
432Dic3⋊C4C22×D314yescomplemented
433C4×Dic3—34no—
434C4×Dic3—34no—
435C4×Dic3C22×D314yescomplemented
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—44no—
442C22×C32C2×#4112yes—
443C22×C32C2511yescharacteristic
444C2×C3⋊D3—28no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—44no—
452C2×C3⋊D3—48no—
453C2×C3⋊D3—48no—
454C2×C3⋊D3C2×#4114yes—
455C2×C3⋊D3H(5,𝔽2)12yes—
456C2×C3⋊D3H(5,𝔽2)12yes—
457C2×C3×D3—24no—
458C2×C3×D3—24no—
459C2×C3×D3—24no—
460D32—84no—
461C32×C4—22no—
462C32×C4—22no—
463C3⋊Dic3—22no—
464C3⋊Dic3—22no—
465C3×Dic3—24no—
466C3×Dic3—24no—
467C3×Dic3—24no—
468C25—91no—
469C2×#41—92no—
470C2×#41—92no—
471C22×D4—92no—
472C22×D4—92no—
473C22×D4—92no—
474C23×C4—91no—
475C23×C4—91no—
476#126—34no—
477#126—94no—
478#124—34no—
479#124—94no—
480#123—34no—
481#123—94no—
482#123—94no—
483#123—94no—
484#123—94no—
485C22⋊Q8—32no—
486C22⋊Q8—92no—
487C22⋊Q8—92no—
488C22⋊Q8—94no—
489C22⋊Q8—92no—
490C22⋊Q8—94no—
491#121—32no—
492#121—34no—
493#121—92no—
494#121—92no—
495#121—92no—
496#121—94no—
497#120—34no—
498#120—94no—
499#120—94no—
500#120—94no—
501#120—94no—
502C4×D4—34no—
503C4×D4—94no—
504C4×D4—94no—
505C4×D4—94no—
506C4×D4—94no—
507C4×D4—94no—
508#117—92no—
509#117—94no—
510#117—92no—
511C2×C22⋊C4—92no—
512C2×C22⋊C4—92no—
513C2×C22⋊C4—92no—
514C2×C22⋊C4—94no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—94no—
519C2×C22⋊C4—94no—
520C2×C22⋊C4D3211yescharacteristic, complemented
521C23×C3—24no—
522C23×C3—24no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—34no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3C23×D314yes—
531C23×C3C23×D312yes—
532C22×D3—34no—
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—38no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—64no—
539C22×D3—62no—
540C22×D3—68no—
541C22×D3—64no—
542C22×D3—64no—
543C22×D3—68no—
544C22×D3—68no—
545C22×D3—68no—
546C22×D3—68no—
547C22×D3—64no—
548C22×D3—64no—
549C22×D3—64no—
550C22×D3—64no—
551C22×D3—68no—
552C22×D3—68no—
553C22×D3—124no—
554C22×D3—124no—
555C22×D3—124no—
556C22×D3—124no—
557C22×D3—124no—
558C22×D3—124no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—124no—
562C22×D3—124no—
563C22×D3—1232no—
564C22×D3—1232no—
565C22×D3—122no—
566C22×D3—122no—
567C22×D3C23×D314yes—
568C3×Q8—122no—
569C3×D4—68no—
570C3×D4—122no—
571C3×D4—124no—
572C3×D4—124no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—34no—
578C2×C3×C4—42no—
579C2×C3×C4—42no—
580C2×C3×C4—42no—
581C2×C3×C4—42no—
582C2×C3×C4—124no—
583C2×C3×C4C23×D314yes—
584C2×C3×C4C23×D312yes—
585C2×C3×C4C23×D312yes—
586#67—28no—
587#67—44no—
588#67—44no—
589#67—68no—
590#67—68no—
591#67—68no—
592#67—124no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—34no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—124no—
599C2×Dic3—122no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3—122no—
603C2×Dic3C23×D314yes—
604C2×Dic3C23×D314yes—
605C2×Dic3C23×D314yes—
606D12—42no—
607D12—68no—
608D12—68no—
609D12—68no—
610C4×D3—44no—
611C4×D3—68no—
612C4×D3—68no—
613C4×D3—64no—
614C4×D3—64no—
615C4×D3—124no—
616C4×D3—124no—
617C4×D3—124no—
618C4×D3—124no—
619C4×D3—124no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—124no—
623C4×D3—124no—
624C4×D3—124no—
625Dic6—42no—
626Dic6—124no—
627C2×C32—22no—
628C2×C32—42no—
629C2×C32C22×#4111yescharacteristic
630C2×C32C2×H(5,𝔽2)11yescharacteristic
631C2×C32C2×H(5,𝔽2)11yescharacteristic
632C3⋊D3—22no—
633C3⋊D3—22no—
634C3⋊D3—24no—
635C3×D3—44no—
636C24—92no—
637C24—91no—
638C24—91no—
639C24—92no—
640C24—92no—
641C24—184no—
642C24—362no—
643C24—362no—
644C24C2×D3211yescharacteristic
645#41—364no—
646#41—364no—
647C2×Q8—32no—
648C2×Q8—92no—
649C2×D4—34no—
650C2×D4—34no—
651C2×D4—34no—
652C2×D4—32no—
653C2×D4—94no—
654C2×D4—94no—
655C2×D4—94no—
656C2×D4—92no—
657C2×D4—188no—
658C2×D4—364no—
659C2×D4—364no—
660C22×C4—34no—
661C22×C4—92no—
662C22×C4—92no—
663C22×C4—92no—
664C22×C4—94no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—92no—
668C22×C4—92no—
669C22×C4—92no—
670C22×C4—92no—
671C22×C4—362no—
672C22×C4—362no—
673C22×C4C2×D3211yescharacteristic
674C22×C4C2×D3211yescharacteristic
675C4⋊C4—34no—
676C4⋊C4—32no—
677C4⋊C4—32no—
678C4⋊C4—34no—
679C4⋊C4—94no—
680C4⋊C4—92no—
681C4⋊C4—92no—
682C4⋊C4—94no—
683C22⋊C4—34no—
684C22⋊C4—34no—
685C22⋊C4—34no—
686C22⋊C4—34no—
687C22⋊C4—34no—
688C22⋊C4—94no—
689C22⋊C4—94no—
690C22⋊C4—94no—
691C22⋊C4—94no—
692C22⋊C4—94no—
693C22⋊C4—94no—
694C22⋊C4—94no—
695C22⋊C4—94no—
696C22⋊C4C2×D3214yes—
697C42—34no—
698C42—94no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—24no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—48no—
712C22×C3—48no—
713C22×C3—64no—
714C22×C3—64no—
715C22×C3—64no—
716C22×C3D3×#4114yes—
717C22×C3C24×D312yes—
718C2×D3—24no—
719C2×D3—24no—
720C2×D3—24no—
721C2×D3—38no—
722C2×D3—34no—
723C2×D3—34no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—64no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—62no—
730C2×D3—62no—
731C2×D3—616no—
732C2×D3—616no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—64no—
738C2×D3—64no—
739C2×D3—122no—
740C2×D3—122no—
741C2×D3—128no—
742C2×D3—1216no—
743C2×D3—1216no—
744C2×D3—1216no—
745C2×D3—1216no—
746C2×D3—128no—
747C2×D3—248no—
748C3×C4—22no—
749C3×C4—24no—
750C3×C4—22no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—64no—
754C3×C4—64no—
755C3×C4—64no—
756Dic3—24no—
757Dic3—24no—
758Dic3—24no—
759Dic3—64no—
760Dic3—62no—
761Dic3—62no—
762Dic3—122no—
763Dic3—122no—
764C32#349011yescharacteristic, complemented, Sylow
765C23—22no—
766C23—34no—
767C23—41no—
768C23—41no—
769C23—92no—
770C23—91no—
771C23—91no—
772C23—94no—
773C23—182no—
774C23—182no—
775C23—184no—
776C23—184no—
777C23—184no—
778C23—184no—
779C23—184no—
780C23—182no—
781C23—361no—
782C23—361no—
783C23—362no—
784C23—362no—
785C23—3616no—
786C23—362no—
787C23—362no—
788C23C22×D3212yes—
789C23C22×D3211yescharacteristic
790Q8—122no—
791Q8—362no—
792D4—68no—
793D4—122no—
794D4—124no—
795D4—124no—
796D4—188no—
797D4—188no—
798D4—188no—
799D4—362no—
800C2×C4—34no—
801C2×C4—34no—
802C2×C4—34no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—92no—
806C2×C4—92no—
807C2×C4—124no—
808C2×C4—184no—
809C2×C4—184no—
810C2×C4—184no—
811C2×C4—362no—
812C2×C4—362no—
813C2×C4—362no—
814C2×C4—362no—
815C2×C4—364no—
816C2×C4—361no—
817C2×C4—361no—
818C2×C4C22×D3212yes—
819C2×C4C22×D3212yes—
820C2×C3—24no—
821C2×C3—24no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—44no—
826C2×C3—44no—
827C2×C3—124no—
828C2×C3C2×D3×#4112yes—
829C2×C3D3×H(5,𝔽2)12yes—
830C2×C3D3×H(5,𝔽2)12yes—
831D3—44no—
832D3—64no—
833D3—64no—
834D3—64no—
835D3—64no—
836D3—68no—
837D3—124no—
838C22—21no—
839C22—21no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—44no—
844C22—64no—
845C22—64no—
846C22—64no—
847C22—94no—
848C22—92no—
849C22—92no—
850C22—188no—
851C22—181no—
852C22—181no—
853C22—181no—
854C22—181no—
855C22—182no—
856C22—182no—
857C22—364no—
858C22—368no—
859C22—368no—
860C22—724no—
861C22#6430612yes—
862C22C23×D3211yescharacteristic
863C4—22no—
864C4—22no—
865C4—64no—
866C4—64no—
867C4—64no—
868C4—182no—
869C4—182no—
870C3—21no—
871C3#8641412yescomplemented
872C2—22no—
873C2—42no—
874C2—124no—
875C2—182no—
876C2—182no—
877C2—184no—
878C2C2×#6430611yescharacteristic
879C2#1059667511yescharacteristic
880C2#1059667511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3490
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊C4×C3⋊D3C2semidirect
2. C3×#5494C2semidirect
3. #10595527C2semidirect
4. #10595508C2semidirect
5. #10595084C2semidirect
6. #10595058C2semidirect
7. #10595016C2semidirect
8. #10594981C2semidirect
9. #10594922C2semidirect
10. #10594285C2semidirect
11. #10594279C2semidirect
12. #10594228C2semidirect
13. #10594153C2semidirect
16. C22×C4×C3⋊D3C22semidirect
17. C22×C4×C3⋊D3C22semidirect
19. C2×#3811C22semidirect
20. C2×#3811C22semidirect
21. C2×#3798C22semidirect
22. C2×#3796C22semidirect
23. C2×C32×C22⋊C4C22semidirect
24. C2×#3757C22semidirect
27. C22⋊C4×C3⋊D3C22semidirect
28. C22⋊C4×C3⋊D3C22semidirect
29. C3×#953C22semidirect
30. C3×#930C22semidirect
31. C3×C4×#67C22semidirect
32. C3×#924C22semidirect
33. C3×#885C22semidirect
34. C3×#884C22semidirect
35. C3×#883C22semidirect
36. C3×#879C22semidirect
37. #63982C22semidirect
40. #63981C22semidirect
41. #63980C22semidirect
43. #63974C22semidirect
44. #63974C22semidirect
45. #67⋊Dic3C22semidirect
46. #63970C22semidirect
47. #63969C22semidirect
48. #63959C22semidirect
49. #63956C22semidirect
50. #63922C22semidirect
51. D3×(C2×D3)⋊C4C22semidirect
52. #63916C22semidirect
53. #63912C22semidirect
54. #63904C22semidirect
55. C4×#626C22semidirect
56. #63895C22semidirect
57. #63888C22semidirect
58. #63881C22semidirect
59. #63880C22semidirect
60. #63874C22semidirect
61. #63871C22semidirect
62. #63865C22semidirect
63. #63854C22semidirect
64. #63853C22semidirect
65. #63853C22semidirect
66. #63849C22semidirect
67. #63836C22semidirect
85. #5494D3semidirect
110. C2×C3×D12C23semidirect
111. C2×C3×C4×D3C23semidirect
112. C2×C3×Dic6C23semidirect
116. C2×#627C23semidirect
120. C2×#625C23semidirect
124. C2×D3×Dic3C23semidirect
134. C3×(C2×D3)⋊C4C23semidirect
135. C3×(C2×D3)⋊C4C23semidirect
136. C3×C4⋊Dic3C23semidirect
137. C3×C4⋊Dic3C23semidirect
138. C3×Dic3⋊C4C23semidirect
139. C3×Dic3⋊C4C23semidirect
140. C3×C4×Dic3C23semidirect
141. #3724C23semidirect
142. #3724C23semidirect
143. Dic3⋊Dic3C23semidirect
144. Dic3⋊Dic3C23semidirect
148. (C2×D3)⋊Dic3C23semidirect
149. (C2×D3)⋊Dic3C23semidirect
150. Dic32C23semidirect
173. C2×C3×C22⋊C4C2×D3semidirect
174. #953C2×D3semidirect
190. #930C2×D3semidirect
193. C4×#67C2×D3semidirect
199. #924C2×D3semidirect
215. #885C2×D3semidirect
217. #884C2×D3semidirect
222. #883C2×D3semidirect
242. #879C2×D3semidirect
265. C22×C3⋊D3#41semidirect
364. C2×D12C22×D3semidirect
383. C2×C4×D3C22×D3semidirect
385. C2×Dic6C22×D3semidirect
421. (C2×D3)⋊C4C22×D3semidirect
422. (C2×D3)⋊C4C22×D3semidirect
425. C4⋊Dic3C22×D3semidirect
426. C4⋊Dic3C22×D3semidirect
431. Dic3⋊C4C22×D3semidirect
432. Dic3⋊C4C22×D3semidirect
435. C4×Dic3C22×D3semidirect
520. C2×C22⋊C4D32semidirect
764. C32#3490semidirect
871. C3#86414semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C3×#54942
#105955272
#105955082
#105950842
#105950582
#105950162
#105949812
#105949222
#105942852
#105942792
#105942282
#105941532
#864143