Finite Group Databasebeta

← #11906187

Subgroups — #11906187

Order 1152.

2311 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5727C212yesmaximal, complemented
3D3×#946C214yesmaximal, complemented
4#10595407C212yesmaximal, complemented
5Q8×#625C212yesmaximal, complemented
6#10594636C214yesmaximal, complemented
7#10594606C212yesmaximal
8#10594534C214yesmaximal, complemented
9#10594460C214yesmaximal, complemented
10#10594351C212yesmaximal, complemented
11C4×#3802C211yesmaximal, characteristic
12#10593960C212yesmaximal, complemented
13#10593882C211yesmaximal, characteristic, complemented
14#86761—32nomaximal
15C2×C3×D3×Q8C2214yescomplemented
16C2×#3802C2211yescharacteristic
17C2×C4×D32C2212yes—
18C32×C4⋊Q8C2211yescharacteristic, complemented
19#64155C2212yes—
20Q8×C3⋊Dic3C2212yescomplemented
21#64106C2212yes—
22#64101C2212yes—
23#64099C2212yescomplemented
24#64096C2212yescomplemented
25C42×C3⋊D3C2211yescharacteristic
26#64078C2211yescharacteristic, complemented
27C3×#946C2214yescomplemented
28C3×#896C2218yescomplemented
29C3×#893C2214yes—
30C3×#888C2214yescomplemented
31C3×C4×D12C2212yes—
32C3×C4×Dic6C2212yescomplemented
33#63921C2212yes—
34D3×(C2×D3)⋊C4C2218yes—
35#63919C2211yescharacteristic, complemented
36C4×#627C2212yescomplemented
37#63902C2214yes—
38#63902C2212yes—
39C4×#625C2214yes—
40C4×#625C2212yes—
41#63900C2211yescharacteristic
42#63898C2212yes—
43#63896C2218yescomplemented
44#63893C2218yescomplemented
45Dic3×D12C2214yes—
46D3×C4⋊Dic3C2214yescomplemented
47#63888C2218yes—
48#63887C2218yescomplemented
49D3×Dic3⋊C4C2218yescomplemented
50#63874C2212yes—
51#63873C2214yescomplemented
52#63873C2211yescharacteristic, complemented
53#63871C2212yes—
54#63870C2214yescomplemented
55#63870C2212yescomplemented
56#63869C2214yescomplemented
57#63865C2212yes—
58#63856C2218yescomplemented
59#63856C2214yescomplemented
60C3×D4×Q8—32no—
61Q8×#67—34no—
62C2×#946—34no—
63#5730—34no—
64#5729—34no—
65#5728—32no—
66#5728—61no—
67#5727D312yescomplemented
68#5636—38no—
69#5635—34no—
70#5634—38no—
71D3×C22⋊Q8—34no—
72#5579—32no—
73#5578—32no—
74#5545—34no—
75C4×D3×D4—32no—
76#5543—32no—
77#5539—34no—
78C22×D32C2312yes—
79C2×C32×Q8C2312yes—
80C2×C4×C3⋊D3C2311yescharacteristic
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×#634C2312yes—
84C3×D3×Q8—48no—
85C2×C3×D12C2312yes—
86C2×C3×C4×D3C2314yes—
87C2×C3×C4×D3C2318yes—
88C2×C3×Dic6C2312yes—
89C2×C3×Dic6C2318yes—
90C2×#627C2312yes—
91C2×#625C2312yes—
92C2×#624C2312yes—
93C2×D3×Dic3C2314yes—
94C2×D3×Dic3C2318yes—
95#3802Q818yescomplemented
96C4×D32—44no—
97C32×C4⋊C4C2312yes—
98C32×C4⋊C4C2312yes—
99C32×C42C2311yescharacteristic
100#3752C2314yes—
101C4⋊(C3⋊Dic3)C2312yes—
102C4⋊(C3⋊Dic3)C2312yes—
103C4⋊(C3⋊Dic3)C2314yes—
104#3750C2314yes—
105C4×C3⋊Dic3C2311yescharacteristic
106C4×C3⋊Dic3C2311yescharacteristic
107C4×C3⋊Dic3C2311yescharacteristic
108C4×C3⋊Dic3C2314yes—
109C3×(C2×D3)⋊C4C2318yes—
110C3×(C2×D3)⋊C4C2314yes—
111C3×C4⋊Dic3C2312yes—
112C3×C4⋊Dic3C2312yes—
113C3×Dic3⋊C4C2318yes—
114C3×Dic3⋊C4C2314yes—
115C3×C4×Dic3C2314yes—
116#3724C2312yes—
117#3724C2318yes—
118#3724C2312yes—
119#3724C2312yes—
120#3724C2312yes—
121Dic3⋊Dic3C2318yes—
122Dic3⋊Dic3C2314yes—
123#3722C2314yes—
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2314yes—
126#3501—91noSylow
127C22×C3×Q8—34no—
128C2×D3×Q8C2×D314yescomplemented
129C2×D3×D4—32no—
130C22×C4×D3—34no—
131C3×C4⋊Q8—21no—
132C3×C4⋊Q8—34no—
133C3×C4⋊Q8C2×D312yescomplemented
134C3×C22⋊Q8—34no—
135C3×C22⋊Q8—38no—
136C3×C4×Q8—32no—
137C3×C4×D4—34no—
138C3×C4×D4—32no—
139#946—34no—
140#946—38no—
141#946—34no—
142#946—38no—
143#946—32no—
144#946—38no—
145#946—62no—
146#946C2×D314yescomplemented
147Q8×Dic3—34no—
148Q8×Dic3—62no—
149#944—38no—
150#944—32no—
151D4×Dic3—32no—
152D4×Dic3—34no—
153C4×#67—34no—
154C4×#67—38no—
155C2×(C2×D3)⋊C4—38no—
156C2×C4⋊Dic3—34no—
157#924—38no—
158#924—34no—
159C2×Dic3⋊C4—38no—
160#897—32no—
161#897—34no—
162#897—38no—
163#897—62no—
164#896—38no—
165#896—38no—
166#896—34no—
167#896C2×D318yescomplemented
168#893—32no—
169#893C2×D314yes—
170#892—34no—
171#892—62no—
172D3×C4⋊C4—34no—
173D3×C4⋊C4—38no—
174D3×C4⋊C4—32no—
175#890—34no—
176#890—34no—
177#890—62no—
178#889—38no—
179#889—34no—
180#888—32no—
181#888C2×D314yescomplemented
182#887—34no—
183#887—62no—
184#67⋊C4—38no—
185#67⋊C4—34no—
186D3×C22⋊C4—38no—
187D3×C22⋊C4—34no—
188#878—38no—
189#878—38no—
190#878—38no—
191C4×D12—34no—
192C4×D12C2×D312yes—
193#872—34no—
194C42×D3—32no—
195C42×D3—61no—
196#870—34no—
197#869—32no—
198#869—61no—
199C4×Dic6—34no—
200C4×Dic6C2×D312yescomplemented
201C22×C3⋊D3C2411yescharacteristic
202C22×C3×D3C2414yes—
203C2×D32—42no—
204C2×D32—42no—
205C2×D32C2×Q818yescomplemented
206C32×Q8—24no—
207C2×C32×C4C2411yescharacteristic
208C2×C32×C4C2414yes—
209C2×C32×C4C2411yescharacteristic
210C2×C32×C4C2411yescharacteristic
211C2×C3⋊Dic3C2411yescharacteristic
212C2×C3⋊Dic3C2414yes—
213C2×C3⋊Dic3C2411yescharacteristic
214C2×C3⋊Dic3C2411yescharacteristic
215C4×C3⋊D3—22no—
216C4×C3⋊D3—41no—
217C4×C3⋊D3C2×Q814yescomplemented
218#634—42no—
219C2×C3×Dic3C2414yes—
220C2×C3×Dic3C2414yes—
221C2×C3×Dic3C2414yes—
222C3×D12C2×Q818yescomplemented
223C3×C4×D3—28no—
224C3×C4×D3—48no—
225C3×Dic6—24no—
226C3×Dic6—48no—
227#627—42no—
228#625C2×Q818yescomplemented
229#624—42no—
230D3×Dic3—44no—
231D3×Dic3—48no—
232#554—92no—
233#554—94no—
234#554—92no—
235#554—94no—
236D4×Q8—32no—
237D4×Q8—92no—
238#544—92no—
239#543—94no—
240#533—91no—
241#533—91no—
242C2×C22⋊Q8—94no—
243#518—92no—
244C2×C4×D4—91no—
245C23×D3—34no—
246C2×C3×Q8—22no—
247C2×C3×Q8—32no—
248C2×C3×Q8—38no—
249C2×C3×Q8—128no—
250C2×C3×Q8C22×D314yes—
251C2×C3×D4—32no—
252C22×C3×C4—34no—
253C22×C3×C4—38no—
254C2×#67—34no—
255C22×Dic3—34no—
256C22×Dic3—38no—
257D3×Q8—48no—
258D3×D4—316no—
259C2×D12C22×D312yes—
260C2×C4×D3—32no—
261C2×C4×D3—32no—
262C2×C4×D3—38no—
263C2×C4×D3—34no—
264C2×C4×D3—32no—
265C2×C4×D3—34no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—128no—
270C2×C4×D3C22×D314yes—
271C2×C4×D3C22×D318yes—
272C2×Dic6—34no—
273C2×Dic6—34no—
274C2×Dic6—62no—
275C2×Dic6C22×D312yes—
276C2×Dic6C22×D318yes—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—32no—
280C3×C4⋊C4—38no—
281C3×C4⋊C4—34no—
282C3×C4⋊C4—32no—
283C3×C4⋊C4C22×D314yes—
284C3×C4⋊C4C22×D314yes—
285C3×C22⋊C4—34no—
286C3×C22⋊C4—38no—
287C3×C42—21no—
288C3×C42—34no—
289C3×C42C22×D312yes—
290#217—34no—
291#217—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—34no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—34no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—64no—
298(C2×D3)⋊C4C22×D314yes—
299(C2×D3)⋊C4C22×D318yes—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—38no—
303C4⋊Dic3—34no—
304C4⋊Dic3—38no—
305C4⋊Dic3—62no—
306C4⋊Dic3—62no—
307C4⋊Dic3—64no—
308C4⋊Dic3C22×D312yes—
309C4⋊Dic3C22×D312yes—
310Dic3⋊C4—38no—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—34no—
316Dic3⋊C4—34no—
317Dic3⋊C4—38no—
318Dic3⋊C4—34no—
319Dic3⋊C4—64no—
320Dic3⋊C4C22×D314yes—
321Dic3⋊C4C22×D318yes—
322C4×Dic3—32no—
323C4×Dic3—32no—
324C4×Dic3—32no—
325C4×Dic3—38no—
326C4×Dic3—61no—
327C4×Dic3—61no—
328C4×Dic3—61no—
329C4×Dic3—64no—
330C4×Dic3C22×D314yes—
331C22×C32C2511yescharacteristic
332C2×C3⋊D3—21no—
333C2×C3⋊D3—21no—
334C2×C3⋊D3C22×Q812yes—
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3C22×Q818yes—
338D32—48no—
339C32×C4—21no—
340C32×C4—24no—
341C32×C4C22×Q812yes—
342C32×C4H(5,𝔽2)12yes—
343C3⋊Dic3—21no—
344C3⋊Dic3—24no—
345C3⋊Dic3—21no—
346C3⋊Dic3C22×Q812yes—
347C3×Dic3—24no—
348C3×Dic3—24no—
349C3×Dic3—24no—
350C22×Q8—34no—
351C22×D4—91no—
352C23×C4—92no—
353C4⋊Q8—34no—
354C4⋊Q8—91no—
355C4⋊Q8—91no—
356C4⋊Q8—94no—
357C4⋊Q8—91no—
358C4⋊Q8D3211yescharacteristic, complemented
359#125—94no—
360#125—92no—
361#125—94no—
362#125—92no—
363C22⋊Q8—34no—
364C22⋊Q8—38no—
365C22⋊Q8—98no—
366C22⋊Q8—98no—
367C22⋊Q8—98no—
368C22⋊Q8—92no—
369C22⋊Q8—92no—
370C22⋊Q8—98no—
371C22⋊Q8—94no—
372C22⋊Q8—98no—
373C22⋊Q8—92no—
374C22⋊Q8—92no—
375C4×Q8—32no—
376C4×Q8—92no—
377C4×Q8—92no—
378C4×Q8—92no—
379C4×D4—34no—
380C4×D4—32no—
381C4×D4—94no—
382C4×D4—92no—
383C4×D4—94no—
384C4×D4—92no—
385C4×D4—92no—
386C4×D4—94no—
387#117—92no—
388#117—92no—
389C2×C4⋊C4—91no—
390C2×C4⋊C4—98no—
391C2×C4⋊C4—94no—
392C2×C22⋊C4—92no—
393C2×C22⋊C4—98no—
394C2×C42—91no—
395C23×C3—34no—
396C22×D3—32no—
397C22×D3—316no—
398C22×D3—61no—
399C22×D3—124no—
400C22×D3—124no—
401C22×D3C23×D314yes—
402C3×Q8—28no—
403C3×Q8—44no—
404C3×Q8—64no—
405C3×Q8—128no—
406C3×D4—38no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—24no—
411C2×C3×C4—34no—
412C2×C3×C4—34no—
413C2×C3×C4—34no—
414C2×C3×C4—68no—
415C2×C3×C4—128no—
416C2×C3×C4C23×D318yes—
417C2×C3×C4C23×D312yes—
418C2×C3×C4C23×D312yes—
419C2×C3×C4C23×D312yes—
420#67—316no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—38no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—64no—
429C2×Dic3—124no—
430C2×Dic3—128no—
431C2×Dic3C23×D314yes—
432C2×Dic3C23×D314yes—
433C2×Dic3C23×D314yes—
434D12D3×Q818yescomplemented
435C4×D3—28no—
436C4×D3—38no—
437C4×D3—48no—
438C4×D3—64no—
439C4×D3—64no—
440C4×D3—122no—
441C4×D3—124no—
442C4×D3—122no—
443C4×D3—128no—
444C4×D3—124no—
445C4×D3—122no—
446Dic6—24no—
447Dic6—48no—
448Dic6—124no—
449Dic6—124no—
450Dic6—124no—
451C2×C32C23×Q811yescharacteristic
452C2×C32C2×H(5,𝔽2)11yescharacteristic
453C2×C32#58511yescharacteristic
454C3⋊D3—22no—
455C3×D3—28no—
456C24—92no—
457C2×Q8—32no—
458C2×Q8—38no—
459C2×Q8—92no—
460C2×Q8—92no—
461C2×Q8—128no—
462C2×Q8C2×D3212yes—
463C2×D4—32no—
464C2×D4—98no—
465C2×D4—92no—
466C22×C4—34no—
467C22×C4—38no—
468C22×C4—92no—
469C22×C4—98no—
470C22×C4—94no—
471C22×C4—91no—
472C22×C4—91no—
473C22×C4—91no—
474C22×C4—364no—
475C4⋊C4—32no—
476C4⋊C4—32no—
477C4⋊C4—38no—
478C4⋊C4—34no—
479C4⋊C4—94no—
480C4⋊C4—92no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—92no—
484C4⋊C4—92no—
485C4⋊C4—92no—
486C4⋊C4—94no—
487C4⋊C4—92no—
488C4⋊C4—92no—
489C4⋊C4—94no—
490C4⋊C4C2×D3212yes—
491C4⋊C4C2×D3212yes—
492C22⋊C4—38no—
493C22⋊C4—34no—
494C22⋊C4—94no—
495C22⋊C4—98no—
496C22⋊C4—94no—
497C22⋊C4—94no—
498C42—34no—
499C42—91no—
500C42—91no—
501C42—91no—
502C42—94no—
503C42C2×D3211yescharacteristic
504C22×C3—21no—
505C22×C3—38no—
506C22×C3—64no—
507C22×C3—64no—
508C22×C3C24×D312yes—
509C2×D3—24no—
510C2×D3—24no—
511C2×D3—34no—
512C2×D3—62no—
513C2×D3—62no—
514C2×D3—62no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—1216no—
518C2×D3C2×D3×Q818yes—
519C3×C4—22no—
520C3×C4—28no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—44no—
525C3×C4—64no—
526C3×C4—64no—
527C3×C4—64no—
528C3×C4#100414yes—
529C3×C4C2×D3×Q814yes—
530Dic3—24no—
531Dic3—24no—
532Dic3—24no—
533Dic3—34no—
534Dic3—62no—
535Dic3—62no—
536Dic3—62no—
537Dic3—68no—
538Dic3—124no—
539Dic3—121no—
540Dic3—121no—
541C32#350111yescharacteristic, complemented, Sylow
542C23—34no—
543C23—98no—
544C23—91no—
545C23—362no—
546C23—362no—
547Q8—24no—
548Q8—64no—
549Q8—128no—
550Q8—362no—
551Q8—362no—
552D4—38no—
553D4—98no—
554C2×C4—34no—
555C2×C4—34no—
556C2×C4—34no—
557C2×C4—68no—
558C2×C4—91no—
559C2×C4—94no—
560C2×C4—91no—
561C2×C4—91no—
562C2×C4—94no—
563C2×C4—128no—
564C2×C4—182no—
565C2×C4—361no—
566C2×C4—362no—
567C2×C4—364no—
568C2×C4—368no—
569C2×C4C22×D3211yescharacteristic
570C2×C4C22×D3214yes—
571C2×C4C22×D3211yescharacteristic
572C2×C4C22×D3211yescharacteristic
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—68no—
577C2×C3C2×#100412yes—
578C2×C3C22×D3×Q812yes—
579C2×C3#596812yes—
580D3—28no—
581D3—64no—
582D3—122no—
583C22—38no—
584C22—64no—
585C22—64no—
586C22—92no—
587C22—181no—
588C22—181no—
589C22—368no—
590C22C23×D3211yescharacteristic
591C4—24no—
592C4—21no—
593C4—64no—
594C4—64no—
595C4—64no—
596C4—92no—
597C4—181no—
598C4—184no—
599C4—181no—
600C4#6431312yes—
601C4D32×Q812yes—
602C3—21no—
603C3#8676112yescomplemented
604C2—68no—
605C2—182no—
606C2C2×#6431311yescharacteristic
607C2C2×D32×Q811yescharacteristic
608C2#1059668911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3802C22
hypercenterC4⋊Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
2. C3×#5727C2semidirect
3. D3×#946C2semidirect
4. #10595407C2semidirect
5. Q8×#625C2semidirect
6. #10594636C2semidirect
8. #10594534C2semidirect
9. #10594460C2semidirect
10. #10594351C2semidirect
12. #10593960C2semidirect
13. #10593882C2semidirect
15. C2×C3×D3×Q8C22semidirect
18. C32×C4⋊Q8C22semidirect
20. Q8×C3⋊Dic3C22semidirect
23. #64099C22semidirect
24. #64096C22semidirect
26. #64078C22semidirect
27. C3×#946C22semidirect
28. C3×#896C22semidirect
30. C3×#888C22semidirect
32. C3×C4×Dic6C22semidirect
35. #63919C22semidirect
36. C4×#627C22semidirect
43. #63896C22semidirect
44. #63893C22semidirect
46. D3×C4⋊Dic3C22semidirect
48. #63887C22semidirect
49. D3×Dic3⋊C4C22semidirect
51. #63873C22semidirect
52. #63873C22semidirect
54. #63870C22semidirect
55. #63870C22semidirect
56. #63869C22semidirect
58. #63856C22semidirect
59. #63856C22semidirect
67. #5727D3semidirect
95. #3802Q8semidirect
128. C2×D3×Q8C2×D3semidirect
133. C3×C4⋊Q8C2×D3semidirect
146. #946C2×D3semidirect
167. #896C2×D3semidirect
181. #888C2×D3semidirect
200. C4×Dic6C2×D3semidirect
205. C2×D32C2×Q8semidirect
217. C4×C3⋊D3C2×Q8semidirect
222. C3×D12C2×Q8semidirect
228. #625C2×Q8semidirect
358. C4⋊Q8D32semidirect
434. D12D3×Q8semidirect
541. C32#3501semidirect
603. C3#86761semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57272
D3×#9462
#105954072
Q8×#6252
#105946362
#105946062
#105945342
#105944602
#105943512
C4×#38022
#105939602
#105938822
#867613