Finite Group Databasebeta

← #11906192

Subgroups — #11906192

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×#5730C212yesmaximal, complemented
3#10595434C214yesmaximal, complemented
4#10595407C214yesmaximal, complemented
5D3×#897C214yesmaximal, complemented
6#10594606C212yesmaximal
7#10594531C212yesmaximal, complemented
8#10594526C212yesmaximal, complemented
9#10594508C212yesmaximal, complemented
10#10594452C214yesmaximal, complemented
11C4×#3802C211yesmaximal, characteristic
12Dic6×D12C212yesmaximal, complemented
13#10593882C211yesmaximal, characteristic, complemented
14#86948—32nomaximal
15C2×#3802C2211yescharacteristic
16C2×C4×D32C2212yes—
17C2×D3×Dic6C2214yescomplemented
18C32×C4⋊Q8C2211yescharacteristic, complemented
19#64155C2212yes—
20Q8×C3⋊Dic3C2212yescomplemented
21#64106C2212yes—
22#64101C2212yes—
23#64099C2212yescomplemented
24#64096C2212yescomplemented
25C42×C3⋊D3C2211yescharacteristic
26#64078C2211yescharacteristic, complemented
27C3×#946C2218yescomplemented
28C3×#897C2214yescomplemented
29C3×#893C2214yes—
30C3×D3×C4⋊C4C2214yescomplemented
31C3×#890C2214yescomplemented
32C3×C4×D12C2212yes—
33C3×C4×Dic6C2212yescomplemented
34#63921C2212yes—
35D3×(C2×D3)⋊C4C2218yes—
36#63919C2214yescomplemented
37#63919C2211yescharacteristic, complemented
38#63918C2214yescomplemented
39C4×#627C2212yescomplemented
40#63902C2214yes—
41#63902C2212yes—
42C4×#625C2214yes—
43C4×#625C2212yes—
44#63900C2211yescharacteristic
45#63899C2218yescomplemented
46#63898C2212yes—
47#63895C2218yes—
48#63893C2218yescomplemented
49#63893C2218yescomplemented
50Dic3×D12C2214yes—
51D3×C4⋊Dic3C2218yescomplemented
52#63874C2212yes—
53#63873C2211yescharacteristic, complemented
54#63871C2212yes—
55#63870C2212yescomplemented
56#63870C2214yescomplemented
57#63865C2212yes—
58#63857C2214yescomplemented
59#63851C2218yescomplemented
60C3×#554—32no—
61#5730D312yescomplemented
62#5728—32no—
63#5728—61no—
64#5690—34no—
65#5689—34no—
66#5635—38no—
67#5634—38no—
68#5632—34no—
69D3×C22⋊Q8—34no—
70#5578—32no—
71Q8×D12—32no—
72#5545—34no—
73C4×D3×D4—32no—
74#5543—34no—
75D4×Dic6—32no—
76#5511—34no—
77C2×#897—34no—
78C22×D32C2312yes—
79C2×C32×Q8C2312yes—
80C2×C4×C3⋊D3C2311yescharacteristic
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×#634C2312yes—
84C2×C3×D12C2312yes—
85C2×C3×C4×D3C2314yes—
86C2×C3×C4×D3C2318yes—
87C2×C3×Dic6C2312yes—
88C2×#627C2318yes—
89C2×#627C2312yes—
90C2×#625C2312yes—
91C2×#624C2312yes—
92C2×D3×Dic3C2318yes—
93C2×D3×Dic3C2314yes—
94#3802Q818yescomplemented
95C4×D32—44no—
96D3×Dic6—48no—
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⋊Dic3C2318yes—
113C3×C4⋊Dic3C2312yes—
114C3×Dic3⋊C4C2318yes—
115C3×Dic3⋊C4C2314yes—
116C3×C4×Dic3C2314yes—
117#3724C2312yes—
118#3724C2312yes—
119#3724C2312yes—
120#3724C2312yes—
121Dic3⋊Dic3C2318yes—
122Dic3⋊Dic3C2314yes—
123#3722C2314yes—
124(C2×D3)⋊Dic3C2314yes—
125(C2×D3)⋊Dic3C2318yes—
126#3501—91noSylow
127C2×D3×Q8—34no—
128C2×D3×D4—32no—
129C22×C4×D3—34no—
130C22×Dic6—34no—
131C3×C4⋊Q8—21no—
132C3×C4⋊Q8C2×D312yescomplemented
133C3×#125—34no—
134C3×C22⋊Q8—38no—
135C3×C22⋊Q8—34no—
136C3×C4×Q8—32no—
137C3×C4×D4—34no—
138C3×C4×D4—32no—
139C2×C3×C4⋊C4—34no—
140#946—34no—
141#946—32no—
142#946—62no—
143#946C2×D318yescomplemented
144Q8×Dic3—34no—
145Q8×Dic3—62no—
146#944—32no—
147D4×Dic3—32no—
148D4×Dic3—34no—
149C4×#67—34no—
150C4×#67—38no—
151C2×(C2×D3)⋊C4—38no—
152C2×C4⋊Dic3—38no—
153#924—34no—
154#924—38no—
155#897—34no—
156#897—32no—
157#897—34no—
158#897—38no—
159#897—38no—
160#897—38no—
161#897—62no—
162#897C2×D314yescomplemented
163#896—38no—
164#896—38no—
165#896—34no—
166#896—38no—
167#893—32no—
168#893C2×D314yes—
169#892—34no—
170#892—62no—
171D3×C4⋊C4—38no—
172D3×C4⋊C4—32no—
173D3×C4⋊C4C2×D314yescomplemented
174#890—34no—
175#890—62no—
176#890C2×D314yescomplemented
177#889—34no—
178#889—38no—
179#888—38no—
180#888—32no—
181#888—34no—
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#869—32no—
197#869—34no—
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—42no—
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—24no—
219C2×C3×Dic3C2414yes—
220C2×C3×Dic3C2414yes—
221C2×C3×Dic3C2414yes—
222C3×D12C2×Q818yescomplemented
223C3×C4×D3—28no—
224C3×C4×D3—48no—
225C3×Dic6—24no—
226#627—48no—
227#627—42no—
228#625C2×Q818yescomplemented
229#624—42no—
230D3×Dic3—48no—
231D3×Dic3—44no—
232#554—32no—
233#554—92no—
234#554—94no—
235#554—94no—
236D4×Q8—92no—
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×Q8C22×D314yes—
249C2×C3×D4—32no—
250C22×C3×C4—34no—
251C22×C3×C4—38no—
252C2×#67—34no—
253C22×Dic3—34no—
254C22×Dic3—38no—
255D3×Q8—128no—
256D3×D4—316no—
257C2×D12C22×D312yes—
258C2×C4×D3—32no—
259C2×C4×D3—32no—
260C2×C4×D3—38no—
261C2×C4×D3—34no—
262C2×C4×D3—32no—
263C2×C4×D3—34no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—128no—
268C2×C4×D3C22×D314yes—
269C2×C4×D3C22×D318yes—
270C2×Dic6—34no—
271C2×Dic6—34no—
272C2×Dic6—38no—
273C2×Dic6—38no—
274C2×Dic6—62no—
275C2×Dic6—128no—
276C2×Dic6C22×D312yes—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—32no—
280C3×C4⋊C4—38no—
281C3×C4⋊C4—32no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—34no—
284C3×C4⋊C4C22×D314yes—
285C3×C4⋊C4C22×D314yes—
286C3×C22⋊C4—38no—
287C3×C22⋊C4—34no—
288C3×C42—21no—
289C3×C42—34no—
290C3×C42C22×D312yes—
291#217—34no—
292#217—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—34no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4C22×D314yes—
300(C2×D3)⋊C4C22×D318yes—
301C4⋊Dic3—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—38no—
304C4⋊Dic3—34no—
305C4⋊Dic3—38no—
306C4⋊Dic3—62no—
307C4⋊Dic3—62no—
308C4⋊Dic3—64no—
309C4⋊Dic3C22×D312yes—
310C4⋊Dic3C22×D312yes—
311C4⋊Dic3C22×D318yes—
312Dic3⋊C4—38no—
313Dic3⋊C4—34no—
314Dic3⋊C4—34no—
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—94no—
351C22×D4—91no—
352C23×C4—92no—
353C4⋊Q8—94no—
354C4⋊Q8—91no—
355C4⋊Q8—94no—
356C4⋊Q8—91no—
357C4⋊Q8—91no—
358C4⋊Q8D3211yescharacteristic, complemented
359#125—34no—
360#125—92no—
361#125—94no—
362#125—92no—
363C22⋊Q8—38no—
364C22⋊Q8—34no—
365C22⋊Q8—98no—
366C22⋊Q8—98no—
367C22⋊Q8—98no—
368C22⋊Q8—98no—
369C22⋊Q8—92no—
370C22⋊Q8—94no—
371C22⋊Q8—98no—
372C22⋊Q8—92no—
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—34no—
390C2×C4⋊C4—91no—
391C2×C4⋊C4—98no—
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—44no—
403C3×Q8—44no—
404C3×Q8—64no—
405C3×D4—38no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—24no—
410C2×C3×C4—34no—
411C2×C3×C4—34no—
412C2×C3×C4—34no—
413C2×C3×C4—68no—
414C2×C3×C4—128no—
415C2×C3×C4C23×D318yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418C2×C3×C4C23×D312yes—
419#67—316no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—38no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—64no—
428C2×Dic3—128no—
429C2×Dic3—124no—
430C2×Dic3C23×D314yes—
431C2×Dic3C23×D314yes—
432C2×Dic3C23×D314yes—
433D12D3×Q818yescomplemented
434C4×D3—28no—
435C4×D3—38no—
436C4×D3—48no—
437C4×D3—64no—
438C4×D3—64no—
439C4×D3—122no—
440C4×D3—124no—
441C4×D3—122no—
442C4×D3—124no—
443C4×D3—128no—
444C4×D3—122no—
445Dic6—24no—
446Dic6—68no—
447Dic6—124no—
448Dic6—124no—
449Dic6—128no—
450Dic6—128no—
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—92no—
459C2×Q8—98no—
460C2×Q8—92no—
461C2×Q8—368no—
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—38no—
477C4⋊C4—32no—
478C4⋊C4—38no—
479C4⋊C4—34no—
480C4⋊C4—94no—
481C4⋊C4—92no—
482C4⋊C4—98no—
483C4⋊C4—92no—
484C4⋊C4—92no—
485C4⋊C4—92no—
486C4⋊C4—94no—
487C4⋊C4—92no—
488C4⋊C4—94no—
489C4⋊C4—92no—
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×C4C2×D3×Q814yes—
529C3×C4#100914yes—
530Dic3—24no—
531Dic3—24no—
532Dic3—24no—
533Dic3—34no—
534Dic3—62no—
535Dic3—68no—
536Dic3—62no—
537Dic3—62no—
538Dic3—124no—
539Dic3—121no—
540Dic3—121no—
541C32#350111yescharacteristic, complemented, Sylow
542C23—34no—
543C23—98no—
544C23—91no—
545C23—362no—
546C23—362no—
547Q8—42no—
548Q8—64no—
549Q8—184no—
550Q8—368no—
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×C3C22×D3×Q812yes—
578C2×C3C2×#100912yes—
579C2×C3#596612yes—
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—181no—
599C4—184no—
600C4D32×Q812yes—
601C4#6432012yes—
602C3—21no—
603C3#8694812yescomplemented
604C2—68no—
605C2—182no—
606C2#1059667911yescharacteristic
607C2C2×D32×Q811yescharacteristic
608C2C2×#6432011yescharacteristic
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×#5730C2semidirect
3. #10595434C2semidirect
4. #10595407C2semidirect
5. D3×#897C2semidirect
7. #10594531C2semidirect
8. #10594526C2semidirect
9. #10594508C2semidirect
10. #10594452C2semidirect
12. Dic6×D12C2semidirect
13. #10593882C2semidirect
17. C2×D3×Dic6C22semidirect
18. C32×C4⋊Q8C22semidirect
20. Q8×C3⋊Dic3C22semidirect
23. #64099C22semidirect
24. #64096C22semidirect
26. #64078C22semidirect
27. C3×#946C22semidirect
28. C3×#897C22semidirect
30. C3×D3×C4⋊C4C22semidirect
31. C3×#890C22semidirect
33. C3×C4×Dic6C22semidirect
36. #63919C22semidirect
37. #63919C22semidirect
38. #63918C22semidirect
39. C4×#627C22semidirect
45. #63899C22semidirect
48. #63893C22semidirect
49. #63893C22semidirect
51. D3×C4⋊Dic3C22semidirect
53. #63873C22semidirect
55. #63870C22semidirect
56. #63870C22semidirect
58. #63857C22semidirect
59. #63851C22semidirect
61. #5730D3semidirect
94. #3802Q8semidirect
132. C3×C4⋊Q8C2×D3semidirect
143. #946C2×D3semidirect
162. #897C2×D3semidirect
173. D3×C4⋊C4C2×D3semidirect
176. #890C2×D3semidirect
200. C4×Dic6C2×D3semidirect
205. C2×D32C2×Q8semidirect
217. C4×C3⋊D3C2×Q8semidirect
222. C3×D12C2×Q8semidirect
228. #625C2×Q8semidirect
358. C4⋊Q8D32semidirect
433. D12D3×Q8semidirect
541. C32#3501semidirect
603. C3#86948semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57302
#105954342
#105954072
D3×#8972
#105946062
#105945312
#105945262
#105945082
#105944522
C4×#38022
Dic6×D122
#105938822
#869483