Finite Group Databasebeta

← #11859249

Subgroups — #11859249

Order 1152.

1197 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63791C211yesmaximal, characteristic, complemented
2C2×D32×C8C211yesmaximal, characteristic, complemented
3C4×#3802C211yesmaximal, characteristic
4C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
5C3×#4836C212yesmaximal, complemented
6#10590935C211yesmaximal, characteristic, complemented
7#10590935C211yesmaximal, characteristic, complemented
8#10590724C212yesmaximal, complemented
9#10590723C212yesmaximal, complemented
10#10590326C212yesmaximal, complemented
11#10590322C211yesmaximal, characteristic, complemented
12D3×#435—32nomaximal
13C2×#3802C411yescharacteristic
14C2×C4×D32C2211yescharacteristic
15C2×C4×D32C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C42×C3⋊D3C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)C2212yescomplemented
20C2×C3×D3×C8C2212yescomplemented
21C3×C4×D12C2212yes—
22#63921C411yescharacteristic
23#63921C411yescharacteristic
24#63902C412yes—
25C4×#625C2212yes—
26#63900C411yescharacteristic
27#63898C412yes—
28C2×#3711C2212yescomplemented
29C2×#3710C2211yescharacteristic
30C2×#3710C2211yescharacteristic
31C2×D3×C3⋊C8C2212yescomplemented
32#63791—24no—
33D32×C8—24no—
34C32×C4⋊C8C2211yescharacteristic, complemented
35#63641C2211yescharacteristic, complemented
36#63641C2211yescharacteristic, complemented
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
38C3×(C2×D3)⋊C8C2212yescomplemented
39C3×(C2×D3)⋊C8C2212yescomplemented
40C3×#803C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43#63555C2212yescomplemented
44C2×D3×M16—32no—
45C22×D3×C8—32no—
46C4×D3×D4—32no—
47C3×#435—32no—
48#5127—32no—
49#5111—32no—
50#5011—32no—
51#4836D312yescomplemented
52D3×C4⋊C8—32no—
53D3×C4⋊C8—61no—
54#4730—32no—
55#4728—32no—
56D3×C22⋊C8—32no—
57D3×C22⋊C8—32no—
58#4706—32no—
59D3×#97—32no—
60C22×D32C2×C411yescharacteristic
61C22×D32C2×C411yescharacteristic
62C2×C4×C3⋊D3C2×C411yescharacteristic
63C2×C4×C3⋊D3C2×C411yescharacteristic
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×C3×D12C2×C412yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×C4×D3C2312yes—
68C2×#625C2×C412yes—
69C2×#624C2×C411yescharacteristic
70C2×#624C2×C411yescharacteristic
71C2×D3×Dic3C2×C412yes—
72C2×D3×Dic3C2×C412yes—
73#3802—24no—
74C4×D32—22no—
75C4×D32—22no—
76C4×D32—22no—
77C4×D32—22no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C42C2311yescharacteristic
81C4×C3⋊Dic3C2×C411yescharacteristic
82C4×C3⋊Dic3C2×C411yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C8×C3⋊D3—22no—
87C8×C3⋊D3—22no—
88C3×(C2×D3)⋊C4C2×C412yes—
89C3×(C2×D3)⋊C4C2×C412yes—
90C3×C4⋊Dic3C2×C412yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×ΓL(1,𝔽25)—24no—
94C3×D3×C8—24no—
95#3724C2×C412yes—
96(C2×D3)⋊Dic3C2×C412yes—
97(C2×D3)⋊Dic3C2×C412yes—
98#3711—24no—
99#3710—22no—
100#3710D414yescomplemented
101D3×C3⋊C8—24no—
102C2×#435—91noSylow
103C2×D3×D4—32no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C2×C3×M16—32no—
107C22×C3×C8—32no—
108C3×C4×D4—32no—
109D4×Dic3—32no—
110C4×#67—32no—
111C4×#67—32no—
112C2×#208—32no—
113C22×C3⋊C8—32no—
114D3×M16—68no—
115C2×ΓL(1,𝔽25)—32no—
116C2×ΓL(1,𝔽25)C2×D312yescomplemented
117C2×D3×C8—32no—
118C2×D3×C8—32no—
119C2×D3×C8—32no—
120C2×D3×C8—32no—
121C2×D3×C8—32no—
122C2×D3×C8—61no—
123C2×D3×C8—61no—
124C2×D3×C8—68no—
125C2×D3×C8C2×D312yescomplemented
126#893—32no—
127D3×C4⋊C4—32no—
128#67⋊C4—32no—
129#67⋊C4—32no—
130D3×C22⋊C4—32no—
131D3×C22⋊C4—32no—
132C4×D12C2×D312yes—
133C42×D3—32no—
134C42×D3—61no—
135C3×C4⋊C8—21no—
136C3×C4⋊C8C2×D312yescomplemented
137C3×C22⋊C8—32no—
138C3×C22⋊C8—32no—
139C3×#97—32no—
140#830—32no—
141#830—32no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8C2×D312yescomplemented
145(C2×D3)⋊C8C2×D312yescomplemented
146#815—32no—
147#815—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—61no—
151Dic3⋊C8—61no—
152C4⋊(C3⋊C8)—32no—
153C4⋊(C3⋊C8)—61no—
154#803C2×D312yescomplemented
155C22×C3⋊D3C22×C411yescharacteristic
156C22×C3×D3C22×C412yes—
157C22×C3×D3C22×C412yes—
158C2×D32—22no—
159C2×D32—22no—
160C2×D32—22no—
161C2×D32—22no—
162C2×D32—22no—
163C2×D32M1614yescomplemented
164C2×C32×C4C22×C411yescharacteristic
165C2×C32×C4C22×C411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3C22×C411yescharacteristic
168C2×C3⋊Dic3C22×C411yescharacteristic
169C2×C3⋊Dic3C22×C411yescharacteristic
170C4×C3⋊D3—22no—
171C4×C3⋊D3—22no—
172C4×C3⋊D3C2×D412yes—
173C4×C3⋊D3#4112yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C3×D12—24no—
177C3×C4×D3—22no—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181#625—24no—
182#624—22no—
183#624—22no—
184D3×Dic3—24no—
185D3×Dic3—24no—
186C32×C8—21no—
187C32×C8—21no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8C2×D414yescomplemented
192C22×M16—91no—
193C23×C8—91no—
194C2×C4×D4—91no—
195#435—32no—
196#435—92no—
197#435—92no—
198#435—92no—
199C2×C4⋊C8—91no—
200C2×C22⋊C8—91no—
201C2×C22⋊C8—91no—
202C2×#97—91no—
203C23×D3—32no—
204C23×D3—32no—
205C2×C3×D4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C2×#67—32no—
209C2×#67—32no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212D3×D4—68no—
213C2×D12C4×D312yes—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3—32no—
218C2×C4×D3—32no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3C22×D312yes—
229C2×C4×D3C22×D312yes—
230C3×M16—64no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—32no—
234C2×C3×C8—32no—
235C2×C3×C8—64no—
236C2×C3×C8C22×D312yes—
237C2×C3×C8C22×D312yes—
238C3×C4⋊C4—32no—
239C3×C22⋊C4—32no—
240C3×C22⋊C4—32no—
241C3×C42—21no—
242C3×C42C22×D312yes—
243#217—32no—
244#217—32no—
245(C2×D3)⋊C4—32no—
246(C2×D3)⋊C4—32no—
247(C2×D3)⋊C4C4×D312yes—
248(C2×D3)⋊C4C4×D312yes—
249C4⋊Dic3C4×D312yes—
250Dic3⋊C4—32no—
251Dic3⋊C4—32no—
252C4×Dic3—32no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258#208—64no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—64no—
264C2×C3⋊C8C22×D312yes—
265C2×C3⋊C8C22×D312yes—
266ΓL(1,𝔽25)—24no—
267ΓL(1,𝔽25)—64no—
268D3×C8—24no—
269D3×C8—38no—
270D3×C8—64no—
271D3×C8—64no—
272D3×C8—64no—
273D3×C8—64no—
274D3×C8—122no—
275D3×C8—122no—
276C22×C32C23×C411yescharacteristic
277C2×C3⋊D3C4×D412yes—
278C2×C3⋊D3C2×M1612yes—
279C2×C3⋊D3#13112yes—
280C2×C3×D3—22no—
281C2×C3×D3—22no—
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3C2×M1614yescomplemented
286D32—28no—
287D32—44no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4C22×D411yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3C4×D412yes—
295C3×Dic3—22no—
296C3×Dic3—22no—
297C22×D4—91no—
298C23×C4—91no—
299C23×C4—91no—
300C2×M16—32no—
301C2×M16—92no—
302C2×M16—184no—
303C22×C8—32no—
304C22×C8—91no—
305C22×C8—91no—
306C22×C8—92no—
307C22×C8—91no—
308C22×C8—91no—
309C22×C8—184no—
310C4×D4—32no—
311C4×D4—92no—
312C4×D4—92no—
313C4×D4—92no—
314C2×C4⋊C4—91no—
315C2×C22⋊C4—91no—
316C2×C22⋊C4—91no—
317C2×C42—91no—
318C4⋊C8—91no—
319C4⋊C8—91no—
320C4⋊C8—91no—
321C4⋊C8D3211yescharacteristic, complemented
322C22⋊C8—32no—
323C22⋊C8—32no—
324C22⋊C8—92no—
325C22⋊C8—92no—
326#97—32no—
327#97—92no—
328C23×C3—32no—
329C23×C3—32no—
330C22×D3—32no—
331C22×D3—38no—
332C22×D3—61no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3C2×C4×D312yes—
339C22×D3C2×C4×D312yes—
340C3×D4—64no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C23×D312yes—
353#67—64no—
354#67—64no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3C2×C4×D312yes—
364C2×Dic3C2×C4×D312yes—
365D12—24no—
366C4×D3—22no—
367C4×D3—22no—
368C4×D3—22no—
369C4×D3—22no—
370C4×D3—34no—
371C4×D3—34no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—64no—
375C4×D3—64no—
376C4×D3—64no—
377C4×D3—64no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—122no—
382C3×C8—22no—
383C3×C8—22no—
384C3×C8—34no—
385C3×C8—41no—
386C3×C8—41no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—62no—
390C3⋊C8—62no—
391C3⋊C8—121no—
392C3⋊C8—121no—
393C3⋊C8D3×D414yescomplemented
394C2×C32C2×C4×D411yescharacteristic
395C2×C32C22×M1611yescharacteristic
396C2×C32C2×#13111yescharacteristic
397C3⋊D3#43514yescomplemented
398C3×D3—24no—
399C3×D3—42no—
400C24—91no—
401C24—91no—
402C2×D4—32no—
403C2×D4—92no—
404C2×D4—184no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—92no—
410C22×C4—92no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—182no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4—182no—
418M16—64no—
419M16—184no—
420C2×C8—32no—
421C2×C8—32no—
422C2×C8—64no—
423C2×C8—94no—
424C2×C8—91no—
425C2×C8—91no—
426C2×C8—182no—
427C2×C8—182no—
428C2×C8—184no—
429C2×C8—182no—
430C2×C8C2×D3211yescharacteristic
431C2×C8C2×D3211yescharacteristic
432C4⋊C4—32no—
433C4⋊C4—92no—
434C22⋊C4—32no—
435C22⋊C4—32no—
436C22⋊C4—92no—
437C22⋊C4—92no—
438C42—91no—
439C42—91no—
440C42—91no—
441C42C2×D3211yescharacteristic
442C22×C3—21no—
443C22×C3—34no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—62no—
449C22×C3C22×C4×D312yes—
450C2×D3—22no—
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—22no—
454C2×D3—22no—
455C2×D3—34no—
456C2×D3—34no—
457C2×D3—34no—
458C2×D3—62no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—616no—
462C2×D3—128no—
463C2×D3D3×M1614yescomplemented
464C3×C4—22no—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—41no—
470C3×C4—62no—
471C3×C4—62no—
472C3×C4C2×D3×D412yes—
473C3×C4D3×#4112yes—
474Dic3—22no—
475Dic3—22no—
476Dic3—34no—
477Dic3—62no—
478Dic3—62no—
479Dic3—62no—
480Dic3—62no—
481Dic3—121no—
482C32C2×#43511yescharacteristic, complemented, Sylow
483C23—32no—
484C23—32no—
485C23—94no—
486C23—91no—
487C23—182no—
488C23—182no—
489C23—182no—
490C23—182no—
491C23—182no—
492D4—64no—
493D4—184no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—91no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—91no—
504C2×C4—91no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—184no—
510C2×C4—184no—
511C2×C4C4×D3211yescharacteristic
512C2×C4C4×D3211yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—21no—
515C8—21no—
516C8—34no—
517C8—62no—
518C8—181no—
519C8—181no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—64no—
524C2×C3—122no—
525C2×C3C4×D3×D412yes—
526C2×C3C2×D3×M1612yes—
527C2×C3D3×#13112yes—
528D3—24no—
529D3—38no—
530D3—42no—
531D3—64no—
532C22—34no—
533C22—62no—
534C22—62no—
535C22—62no—
536C22—62no—
537C22—62no—
538C22—92no—
539C22—92no—
540C22—92no—
541C22—188no—
542C22—364no—
543C22C2×C4×D3211yescharacteristic
544C4—21no—
545C4—21no—
546C4—62no—
547C4—62no—
548C4—92no—
549C4—181no—
550C4—181no—
551C4D32×D411yescharacteristic
552C4#6431911yescharacteristic
553C3—21no—
554C3D3×#43512yescomplemented
555C2—64no—
556C2—94no—
557C2—122no—
558C2#1059460511yescharacteristic
559C2#1059466911yescharacteristic
560C2D32×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC2×#3802C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63791C2semidirect
2. C2×D32×C8C2semidirect
4. C3⋊D3×C4⋊C8C2semidirect
5. C3×#4836C2semidirect
6. #10590935C2semidirect
7. #10590935C2semidirect
8. #10590724C2semidirect
9. #10590723C2semidirect
10. #10590326C2semidirect
11. #10590322C2semidirect
19. C2×C3×ΓL(1,𝔽25)C22semidirect
20. C2×C3×D3×C8C22semidirect
28. C2×#3711C22semidirect
31. C2×D3×C3⋊C8C22semidirect
34. C32×C4⋊C8C22semidirect
35. #63641C22semidirect
36. #63641C22semidirect
37. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×(C2×D3)⋊C8C22semidirect
39. C3×(C2×D3)⋊C8C22semidirect
40. C3×#803C22semidirect
41. (C2×D3)⋊(C3⋊C8)C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
43. #63555C22semidirect
51. #4836D3semidirect
100. #3710D4semidirect
116. C2×ΓL(1,𝔽25)C2×D3semidirect
125. C2×D3×C8C2×D3semidirect
136. C3×C4⋊C8C2×D3semidirect
144. (C2×D3)⋊C8C2×D3semidirect
145. (C2×D3)⋊C8C2×D3semidirect
154. #803C2×D3semidirect
163. C2×D32M16semidirect
191. C3×C3⋊C8C2×D4semidirect
285. C2×C3×D3C2×M16semidirect
321. C4⋊C8D32semidirect
393. C3⋊C8D3×D4semidirect
397. C3⋊D3#435semidirect
463. C2×D3D3×M16semidirect
482. C32C2×#435semidirect
554. C3D3×#435semidirect

Maximal subgroups

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

subgroupindex
C2×#637912
C2×D32×C82
C4×#38022
C3⋊D3×C4⋊C82
C3×#48362
#105909352
#105907242
#105907232
#105903262
#105903222
D3×#4353