Finite Group Databasebeta

← #11868697

Subgroups — #11868697

Order 1152.

991 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596159C211yesmaximal, characteristic, complemented
2C4×#3802C211yesmaximal, characteristic
3C3×#5066C212yesmaximal, complemented
4#10590594C211yesmaximal, characteristic
5#10590594C211yesmaximal, characteristic
6#10590584C211yesmaximal, characteristic, complemented
7#10590582C211yesmaximal, characteristic, complemented
8#10590472C212yesmaximal, complemented
9#10590471C212yesmaximal, complemented
10#10590340C211yesmaximal, characteristic, complemented
11#10590271C212yesmaximal, complemented
12#81166—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×C4×D32—21no—
15C32×#125C2211yescharacteristic, complemented
16#64105—21no—
17#64105—21no—
18#64101C2211yescharacteristic
19#64101C2211yescharacteristic
20#64097C2211yescharacteristic, complemented
21#64097C2211yescharacteristic, complemented
22#64096—21no—
23#64096—21no—
24C42×C3⋊D3C2211yescharacteristic
25#64079C2211yescharacteristic, complemented
26C3×C4×D12C2212yes—
27#63921—21no—
28#63902—21no—
29C4×#625—21no—
30#63900C2211yescharacteristic
31#63898C2212yes—
32C2×#3712C2211yescharacteristic
33C2×#3712C2211yescharacteristic
34C3×#809C2212yes—
35C3×#809C2212yes—
36C3×#808C2212yescomplemented
37C3×#807C2212yescomplemented
38C3×C4⋊(C3⋊C8)C2212yescomplemented
39#63575C2212yescomplemented
40#63573C2212yescomplemented
41#63572C2212yescomplemented
42#63563C2212yes—
43#63563C2212yes—
44#5688—32no—
45#5688—61no—
46C4×D3×D4—32no—
47C3×#478—32no—
48#5066D312yescomplemented
49#5009—32no—
50#4890—32no—
51#4881—32no—
52#4870—32no—
53#4861—32no—
54#4847—32no—
55#4837—32no—
56#4770—32no—
57#4770—32no—
58#4761—32no—
59#4759—32no—
60C22×D32—21no—
61C2×C4×C3⋊D3D411yescharacteristic
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3C2311yescharacteristic
64C2×#634—21no—
65C2×#634—21no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×#625—21no—
69C2×#624—21no—
70C2×D3×Dic3—22no—
71#3802—22no—
72#3802Q814yescomplemented
73C4×D32—44no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3752—21no—
80#3752—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84#3750—21no—
85#3750—21no—
86#3750—21no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2312yes—
96#3724—21no—
97(C2×D3)⋊Dic3—22no—
98#3712—22no—
99#3712—22no—
100#3077—91noSylow
101C2×D3×D4—32no—
102C22×C4×D3—62no—
103C3×#125—21no—
104C3×#125C2×D312yescomplemented
105C3×C4×D4—32no—
106D4×Dic3—32no—
107C4×#67—62no—
108C2×ΓL(1,𝔽25)—32no—
109C2×ΓL(1,𝔽25)—32no—
110#896—62no—
111#896—62no—
112#896—62no—
113#896—62no—
114#893—32no—
115#892—32no—
116#892—32no—
117#892—61no—
118#892—61no—
119D3×C4⋊C4—32no—
120#888—32no—
121#888—32no—
122#888—61no—
123#888—61no—
124#887—62no—
125#887—62no—
126#887—62no—
127#887—62no—
128#67⋊C4—62no—
129D3×C22⋊C4—62no—
130C4×D12C2×D312yes—
131C42×D3—32no—
132C42×D3—61no—
133#870—32no—
134#870—61no—
135C3×#107—32no—
136C3×#106—32no—
137C3×C4⋊C8—32no—
138C3×#102—32no—
139C3×#102—32no—
140#832—32no—
141#832—32no—
142#821—32no—
143#821—32no—
144#818—32no—
145#817—32no—
146Dic3⋊C8—32no—
147Dic3⋊C8—32no—
148#809C2×D312yes—
149#809C2×D312yes—
150#808—32no—
151#808C2×D312yescomplemented
152#807—32no—
153#807C2×D312yescomplemented
154C4⋊(C3⋊C8)C2×D312yescomplemented
155C22×C3⋊D3C2×D411yescharacteristic
156C22×C3×D3—22no—
157C2×D32—24no—
158C2×D32—42no—
159C2×D32—42no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3C2×D411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C4×C3⋊D3—22no—
171C4×C3⋊D3—41no—
172C4×C3⋊D3C2×Q812yes—
173C4×C3⋊D3#4112yes—
174#634—42no—
175#634—42no—
176C2×C3×Dic3—22no—
177C3×D12—22no—
178C3×D12C2×Q814yes—
179C3×C4×D3—44no—
180#625—24no—
181#624—42no—
182D3×Dic3—44no—
183C3×C3⋊C8—22no—
184C3×C3⋊C8—22no—
185#533—91no—
186C2×C4×D4—91no—
187#478—32no—
188#478—92no—
189#476—92no—
190#474—92no—
191#428—91no—
192#428—91no—
193#423—91no—
194#418—91no—
195#418—91no—
196C23×D3—62no—
197C2×C3×D4—32no—
198C22×C3×C4—62no—
199C2×#67—62no—
200C22×Dic3—62no—
201D3×D4—38no—
202D3×D4—64no—
203C2×D12C22×D312yes—
204C2×C4×D3—22no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—128no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×C3×C8—32no—
219C2×C3×C8—32no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4C22×D312yes—
228C3×C4⋊C4C22×D312yes—
229C3×C22⋊C4—62no—
230C3×C42—21no—
231C3×C42C22×D312yes—
232#217—62no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3C22×D312yes—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—32no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—61no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C2×C3⋊C8C22×D312yes—
264C2×C3⋊C8C22×D312yes—
265ΓL(1,𝔽25)—64no—
266ΓL(1,𝔽25)—64no—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—21no—
269C2×C3⋊D3—21no—
270C2×C3⋊D3C22⋊Q812yes—
271C2×C3×D3—24no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274D32—48no—
275C32×C4—21no—
276C32×C4—21no—
277C32×C4—41no—
278C32×C4—41no—
279C32×C4C22×Q811yescharacteristic
280C32×C4C2×#4111yescharacteristic
281C3⋊Dic3—21no—
282C3⋊Dic3—41no—
283C3⋊Dic3—41no—
284C3⋊Dic3C22⋊Q812yes—
285C3⋊Dic3AGL(1,ℤ/8)12yes—
286C3×Dic3—42no—
287C22×D4—91no—
288C23×C4—181no—
289C2×M16—91no—
290C2×M16—91no—
291C4⋊Q8—91no—
292C4⋊Q8—91no—
293#125—91no—
294#125D3211yescharacteristic, complemented
295C22⋊Q8—181no—
296C22⋊Q8—181no—
297C4×Q8—181no—
298C4×Q8—181no—
299C4×D4—32no—
300C4×D4—92no—
301C4×D4—181no—
302C4×D4—181no—
303#117—91no—
304#117—91no—
305C2×C4⋊C4—91no—
306C2×C22⋊C4—181no—
307C2×C42—91no—
308#107—32no—
309#107—92no—
310#106—32no—
311#106—92no—
312C4⋊C8—32no—
313C4⋊C8—92no—
314#102—32no—
315#102—32no—
316#102—92no—
317#102—92no—
318C23×C3—62no—
319C22×D3—22no—
320C22×D3—32no—
321C22×D3—61no—
322C22×D3—68no—
323C22×D3—124no—
324C22×D3—124no—
325C3×D4—34no—
326C3×D4—62no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—62no—
335C2×C3×C4—124no—
336C2×C3×C4D3×D412yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4C23×D312yes—
339#67—68no—
340C2×Dic3—22no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—124no—
352D12—22no—
353D12D3×Q814yes—
354C4×D3—34no—
355C4×D3—34no—
356C4×D3—44no—
357C4×D3—62no—
358C4×D3—62no—
359C4×D3—64no—
360C4×D3—122no—
361C4×D3—124no—
362C4×D3—124no—
363C4×D3—122no—
364C4×D3—122no—
365Dic6—124no—
366Dic6—124no—
367Dic6—124no—
368Dic6—124no—
369C3×C8—62no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—22no—
373C2×C32C2×C22⋊Q811yescharacteristic
374C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
375C2×C32#57511yescharacteristic
376C3⋊D3—22no—
377C3×D3—44no—
378C24—181no—
379C2×Q8—181no—
380C2×Q8—181no—
381C2×D4—32no—
382C2×D4—94no—
383C2×D4—182no—
384C2×D4—181no—
385C22×C4—62no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—181no—
390C22×C4—182no—
391C22×C4—364no—
392M16—182no—
393M16—182no—
394C2×C8—32no—
395C2×C8—32no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—32no—
399C4⋊C4—91no—
400C4⋊C4—91no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4—181no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C4⋊C4C2×D3211yescharacteristic
407C4⋊C4C2×D3211yescharacteristic
408C22⋊C4—62no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—182no—
412C42—91no—
413C42—91no—
414C42—91no—
415C42—181no—
416C42—181no—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3—64no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3C2×D3×D412yes—
423C2×D3—24no—
424C2×D3—34no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—1216no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—122no—
444C3×C4C2×D3×Q812yes—
445C3×C4D3×#4112yes—
446Dic3—34no—
447Dic3—34no—
448Dic3—42no—
449Dic3—62no—
450Dic3—62no—
451Dic3—62no—
452Dic3—62no—
453Dic3—122no—
454Dic3—122no—
455Dic3—122no—
456Dic3—122no—
457C32#307711yescharacteristic, complemented, Sylow
458C23—62no—
459C23—91no—
460C23—184no—
461C23—362no—
462C23—362no—
463Q8—362no—
464Q8—362no—
465D4—34no—
466D4—62no—
467D4—184no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—62no—
471C2×C4—91no—
472C2×C4—91no—
473C2×C4—92no—
474C2×C4—92no—
475C2×C4—91no—
476C2×C4—124no—
477C2×C4—182no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—361no—
481C2×C4—364no—
482C2×C4—362no—
483C2×C4#381111yescharacteristic
484C2×C4#381111yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—62no—
487C8—62no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—124no—
492C2×C3D3×C22⋊Q812yes—
493C2×C3#576812yes—
494C2×C3D3×AGL(1,ℤ/8)12yes—
495D3—44no—
496D3—64no—
497D3—122no—
498C22—64no—
499C22—92no—
500C22—122no—
501C22—122no—
502C22—181no—
503C22—181no—
504C22—368no—
505C22C2×#381111yescharacteristic
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—92no—
511C4—92no—
512C4—122no—
513C4—181no—
514C4—361no—
515C4—361no—
516C4D32×Q811yescharacteristic
517C4#6431911yescharacteristic
518C3—21no—
519C3#8116612yescomplemented
520C2—124no—
521C2—182no—
522C2#1059542911yescharacteristic
523C2#1059545811yescharacteristic
524C2#1059546011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#125D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596159C2semidirect
3. C3×#5066C2semidirect
6. #10590584C2semidirect
7. #10590582C2semidirect
8. #10590472C2semidirect
9. #10590471C2semidirect
10. #10590340C2semidirect
11. #10590271C2semidirect
15. C32×#125C22semidirect
20. #64097C22semidirect
21. #64097C22semidirect
25. #64079C22semidirect
36. C3×#808C22semidirect
37. C3×#807C22semidirect
38. C3×C4⋊(C3⋊C8)C22semidirect
39. #63575C22semidirect
40. #63573C22semidirect
41. #63572C22semidirect
48. #5066D3semidirect
72. #3802Q8semidirect
104. C3×#125C2×D3semidirect
151. #808C2×D3semidirect
153. #807C2×D3semidirect
154. C4⋊(C3⋊C8)C2×D3semidirect
294. #125D32semidirect
457. C32#3077semidirect
519. C3#81166semidirect

Maximal subgroups

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

subgroupindex
#105961592
C4×#38022
C3×#50662
#105905942
#105905842
#105905822
#105904722
#105904712
#105903402
#105902712
#811663