Finite Group Databasebeta

← #28404227

Subgroups — #28404227

Order 14464.

1536 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813669C211yesmaximal, characteristic, complemented
2C2×#41×D113C211yesmaximal, characteristic, complemented
3#20299268C213yesmaximal, complemented
4#20299267C211yesmaximal, characteristic, complemented
5#20299266C213yesmaximal, complemented
6#20299260C211yesmaximal, characteristic, complemented
7#20299257C213yesmaximal, complemented
8#20299255C211yesmaximal, characteristic, complemented
9#20299254C213yesmaximal, complemented
10#20299164C213yesmaximal, complemented
11#20299161C213yesmaximal, complemented
12#20299108C213yesmaximal, complemented
13#20299107C213yesmaximal, complemented
14#20299074C211yesmaximal, characteristic, complemented
15#550×C113C211yesmaximal, characteristic, complemented
16#16813669—28no—
17C2×#14268648C2211yescharacteristic
18C2×#14268647C2213yes—
19C2×#14268647C2213yes—
20C2×#14268646C2213yes—
21C2×#14268646C2213yes—
22C2×#14268646C2213yescomplemented
23#41×D113—28no—
24C22×Dic226C2213yescomplemented
25C2×Q8×D113C2211yescharacteristic
26C2×Q8×D113C2211yescharacteristic, complemented
27C2×D4×D113C2213yes—
28C22×C4×D113C2213yes—
29#16813618C2213yescomplemented
30#16813618C2216yescomplemented
31#16813610C2213yescomplemented
32#16813609C2213yescomplemented
33#16813608C2216yescomplemented
34#16813607C2211yescharacteristic
35#16813604C2213yes—
36#16813602C2213yescomplemented
37#16813601C2213yescomplemented
38#16813600C2213yescomplemented
39#16813599C2213yescomplemented
40#16813597C2213yescomplemented
41#16813596C2213yescomplemented
42#16813595C2213yescomplemented
43#16813594C2216yescomplemented
44#16813594C2213yescomplemented
45#16813594C2216yescomplemented
46#16813593C2213yescomplemented
47#16813593C2213yescomplemented
48#16813592C2213yes—
49#16813590C2213yes—
50#16813590C2216yes—
51Q8×Dic113C2211yescharacteristic, complemented
52C4×Dic226C2213yescomplemented
53#16813587C2213yescomplemented
54C4×D452C2213yescomplemented
55D4×Dic113C2216yescomplemented
56C4×C22⋊D113C2213yescomplemented
57C4×C22⋊D113C2213yescomplemented
58#16813582C2216yescomplemented
59#16813580C2213yes—
60#16813579C2213yes—
61C2×#41×C113C2211yescharacteristic
62C2×#41×C113C2211yescharacteristic, complemented
63#127×C113C2213yescomplemented
64#121×C113C2213yescomplemented
65#121×C113C2213yescomplemented
66C4×Q8×C113C2211yescharacteristic, complemented
67C4×D4×C113C2213yescomplemented
68C23×D113C2313yes—
69#14268648—24no—
70#14268647—212no—
71#14268647—212no—
72#14268646—212no—
73#14268646—212no—
74#14268646—212no—
75C2×Dic226—212no—
76C2×Dic226C2313yes—
77C2×Dic226C2313yes—
78C2×Dic226C2313yes—
79Q8×D113—24no—
80Q8×D113D418yescomplemented
81C2×D452C2311yescharacteristic
82C2×D452C2313yes—
83C2×D452C2313yes—
84C2×C22⋊D113C2313yes—
85C2×C22⋊D113C2316yes—
86C2×C22⋊D113C2313yes—
87C2×C22⋊D113C2316yes—
88C2×C22⋊D113C2313yes—
89C2×C22⋊D113C2313yes—
90D4×D113—212no—
91C22×Dic113C2316yes—
92C22×Dic113C2313yes—
93C2×C4×D113—212no—
94C2×C4×D113C2313yes—
95C2×C4×D113C2313yes—
96C2×C4×D113C2313yes—
97C2×C4×D113C2311yescharacteristic
98C2×C4×D113C2313yes—
99C4⋊Dic113C2313yes—
100C4⋊Dic113C2313yes—
101#14268626C2313yes—
102#14268626C2313yes—
103#14268626C2313yes—
104#14268626C2311yescharacteristic
105C22⋊Dic113C2313yes—
106C22⋊Dic113C2313yes—
107C22⋊Dic113C2316yes—
108#14268624C2311yescharacteristic
109#14268624C2313yes—
110#14268624C2316yes—
111#14268624C2311yescharacteristic
112#14268624C2313yes—
113#14268624C2311yescharacteristic
114#14268624C2313yes—
115C4×Dic113C2313yes—
116C4×Dic113C2316yes—
117#41×C113—24no—
118#41×C113—24no—
119C2×Q8×C113C2311yescharacteristic
120C2×D4×C113C2313yes—
121C2×D4×C113C2313yes—
122C2×D4×C113C2316yes—
123C2×D4×C113C2313yes—
124C22×C4×C113C2313yes—
125C22×C4×C113C2313yes—
126C4⋊C4×C113C2313yes—
127C4⋊C4×C113C2311yescharacteristic
128C22⋊C4×C113C2313yes—
129C22⋊C4×C113C2313yes—
130C42×C113C2313yes—
131C23×C113C2413yes—
132C23×C113C2413yes—
133C22×D113—26no—
134C22×D113—43no—
135C22×D113—43no—
136C22×D113C2413yes—
137C22×D113C2411yescharacteristic
138C22×D113C2411yescharacteristic
139Q8×C113C2×D414yes—
140D4×C113—26no—
141D4×C113—26no—
142D4×C113—46no—
143D4×C113—43no—
144C2×C4×C113—26no—
145C2×C4×C113—26no—
146C2×C4×C113C2411yescharacteristic
147C2×C4×C113C2413yes—
148C2×C4×C113C2411yescharacteristic
149C2×C4×C113C2411yescharacteristic
150C2×C4×C113C2413yes—
151C22⋊D113—26no—
152C22⋊D113—212no—
153C22⋊D113—26no—
154C22⋊D113—43no—
155C22⋊D113—43no—
156C22⋊D113—46no—
157C2×Dic113—26no—
158C2×Dic113—212no—
159C2×Dic113C2411yescharacteristic
160C2×Dic113C2413yes—
161C2×Dic113C2413yes—
162C2×Dic113C2411yescharacteristic
163C2×Dic113C2413yes—
164D452—22no—
165D452—26no—
166D452—43no—
167C4×D113—22no—
168C4×D113—26no—
169C4×D113—26no—
170C4×D113—26no—
171C4×D113C2×D4112yes—
172Dic226—26no—
173Dic226—26no—
174Dic226C2×D4112yes—
175C22×C113—23no—
176C22×C113—23no—
177C22×C113—23no—
178C22×C113—23no—
179C22×C113—23no—
180C22×C113—23no—
181C22×C113C2511yescharacteristic
182C2×D113—21no—
183C2×D113—21no—
184C2×D113—21no—
185C2×D113—23no—
186C2×D113—21no—
187C2×D113—23no—
188C2×D113—21no—
189C2×D113—23no—
190C2×D113—412no—
191C2×D113C22×D412yes—
192C4×C113—21no—
193C4×C113—21no—
194C4×C113—23no—
195C4×C113—21no—
196C4×C113C22×D416yes—
197Dic113—23no—
198Dic113—21no—
199Dic113—21no—
200Dic113—23no—
201Dic113C22×D416yes—
202C2×C113—43no—
203C2×C113—43no—
204C2×C113C23×D411yescharacteristic
205C2×C113#58511yescharacteristic
206C2×C113#58511yescharacteristic
207D113—22no—
208D113—41no—
209D113—43no—
210#3487—1131nomaximal, Sylow
211C113#348711yescharacteristic, complemented, Sylow
212C2×2−1+4—1131no—
213C22×#41—1131no—
214#550—1131no—
215#550—1133no—
216#550—1133no—
217#550D11311yescharacteristic, complemented
218#548—1131no—
219#548—1133no—
220#548—1131no—
221#548—1133no—
222#535—1133no—
223#535—1133no—
224#525—1133no—
225#525—1133no—
226#519—1131no—
2272−1+4—2268no—
228C2×#41—1131no—
229C2×#41—1133no—
230C2×#41—1133no—
231C2×#41—1133no—
232C2×#41—1133no—
233C2×#41—1133no—
234C2×#41—2268no—
235C2×#41C2×D11311yescharacteristic
236C2×#41C2×D11311yescharacteristic, complemented
237C22×Q8—1131no—
238C22×Q8—1131no—
239C22×Q8—1133no—
240C22×D4—1133no—
241C23×C4—1133no—
242#127—1133no—
243#127—1136no—
244#127C2×D11313yescomplemented
245#124—1133no—
246#124—1136no—
247#124—1133no—
248#123—1131no—
249#123—1133no—
250C22⋊Q8—1133no—
251C22⋊Q8—1133no—
252C22⋊Q8—1133no—
253C22⋊Q8—1133no—
254#121—1133no—
255#121—1133no—
256#121—1133no—
257#121—1136no—
258#121—1136no—
259#121—1133no—
260#121—1133no—
261#121—1133no—
262#121C2×D11313yescomplemented
263#121C2×D11313yescomplemented
264#120—1136no—
265#120—1133no—
266#120—1133no—
267C4×Q8—1131no—
268C4×Q8—1133no—
269C4×Q8—1133no—
270C4×Q8C2×D11311yescharacteristic, complemented
271C4×D4—1136no—
272C4×D4—1133no—
273C4×D4—1133no—
274C4×D4—1136no—
275C4×D4—1133no—
276C4×D4C2×D11313yescomplemented
277#117—1133no—
278#117—1133no—
279C24—1133no—
280#41—24no—
281#41—24no—
282#41—22612no—
283#41—22612no—
284#41—22612no—
285#41—22612no—
286#41—22612no—
287#41—2264no—
288C2×Q8—1138no—
289C2×Q8—1133no—
290C2×Q8—1133no—
291C2×Q8—1133no—
292C2×Q8—22612no—
293C2×Q8—2264no—
294C2×Q8C22×D11311yescharacteristic
295C2×D4—1133no—
296C2×D4—1136no—
297C2×D4—1133no—
298C2×D4—1133no—
299C2×D4—1136no—
300C2×D4—1133no—
301C2×D4—1133no—
302C2×D4—1131no—
303C2×D4—1133no—
304C2×D4—22612no—
305C2×D4C22×D11313yes—
306C2×D4C22×D11313yes—
307C2×D4C22×D11316yes—
308C2×D4C22×D11313yes—
309C22×C4—1133no—
310C22×C4—1136no—
311C22×C4—1133no—
312C22×C4—1133no—
313C22×C4—1133no—
314C22×C4—1133no—
315C22×C4—1131no—
316C22×C4—22612no—
317C22×C4C22×D11313yes—
318C22×C4C22×D11313yes—
319C4⋊C4—1133no—
320C4⋊C4—1133no—
321C4⋊C4—1133no—
322C4⋊C4—1133no—
323C4⋊C4—1131no—
324C4⋊C4—1133no—
325C4⋊C4C22×D11313yes—
326C4⋊C4C22×D11311yescharacteristic
327C22⋊C4—1133no—
328C22⋊C4—1136no—
329C22⋊C4—1133no—
330C22⋊C4—1133no—
331C22⋊C4—1131no—
332C22⋊C4—1131no—
333C22⋊C4—1131no—
334C22⋊C4—1133no—
335C22⋊C4—1136no—
336C22⋊C4—1133no—
337C22⋊C4C22×D11313yes—
338C22⋊C4C22×D11313yes—
339C42—1136no—
340C42—1133no—
341C42C22×D11313yes—
342C23—1131no—
343C23—1133no—
344C23—1131no—
345C23—4523no—
346C23—4523no—
347C23—2266no—
348C23C23×D11313yes—
349C23C23×D11313yes—
350Q8—11312no—
351Q8—2266no—
352Q8—2266no—
353Q8D4×D11314yes—
354D4—26no—
355D4—26no—
356D4—46no—
357D4—43no—
358D4—4523no—
359D4—4523no—
360D4—4526no—
361D4—4523no—
362D4—2262no—
363D4—22612no—
364D4—2266no—
365D4—2266no—
366D4—2266no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—1133no—
370C2×C4—11312no—
371C2×C4—1131no—
372C2×C4—1133no—
373C2×C4—1133no—
374C2×C4—1131no—
375C2×C4—2266no—
376C2×C4—2262no—
377C2×C4—2266no—
378C2×C4—22612no—
379C2×C4—2266no—
380C2×C4—2266no—
381C2×C4C23×D11313yes—
382C2×C4C23×D11311yescharacteristic
383C2×C4C23×D11311yescharacteristic
384C2×C4C23×D11311yescharacteristic
385C2×C4C23×D11313yes—
386C22—23no—
387C22—23no—
388C22—23no—
389C22—23no—
390C22—23no—
391C22—23no—
392C22—1132no—
393C22—45212no—
394C22—2261no—
395C22—2263no—
396C22—2261no—
397C22—2263no—
398C22—2261no—
399C22—2263no—
400C22—2261no—
401C22—2261no—
402C22C24×D11311yescharacteristic
403C4—21no—
404C4—21no—
405C4—23no—
406C4—21no—
407C4—1136no—
408C4—2261no—
409C4—2263no—
410C4—2261no—
411C4—2263no—
412C4C2×D4×D11316yes—
413C2—43no—
414C2—43no—
415C2—4523no—
416C2—4521no—
417C2—2262no—
418C2C22×D4×D11311yescharacteristic
419C2#2029943311yescharacteristic
420C2#2029943411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#550×C113C2
hypercenter#550D113
hypocenterC113#3487
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#16813669C2semidirect
2. C2×#41×D113C2semidirect
3. #20299268C2semidirect
4. #20299267C2semidirect
5. #20299266C2semidirect
6. #20299260C2semidirect
7. #20299257C2semidirect
8. #20299255C2semidirect
9. #20299254C2semidirect
10. #20299164C2semidirect
11. #20299161C2semidirect
12. #20299108C2semidirect
13. #20299107C2semidirect
14. #20299074C2semidirect
15. #550×C113C2semidirect
22. C2×#14268646C22semidirect
24. C22×Dic226C22semidirect
26. C2×Q8×D113C22semidirect
29. #16813618C22semidirect
30. #16813618C22semidirect
31. #16813610C22semidirect
32. #16813609C22semidirect
33. #16813608C22semidirect
36. #16813602C22semidirect
37. #16813601C22semidirect
38. #16813600C22semidirect
39. #16813599C22semidirect
40. #16813597C22semidirect
41. #16813596C22semidirect
42. #16813595C22semidirect
43. #16813594C22semidirect
44. #16813594C22semidirect
45. #16813594C22semidirect
46. #16813593C22semidirect
47. #16813593C22semidirect
51. Q8×Dic113C22semidirect
52. C4×Dic226C22semidirect
53. #16813587C22semidirect
54. C4×D452C22semidirect
55. D4×Dic113C22semidirect
56. C4×C22⋊D113C22semidirect
57. C4×C22⋊D113C22semidirect
58. #16813582C22semidirect
62. C2×#41×C113C22semidirect
63. #127×C113C22semidirect
64. #121×C113C22semidirect
65. #121×C113C22semidirect
66. C4×Q8×C113C22semidirect
67. C4×D4×C113C22semidirect
80. Q8×D113D4semidirect
211. C113#3487semidirect
217. #550D113semidirect
236. C2×#41C2×D113semidirect
244. #127C2×D113semidirect
262. #121C2×D113semidirect
263. #121C2×D113semidirect
270. C4×Q8C2×D113semidirect
276. C4×D4C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136692
C2×#41×D1132
#202992682
#202992672
#202992662
#202992602
#202992572
#202992552
#202992542
#202991642
#202991612
#202991082
#202991072
#202990742
#550×C1132
#3487113