Finite Group Databasebeta

← #27205984

Subgroups — #27205984

Order 13184.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268303C211yesmaximal, characteristic, complemented
2#20268301C211yesmaximal, characteristic, complemented
3#20268134C211yesmaximal, characteristic, complemented
4#20268132C211yesmaximal, characteristic, complemented
5#20268117C211yesmaximal, characteristic, complemented
6#20268050C211yesmaximal, characteristic, complemented
7#20268043C211yesmaximal, characteristic, complemented
8#20268038C211yesmaximal, characteristic, complemented
9#20268036C211yesmaximal, characteristic, complemented
10#20267955C211yesmaximal, characteristic, complemented
11#20267954C211yesmaximal, characteristic, complemented
12#20267937C211yesmaximal, characteristic, complemented
13#20267934C211yesmaximal, characteristic, complemented
14#20267753C211yesmaximal, characteristic, complemented
15#482×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×#13110104C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C2×Dic412C2211yescharacteristic, complemented
20C2×#13110094C2211yescharacteristic, complemented
21C2×#13110093C2211yescharacteristic, complemented
22C2×#13110090C2211yescharacteristic, complemented
23C2×#13110088C2211yescharacteristic
24C2×#13110088C2211yescharacteristic
25#15693005—21no—
26#15693003—21no—
27#15693001C2211yescharacteristic
28#15693001C2211yescharacteristic
29#15693001C2211yescharacteristic
30#15693000C2211yescharacteristic
31#15692996C2211yescharacteristic
32#15692996C2211yescharacteristic
33#15692992C2211yescharacteristic
34#15692991—21no—
35#15692989—21no—
36C4×D412—21no—
37C4×D412—21no—
38D4×Dic103—21no—
39(C22⋊D103)⋊C4—21no—
40#15692979C2211yescharacteristic
41#15692954C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692944C2211yescharacteristic, complemented
45#15692944C2211yescharacteristic, complemented
46#15692944C2211yescharacteristic, complemented
47#15692943C2211yescharacteristic, complemented
48#15692941C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51(C2×D103)⋊C8C2211yescharacteristic
52#121×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56#102×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103D411yescharacteristic
60#13110105—41no—
61#13110105—41no—
62#13110104—41no—
63#13110104—41no—
64C2×Dic206C2311yescharacteristic
65C2×Dic206C2311yescharacteristic
66C2×D412—21no—
67C2×D412—21no—
68C2×D412C2311yescharacteristic
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C22×Dic103—21no—
73C22×Dic103D411yescharacteristic
74C2×C4×D103—21no—
75C2×C4×D103—41no—
76C2×C4×D103—41no—
77C2×C4×D103D411yescharacteristic
78C2×C4×D103D411yescharacteristic
79C2×C4×D103C2311yescharacteristic
80C2×C4×D103C2311yescharacteristic
81Dic412—41no—
82#13110094—41no—
83#13110093—41no—
84#13110090—41no—
85#13110088—41no—
86#13110088—41no—
87C2×C103⋊C8C2311yescharacteristic
88C2×C103⋊C8C2311yescharacteristic
89C4⋊Dic103—21no—
90C4⋊Dic103—21no—
91C4⋊Dic103—21no—
92C4⋊Dic103C2311yescharacteristic
93Dic103⋊C4—21no—
94C22⋊Dic103—21no—
95C22⋊Dic103—21no—
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4—21no—
98(C2×D103)⋊C4—21no—
99(C2×D103)⋊C4—21no—
100(C2×D103)⋊C4—21no—
101(C2×D103)⋊C4—21no—
102C4×Dic103—21no—
103C2×D4×C103—21no—
104C2×D4×C103C2311yescharacteristic
105C22×C4×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C2×C8×C103C2311yescharacteristic
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C4⋊C4×C103C2311yescharacteristic
111C22⋊C4×C103—21no—
112C22⋊C4×C103—21no—
113C42×C103—21no—
114C23×C103—21no—
115C23×C103C2×D411yescharacteristic
116C22×D103—21no—
117C22×D103—41no—
118C22×D103—41no—
119C22×D103—41no—
120C22×D103C2×D411yescharacteristic
121C22×D103C2×D411yescharacteristic
122D4×C103—21no—
123D4×C103—21no—
124D4×C103—42no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2411yescharacteristic
132C22⋊D103—42no—
133C22⋊D103—42no—
134C22⋊D103—42no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—41no—
139C2×Dic103—42no—
140C2×Dic103C2×D411yescharacteristic
141C2×Dic103C2×D411yescharacteristic
142D412—21no—
143D412—21no—
144D412—42no—
145D412—42no—
146C4×D103—21no—
147C4×D103—21no—
148C4×D103—21no—
149C4×D103—21no—
150C4×D103—41no—
151C4×D103—41no—
152C4×D103—42no—
153Dic206—21no—
154Dic206—21no—
155Dic206—21no—
156Dic206—21no—
157C8×C103—21no—
158C8×C103—21no—
159C103⋊C8—21no—
160C103⋊C8—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103—21no—
164C22×C103—41no—
165C22×C103—41no—
166C22×C103—41no—
167C22×C103C22×D411yescharacteristic
168C2×D103—21no—
169C2×D103—21no—
170C2×D103—21no—
171C2×D103—21no—
172C2×D103—21no—
173C2×D103—21no—
174C2×D103—44no—
175C2×D103—41no—
176C2×D103—41no—
177C2×D103—41no—
178C4×C103—21no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103—41no—
182C4×C103H(5,𝔽2)11yescharacteristic
183C4×C103H(5,𝔽2)11yescharacteristic
184Dic103—21no—
185Dic103—21no—
186Dic103—41no—
187Dic103—41no—
188Dic103—41no—
189C2×C103—41no—
190C2×C103—81no—
191C2×C103#53411yescharacteristic
192C2×C103#57511yescharacteristic
193C2×C103#57511yescharacteristic
194D103—41no—
195D103—41no—
196D103—81no—
197#3197—1031nomaximal, Sylow
198C103#319711yescharacteristic, complemented, Sylow
199#525—1031no—
200#525—1031no—
201#485—1031no—
202#485—1031no—
203#482—1031no—
204#482D10311yescharacteristic, complemented
205#470—1031no—
206#469—1031no—
207#468—1031no—
208#468—1031no—
209#452—1031no—
210#452—1031no—
211#449—1031no—
212#449—1031no—
213#407—1031no—
214C2×#41—1031no—
215C2×#41—1031no—
216C23×C4—1031no—
217C2×Q16—1031no—
218C2×SD16—1031no—
219C2×SD16—1031no—
220C2×D8—1031no—
221C2×M16—1031no—
222C2×M16—1031no—
223#123—2061no—
224#123—2061no—
225C22⋊Q8—1031no—
226C22⋊Q8—1031no—
227C22⋊Q8—1031no—
228C22⋊Q8—1031no—
229#121—1031no—
230#121—1031no—
231#121—1031no—
232#121C2×D10311yescharacteristic
233#120—2061no—
234#120—2061no—
235C4×D4—2061no—
236C4×D4—2061no—
237C4×D4—2061no—
238C4×D4—2061no—
239#117—1031no—
240#117C2×D10311yescharacteristic
241#107—1031no—
242#107C2×D10311yescharacteristic, complemented
243#106—1031no—
244#106C2×D10311yescharacteristic, complemented
245#103—1031no—
246#103—1031no—
247#103—1031no—
248#103—1031no—
249#102—1031no—
250#102—1031no—
251#102C2×D10311yescharacteristic, complemented
252#102C2×D10311yescharacteristic, complemented
253C22⋊C8—1031no—
254C22⋊C8—1031no—
255C22⋊C8—1031no—
256C22⋊C8C2×D10311yescharacteristic
257C24—1031no—
258#41—4121no—
259#41—4121no—
260#41—4121no—
261#41—4121no—
262C2×Q8—1031no—
263C2×Q8—1031no—
264C2×D4—21no—
265C2×D4—1031no—
266C2×D4—2061no—
267C2×D4—2061no—
268C2×D4—2061no—
269C2×D4—2061no—
270C2×D4—2061no—
271C2×D4C22×D10311yescharacteristic
272C22×C4—1031no—
273C22×C4—1031no—
274C22×C4—1031no—
275C22×C4—1031no—
276C22×C4—1031no—
277C22×C4—4121no—
278C22×C4—4121no—
279C22×C4—2061no—
280C22×C4—2061no—
281C22×C4C22×D10311yescharacteristic
282Q16—4121no—
283SD16—4121no—
284SD16—4121no—
285D8—4121no—
286M16—4121no—
287M16—4121no—
288C2×C8—1031no—
289C2×C8—1031no—
290C2×C8C22×D10311yescharacteristic
291C2×C8C22×D10311yescharacteristic
292C4⋊C4—1031no—
293C4⋊C4—2061no—
294C4⋊C4—2061no—
295C4⋊C4—2061no—
296C4⋊C4—2061no—
297C4⋊C4C22×D10311yescharacteristic
298C4⋊C4C22×D10311yescharacteristic
299C4⋊C4C22×D10311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2061no—
303C22⋊C4—2061no—
304C22⋊C4—2061no—
305C22⋊C4—2061no—
306C22⋊C4—2061no—
307C22⋊C4—2061no—
308C22⋊C4—2061no—
309C22⋊C4—2061no—
310C42—21no—
311C42—2061no—
312C23—21no—
313C23—1031no—
314C23—1031no—
315C23—4121no—
316C23—4121no—
317C23—4121no—
318C23—2061no—
319C23D4×D10311yescharacteristic
320Q8—2061no—
321Q8—2061no—
322Q8—2061no—
323Q8—2061no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—4122no—
328D4—4122no—
329D4—4122no—
330D4—4122no—
331D4—4122no—
332D4—2061no—
333D4—2061no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—1031no—
340C2×C4—1031no—
341C2×C4—4122no—
342C2×C4—4121no—
343C2×C4—4121no—
344C2×C4—4122no—
345C2×C4—4121no—
346C2×C4—2061no—
347C2×C4—2061no—
348C2×C4—2061no—
349C2×C4—2061no—
350C2×C4—2061no—
351C2×C4—2061no—
352C2×C4—2061no—
353C2×C4D4×D10311yescharacteristic
354C2×C4C23×D10311yescharacteristic
355C8—21no—
356C8—21no—
357C8—2061no—
358C8—2061no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—4124no—
366C22—4121no—
367C22—4121no—
368C22—4121no—
369C22—2061no—
370C22—2061no—
371C22—2061no—
372C22—2061no—
373C22—2061no—
374C22—2061no—
375C22C2×D4×D10311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4121no—
381C4—4121no—
382C4—4121no—
383C4—2061no—
384C4—2061no—
385C4#1569306711yescharacteristic
386C4#1569306711yescharacteristic
387C2—41no—
388C2—81no—
389C2—8241no—
390C2—4121no—
391C2—4121no—
392C2#2026835211yescharacteristic
393C2#2026858711yescharacteristic
394C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#482×C103C2
socleC22×C103C22×D4
hypercenter#482D103
hypocenterC103#3197
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20268303C2semidirect
2. #20268301C2semidirect
3. #20268134C2semidirect
4. #20268132C2semidirect
5. #20268117C2semidirect
6. #20268050C2semidirect
7. #20268043C2semidirect
8. #20268038C2semidirect
9. #20268036C2semidirect
10. #20267955C2semidirect
11. #20267954C2semidirect
12. #20267937C2semidirect
13. #20267934C2semidirect
14. #20267753C2semidirect
15. #482×C103C2semidirect
19. C2×Dic412C22semidirect
20. C2×#13110094C22semidirect
21. C2×#13110093C22semidirect
22. C2×#13110090C22semidirect
41. #15692954C22semidirect
42. #15692952C22semidirect
43. #15692946C22semidirect
44. #15692944C22semidirect
45. #15692944C22semidirect
46. #15692944C22semidirect
47. #15692943C22semidirect
48. #15692941C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. #102×C103C22semidirect
57. #102×C103C22semidirect
198. C103#3197semidirect
204. #482D103semidirect
242. #107C2×D103semidirect
244. #106C2×D103semidirect
251. #102C2×D103semidirect
252. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683032
#202683012
#202681342
#202681322
#202681172
#202680502
#202680432
#202680382
#202680362
#202679552
#202679542
#202679372
#202679342
#202677532
#482×C1032
#3197103