Finite Group Databasebeta

← #27205978

Subgroups — #27205978

Order 13184.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268303C211yesmaximal, characteristic
2C22⋊Q8×D103C211yesmaximal, characteristic, complemented
3#20268132C211yesmaximal, characteristic, complemented
4#20268128C211yesmaximal, characteristic, complemented
5#20268111C211yesmaximal, characteristic, complemented
6#20268050C211yesmaximal, characteristic, complemented
7#20268048C211yesmaximal, characteristic, complemented
8#20268040C211yesmaximal, characteristic, complemented
9#20268038C211yesmaximal, characteristic, complemented
10#20267955C211yesmaximal, characteristic, complemented
11#20267951C211yesmaximal, characteristic, complemented
12#20267948C211yesmaximal, characteristic, complemented
13#20267931C211yesmaximal, characteristic, complemented
14#20267753C211yesmaximal, characteristic, complemented
15#485×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×Q8×D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C2×Dic412C2211yescharacteristic, complemented
20C2×#13110095C2211yescharacteristic, complemented
21C2×#13110094C2211yescharacteristic, complemented
22C2×#13110092C2211yescharacteristic, complemented
23C2×#13110088C2211yescharacteristic
24C2×#13110088C2211yescharacteristic
25#15693005—21no—
26#15693001C2211yescharacteristic
27#15693001C2211yescharacteristic
28#15693001C2211yescharacteristic
29#15693000C2211yescharacteristic
30#15692999—21no—
31#15692998—21no—
32#15692997C2211yescharacteristic
33#15692996C2211yescharacteristic
34#15692996C2211yescharacteristic
35#15692991—21no—
36C4×D412—21no—
37C4×D412—21no—
38C4⋊C4×D103—21no—
39C4⋊C4×D103C2211yescharacteristic
40C22⋊C4×D103—21no—
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
52C22⋊Q8×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103D411yescharacteristic
60#13110105—41no—
61#13110105—41no—
62C2×Dic206—21no—
63C2×Dic206C2311yescharacteristic
64C2×Dic206C2311yescharacteristic
65Q8×D103—41no—
66Q8×D103—41no—
67C2×D412—21no—
68C2×D412—21no—
69C2×D412C2311yescharacteristic
70C2×C22⋊D103—21no—
71C22×Dic103D411yescharacteristic
72C2×C4×D103—21no—
73C2×C4×D103—21no—
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#13110095—41no—
83#13110094—41no—
84#13110092—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—
94Dic103⋊C4—21no—
95Dic103⋊C4—21no—
96C22⋊Dic103—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—
102(C2×D103)⋊C4—21no—
103C2×Q8×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103—21no—
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C4⋊C4×C103C2311yescharacteristic
111C22⋊C4×C103—21no—
112C22⋊C4×C103—21no—
113C42×C103—21no—
114C23×C103C2×D411yescharacteristic
115C22×D103—22no—
116C22×D103—21no—
117C22×D103—41no—
118C22×D103—41no—
119C22×D103C2×D411yescharacteristic
120C22×D103C2×D411yescharacteristic
121Q8×C103—21no—
122Q8×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2411yescharacteristic
131C22⋊D103—42no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—41no—
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138D412—21no—
139D412—21no—
140D412—42no—
141D412—42no—
142C4×D103—21no—
143C4×D103—21no—
144C4×D103—21no—
145C4×D103—21no—
146C4×D103—41no—
147C4×D103—41no—
148C4×D103—42no—
149C4×D103—42no—
150C4×D103—42no—
151Dic206—21no—
152Dic206—21no—
153Dic206—21no—
154Dic206—21no—
155Dic206—42no—
156C8×C103—21no—
157C8×C103—21no—
158C103⋊C8—21no—
159C103⋊C8—21no—
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103C22×D411yescharacteristic
164C2×D103—21no—
165C2×D103—21no—
166C2×D103—21no—
167C2×D103—21no—
168C2×D103—21no—
169C2×D103—44no—
170C2×D103—41no—
171C2×D103—41no—
172C2×D103—41no—
173C2×D103#13712yes—
174C4×C103—21no—
175C4×C103—41no—
176C4×C103—41no—
177C4×C103—41no—
178C4×C103—41no—
179C4×C103H(5,𝔽2)11yescharacteristic
180C4×C103H(5,𝔽2)11yescharacteristic
181Dic103—21no—
182Dic103—21no—
183Dic103—41no—
184Dic103—41no—
185Dic103—41no—
186C2×C103—41no—
187C2×C103#53411yescharacteristic
188C2×C103C2×#13711yescharacteristic
189C2×C103#57511yescharacteristic
190D103—22no—
191D103—41no—
192D103—81no—
193#3196—1031nomaximal, Sylow
194C103#319611yescharacteristic, complemented, Sylow
195#525—1031no—
196C2×C22⋊Q8—1031no—
197#485—1031no—
198#485D10311yescharacteristic, complemented
199#484—1031no—
200#481—1031no—
201#470—1031no—
202#470—1031no—
203#468—1031no—
204#468—1031no—
205#452—1031no—
206#452—1031no—
207#451—1031no—
208#448—1031no—
209#407—1031no—
210C2×#41—1031no—
211C22×Q8—1031no—
212C23×C4—1031no—
213C2×Q16—1031no—
214C2×Q16—1031no—
215C2×SD16—1031no—
216C2×SD16—1031no—
217C2×M16—1031no—
218C2×M16—1031no—
219#123—2061no—
220C22⋊Q8—1031no—
221C22⋊Q8—1031no—
222C22⋊Q8—1031no—
223C22⋊Q8—1031no—
224C22⋊Q8—1031no—
225C22⋊Q8—2061no—
226C22⋊Q8—2061no—
227C22⋊Q8C2×D10311yescharacteristic
228#121—1031no—
229#121—1031no—
230#120—2061no—
231C4×D4—2061no—
232C4×D4—2061no—
233#117C2×D10311yescharacteristic
234C2×C4⋊C4—1031no—
235C2×C4⋊C4—2061no—
236C2×C22⋊C4—2061no—
237#107—1031no—
238#107C2×D10311yescharacteristic, complemented
239#106—1031no—
240#106C2×D10311yescharacteristic, complemented
241#103—1031no—
242#103—1031no—
243#103—1031no—
244#103—1031no—
245#103C2×D10311yescharacteristic, complemented
246#103C2×D10311yescharacteristic, complemented
247#102—1031no—
248#102—1031no—
249C22⋊C8—1031no—
250C22⋊C8—1031no—
251C22⋊C8—1031no—
252C22⋊C8C2×D10311yescharacteristic
253C24—1031no—
254#41—4121no—
255#41—4121no—
256C2×Q8—1031no—
257C2×Q8—1031no—
258C2×Q8—4121no—
259C2×Q8—4121no—
260C2×Q8—2061no—
261C2×Q8C22×D10311yescharacteristic
262C2×D4—1031no—
263C2×D4—2061no—
264C2×D4—2061no—
265C2×D4—2061no—
266C22×C4—1031no—
267C22×C4—1031no—
268C22×C4—1031no—
269C22×C4—1031no—
270C22×C4—1031no—
271C22×C4—4121no—
272C22×C4—4121no—
273C22×C4—2061no—
274C22×C4—2061no—
275C22×C4—2061no—
276C22×C4C22×D10311yescharacteristic
277Q16—4121no—
278Q16—4121no—
279SD16—4121no—
280SD16—4121no—
281M16—4121no—
282M16—4121no—
283C2×C8—1031no—
284C2×C8—1031no—
285C2×C8C22×D10311yescharacteristic
286C2×C8C22×D10311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—1031no—
289C4⋊C4—2061no—
290C4⋊C4—2061no—
291C4⋊C4—2061no—
292C4⋊C4—2061no—
293C4⋊C4—2061no—
294C4⋊C4—2061no—
295C4⋊C4C22×D10311yescharacteristic
296C4⋊C4C22×D10311yescharacteristic
297C4⋊C4C22×D10311yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—2061no—
301C22⋊C4—2061no—
302C22⋊C4—2061no—
303C22⋊C4—2061no—
304C22⋊C4—2061no—
305C22⋊C4—2061no—
306C22⋊C4—2061no—
307C42—21no—
308C23—1031no—
309C23—1031no—
310C23—4121no—
311C23—4121no—
312C23—2062no—
313C23—2061no—
314C23D4×D10311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—4122no—
318Q8—2061no—
319Q8—2061no—
320Q8—2061no—
321Q8—2061no—
322D4—4122no—
323D4—4122no—
324D4—4122no—
325D4—2061no—
326D4—2061no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—1031no—
334C2×C4—1031no—
335C2×C4—4122no—
336C2×C4—4121no—
337C2×C4—4121no—
338C2×C4—4122no—
339C2×C4—4122no—
340C2×C4—4121no—
341C2×C4—2061no—
342C2×C4—2061no—
343C2×C4—2061no—
344C2×C4—2061no—
345C2×C4—2061no—
346C2×C4—2061no—
347C2×C4—2061no—
348C2×C4D4×D10311yescharacteristic
349C2×C4C23×D10311yescharacteristic
350C8—21no—
351C8—21no—
352C8—2061no—
353C8—2061no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—1032no—
358C22—4124no—
359C22—4121no—
360C22—4121no—
361C22—4121no—
362C22—2061no—
363C22—2061no—
364C22—2061no—
365C22—2061no—
366C22—2061no—
367C22C2×D4×D10311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—4121no—
374C4—4121no—
375C4—4121no—
376C4—2061no—
377C4—2061no—
378C4#1569306711yescharacteristic
379C4#1569306711yescharacteristic
380C2—41no—
381C2—8241no—
382C2—4121no—
383C2—2062no—
384C2#2026835211yescharacteristic
385C2#137×D10311yescharacteristic
386C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#485×C103C2
socleC22×C103C22×D4
prime radical#20268303C2
hypercenter#485D103
hypocenterC103#3196
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D103C2semidirect
3. #20268132C2semidirect
4. #20268128C2semidirect
5. #20268111C2semidirect
6. #20268050C2semidirect
7. #20268048C2semidirect
8. #20268040C2semidirect
9. #20268038C2semidirect
10. #20267955C2semidirect
11. #20267951C2semidirect
12. #20267948C2semidirect
13. #20267931C2semidirect
14. #20267753C2semidirect
15. #485×C103C2semidirect
19. C2×Dic412C22semidirect
20. C2×#13110095C22semidirect
21. C2×#13110094C22semidirect
22. C2×#13110092C22semidirect
41. #15692954C22semidirect
42. #15692952C22semidirect
43. #15692946C22semidirect
44. #15692944C22semidirect
45. #15692944C22semidirect
46. #15692944C22semidirect
47. #15692943C22semidirect
48. #15692941C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. #103×C103C22semidirect
57. #103×C103C22semidirect
194. C103#3196semidirect
198. #485D103semidirect
238. #107C2×D103semidirect
240. #106C2×D103semidirect
245. #103C2×D103semidirect
246. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683032
C22⋊Q8×D1032
#202681322
#202681282
#202681112
#202680502
#202680482
#202680402
#202680382
#202679552
#202679512
#202679482
#202679312
#202677532
#485×C1032
#3196103