Finite Group Databasebeta

← #27206973

Subgroups — #27206973

Order 13184.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268437C211yesmaximal, characteristic
2#20268148C211yesmaximal, characteristic, complemented
3#20268121C211yesmaximal, characteristic, complemented
4#20268115C211yesmaximal, characteristic, complemented
5#20268088C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268022C211yesmaximal, characteristic, complemented
8#20268013C211yesmaximal, characteristic, complemented
9#20267951C211yesmaximal, characteristic, complemented
10#20267941C211yesmaximal, characteristic, complemented
11C4×#13110092C211yesmaximal, characteristic, complemented
12D4×C103⋊C8C211yesmaximal, characteristic, complemented
13#20267785C211yesmaximal, characteristic, complemented
14C2×#15692941C211yesmaximal, characteristic, complemented
15#552×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C2×#13110095C2211yescharacteristic, complemented
19C2×#13110092C2211yescharacteristic
20C2×#13110092C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22C22×C103⋊C8C2211yescharacteristic, complemented
23#15693009C2211yescharacteristic
24#15693006—21no—
25#15693000C2211yescharacteristic
26#15692995C2211yescharacteristic
27#15692994—21no—
28#15692989—21no—
29C4×D412C2211yescharacteristic
30C22⋊C4×D103—21no—
31#15692954C2211yescharacteristic, complemented
32#15692952C2211yescharacteristic, complemented
33#15692952C2211yescharacteristic, complemented
34C4⋊(C103⋊C8)C2211yescharacteristic, complemented
35#15692945C2211yescharacteristic, complemented
36#15692944C2211yescharacteristic, complemented
37#15692944C2211yescharacteristic, complemented
38#15692944C2211yescharacteristic, complemented
39#15692941C2211yescharacteristic
40#15692941C2211yescharacteristic
41#15692941C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44#15692941C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic, complemented
47C4×C103⋊C8C2211yescharacteristic, complemented
48#126×C103—21no—
49#125×C103—21no—
50#125×C103C2211yescharacteristic, complemented
51#123×C103—21no—
52C22⋊Q8×C103C2211yescharacteristic
53C22⋊Q8×C103C2211yescharacteristic, complemented
54C4×Q8×C103C2211yescharacteristic, complemented
55C4×D4×C103C2211yescharacteristic
56#117×C103—21no—
57#117×C103C2211yescharacteristic, complemented
58C2×C4⋊C4×C103C2211yescharacteristic
59C23×D103—21no—
60#13110105—22no—
61#13110105—41no—
62C2×Dic206C2311yescharacteristic
63C2×D412—22no—
64C2×D412—21no—
65C2×D412—41no—
66C2×D412C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72#13110095—41no—
73#13110092—22no—
74#13110092—41no—
75C2×C103⋊C8—41no—
76C2×C103⋊C8—41no—
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C2×C103⋊C8C2311yescharacteristic
81C4⋊Dic103C2311yescharacteristic
82Dic103⋊C4—21no—
83C22⋊Dic103—21no—
84(C2×D103)⋊C4—21no—
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87(C2×D103)⋊C4—21no—
88C2×Q8×C103C2311yescharacteristic
89C2×D4×C103D411yescharacteristic
90C22×C4×C103—21no—
91C22×C4×C103C2311yescharacteristic
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—21no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103—21no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103D411yescharacteristic
100C4⋊C4×C103C2311yescharacteristic
101C4⋊C4×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C22⋊C4×C103—21no—
104C22⋊C4×C103—21no—
105C22⋊C4×C103—21no—
106C22⋊C4×C103D411yescharacteristic
107C22⋊C4×C103D411yescharacteristic
108C42×C103—21no—
109C42×C103—21no—
110C42×C103C2311yescharacteristic
111C23×C103C2×D411yescharacteristic
112C23×C103C2×D411yescharacteristic
113C22×D103—21no—
114C22×D103—21no—
115C22×D103—42no—
116C22×D103—42no—
117C22×D103—81no—
118Q8×C103—21no—
119Q8×C103—21no—
120D4×C103—22no—
121C2×C4×C103—21no—
122C2×C4×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×C103—42no—
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2×D411yescharacteristic
132C2×C4×C103C2×D411yescharacteristic
133C2×C4×C103C2×D411yescharacteristic
134C2×C4×C103C2411yescharacteristic
135C22⋊D103—42no—
136C22⋊D103—81no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139D412—21no—
140D412—21no—
141D412—21no—
142D412—42no—
143D412#4112yes—
144C4×D103—42no—
145C4×D103—81no—
146Dic206—21no—
147Dic206—21no—
148C103⋊C8—21no—
149C103⋊C8—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103#13512yes—
158C22×C103C22×D411yescharacteristic
159C2×D103—22no—
160C2×D103—41no—
161C2×D103—41no—
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—41no—
165C2×D103—84no—
166C4×C103—21no—
167C4×C103—21no—
168C4×C103—21no—
169C4×C103—21no—
170C4×C103—41no—
171C4×C103—41no—
172C4×C103—41no—
173C4×C103—41no—
174C4×C103C2×#4111yescharacteristic
175C4×C103H(5,𝔽2)11yescharacteristic
176Dic103—41no—
177Dic103—41no—
178C2×C103—22no—
179C2×C103—41no—
180C2×C103#54611yescharacteristic
181C2×C103C2×#13511yescharacteristic
182C2×C103#57711yescharacteristic
183D103—42no—
184D103—81no—
185#3296—1031nomaximal, Sylow
186C103#329611yescharacteristic, complemented, Sylow
187#552D10311yescharacteristic, complemented
188#546—1031no—
189#488—1031no—
190#483—1031no—
191#482—1031no—
192#478—1031no—
193#467—1031no—
194#465—1031no—
195#464—1031no—
196#452—1031no—
197#450—1031no—
198C4×SD16—1031no—
199C8×D4—1031no—
200#416—1031no—
201C2×#102—1031no—
202C2×#41—1031no—
203C22×D4—1031no—
204C2×Q16—1031no—
205C2×SD16—1031no—
206C2×SD16—1031no—
207C22×C8—1031no—
208C22×C8—1031no—
209#126—21no—
210#125—21no—
211#125C2×D10311yescharacteristic, complemented
212#124—1031no—
213#123—21no—
214#123—2061no—
215C22⋊Q8—1031no—
216C22⋊Q8C2×D10311yescharacteristic
217C22⋊Q8C2×D10311yescharacteristic, complemented
218#121—1031no—
219#121—2061no—
220#120—2061no—
221C4×Q8C2×D10311yescharacteristic, complemented
222C4×D4—1031no—
223C4×D4C2×D10311yescharacteristic
224#117—21no—
225#117C2×D10311yescharacteristic, complemented
226C2×C4⋊C4C2×D10311yescharacteristic
227C2×C22⋊C4—2061no—
228#107—1031no—
229#106—1031no—
230#106—1031no—
231C4⋊C8—1031no—
232#103—1031no—
233#103—1031no—
234#103—1031no—
235#103—1031no—
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241#102—1031no—
242C22⋊C8—1031no—
243C22⋊C8—1031no—
244C4×C8—1031no—
245C24—2061no—
246#41—4121no—
247#41—2062no—
248C2×Q8—1031no—
249C2×Q8C22×D10311yescharacteristic
250C2×D4—1031no—
251C2×D4—1031no—
252C2×D4—4121no—
253C2×D4—2062no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4—2061no—
257C2×D4C22⋊D10311yescharacteristic
258C22×C4—21no—
259C22×C4—2061no—
260C22×C4—2061no—
261C22×C4C22×D10311yescharacteristic
262C22×C4C22×D10311yescharacteristic
263Q16—4121no—
264SD16—4121no—
265SD16—2062no—
266C2×C8—1031no—
267C2×C8—1031no—
268C2×C8—1031no—
269C2×C8—1031no—
270C2×C8—4121no—
271C2×C8—4121no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—1031no—
279C4⋊C4—2061no—
280C4⋊C4C22⋊D10311yescharacteristic
281C4⋊C4C22×D10311yescharacteristic
282C4⋊C4C22×D10311yescharacteristic
283C4⋊C4C22×D10311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4C22⋊D10311yescharacteristic
293C22⋊C4C22⋊D10311yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D10311yescharacteristic
297C23—8241no—
298C23—4122no—
299C23—4122no—
300C23—2061no—
301C23—2061no—
302C23C2×C22⋊D10311yescharacteristic
303C23C2×C22⋊D10311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2061no—
307Q8—2061no—
308D4—22no—
309D4—8241no—
310D4—1032no—
311D4—4122no—
312D4—4122no—
313D4—2061no—
314D4—2061no—
315D4—2061no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—8241no—
326C2×C4—4122no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4C2×C22⋊D10311yescharacteristic
330C2×C4C2×C22⋊D10311yescharacteristic
331C2×C4C2×C22⋊D10311yescharacteristic
332C2×C4C2×C22⋊D10311yescharacteristic
333C2×C4C23×D10311yescharacteristic
334C8—2061no—
335C8—2061no—
336C8—2061no—
337C8—2061no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—8244no—
344C22—4121no—
345C22—4121no—
346C22—4121no—
347C22—4121no—
348C22—4121no—
349C22—2062no—
350C22#1569304112yes—
351C22C22×C22⋊D10311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—4121no—
361C4—4121no—
362C4#41×D10311yescharacteristic
363C4#1569306711yescharacteristic
364C2—22no—
365C2—41no—
366C2—8241no—
367C2—4122no—
368C2#2026842911yescharacteristic
369C2C2×#1569304111yescharacteristic
370C2#2026859911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#552×C103C2
socleC22×C103C22×D4
prime radical#20268437C2
hypercenter#552D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #20268148C2semidirect
3. #20268121C2semidirect
4. #20268115C2semidirect
5. #20268088C2semidirect
6. #20268030C2semidirect
7. #20268022C2semidirect
8. #20268013C2semidirect
9. #20267951C2semidirect
10. #20267941C2semidirect
11. C4×#13110092C2semidirect
12. D4×C103⋊C8C2semidirect
13. #20267785C2semidirect
14. C2×#15692941C2semidirect
15. #552×C103C2semidirect
18. C2×#13110095C22semidirect
22. C22×C103⋊C8C22semidirect
31. #15692954C22semidirect
32. #15692952C22semidirect
33. #15692952C22semidirect
34. C4⋊(C103⋊C8)C22semidirect
35. #15692945C22semidirect
36. #15692944C22semidirect
37. #15692944C22semidirect
38. #15692944C22semidirect
46. C22⋊(C103⋊C8)C22semidirect
47. C4×C103⋊C8C22semidirect
50. #125×C103C22semidirect
53. C22⋊Q8×C103C22semidirect
54. C4×Q8×C103C22semidirect
57. #117×C103C22semidirect
186. C103#3296semidirect
187. #552D103semidirect
211. #125C2×D103semidirect
217. C22⋊Q8C2×D103semidirect
221. C4×Q8C2×D103semidirect
225. #117C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684372
#202681482
#202681212
#202681152
#202680882
#202680302
#202680222
#202680132
#202679512
#202679412
C4×#131100922
D4×C103⋊C82
#202677852
C2×#156929412
#552×C1032
#3296103