Finite Group Databasebeta

← #27205814

Subgroups — #27205814

Order 13184.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268412C211yesmaximal, characteristic
2#20268201C211yesmaximal, characteristic, complemented
3#20268183C211yesmaximal, characteristic, complemented
4#20268148C211yesmaximal, characteristic, complemented
5#20268141C211yesmaximal, characteristic, complemented
6#20268047C211yesmaximal, characteristic, complemented
7#20268039C211yesmaximal, characteristic
8#20268030C211yesmaximal, characteristic, complemented
9#20268022C211yesmaximal, characteristic
10#20267896C211yesmaximal, characteristic, complemented
11#20267889C211yesmaximal, characteristic, complemented
12C4×#13110095C211yesmaximal, characteristic, complemented
13C4×#13110092C211yesmaximal, characteristic, complemented
14#20267747C211yesmaximal, characteristic, complemented
15#541×C103C211yesmaximal, characteristic, complemented
16C2×#13110095C2211yescharacteristic
17C2×#13110095C2211yescharacteristic
18C2×#13110092C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C2×#13110089C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22#15693021C2211yescharacteristic
23#15693016—21no—
24#15693009C2211yescharacteristic
25#15693007—21no—
26#15693003—21no—
27#15693000C2211yescharacteristic
28#15692999—21no—
29#15692995C2211yescharacteristic
30C4×Dic206C2211yescharacteristic
31C4×D412C2211yescharacteristic
32#15692954C2211yescharacteristic
33#15692954C2211yescharacteristic
34#15692952C2211yescharacteristic
35#15692952C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692945C2211yescharacteristic
39#15692945C2211yescharacteristic
40#15692944C2211yescharacteristic
41#15692944C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44#15692932C2211yescharacteristic
45#15692932C2211yescharacteristic
46C4×C103⋊C8C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48C4⋊Q8×C103C2211yescharacteristic
49#126×C103—21no—
50#126×C103—21no—
51#125×C103—21no—
52#125×C103—21no—
53#125×C103C2211yescharacteristic
54C22⋊Q8×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56C4×Q8×C103C2211yescharacteristic
57C4×Q8×C103C2211yescharacteristic
58#117×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206C2311yescharacteristic
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C2×C4×D103—21no—
64#13110095—22no—
65#13110095—22no—
66#13110092—22no—
67#13110092—22no—
68#13110089—22no—
69C2×C103⋊C8—22no—
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C4⋊Dic103—21no—
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83(C2×D103)⋊C4—21no—
84C4×Dic103—21no—
85C2×Q8×C103C2311yescharacteristic
86C2×Q8×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C4⋊C4×C103—21no—
89C4⋊C4×C103—21no—
90C4⋊C4×C103—21no—
91C4⋊C4×C103—21no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103D411yescharacteristic
97C4⋊C4×C103D411yescharacteristic
98C4⋊C4×C103C2311yescharacteristic
99C4⋊C4×C103C2311yescharacteristic
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103D411yescharacteristic
103C22⋊C4×C103D411yescharacteristic
104C42×C103—21no—
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103C2×D411yescharacteristic
109C22×D103—21no—
110Q8×C103—21no—
111Q8×C103—21no—
112Q8×C103—21no—
113Q8×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103C2×D411yescharacteristic
121C2×C4×C103C2×D411yescharacteristic
122C2×C4×C103C2×D411yescharacteristic
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C22⋊D103—81no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103—21no—
130D412—21no—
131D412—21no—
132C4×D103—81no—
133Dic206—21no—
134Dic206—21no—
135Dic206—81no—
136C103⋊C8—21no—
137C103⋊C8—21no—
138C103⋊C8#4112yes—
139C103⋊C8#4112yes—
140C22×C103—21no—
141C22×C103—21no—
142C22×C103—21no—
143C22×C103C22×D411yescharacteristic
144C2×D103—41no—
145C2×D103—41no—
146C2×D103—41no—
147C4×C103—21no—
148C4×C103—21no—
149C4×C103—21no—
150C4×C103—21no—
151C4×C103—21no—
152C4×C103—41no—
153C4×C103—41no—
154C4×C103—41no—
155C4×C103—41no—
156C4×C103C2×#4111yescharacteristic
157C4×C103C2×#4111yescharacteristic
158Dic103—41no—
159Dic103—41no—
160Dic103—41no—
161C2×C103—41no—
162C2×C103#53211yescharacteristic
163C2×C103#57711yescharacteristic
164C2×C103#57811yescharacteristic
165D103—81no—
166#3178—1031nomaximal, Sylow
167C103#317811yescharacteristic, complemented, Sylow
168#542—1031no—
169#541D10311yescharacteristic, complemented
170#501—1031no—
171#497—1031no—
172#488—1031no—
173#487—1031no—
174#470—1031no—
175#468—1031no—
176#467—1031no—
177#465—1031no—
178#441—1031no—
179#440—1031no—
180C4×Q16—1031no—
181C4×SD16—1031no—
182#405—1031no—
183C2×Q16—1031no—
184C2×Q16—1031no—
185C2×SD16—1031no—
186C2×SD16—1031no—
187C2×M16—1031no—
188C22×C8—1031no—
189C4⋊Q8—1031no—
190C4⋊Q8C2×D10311yescharacteristic
191#126—21no—
192#126—21no—
193#126—2061no—
194#125—21no—
195#125—21no—
196#125C2×D10311yescharacteristic
197#124—1031no—
198#124—2061no—
199#123—2061no—
200C22⋊Q8—1031no—
201C22⋊Q8—2061no—
202C22⋊Q8C2×D10311yescharacteristic
203C22⋊Q8C2×D10311yescharacteristic
204#121—1031no—
205C4×Q8—1031no—
206C4×Q8C2×D10311yescharacteristic
207C4×Q8C2×D10311yescharacteristic
208C4×D4—1031no—
209#117C2×D10311yescharacteristic
210#107—1031no—
211#107—1031no—
212#106—1031no—
213#106—1031no—
214#103—1031no—
215#103—1031no—
216#103—1031no—
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#102—1031no—
221#102—1031no—
222#97—1031no—
223#97—1031no—
224C4×C8—1031no—
225C4×C8—1031no—
226C2×Q8—1031no—
227C2×Q8—2061no—
228C2×Q8C22×D10311yescharacteristic
229C2×Q8C22×D10311yescharacteristic
230C2×D4—1031no—
231C2×D4—2061no—
232C22×C4—2061no—
233C22×C4C22×D10311yescharacteristic
234Q16—2062no—
235Q16—2062no—
236SD16—2062no—
237SD16—2062no—
238M16—2062no—
239C2×C8—1031no—
240C2×C8—1031no—
241C2×C8—1031no—
242C2×C8—1031no—
243C2×C8—2062no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—1031no—
253C4⋊C4—1031no—
254C4⋊C4—2061no—
255C4⋊C4—2061no—
256C4⋊C4—2061no—
257C4⋊C4C22⋊D10311yescharacteristic
258C4⋊C4C22⋊D10311yescharacteristic
259C4⋊C4C22×D10311yescharacteristic
260C4⋊C4C22×D10311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—2061no—
264C22⋊C4—2061no—
265C22⋊C4—2061no—
266C22⋊C4—2061no—
267C22⋊C4—2061no—
268C22⋊C4C22⋊D10311yescharacteristic
269C22⋊C4C22⋊D10311yescharacteristic
270C42—21no—
271C42—21no—
272C42—2061no—
273C42C22×D10311yescharacteristic
274C42C22×D10311yescharacteristic
275C23—2061no—
276C23C2×C22⋊D10311yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—8241no—
282Q8—2061no—
283Q8—2061no—
284D4—8241no—
285D4—2061no—
286D4—2061no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—8241no—
294C2×C4—2061no—
295C2×C4—2061no—
296C2×C4—2061no—
297C2×C4C2×C22⋊D10311yescharacteristic
298C2×C4C2×C22⋊D10311yescharacteristic
299C2×C4C2×C22⋊D10311yescharacteristic
300C2×C4C2×C22⋊D10311yescharacteristic
301C2×C4C2×C22⋊D10311yescharacteristic
302C2×C4C23×D10311yescharacteristic
303C8—1032no—
304C8—1032no—
305C8—2061no—
306C8—2061no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—4121no—
311C22—4121no—
312C22—4121no—
313C22C22×C22⋊D10311yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—4121no—
324C4—4121no—
325C4—4121no—
326C4#41×D10311yescharacteristic
327C4#41×D10311yescharacteristic
328C2—41no—
329C2—8241no—
330C2#2026833711yescharacteristic
331C2#2026859911yescharacteristic
332C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#541×C103C2
socleC22×C103C22×D4
prime radical#15692995C22
hypercenter#541D103
hypocenterC103#3178
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20268201C2semidirect
3. #20268183C2semidirect
4. #20268148C2semidirect
5. #20268141C2semidirect
6. #20268047C2semidirect
8. #20268030C2semidirect
10. #20267896C2semidirect
11. #20267889C2semidirect
12. C4×#13110095C2semidirect
13. C4×#13110092C2semidirect
14. #20267747C2semidirect
15. #541×C103C2semidirect
167. C103#3178semidirect
169. #541D103semidirect

Maximal subgroups

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

subgroupindex
#202684122
#202682012
#202681832
#202681482
#202681412
#202680472
#202680392
#202680302
#202680222
#202678962
#202678892
C4×#131100952
C4×#131100922
#202677472
#541×C1032
#3178103