Finite Group Databasebeta

← #27205848

Subgroups — #27205848

Order 13184.

366 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268343C211yesmaximal, characteristic, complemented
2#20268327C211yesmaximal, characteristic
3#20268199C211yesmaximal, characteristic, complemented
4#20268184C211yesmaximal, characteristic, complemented
5#20268158C211yesmaximal, characteristic, complemented
6#20268152C211yesmaximal, characteristic, complemented
7#20268030C211yesmaximal, characteristic, complemented
8#20268022C211yesmaximal, characteristic
9#20268020C211yesmaximal, characteristic
10#20267898C211yesmaximal, characteristic, complemented
11#20267895C211yesmaximal, characteristic, complemented
12#20267894C211yesmaximal, characteristic, complemented
13#20267890C211yesmaximal, characteristic, complemented
14C2×#15692931C211yesmaximal, characteristic, complemented
15#467×C103C211yesmaximal, characteristic, complemented
16C2×#13110095C2211yescharacteristic
17C2×#13110094C2211yescharacteristic
18C2×#13110092C2211yescharacteristic
19C22×C103⋊C8C2211yescharacteristic
20#15693020C2211yescharacteristic
21#15693019C2211yescharacteristic
22#15693016—21no—
23#15693012C2211yescharacteristic
24#15693011—21no—
25#15693010C2211yescharacteristic
26#15693005—21no—
27#15693000C2211yescharacteristic
28#15692998—21no—
29#15692995C2211yescharacteristic
30Q8×Dic103C2211yescharacteristic
31Q8×Dic103C2211yescharacteristic
32#15692986—21no—
33#15692986C2211yescharacteristic
34#15692983C2211yescharacteristic
35(C22⋊D103)⋊C4—21no—
36#15692979—21no—
37#15692977—21no—
38C2×C4×Dic103C2211yescharacteristic
39#15692954C2211yescharacteristic
40#15692953C2211yescharacteristic
41#15692952C2211yescharacteristic
42#15692946C2211yescharacteristic
43#15692945C2211yescharacteristic
44#15692945C2211yescharacteristic
45#15692944C2211yescharacteristic
46#15692943C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692931C2211yescharacteristic
49#15692931C2211yescharacteristic
50#15692931C2211yescharacteristic
51#15692931C2211yescharacteristic
52C2×Q16×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic
54C22⋊Q8×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56#107×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58#103×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206C2311yescharacteristic
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C22×Dic103D411yescharacteristic
64C22×Dic103D411yescharacteristic
65C2×C4×D103—21no—
66#13110095—22no—
67#13110094—22no—
68#13110092—22no—
69C2×C103⋊C8—22no—
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C4⋊Dic103—21no—
73C4⋊Dic103—21no—
74C4⋊Dic103—21no—
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
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—
88C4×Dic103—21no—
89C4×Dic103—21no—
90C4×Dic103—21no—
91C4×Dic103D411yescharacteristic
92C4×Dic103D411yescharacteristic
93C4×Dic103C2311yescharacteristic
94C4×Dic103C2311yescharacteristic
95C2×Q8×C103C2311yescharacteristic
96C2×Q8×C103C2311yescharacteristic
97C22×C4×C103C2311yescharacteristic
98Q16×C103—22no—
99C2×C8×C103—22no—
100C2×C8×C103C2311yescharacteristic
101C2×C8×C103C2311yescharacteristic
102C4⋊C4×C103—21no—
103C4⋊C4×C103—21no—
104C4⋊C4×C103C2311yescharacteristic
105C4⋊C4×C103C2311yescharacteristic
106C22⋊C4×C103—21no—
107C22⋊C4×C103—21no—
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×C103C2411yescharacteristic
122C22⋊D103—42no—
123C2×Dic103—22no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—41no—
128C2×Dic103C2×D411yescharacteristic
129C2×Dic103C2×D411yescharacteristic
130C2×Dic103C2×D411yescharacteristic
131C2×Dic103C2×D411yescharacteristic
132D412—21no—
133D412—21no—
134C4×D103—42no—
135Dic206—21no—
136Dic206—21no—
137Dic206—42no—
138C8×C103—21no—
139C8×C103#4112yes—
140C103⋊C8—21no—
141C103⋊C8#4112yes—
142C22×C103—21no—
143C22×C103—21no—
144C22×C103#13712yes—
145C22×C103C22×D411yescharacteristic
146C2×D103—41no—
147C2×D103—41no—
148C2×D103—41no—
149C4×C103—21no—
150C4×C103—41no—
151C4×C103—41no—
152C4×C103—41no—
153C4×C103—41no—
154C4×C103C2×#4111yescharacteristic
155C4×C103C2×#4111yescharacteristic
156Dic103—21no—
157Dic103—21no—
158Dic103—21no—
159Dic103—21no—
160Dic103—41no—
161Dic103—41no—
162Dic103—41no—
163C2×C103—22no—
164C2×C103#53211yescharacteristic
165C2×C103C2×#13711yescharacteristic
166C2×C103#57511yescharacteristic
167D103—81no—
168#3181—1031nomaximal, Sylow
169C103#318111yescharacteristic, complemented, Sylow
170#533—1031no—
171#529—1031no—
172#501—1031no—
173#497—1031no—
174#491—1031no—
175#489—1031no—
176#467—1031no—
177#467D10311yescharacteristic, complemented
178#465—1031no—
179#465—1031no—
180#441—1031no—
181#441—1031no—
182#440—1031no—
183#440—1031no—
184C2×#97—1031no—
185C2×Q16—1031no—
186C2×Q16C2×D10311yescharacteristic
187C2×SD16—1031no—
188C2×SD16—1031no—
189C22×C8—1031no—
190C22×C8C2×D10311yescharacteristic
191C4⋊Q8—1031no—
192C4⋊Q8—1031no—
193#126—2061no—
194#125—1031no—
195#125—2061no—
196#124—1031no—
197#123—2061no—
198C22⋊Q8—1031no—
199C22⋊Q8—2061no—
200C22⋊Q8C2×D10311yescharacteristic
201C22⋊Q8C2×D10311yescharacteristic
202#121—1031no—
203C4×Q8—1031no—
204C4×Q8—1031no—
205C4×Q8—1031no—
206C4×Q8—2061no—
207C4×D4—1031no—
208C4×D4—2061no—
209#117—2061no—
210#117—2061no—
211C2×C42—1031no—
212#107—1031no—
213#107C2×D10311yescharacteristic
214#106—1031no—
215#106—1031no—
216#103—1031no—
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#103C2×D10311yescharacteristic
221#103C2×D10311yescharacteristic
222#102—1031no—
223#102—1031no—
224#97—1031no—
225#97—1031no—
226#97—1031no—
227#97—1031no—
228C2×Q8—1031no—
229C2×Q8—2061no—
230C2×Q8C22×D10311yescharacteristic
231C2×Q8C22×D10311yescharacteristic
232C2×D4—1031no—
233C2×D4—2061no—
234C22×C4—1031no—
235C22×C4—1031no—
236C22×C4—2061no—
237C22×C4C22×D10311yescharacteristic
238Q16—22no—
239Q16—2062no—
240SD16—2062no—
241SD16—2062no—
242C2×C8—22no—
243C2×C8—1031no—
244C2×C8—1031no—
245C2×C8—2062no—
246C2×C8C22×D10311yescharacteristic
247C2×C8C22×D10311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1031no—
251C4⋊C4—1031no—
252C4⋊C4—2061no—
253C4⋊C4—2061no—
254C4⋊C4—2061no—
255C4⋊C4—2061no—
256C4⋊C4—2061no—
257C4⋊C4—2061no—
258C4⋊C4—2061no—
259C4⋊C4—2061no—
260C4⋊C4—2061no—
261C4⋊C4C22×D10311yescharacteristic
262C4⋊C4C22×D10311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—2061no—
266C22⋊C4—2061no—
267C22⋊C4—2061no—
268C22⋊C4—2061no—
269C22⋊C4—2061no—
270C42—1031no—
271C42—1031no—
272C42—1031no—
273C42—1031no—
274C42—2061no—
275C42—2061no—
276C42—2061no—
277C23—2061no—
278C23D4×D10311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—4122no—
284Q8—2061no—
285Q8—2061no—
286D4—4122no—
287D4—2061no—
288D4—2061no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—1031no—
296C2×C4—1031no—
297C2×C4—1031no—
298C2×C4—1031no—
299C2×C4—4122no—
300C2×C4—4121no—
301C2×C4—2061no—
302C2×C4—2061no—
303C2×C4—2061no—
304C2×C4—2062no—
305C2×C4D4×D10311yescharacteristic
306C2×C4C23×D10311yescharacteristic
307C8—21no—
308C8—1032no—
309C8—2061no—
310C8#1311010412yes—
311C22—21no—
312C22—21no—
313C22—4121no—
314C22—4121no—
315C22—4121no—
316C22#1569305312yes—
317C22C2×D4×D10311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—4121no—
324C4—4121no—
325C4—4121no—
326C4—2061no—
327C4—2061no—
328C4—2061no—
329C4—2061no—
330C4#41×D10311yescharacteristic
331C4C2×#1311010411yescharacteristic
332C2—22no—
333C2—8241no—
334C2#2026833611yescharacteristic
335C2C2×#1569305311yescharacteristic
336C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#467×C103C2
socleC22×C103C22×D4
prime radical#15692995C22
hypercenter#467D103
hypocenterC103#3181
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #20268343C2semidirect
3. #20268199C2semidirect
4. #20268184C2semidirect
5. #20268158C2semidirect
6. #20268152C2semidirect
7. #20268030C2semidirect
10. #20267898C2semidirect
11. #20267895C2semidirect
12. #20267894C2semidirect
13. #20267890C2semidirect
14. C2×#15692931C2semidirect
15. #467×C103C2semidirect
169. C103#3181semidirect
177. #467D103semidirect

Maximal subgroups

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

subgroupindex
#202683432
#202683272
#202681992
#202681842
#202681582
#202681522
#202680302
#202680222
#202680202
#202678982
#202678952
#202678942
#202678902
C2×#156929312
#467×C1032
#3181103