Finite Group Databasebeta

← #27204928

Subgroups — #27204928

Order 13184.

388 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268344C211yesmaximal, characteristic, complemented
2#41×Dic103C211yesmaximal, characteristic
3#20268100C211yesmaximal, characteristic, complemented
4#20268096C211yesmaximal, characteristic, complemented
5#20268093C211yesmaximal, characteristic, complemented
6#20268089C211yesmaximal, characteristic, complemented
7#20268084C211yesmaximal, characteristic, complemented
8#20268079C211yesmaximal, characteristic, complemented
9#20268074C211yesmaximal, characteristic, complemented
10#20268069C211yesmaximal, characteristic, complemented
11#20267829C211yesmaximal, characteristic, complemented
12#20267827C211yesmaximal, characteristic, complemented
13C2×Dic103⋊C8C211yesmaximal, characteristic, complemented
14#20267787C211yesmaximal, characteristic
15#416×C103C211yesmaximal, characteristic
16C22×C103⋊C8C2211yescharacteristic
17#15693020C2211yescharacteristic
18#15693020C2211yescharacteristic
19#15693012C2211yescharacteristic
20#15693012C2211yescharacteristic
21#15692998—21no—
22#15692998—21no—
23Q8×Dic103C2211yescharacteristic
24Q8×Dic103C2211yescharacteristic
25C4×Dic206—21no—
26C4×Dic206—21no—
27D4×Dic103—21no—
28D4×Dic103—21no—
29D4×Dic103C2211yescharacteristic
30D4×Dic103C2211yescharacteristic
31#15692980—21no—
32#15692980C2211yescharacteristic
33#15692980C2211yescharacteristic
34C2×C4×Dic103—21no—
35C2×C4×Dic103C2211yescharacteristic
36#15692955C2211yescharacteristic
37#15692955C2211yescharacteristic
38#15692954C2211yescharacteristic
39#15692954C2211yescharacteristic
40#15692953C2211yescharacteristic
41#15692953C2211yescharacteristic
42#15692952C2211yescharacteristic
43#15692952C2211yescharacteristic
44Dic103⋊C8C2211yescharacteristic
45Dic103⋊C8C2211yescharacteristic
46Dic103⋊C8C2211yescharacteristic
47Dic103⋊C8C2211yescharacteristic
48#15692945C2211yescharacteristic
49#15692945C2211yescharacteristic
50#15692942C2211yescharacteristic
51#15692942C2211yescharacteristic
52C2×#41×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic
54#117×C103C2211yescharacteristic
55#103×C103C2211yescharacteristic
56#103×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206—21no—
61C22×Dic103—21no—
62C22×Dic103—21no—
63C22×Dic103D411yescharacteristic
64C22×Dic103D411yescharacteristic
65C2×C103⋊C8—22no—
66C2×C103⋊C8C2311yescharacteristic
67C2×C103⋊C8C2311yescharacteristic
68C4⋊Dic103—21no—
69C4⋊Dic103—21no—
70C4⋊Dic103—21no—
71C4⋊Dic103—21no—
72C4⋊Dic103C2311yescharacteristic
73C4⋊Dic103C2311yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76Dic103⋊C4—21no—
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79Dic103⋊C4—21no—
80C22⋊Dic103—21no—
81C22⋊Dic103—21no—
82C22⋊Dic103—21no—
83C22⋊Dic103—21no—
84C4×Dic103—21no—
85C4×Dic103—21no—
86C4×Dic103—21no—
87C4×Dic103—21no—
88C4×Dic103D411yescharacteristic
89C4×Dic103D411yescharacteristic
90C4×Dic103C2311yescharacteristic
91C4×Dic103C2311yescharacteristic
92#41×C103—22no—
93#41×C103Q814yescomplemented
94C2×Q8×C103C2311yescharacteristic
95C2×D4×C103—21no—
96C2×D4×C103C2311yescharacteristic
97C22×C4×C103—21no—
98C22×C4×C103C2311yescharacteristic
99C2×C8×C103—22no—
100C2×C8×C103C2311yescharacteristic
101C2×C8×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C22⋊C4×C103—21no—
105C42×C103—21no—
106C23×C103—21no—
107C23×C103C2×D411yescharacteristic
108Q8×C103—21no—
109Q8×C103C2×Q812yes—
110D4×C103—24no—
111D4×C103—21no—
112D4×C103C2×Q812yes—
113C2×C4×C103—21no—
114C2×C4×C103—24no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103C2×D411yescharacteristic
118C2×C4×C103C2×Q812yes—
119C2×C4×C103#4112yes—
120C2×C4×C103C2411yescharacteristic
121C2×Dic103—22no—
122C2×Dic103—21no—
123C2×Dic103—21no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—41no—
127C2×Dic103—42no—
128C2×Dic103—42no—
129C2×Dic103C2×D411yescharacteristic
130C2×Dic103C2×D411yescharacteristic
131C2×Dic103C2×D411yescharacteristic
132C2×Dic103C2×D411yescharacteristic
133Dic206—42no—
134Dic206—42no—
135C8×C103—21no—
136C8×C103—21no—
137C103⋊C8—21no—
138C103⋊C8—21no—
139C22×C103—21no—
140C22×C103—21no—
141C22×C103—22no—
142C22×C103—41no—
143C22×C103—41no—
144C22×C103C22⋊Q812yes—
145C22×C103C22×D411yescharacteristic
146C4×C103—22no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103C22⋊Q812yes—
150C4×C103C22×Q811yescharacteristic
151C4×C103C2×#4111yescharacteristic
152Dic103—21no—
153Dic103—21no—
154Dic103—21no—
155Dic103—41no—
156Dic103—41no—
157Dic103—41no—
158Dic103—41no—
159Dic103#13512yes—
160C2×C103—22no—
161C2×C103—42no—
162C2×C103C2×C22⋊Q811yescharacteristic
163C2×C103C2×#13511yescharacteristic
164C2×C103#57511yescharacteristic
165#3076—1031nomaximal, Sylow
166C103#307611yescharacteristic, complemented, Sylow
167#533—1031no—
168C4×#41—1031no—
169#479—1031no—
170#479—1031no—
171#478—1031no—
172#478—1031no—
173#477—1031no—
174#476—1031no—
175#475—1031no—
176#474—1031no—
177#427—1031no—
178#427—1031no—
179C2×C4⋊C8—1031no—
180#416—1031no—
181#416D10311yescharacteristic
182C2×#41C2×D10311yescharacteristic
183C22×C8—1031no—
184C22×C8C2×D10311yescharacteristic
185C4⋊Q8—1031no—
186C4⋊Q8—1031no—
187#125—1031no—
188#125—1031no—
189C22⋊Q8—2061no—
190C22⋊Q8—2061no—
191C4×Q8—1031no—
192C4×Q8—1031no—
193C4×Q8—2061no—
194C4×Q8—2061no—
195C4×D4—1031no—
196C4×D4—1031no—
197C4×D4—2061no—
198C4×D4—2061no—
199#117—1031no—
200#117—1031no—
201#117—2061no—
202#117C2×D10311yescharacteristic
203C2×C42—1031no—
204C2×C42—2061no—
205#107—1031no—
206#107—1031no—
207#107—1031no—
208#107—1031no—
209#106—1031no—
210#106—1031no—
211#106—1031no—
212#106—1031no—
213C4⋊C8—1031no—
214C4⋊C8—1031no—
215C4⋊C8—1031no—
216C4⋊C8—1031no—
217#103—1031no—
218#103—1031no—
219#103C2×D10311yescharacteristic
220#103C2×D10311yescharacteristic
221#102—1031no—
222#102—1031no—
223#102C2×D10311yescharacteristic
224#102C2×D10311yescharacteristic
225#41—22no—
226#41Dic20614yescomplemented
227C2×Q8—2061no—
228C2×Q8—2061no—
229C2×Q8C22×D10311yescharacteristic
230C2×D4—21no—
231C2×D4C22×D10311yescharacteristic
232C22×C4—21no—
233C22×C4—1031no—
234C22×C4—1031no—
235C22×C4—2061no—
236C22×C4—2061no—
237C22×C4C22×D10311yescharacteristic
238C2×C8—22no—
239C2×C8—1031no—
240C2×C8—1031no—
241C2×C8—2062no—
242C2×C8C22×D10311yescharacteristic
243C2×C8C22×D10311yescharacteristic
244C4⋊C4—1031no—
245C4⋊C4—1031no—
246C4⋊C4—1031no—
247C4⋊C4—1031no—
248C4⋊C4—2061no—
249C4⋊C4—2061no—
250C4⋊C4—2061no—
251C4⋊C4—2061no—
252C4⋊C4—2061no—
253C4⋊C4—2061no—
254C4⋊C4—2061no—
255C4⋊C4—2061no—
256C4⋊C4C22×D10311yescharacteristic
257C4⋊C4C22×D10311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—2061no—
260C22⋊C4—2061no—
261C22⋊C4—2061no—
262C22⋊C4—2061no—
263C42—21no—
264C42—1031no—
265C42—1031no—
266C42—1031no—
267C42—1031no—
268C42—2061no—
269C42—2061no—
270C42—2061no—
271C42—2061no—
272C23—21no—
273C23D4×D10311yescharacteristic
274Q8—21no—
275Q8—4122no—
276Q8—4122no—
277Q8C2×Dic20612yes—
278D4—24no—
279D4—21no—
280D4C2×Dic20612yes—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—1031no—
286C2×C4—1031no—
287C2×C4—1031no—
288C2×C4—1031no—
289C2×C4—4122no—
290C2×C4—4122no—
291C2×C4—4121no—
292C2×C4—2062no—
293C2×C4—2061no—
294C2×C4—2061no—
295C2×C4—2061no—
296C2×C4—2061no—
297C2×C4D4×D10311yescharacteristic
298C2×C4C2×Dic20612yes—
299C2×C4#1311010412yes—
300C2×C4C23×D10311yescharacteristic
301C8—21no—
302C8—21no—
303C8—2061no—
304C8—2061no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—41no—
309C22—41no—
310C22#1569299812yes—
311C22C2×D4×D10311yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—1032no—
316C4—4121no—
317C4—4121no—
318C4—4121no—
319C4—4121no—
320C4—2061no—
321C4—2061no—
322C4—2061no—
323C4#1569299812yes—
324C4C22×Dic20611yescharacteristic
325C4C2×#1311010411yescharacteristic
326C2—22no—
327C2—42no—
328C2C2×#1569299811yescharacteristic
329C2#135×D10311yescharacteristic
330C2#2026858811yescharacteristic
subgroupG/H
centerC2×C4D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#416×C103C2
socleC22×C103C22×D4
prime radicalC2×#41×C103C22
hypercenter#416D103
hypocenterC103#3076
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20268344C2semidirect
3. #20268100C2semidirect
4. #20268096C2semidirect
5. #20268093C2semidirect
6. #20268089C2semidirect
7. #20268084C2semidirect
8. #20268079C2semidirect
9. #20268074C2semidirect
10. #20268069C2semidirect
11. #20267829C2semidirect
12. #20267827C2semidirect
13. C2×Dic103⋊C8C2semidirect
93. #41×C103Q8semidirect
166. C103#3076semidirect
226. #41Dic206semidirect

Maximal subgroups

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

subgroupindex
#202683442
#41×Dic1032
#202681002
#202680962
#202680932
#202680892
#202680842
#202680792
#202680742
#202680692
#202678292
#202678272
C2×Dic103⋊C82
#202677872
#416×C1032
#3076103