Finite Group Databasebeta

← #27198098

Subgroups — #27198098

Order 13184.

480 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
1C2×#15692986C211yesmaximal, characteristic
2#20267695C211yesmaximal, characteristic
3#20267695C211yesmaximal, characteristic
4#20267678C211yesmaximal, characteristic
5#20267677C211yesmaximal, characteristic
6#20267672C211yesmaximal, characteristic
7#20267660C211yesmaximal, characteristic
8#20267655C211yesmaximal, characteristic
9#20267655C211yesmaximal, characteristic
10C4×Dic103⋊C4C211yesmaximal, characteristic
11C4×Dic103⋊C4C211yesmaximal, characteristic
12#20267642C211yesmaximal, characteristic
13#20267642C211yesmaximal, characteristic
14#20267642C211yesmaximal, characteristic
15#387×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17#15692986C418yescomplemented
18C2×C4⋊Dic103C2211yescharacteristic
19C2×Dic103⋊C4C2211yescharacteristic
20C2×Dic103⋊C4C2211yescharacteristic
21C2×Dic103⋊C4C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×C4×Dic103C2211yescharacteristic
28C2×C4×Dic103C2211yescharacteristic
29C2×C4×Dic103C2211yescharacteristic
30C2×C4×Dic103C2211yescharacteristic
31C2×C4×Dic103C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C2×C4×Dic103C2211yescharacteristic
34C2×C4×Dic103C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C2×C4⋊C4×C103C2211yescharacteristic
46C2×C4⋊C4×C103C2211yescharacteristic
47C2×C42×C103C2211yescharacteristic
48#95×C103C2211yescharacteristic
49#95×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C2×Dic206—22no—
53C2×Dic206—22no—
54C2×Dic206C2×C414yes—
55C22×Dic103C2311yescharacteristic
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C4⋊Dic103—41no—
64Dic103⋊C4—22no—
65Dic103⋊C4—22no—
66Dic103⋊C4—22no—
67Dic103⋊C4—22no—
68Dic103⋊C4—22no—
69Dic103⋊C4C2×C414yes—
70Dic103⋊C4C2×C414yes—
71Dic103⋊C4Q814yescomplemented
72C4×Dic103—22no—
73C4×Dic103—22no—
74C4×Dic103—41no—
75C4×Dic103—41no—
76C4×Dic103—41no—
77C4×Dic103C2×C414yes—
78C4×Dic103C2×C414yes—
79C4×Dic103C2×C414yes—
80C22×C4×C103C2311yescharacteristic
81C22×C4×C103C2311yescharacteristic
82C22×C4×C103C2311yescharacteristic
83C22×C4×C103C2311yescharacteristic
84C22×C4×C103C2311yescharacteristic
85C22×C4×C103C2311yescharacteristic
86C22×C4×C103C2311yescharacteristic
87C4⋊C4×C103—41no—
88C4⋊C4×C103C2×C414yes—
89C42×C103—41no—
90C23×C103C2411yescharacteristic
91C2×C4×C103—21no—
92C2×C4×C103—21no—
93C2×C4×C103—21no—
94C2×C4×C103—21no—
95C2×C4×C103—21no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103C22×C412yes—
109C2×C4×C103C22×C412yes—
110C2×C4×C103C22×C412yes—
111C2×C4×C103C2×Q812yes—
112C2×Dic103—21no—
113C2×Dic103—21no—
114C2×Dic103—21no—
115C2×Dic103—21no—
116C2×Dic103—21no—
117C2×Dic103—21no—
118C2×Dic103—21no—
119C2×Dic103—21no—
120C2×Dic103—21no—
121C2×Dic103—21no—
122C2×Dic103—21no—
123C2×Dic103—21no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103C22×C412yes—
128C2×Dic103C22×C412yes—
129C2×Dic103C22×C412yes—
130C2×Dic103C22×C412yes—
131C2×Dic103C2×Q812yes—
132C2×Dic103C2×Q812yes—
133C2×Dic103#4112yes—
134C2×Dic103#4112yes—
135C2×Dic103#4112yes—
136Dic206—28no—
137C22×C103C23×C411yescharacteristic
138C22×C103C22×Q811yescharacteristic
139C22×C103C2×#4111yescharacteristic
140C22×C103C2×#4111yescharacteristic
141C22×C103C2×#4111yescharacteristic
142C22×C103H(5,𝔽2)11yescharacteristic
143C22×C1032−1+411yescharacteristic
144C4×C103—22no—
145C4×C103—22no—
146C4×C103—22no—
147C4×C103—22no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103—41no—
151Dic103—22no—
152Dic103—22no—
153Dic103—22no—
154Dic103—41no—
155Dic103—41no—
156Dic103—41no—
157Dic103#11714yes—
158Dic103C4×Q814yes—
159C2×C103C2×#11711yescharacteristic
160C2×C103C2×C4×Q811yescharacteristic
161C2×C103#52011yescharacteristic
162C2×C103#55411yescharacteristic
163C2×C103#55611yescharacteristic
164C2×C103#55711yescharacteristic
165C2×C103#55911yescharacteristic
166#2355—1031nomaximal, Sylow
167C103#235511yescharacteristic, complemented, Sylow
168C2×C4×Q8—1031no—
169#391—1031no—
170#391—1031no—
171#387—1031no—
172#387—1031no—
173#387—1031no—
174#387D10311yescharacteristic
175#384—1031no—
176#382—1031no—
177#382—1031no—
178C4×C4⋊C4—1031no—
179C4×C4⋊C4—1031no—
180C4×C4⋊C4—1031no—
181C4×C4⋊C4—1031no—
182C4×C4⋊C4—1031no—
183C22×Q8—1031no—
184C4×Q8—1038no—
185C2×C4⋊C4—1031no—
186C2×C4⋊C4—1031no—
187C2×C4⋊C4—1031no—
188C2×C4⋊C4—1031no—
189C2×C4⋊C4—1031no—
190C2×C4⋊C4—1031no—
191C2×C4⋊C4—1031no—
192C2×C4⋊C4—1031no—
193C2×C4⋊C4—1031no—
194C2×C4⋊C4C2×D10311yescharacteristic
195C2×C4⋊C4C2×D10311yescharacteristic
196C2×C42—1031no—
197C2×C42—1031no—
198C2×C42—1031no—
199C2×C42—1031no—
200C2×C42—1031no—
201C2×C42—1031no—
202C2×C42—1031no—
203C2×C42—1031no—
204C2×C42C2×D10311yescharacteristic
205#95—1031no—
206#95—1031no—
207#95—1031no—
208#95—1031no—
209#95—1031no—
210#95—1031no—
211#95—1031no—
212#95—1031no—
213#95—1031no—
214#95—1031no—
215#95C2×D10311yescharacteristic
216#95C2×D10311yescharacteristic
217#95C2×D10311yescharacteristic
218#95C2×D10311yescharacteristic
219C2×Q8—1034no—
220C2×Q8—2062no—
221C2×Q8—2062no—
222C22×C4—1031no—
223C22×C4—1031no—
224C22×C4—1031no—
225C22×C4—1031no—
226C22×C4—1031no—
227C22×C4—1031no—
228C22×C4—1031no—
229C22×C4—1031no—
230C22×C4C22×D10311yescharacteristic
231C22×C4C22×D10311yescharacteristic
232C22×C4C22×D10311yescharacteristic
233C22×C4C22×D10311yescharacteristic
234C22×C4C22×D10311yescharacteristic
235C22×C4C22×D10311yescharacteristic
236C22×C4C22×D10311yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—1034no—
239C4⋊C4—1034no—
240C4⋊C4—1034no—
241C4⋊C4—4121no—
242C4⋊C4—2062no—
243C4⋊C4—2062no—
244C4⋊C4—2062no—
245C4⋊C4—2062no—
246C4⋊C4—2062no—
247C4⋊C4C4×D10314yes—
248C42—41no—
249C42—1034no—
250C42—1034no—
251C42—1034no—
252C42—4121no—
253C42—4121no—
254C42—4121no—
255C42—2062no—
256C42—2062no—
257C23C23×D10311yescharacteristic
258Q8—2068no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—1032no—
277C2×C4—1032no—
278C2×C4—1032no—
279C2×C4—1032no—
280C2×C4—1032no—
281C2×C4—1032no—
282C2×C4—1032no—
283C2×C4—1032no—
284C2×C4—1032no—
285C2×C4—2061no—
286C2×C4—2061no—
287C2×C4—2061no—
288C2×C4—2061no—
289C2×C4—2061no—
290C2×C4—2061no—
291C2×C4—2061no—
292C2×C4—2061no—
293C2×C4—2061no—
294C2×C4—2061no—
295C2×C4—2061no—
296C2×C4—2061no—
297C2×C4—2061no—
298C2×C4—2061no—
299C2×C4—2061no—
300C2×C4C2×C4×D10312yes—
301C2×C4C2×C4×D10312yes—
302C2×C4C2×C4×D10312yes—
303C2×C4Q8×D10312yes—
304C22C22×C4×D10311yescharacteristic
305C22C2×Q8×D10311yescharacteristic
306C22#41×D10311yescharacteristic
307C22#41×D10311yescharacteristic
308C22#41×D10311yescharacteristic
309C22#1569306611yescharacteristic
310C22#1569306811yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—1034no—
319C4—1034no—
320C4—4121no—
321C4—4121no—
322C4—4121no—
323C4—2062no—
324C4—2062no—
325C4—2062no—
326C2#117×D10311yescharacteristic
327C2C4×Q8×D10311yescharacteristic
328C2#2026827011yescharacteristic
329C2#2026849511yescharacteristic
330C2#2026850811yescharacteristic
331C2#2026851811yescharacteristic
332C2#2026852511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#387×C103C2
socle, prime radical, cosocleC23×C103C24
hypercenter#387D103
hypocenterC103#2355
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #15692986C4semidirect
71. Dic103⋊C4Q8semidirect
167. C103#2355semidirect

Maximal subgroups

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

subgroupindex
C2×#156929862
#202676952
#202676782
#202676772
#202676722
#202676602
#202676552
C4×Dic103⋊C42
#202676422
#387×C1032
#2355103