Finite Group Databasebeta

← #27197882

Subgroups — #27197882

Order 13184.

444 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
1C2×#15693011C211yesmaximal, characteristic
2#20267688C211yesmaximal, characteristic
3#20267687C211yesmaximal, characteristic
4#20267686C211yesmaximal, characteristic
5#20267686C211yesmaximal, characteristic
6#20267686C211yesmaximal, characteristic
7#20267677C211yesmaximal, characteristic
8#20267675C211yesmaximal, characteristic
9#20267674C211yesmaximal, characteristic
10#20267672C211yesmaximal, characteristic
11#20267660C211yesmaximal, characteristic
12C4×Dic103⋊C4C211yesmaximal, characteristic
13#20267642C211yesmaximal, characteristic
14#20267636C211yesmaximal, characteristic
15#389×C103C211yesmaximal, characteristic
16#15693011C418yescomplemented
17C2×C4⋊Dic103C2211yescharacteristic
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×Dic103⋊C4C2211yescharacteristic
28C2×Dic103⋊C4C2211yescharacteristic
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×C4⋊C4×C103C2211yescharacteristic
48C2×C4⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C22×Dic103C2311yescharacteristic
53C22×Dic103C2311yescharacteristic
54C22×Dic103C2311yescharacteristic
55C22×Dic103C2311yescharacteristic
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C4⋊Dic103—41no—
61C4⋊Dic103C2×C414yes—
62Dic103⋊C4—22no—
63Dic103⋊C4—22no—
64Dic103⋊C4—41no—
65Dic103⋊C4—41no—
66Dic103⋊C4—41no—
67Dic103⋊C4—41no—
68Dic103⋊C4C2×C414yes—
69Dic103⋊C4C2×C414yes—
70Dic103⋊C4C2×C414yes—
71Dic103⋊C4C2×C414yes—
72C4×Dic103—22no—
73C4×Dic103—41no—
74C4×Dic103—41no—
75C4×Dic103—41no—
76C4×Dic103C2×C414yes—
77C4×Dic103Q814yes—
78C22×C4×C103C2311yescharacteristic
79C22×C4×C103C2311yescharacteristic
80C22×C4×C103C2311yescharacteristic
81C22×C4×C103C2311yescharacteristic
82C22×C4×C103C2311yescharacteristic
83C22×C4×C103C2311yescharacteristic
84C22×C4×C103C2311yescharacteristic
85C4⋊C4×C103—41no—
86C4⋊C4×C103—41no—
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×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103C22×C412yes—
130C2×Dic103C22×C412yes—
131C2×Dic103C22×C412yes—
132C2×Dic103C22×C412yes—
133C2×Dic103C2×Q812yes—
134C2×Dic103C2×Q812yes—
135C2×Dic103#4112yes—
136C22×C103C23×C411yescharacteristic
137C22×C103C22×Q811yescharacteristic
138C22×C103C2×#4111yescharacteristic
139C22×C103H(5,𝔽2)11yescharacteristic
140C22×C103H(5,𝔽2)11yescharacteristic
141C22×C1032−1+411yescharacteristic
142C22×C1032−1+411yescharacteristic
143C4×C103—22no—
144C4×C103—22no—
145C4×C103—22no—
146C4×C103—22no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103—41no—
150Dic103—22no—
151Dic103—22no—
152Dic103—22no—
153Dic103—22no—
154Dic103—41no—
155Dic103—41no—
156Dic103—41no—
157Dic103C4×Q814yes—
158C2×C103C2×C4×Q811yescharacteristic
159C2×C103#52011yescharacteristic
160C2×C103#52011yescharacteristic
161C2×C103#54011yescharacteristic
162C2×C103#54111yescharacteristic
163C2×C103#54411yescharacteristic
164C2×C103#54411yescharacteristic
165#2330—1031nomaximal, Sylow
166C103#233011yescharacteristic, complemented, Sylow
167C2×#125—1031no—
168#389—1031no—
169#389—1031no—
170#389—1031no—
171#389—1031no—
172#389—1031no—
173#389D10311yescharacteristic
174#387—1031no—
175#387—1031no—
176#387—1031no—
177#387—1031no—
178#384—1031no—
179C4×C4⋊C4—1031no—
180C4×C4⋊C4—1031no—
181#376—1031no—
182#125—1038no—
183C2×C4⋊C4—1031no—
184C2×C4⋊C4—1031no—
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⋊C4—1031no—
195C2×C4⋊C4C2×D10311yescharacteristic
196C2×C4⋊C4C2×D10311yescharacteristic
197C2×C4⋊C4C2×D10311yescharacteristic
198C2×C4⋊C4C2×D10311yescharacteristic
199C2×C42—1031no—
200C2×C42—1031no—
201C2×C42—1031no—
202C2×C42—1031no—
203C2×C42—1031no—
204C2×C42—1031no—
205C2×C42C2×D10311yescharacteristic
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#95—1031no—
216#95C2×D10311yescharacteristic
217#95C2×D10311yescharacteristic
218C22×C4—1031no—
219C22×C4—1031no—
220C22×C4—1031no—
221C22×C4—1031no—
222C22×C4—1031no—
223C22×C4—1031no—
224C22×C4—1031no—
225C22×C4—1031no—
226C22×C4C22×D10311yescharacteristic
227C22×C4C22×D10311yescharacteristic
228C22×C4C22×D10311yescharacteristic
229C22×C4C22×D10311yescharacteristic
230C22×C4C22×D10311yescharacteristic
231C22×C4C22×D10311yescharacteristic
232C22×C4C22×D10311yescharacteristic
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—1034no—
237C4⋊C4—1034no—
238C4⋊C4—1034no—
239C4⋊C4—1034no—
240C4⋊C4—1034no—
241C4⋊C4—4121no—
242C4⋊C4—4121no—
243C4⋊C4—4121no—
244C4⋊C4—4121no—
245C4⋊C4—4121no—
246C4⋊C4—2062no—
247C4⋊C4—2062no—
248C4⋊C4C4×D10314yes—
249C42—41no—
250C42—1034no—
251C42—1034no—
252C42—4121no—
253C42—4121no—
254C42—4121no—
255C42—2062no—
256C23C23×D10311yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
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—1032no—
275C2×C4—1032no—
276C2×C4—1032no—
277C2×C4—1032no—
278C2×C4—1032no—
279C2×C4—1032no—
280C2×C4—1032no—
281C2×C4—2061no—
282C2×C4—2061no—
283C2×C4—2061no—
284C2×C4—2061no—
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×C4C2×C4×D10312yes—
299C2×C4C2×C4×D10312yes—
300C2×C4C2×C4×D10312yes—
301C2×C4Q8×D10312yes—
302C22C22×C4×D10311yescharacteristic
303C22C2×Q8×D10311yescharacteristic
304C22#41×D10311yescharacteristic
305C22#1569306611yescharacteristic
306C22#1569306611yescharacteristic
307C22#1569306811yescharacteristic
308C22#1569306911yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—1034no—
317C4—4121no—
318C4—4121no—
319C4—4121no—
320C4—2062no—
321C4—2062no—
322C4—2062no—
323C4—2062no—
324C2C4×Q8×D10311yescharacteristic
325C2#2026827011yescharacteristic
326C2#2026827211yescharacteristic
327C2#2026839111yescharacteristic
328C2#2026840011yescharacteristic
329C2#2026841811yescharacteristic
330C2#2026842011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#389×C103C2
socle, prime radical, cosocleC23×C103C24
hypercenter#389D103
hypocenterC103#2330
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
16. #15693011C4semidirect
166. C103#2330semidirect

Maximal subgroups

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

subgroupindex
C2×#156930112
#202676882
#202676872
#202676862
#202676772
#202676752
#202676742
#202676722
#202676602
C4×Dic103⋊C42
#202676422
#202676362
#389×C1032
#2330103