Finite Group Databasebeta

← #27203405

Subgroups — #27203405

Order 13184.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20267732C211yesmaximal, characteristic, complemented
2#20267729C211yesmaximal, characteristic, complemented
3#20267727C211yesmaximal, characteristic
4#20267724C211yesmaximal, characteristic, complemented
5#20267722C211yesmaximal, characteristic, complemented
6#20267722C211yesmaximal, characteristic, complemented
7#20267721C211yesmaximal, characteristic, complemented
8#20267714C211yesmaximal, characteristic
9#20267712C211yesmaximal, characteristic, complemented
10#20267711C211yesmaximal, characteristic, complemented
11#20267703C211yesmaximal, characteristic
12#20267652C211yesmaximal, characteristic
13#20267649C211yesmaximal, characteristic
14#20267649C211yesmaximal, characteristic
15#396×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C23×Dic103C2211yescharacteristic
18C2×C4⋊Dic103C2211yescharacteristic
19C2×C4⋊Dic103C2211yescharacteristic
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×C22⋊Dic103C2211yescharacteristic
29C2×C22⋊Dic103C2211yescharacteristic
30C2×C22⋊Dic103C2211yescharacteristic
31C103⋊#95C2211yescharacteristic
32C103⋊#95C2211yescharacteristic
33C103⋊#95C2211yescharacteristic
34C103⋊#95C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C2×C4⋊C4×C103C2211yescharacteristic
45C2×C4⋊C4×C103C2211yescharacteristic
46C2×C4⋊C4×C103C2211yescharacteristic
47C2×C22⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C22⋊C4×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51C2×Dic206—41no—
52C2×Dic206—41no—
53C2×Dic206—41no—
54C22×Dic103—41no—
55C22×Dic103—41no—
56C22×Dic103Q814yescomplemented
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C4⋊Dic103—41no—
66C4⋊Dic103—41no—
67Dic103⋊C4—41no—
68Dic103⋊C4—41no—
69Dic103⋊C4—41no—
70Dic103⋊C4—41no—
71Dic103⋊C4—41no—
72Dic103⋊C4—41no—
73Dic103⋊C4—41no—
74Dic103⋊C4—41no—
75C22⋊Dic103—41no—
76C22⋊Dic103—41no—
77C22⋊Dic103—41no—
78C24×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—
88C22⋊C4×C103—41no—
89C22⋊C4×C103—41no—
90C22⋊C4×C103—41no—
91C23×C103—21no—
92C23×C103—21no—
93C23×C103—21no—
94C23×C103—21no—
95C23×C103—21no—
96C23×C103—21no—
97C23×C103C2×Q812yes—
98C23×C103C2411yescharacteristic
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×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—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×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139C2×Dic103—44no—
140C2×Dic103C2×Q812yes—
141C2×Dic103C2×Q812yes—
142Dic206—44no—
143C22×C103—22no—
144C22×C103—22no—
145C22×C103—22no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103—41no—
149C22×C103—41no—
150C22×C103C22×Q811yescharacteristic
151C22×C103H(5,𝔽2)11yescharacteristic
152C22×C103H(5,𝔽2)11yescharacteristic
153C22×C103H(5,𝔽2)11yescharacteristic
154C22×C103H(5,𝔽2)11yescharacteristic
155C22×C1032−1+411yescharacteristic
156C22×C1032−1+411yescharacteristic
157C4×C103—41no—
158C4×C103—41no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103—41no—
162C4×C103—41no—
163Dic103—22no—
164Dic103—22no—
165Dic103—41no—
166Dic103—41no—
167Dic103—41no—
168Dic103—41no—
169Dic103—41no—
170Dic103—41no—
171C2×C103—42no—
172C2×C103#54311yescharacteristic
173C2×C103#54411yescharacteristic
174C2×C103#54411yescharacteristic
175C2×C103#56011yescharacteristic
176C2×C103#56211yescharacteristic
177C2×C103#56211yescharacteristic
178C2×C103#56311yescharacteristic
179#2841—1031nomaximal, Sylow
180C103#284111yescharacteristic, complemented, Sylow
181#400—1031no—
182#400—1031no—
183#399—1031no—
184#398—1031no—
185#398—1031no—
186#398—1031no—
187#398—1031no—
188#396—1031no—
189#396D10311yescharacteristic
190#395—1031no—
191#395—1031no—
192#393—1031no—
193#381—1031no—
194#380—1031no—
195#380—1031no—
196C22×Q8—1031no—
197C23×C4—1031no—
198C2×C4⋊C4—1031no—
199C2×C4⋊C4—1031no—
200C2×C4⋊C4—1031no—
201C2×C4⋊C4—1031no—
202C2×C4⋊C4—1031no—
203C2×C4⋊C4—1031no—
204C2×C4⋊C4—1031no—
205C2×C4⋊C4—1031no—
206C2×C4⋊C4—1031no—
207C2×C4⋊C4—1031no—
208C2×C4⋊C4C2×D10311yescharacteristic
209C2×C4⋊C4C2×D10311yescharacteristic
210C2×C4⋊C4C2×D10311yescharacteristic
211C2×C22⋊C4—1031no—
212C2×C22⋊C4—1031no—
213C2×C22⋊C4—1031no—
214C2×C22⋊C4C2×D10311yescharacteristic
215C2×C22⋊C4C2×D10311yescharacteristic
216C2×C22⋊C4C2×D10311yescharacteristic
217#95—1031no—
218#95—1031no—
219#95—1031no—
220#95—1031no—
221#95—1031no—
222#95—1031no—
223#95—1031no—
224#95—1031no—
225#95—1031no—
226#95—1031no—
227#95—1031no—
228#95—1031no—
229#95—1031no—
230#95C2×D10311yescharacteristic
231C24C22×D10311yescharacteristic
232C2×Q8—4121no—
233C2×Q8—4121no—
234C2×Q8—4121no—
235C22×C4—1034no—
236C22×C4—1031no—
237C22×C4—1031no—
238C22×C4—1031no—
239C22×C4—1031no—
240C22×C4—1031no—
241C22×C4—1031no—
242C22×C4—1031no—
243C22×C4—1031no—
244C22×C4—4121no—
245C22×C4—4121no—
246C22×C4C22×D10311yescharacteristic
247C22×C4C22×D10311yescharacteristic
248C22×C4C22×D10311yescharacteristic
249C22×C4C22×D10311yescharacteristic
250C22×C4C22×D10311yescharacteristic
251C22×C4C22×D10311yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—4121no—
256C4⋊C4—4121no—
257C4⋊C4—4121no—
258C4⋊C4—4121no—
259C4⋊C4—4121no—
260C4⋊C4—4121no—
261C4⋊C4—4121no—
262C4⋊C4—4121no—
263C4⋊C4—4121no—
264C4⋊C4—4121no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—4121no—
269C22⋊C4—4121no—
270C22⋊C4—4121no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23Q8×D10312yes—
278C23C23×D10311yescharacteristic
279Q8—4124no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—1032no—
299C2×C4—1032no—
300C2×C4—4124no—
301C2×C4—2061no—
302C2×C4—2061no—
303C2×C4—2061no—
304C2×C4—2061no—
305C2×C4—2061no—
306C2×C4—2061no—
307C2×C4—2061no—
308C2×C4—2061no—
309C2×C4—2061no—
310C2×C4—2061no—
311C2×C4—2061no—
312C2×C4—2061no—
313C2×C4—2061no—
314C2×C4—2061no—
315C2×C4—2061no—
316C2×C4—2061no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4—2061no—
322C2×C4—2061no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×Q8×D10311yescharacteristic
331C22#1569306611yescharacteristic
332C22#1569306611yescharacteristic
333C22#1569306611yescharacteristic
334C22#1569306711yescharacteristic
335C22#1569306811yescharacteristic
336C22#1569306811yescharacteristic
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4121no—
344C4—4121no—
345C4—4121no—
346C4—4121no—
347C4—4121no—
348C4—4121no—
349C4—2062no—
350C4—2062no—
351C2—42no—
352C2#2026841611yescharacteristic
353C2#2026842011yescharacteristic
354C2#2026842011yescharacteristic
355C2#2026852911yescharacteristic
356C2#2026853611yescharacteristic
357C2#2026853611yescharacteristic
358C2#2026854311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutator, socle, cosocleC23×C103C24
Fitting#396×C103C2
prime radicalC24×C103C23
hypercenter#396D103
hypocenterC103#2841
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #20267732C2semidirect
2. #20267729C2semidirect
4. #20267724C2semidirect
5. #20267722C2semidirect
6. #20267722C2semidirect
7. #20267721C2semidirect
9. #20267712C2semidirect
10. #20267711C2semidirect
56. C22×Dic103Q8semidirect
180. C103#2841semidirect

Maximal subgroups

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

subgroupindex
#202677322
#202677292
#202677272
#202677242
#202677222
#202677212
#202677142
#202677122
#202677112
#202677032
#202676522
#202676492
#396×C1032
#2841103