Finite Group Databasebeta

← #27198331

Subgroups — #27198331

Order 13184.

456 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
1C2×#15693014C211yesmaximal, characteristic
2#20267689C211yesmaximal, characteristic, complemented
3#20267688C211yesmaximal, characteristic, complemented
4#20267686C211yesmaximal, characteristic, complemented
5#20267685C211yesmaximal, characteristic
6#20267679C211yesmaximal, characteristic
7#20267678C211yesmaximal, characteristic, complemented
8#20267676C211yesmaximal, characteristic, complemented
9#20267675C211yesmaximal, characteristic, complemented
10#20267666C211yesmaximal, characteristic
11#20267663C211yesmaximal, characteristic
12#20267663C211yesmaximal, characteristic
13#20267660C211yesmaximal, characteristic, complemented
14#20267658C211yesmaximal, characteristic, complemented
15#388×C103C211yesmaximal, characteristic
16C23×Dic103C2211yescharacteristic
17#15693014C418yescomplemented
18C2×C4⋊Dic103C2211yescharacteristic
19C2×C4⋊Dic103C2211yescharacteristic
20C2×C4⋊Dic103C2211yescharacteristic
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×C22⋊Dic103C2211yescharacteristic
30C2×C22⋊Dic103C2211yescharacteristic
31C2×C22⋊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×C22⋊C4×C103C2211yescharacteristic
47C2×C22⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C22×Dic103—41no—
53C22×Dic103—41no—
54C22×Dic103—41no—
55C22×Dic103C2311yescharacteristic
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C4⋊Dic103—41no—
64C4⋊Dic103—41no—
65C4⋊Dic103C2×C414yescomplemented
66Dic103⋊C4—41no—
67Dic103⋊C4—41no—
68Dic103⋊C4—41no—
69Dic103⋊C4—41no—
70Dic103⋊C4—41no—
71Dic103⋊C4—41no—
72Dic103⋊C4C2×C414yescomplemented
73Dic103⋊C4C2×C414yescomplemented
74C22⋊Dic103—41no—
75C22⋊Dic103C2×C414yes—
76C22⋊Dic103C2×C414yes—
77C4×Dic103—41no—
78C4×Dic103—41no—
79C4×Dic103C2×C414yescomplemented
80C24×C103C2311yescharacteristic
81C22×C4×C103C2311yescharacteristic
82C22×C4×C103C2311yescharacteristic
83C22×C4×C103C2311yescharacteristic
84C22×C4×C103C2311yescharacteristic
85C22×C4×C103C2311yescharacteristic
86C22×C4×C103C2311yescharacteristic
87C4⋊C4×C103—41no—
88C22⋊C4×C103—41no—
89C22⋊C4×C103—41no—
90C22⋊C4×C103C2×C414yes—
91C42×C103—41no—
92C23×C103—21no—
93C23×C103—21no—
94C23×C103—21no—
95C23×C103—21no—
96C23×C103—21no—
97C23×C103—21no—
98C23×C103C22×C412yes—
99C23×C103C2411yescharacteristic
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×C103C22×C412yes—
117C2×C4×C103C22×C412yes—
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—44no—
139C2×Dic103C22×C412yes—
140C2×Dic103C22×C412yes—
141C2×Dic103C22×C412yes—
142C2×Dic103C22×C412yes—
143C22×C103—22no—
144C22×C103—22no—
145C22×C103—22no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103—41no—
149C22×C103—41no—
150C22×C103C23×C411yescharacteristic
151C22×C103H(5,𝔽2)11yescharacteristic
152C22×C103H(5,𝔽2)11yescharacteristic
153C22×C103H(5,𝔽2)11yescharacteristic
154C22×C1032−1+411yescharacteristic
155C22×C1032−1+411yescharacteristic
156C22×C1032−1+411yescharacteristic
157C4×C103—22no—
158C4×C103—22no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103—41no—
162C4×C103—41no—
163Dic103—22no—
164Dic103—22no—
165Dic103—22no—
166Dic103—22no—
167Dic103—41no—
168Dic103—41no—
169Dic103—41no—
170Dic103—41no—
171C2×C103—42no—
172C2×C103#52011yescharacteristic
173C2×C103#52011yescharacteristic
174C2×C103#52011yescharacteristic
175C2×C103#56011yescharacteristic
176C2×C103#56311yescharacteristic
177C2×C103#56311yescharacteristic
178C2×C103#56311yescharacteristic
179#2383—1031nomaximal, Sylow
180C103#238311yescharacteristic, complemented, Sylow
181C2×#126—1031no—
182#389—1031no—
183#389—1031no—
184#389—1031no—
185#388—1031no—
186#388—1031no—
187#388D10311yescharacteristic
188#387—1031no—
189#387—1031no—
190#387—1031no—
191#385—1031no—
192#385—1031no—
193#385—1031no—
194#384—1031no—
195#383—1031no—
196C23×C4—1031no—
197#126—1038no—
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⋊C4—1031no—
209C2×C4⋊C4C2×D10311yescharacteristic
210C2×C22⋊C4—1031no—
211C2×C22⋊C4—1031no—
212C2×C22⋊C4—1031no—
213C2×C22⋊C4C2×D10311yescharacteristic
214C2×C22⋊C4C2×D10311yescharacteristic
215C2×C22⋊C4C2×D10311yescharacteristic
216C2×C42—1031no—
217C2×C42—1031no—
218C2×C42—1031no—
219C2×C42C2×D10311yescharacteristic
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
231#95C2×D10311yescharacteristic
232C24C22×D10311yescharacteristic
233C22×C4—1031no—
234C22×C4—1031no—
235C22×C4—1031no—
236C22×C4—1031no—
237C22×C4—1031no—
238C22×C4—1031no—
239C22×C4—1031no—
240C22×C4—1031no—
241C22×C4—4121no—
242C22×C4—4121no—
243C22×C4—4121no—
244C22×C4C22×D10311yescharacteristic
245C22×C4C22×D10311yescharacteristic
246C22×C4C22×D10311yescharacteristic
247C22×C4C22×D10311yescharacteristic
248C22×C4C22×D10311yescharacteristic
249C22×C4C22×D10311yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—1034no—
252C4⋊C4—1034no—
253C4⋊C4—1034no—
254C4⋊C4—4121no—
255C4⋊C4—4121no—
256C4⋊C4—4121no—
257C4⋊C4—4121no—
258C4⋊C4—4121no—
259C4⋊C4—4121no—
260C4⋊C4—4121no—
261C4⋊C4—4121no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—1034no—
265C22⋊C4—1034no—
266C22⋊C4—4121no—
267C22⋊C4C4×D10314yes—
268C42—41no—
269C42—1034no—
270C42—4121no—
271C42—4121no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D10312yes—
279C23C23×D10311yescharacteristic
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—1032no—
297C2×C4—1032no—
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×C4C2×C4×D10312yes—
322C2×C4C2×C4×D10312yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D10311yescharacteristic
331C22#1569306611yescharacteristic
332C22#1569306611yescharacteristic
333C22#1569306711yescharacteristic
334C22#1569306811yescharacteristic
335C22#1569306811yescharacteristic
336C22#1569306811yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4121no—
344C4—4121no—
345C4—4121no—
346C4—4121no—
347C4—2062no—
348C4—2062no—
349C4—2062no—
350C4—2062no—
351C2—42no—
352C2#2026827011yescharacteristic
353C2#2026827011yescharacteristic
354C2#2026827111yescharacteristic
355C2#2026852911yescharacteristic
356C2#2026854111yescharacteristic
357C2#2026854311yescharacteristic
358C2#2026854411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#388×C103C2
socle, cosocleC23×C103C24
prime radicalC24×C103C23
hypercenter#388D103
hypocenterC103#2383
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20267689C2semidirect
3. #20267688C2semidirect
4. #20267686C2semidirect
7. #20267678C2semidirect
8. #20267676C2semidirect
9. #20267675C2semidirect
13. #20267660C2semidirect
14. #20267658C2semidirect
17. #15693014C4semidirect
65. C4⋊Dic103C2×C4semidirect
72. Dic103⋊C4C2×C4semidirect
73. Dic103⋊C4C2×C4semidirect
79. C4×Dic103C2×C4semidirect
180. C103#2383semidirect

Maximal subgroups

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

subgroupindex
C2×#156930142
#202676892
#202676882
#202676862
#202676852
#202676792
#202676782
#202676762
#202676752
#202676662
#202676632
#202676602
#202676582
#388×C1032
#2383103