Finite Group Databasebeta

← #27203402

Subgroups — #27203402

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#20267730C211yesmaximal, characteristic, complemented
2#20267729C211yesmaximal, characteristic, complemented
3#20267726C211yesmaximal, characteristic
4#20267725C211yesmaximal, characteristic, complemented
5#20267725C211yesmaximal, characteristic, complemented
6#20267721C211yesmaximal, characteristic, complemented
7#20267713C211yesmaximal, characteristic
8#20267713C211yesmaximal, characteristic
9#20267712C211yesmaximal, characteristic, complemented
10#20267711C211yesmaximal, characteristic, complemented
11#20267704C211yesmaximal, characteristic
12#20267653C211yesmaximal, characteristic
13#20267650C211yesmaximal, characteristic
14#20267648C211yesmaximal, characteristic
15#398×C103C211yesmaximal, characteristic, complemented
16C22×Dic206C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
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×(C2×D103)⋊C4C2211yescharacteristic
28C2×(C2×D103)⋊C4C2211yescharacteristic
29C2×(C2×D103)⋊C4C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
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×C4⋊C4×C103C2211yescharacteristic
48#95×C103C2211yescharacteristic
49#95×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51C23×D103C2311yescharacteristic
52C2×Dic206—41no—
53C2×Dic206—41no—
54C2×Dic206—41no—
55C22×Dic103C2311yescharacteristic
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C2×C4×D103—41no—
63C2×C4×D103—41no—
64C2×C4×D103Q814yescomplemented
65C4⋊Dic103—41no—
66C4⋊Dic103—41no—
67C4⋊Dic103—41no—
68Dic103⋊C4—41no—
69Dic103⋊C4—41no—
70Dic103⋊C4—41no—
71Dic103⋊C4—41no—
72Dic103⋊C4—41no—
73Dic103⋊C4—41no—
74(C2×D103)⋊C4—41no—
75(C2×D103)⋊C4—41no—
76(C2×D103)⋊C4—41no—
77(C2×D103)⋊C4—41no—
78(C2×D103)⋊C4—41no—
79(C2×D103)⋊C4—41no—
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×C103—41no—
89C4⋊C4×C103—41no—
90C4⋊C4×C103—41no—
91C23×C103C2411yescharacteristic
92C22×D103—21no—
93C22×D103—21no—
94C22×D103—21no—
95C22×D103—21no—
96C22×D103—21no—
97C22×D103—21no—
98C22×D103C2×Q812yes—
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×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103C2×Q812yes—
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—21no—
140C2×Dic103C2×Q812yes—
141C4×D103—44no—
142Dic206—44no—
143C22×C103C22×Q811yescharacteristic
144C22×C103H(5,𝔽2)11yescharacteristic
145C22×C103H(5,𝔽2)11yescharacteristic
146C22×C103H(5,𝔽2)11yescharacteristic
147C22×C103H(5,𝔽2)11yescharacteristic
148C22×C1032−1+411yescharacteristic
149C22×C1032−1+411yescharacteristic
150C2×D103—22no—
151C2×D103—22no—
152C2×D103—22no—
153C2×D103—41no—
154C2×D103—41no—
155C2×D103—41no—
156C2×D103—41no—
157C4×C103—22no—
158C4×C103—41no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103—41no—
162C4×C103—41no—
163C4×C103—41no—
164Dic103—22no—
165Dic103—41no—
166Dic103—41no—
167Dic103—41no—
168Dic103—41no—
169Dic103—41no—
170Dic103—41no—
171C2×C103#54311yescharacteristic
172C2×C103#54411yescharacteristic
173C2×C103#54411yescharacteristic
174C2×C103#56011yescharacteristic
175C2×C103#56211yescharacteristic
176C2×C103#56211yescharacteristic
177C2×C103#56311yescharacteristic
178D103—42no—
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#398D10311yescharacteristic, complemented
188#396—1031no—
189#396—1031no—
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⋊C4C2×D10311yescharacteristic
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⋊C4—1031no—
215C2×C22⋊C4—1031no—
216C2×C22⋊C4—1031no—
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#95C2×D10311yescharacteristic
229#95C2×D10311yescharacteristic
230#95C2×D10311yescharacteristic
231C24—1031no—
232C2×Q8—4121no—
233C2×Q8—4121no—
234C2×Q8—4121no—
235C22×C4—1031no—
236C22×C4—1034no—
237C22×C4—1031no—
238C22×C4—1031no—
239C22×C4—1031no—
240C22×C4—1031no—
241C22×C4—1031no—
242C22×C4—1031no—
243C22×C4—4121no—
244C22×C4—4121no—
245C22×C4C22×D10311yescharacteristic
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—41no—
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—4121no—
266C22⋊C4—4121no—
267C22⋊C4—4121no—
268C22⋊C4—4121no—
269C22⋊C4—4121no—
270C22⋊C4—4121no—
271C23—1032no—
272C23—2061no—
273C23—2061no—
274C23—2061no—
275C23—2061no—
276C23—2061no—
277C23—2061no—
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—21no—
299C2×C4—21no—
300C2×C4—1032no—
301C2×C4—4124no—
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×C4Q8×D10312yes—
323C22—4121no—
324C22—4121no—
325C22—4121no—
326C22—4121no—
327C22—2062no—
328C22—2062no—
329C22—2062no—
330C22C2×Q8×D10311yescharacteristic
331C22#1569306611yescharacteristic
332C22#1569306611yescharacteristic
333C22#1569306711yescharacteristic
334C22#1569306711yescharacteristic
335C22#1569306811yescharacteristic
336C22#1569306911yescharacteristic
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—4121no—
345C4—4121no—
346C4—4121no—
347C4—4121no—
348C4—4121no—
349C4—4121no—
350C4—2062no—
351C2—4122no—
352C2#2026841611yescharacteristic
353C2#2026841811yescharacteristic
354C2#2026842111yescharacteristic
355C2#2026853111yescharacteristic
356C2#2026853611yescharacteristic
357C2#2026853711yescharacteristic
358C2#2026854511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutator, socle, cosocleC23×C103C24
Fitting#398×C103C2
prime radicalC23×D103C23
hypercenter#398D103
hypocenterC103#2841
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #20267730C2semidirect
2. #20267729C2semidirect
4. #20267725C2semidirect
5. #20267725C2semidirect
6. #20267721C2semidirect
9. #20267712C2semidirect
10. #20267711C2semidirect
15. #398×C103C2semidirect
64. C2×C4×D103Q8semidirect
180. C103#2841semidirect
187. #398D103semidirect

Maximal subgroups

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

subgroupindex
#202677302
#202677292
#202677262
#202677252
#202677212
#202677132
#202677122
#202677112
#202677042
#202676532
#202676502
#202676482
#398×C1032
#2841103