Finite Group Databasebeta

← #31814665

Subgroups — #31814665

Order 17792.

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#22580894C211yesmaximal, characteristic, complemented
2#22580891C211yesmaximal, characteristic, complemented
3#22580889C211yesmaximal, characteristic
4#22580886C211yesmaximal, characteristic, complemented
5#22580884C211yesmaximal, characteristic, complemented
6#22580884C211yesmaximal, characteristic, complemented
7#22580883C211yesmaximal, characteristic, complemented
8#22580876C211yesmaximal, characteristic
9#22580874C211yesmaximal, characteristic, complemented
10#22580873C211yesmaximal, characteristic, complemented
11#22580865C211yesmaximal, characteristic
12#22580814C211yesmaximal, characteristic
13#22580811C211yesmaximal, characteristic
14#22580811C211yesmaximal, characteristic
15#396×C139C211yesmaximal, characteristic
16C22×Dic278C2211yescharacteristic
17C23×Dic139C2211yescharacteristic
18C2×C4⋊Dic139C2211yescharacteristic
19C2×C4⋊Dic139C2211yescharacteristic
20C2×Dic139⋊C4C2211yescharacteristic
21C2×Dic139⋊C4C2211yescharacteristic
22C2×Dic139⋊C4C2211yescharacteristic
23C2×Dic139⋊C4C2211yescharacteristic
24C2×Dic139⋊C4C2211yescharacteristic
25C2×Dic139⋊C4C2211yescharacteristic
26C2×Dic139⋊C4C2211yescharacteristic
27C2×Dic139⋊C4C2211yescharacteristic
28C2×C22⋊Dic139C2211yescharacteristic
29C2×C22⋊Dic139C2211yescharacteristic
30C2×C22⋊Dic139C2211yescharacteristic
31C139⋊#95C2211yescharacteristic
32C139⋊#95C2211yescharacteristic
33C139⋊#95C2211yescharacteristic
34C139⋊#95C2211yescharacteristic
35C139⋊#95C2211yescharacteristic
36C139⋊#95C2211yescharacteristic
37C139⋊#95C2211yescharacteristic
38C139⋊#95C2211yescharacteristic
39C139⋊#95C2211yescharacteristic
40C139⋊#95C2211yescharacteristic
41C139⋊#95C2211yescharacteristic
42C139⋊#95C2211yescharacteristic
43C139⋊#95C2211yescharacteristic
44C2×C4⋊C4×C139C2211yescharacteristic
45C2×C4⋊C4×C139C2211yescharacteristic
46C2×C4⋊C4×C139C2211yescharacteristic
47C2×C22⋊C4×C139C2211yescharacteristic
48C2×C22⋊C4×C139C2211yescharacteristic
49C2×C22⋊C4×C139C2211yescharacteristic
50#95×C139C2211yescharacteristic
51C2×Dic278—41no—
52C2×Dic278—41no—
53C2×Dic278—41no—
54C22×Dic139—41no—
55C22×Dic139—41no—
56C22×Dic139Q814yescomplemented
57C22×Dic139C2311yescharacteristic
58C22×Dic139C2311yescharacteristic
59C22×Dic139C2311yescharacteristic
60C22×Dic139C2311yescharacteristic
61C22×Dic139C2311yescharacteristic
62C22×Dic139C2311yescharacteristic
63C22×Dic139C2311yescharacteristic
64C22×Dic139C2311yescharacteristic
65C4⋊Dic139—41no—
66C4⋊Dic139—41no—
67Dic139⋊C4—41no—
68Dic139⋊C4—41no—
69Dic139⋊C4—41no—
70Dic139⋊C4—41no—
71Dic139⋊C4—41no—
72Dic139⋊C4—41no—
73Dic139⋊C4—41no—
74Dic139⋊C4—41no—
75C22⋊Dic139—41no—
76C22⋊Dic139—41no—
77C22⋊Dic139—41no—
78C24×C139C2311yescharacteristic
79C22×C4×C139C2311yescharacteristic
80C22×C4×C139C2311yescharacteristic
81C22×C4×C139C2311yescharacteristic
82C22×C4×C139C2311yescharacteristic
83C22×C4×C139C2311yescharacteristic
84C22×C4×C139C2311yescharacteristic
85C4⋊C4×C139—41no—
86C4⋊C4×C139—41no—
87C4⋊C4×C139—41no—
88C22⋊C4×C139—41no—
89C22⋊C4×C139—41no—
90C22⋊C4×C139—41no—
91Dic278—44no—
92C2×Dic139—21no—
93C2×Dic139—21no—
94C2×Dic139—21no—
95C2×Dic139—21no—
96C2×Dic139—21no—
97C2×Dic139—21no—
98C2×Dic139—21no—
99C2×Dic139—21no—
100C2×Dic139—21no—
101C2×Dic139—21no—
102C2×Dic139—21no—
103C2×Dic139—21no—
104C2×Dic139—21no—
105C2×Dic139—21no—
106C2×Dic139—21no—
107C2×Dic139—21no—
108C2×Dic139—21no—
109C2×Dic139—21no—
110C2×Dic139—21no—
111C2×Dic139—21no—
112C2×Dic139—21no—
113C2×Dic139—21no—
114C2×Dic139—44no—
115C2×Dic139C2×Q812yes—
116C2×Dic139C2×Q812yes—
117C23×C139—21no—
118C23×C139—21no—
119C23×C139—21no—
120C23×C139—21no—
121C23×C139—21no—
122C23×C139—21no—
123C23×C139C2×Q812yes—
124C23×C139C2411yescharacteristic
125C2×C4×C139—21no—
126C2×C4×C139—21no—
127C2×C4×C139—21no—
128C2×C4×C139—21no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C22×C139—22no—
144C22×C139—22no—
145C22×C139—22no—
146C22×C139—41no—
147C22×C139—41no—
148C22×C139—41no—
149C22×C139—41no—
150C22×C139C22×Q811yescharacteristic
151C22×C139H(5,𝔽2)11yescharacteristic
152C22×C139H(5,𝔽2)11yescharacteristic
153C22×C139H(5,𝔽2)11yescharacteristic
154C22×C139H(5,𝔽2)11yescharacteristic
155C22×C1392−1+411yescharacteristic
156C22×C1392−1+411yescharacteristic
157C4×C139—41no—
158C4×C139—41no—
159C4×C139—41no—
160C4×C139—41no—
161C4×C139—41no—
162C4×C139—41no—
163Dic139—22no—
164Dic139—22no—
165Dic139—41no—
166Dic139—41no—
167Dic139—41no—
168Dic139—41no—
169Dic139—41no—
170Dic139—41no—
171C2×C139—42no—
172C2×C139#54311yescharacteristic
173C2×C139#54411yescharacteristic
174C2×C139#54411yescharacteristic
175C2×C139#56011yescharacteristic
176C2×C139#56211yescharacteristic
177C2×C139#56211yescharacteristic
178C2×C139#56311yescharacteristic
179C139#284111yescharacteristic, complemented, Sylow
180#2841—1391nomaximal, Sylow
181#400—1391no—
182#400—1391no—
183#399—1391no—
184#398—1391no—
185#398—1391no—
186#398—1391no—
187#398—1391no—
188#396—1391no—
189#396D13911yescharacteristic
190#395—1391no—
191#395—1391no—
192#393—1391no—
193#381—1391no—
194#380—1391no—
195#380—1391no—
196C22×Q8—1391no—
197C23×C4—1391no—
198C2×C4⋊C4—1391no—
199C2×C4⋊C4—1391no—
200C2×C4⋊C4—1391no—
201C2×C4⋊C4—1391no—
202C2×C4⋊C4—1391no—
203C2×C4⋊C4—1391no—
204C2×C4⋊C4—1391no—
205C2×C4⋊C4—1391no—
206C2×C4⋊C4—1391no—
207C2×C4⋊C4—1391no—
208C2×C4⋊C4C2×D13911yescharacteristic
209C2×C4⋊C4C2×D13911yescharacteristic
210C2×C4⋊C4C2×D13911yescharacteristic
211C2×C22⋊C4—1391no—
212C2×C22⋊C4—1391no—
213C2×C22⋊C4—1391no—
214C2×C22⋊C4C2×D13911yescharacteristic
215C2×C22⋊C4C2×D13911yescharacteristic
216C2×C22⋊C4C2×D13911yescharacteristic
217#95—1391no—
218#95—1391no—
219#95—1391no—
220#95—1391no—
221#95—1391no—
222#95—1391no—
223#95—1391no—
224#95—1391no—
225#95—1391no—
226#95—1391no—
227#95—1391no—
228#95—1391no—
229#95—1391no—
230#95C2×D13911yescharacteristic
231C24C22×D13911yescharacteristic
232C2×Q8—5561no—
233C2×Q8—5561no—
234C2×Q8—5561no—
235C22×C4—5561no—
236C22×C4—5561no—
237C22×C4—1391no—
238C22×C4—1391no—
239C22×C4—1391no—
240C22×C4—1391no—
241C22×C4—1391no—
242C22×C4—1391no—
243C22×C4—1391no—
244C22×C4—1391no—
245C22×C4—1394no—
246C22×C4C22×D13911yescharacteristic
247C22×C4C22×D13911yescharacteristic
248C22×C4C22×D13911yescharacteristic
249C22×C4C22×D13911yescharacteristic
250C22×C4C22×D13911yescharacteristic
251C22×C4C22×D13911yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—5561no—
256C4⋊C4—5561no—
257C4⋊C4—5561no—
258C4⋊C4—5561no—
259C4⋊C4—5561no—
260C4⋊C4—5561no—
261C4⋊C4—5561no—
262C4⋊C4—5561no—
263C4⋊C4—5561no—
264C4⋊C4—5561no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—5561no—
269C22⋊C4—5561no—
270C22⋊C4—5561no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23Q8×D13912yes—
278C23C23×D13911yescharacteristic
279Q8—5564no—
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—2781no—
299C2×C4—2781no—
300C2×C4—2781no—
301C2×C4—2781no—
302C2×C4—2781no—
303C2×C4—2781no—
304C2×C4—2781no—
305C2×C4—2781no—
306C2×C4—2781no—
307C2×C4—2781no—
308C2×C4—2781no—
309C2×C4—2781no—
310C2×C4—2781no—
311C2×C4—2781no—
312C2×C4—2781no—
313C2×C4—2781no—
314C2×C4—2781no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—2781no—
318C2×C4—2781no—
319C2×C4—2781no—
320C2×C4—5564no—
321C2×C4—1392no—
322C2×C4—1392no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×Q8×D13911yescharacteristic
331C22#1798488711yescharacteristic
332C22#1798488711yescharacteristic
333C22#1798488711yescharacteristic
334C22#1798488811yescharacteristic
335C22#1798488911yescharacteristic
336C22#1798488911yescharacteristic
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2782no—
344C4—2782no—
345C4—5561no—
346C4—5561no—
347C4—5561no—
348C4—5561no—
349C4—5561no—
350C4—5561no—
351C2—42no—
352C2#2258157811yescharacteristic
353C2#2258158211yescharacteristic
354C2#2258158211yescharacteristic
355C2#2258169111yescharacteristic
356C2#2258169811yescharacteristic
357C2#2258169811yescharacteristic
358C2#2258170511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#396×C139C2
prime radicalC24×C139C23
hypercenter#396D139
hypocenterC139#2841
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #22580894C2semidirect
2. #22580891C2semidirect
4. #22580886C2semidirect
5. #22580884C2semidirect
6. #22580884C2semidirect
7. #22580883C2semidirect
9. #22580874C2semidirect
10. #22580873C2semidirect
56. C22×Dic139Q8semidirect
179. C139#2841semidirect

Maximal subgroups

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

subgroupindex
#225808942
#225808912
#225808892
#225808862
#225808842
#225808832
#225808762
#225808742
#225808732
#225808652
#225808142
#225808112
#396×C1392
#2841139