Finite Group Databasebeta

← #31814640

Subgroups — #31814640

Order 17792.

366 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C139⋊#401C211yesmaximal, characteristic, complemented
2#22580895C211yesmaximal, characteristic, complemented
3#22580888C211yesmaximal, characteristic
4#22580883C211yesmaximal, characteristic, complemented
5#22580882C211yesmaximal, characteristic
6#22580882C211yesmaximal, characteristic
7#22580880C211yesmaximal, characteristic
8#22580875C211yesmaximal, characteristic
9#22580874C211yesmaximal, characteristic, complemented
10#22580873C211yesmaximal, characteristic, complemented
11#22580866C211yesmaximal, characteristic
12#22580850C211yesmaximal, characteristic, complemented
13#22580845C211yesmaximal, characteristic
14#22580836C211yesmaximal, characteristic, complemented
15#400×C139C211yesmaximal, characteristic, complemented
16C22×Dic278C2211yescharacteristic
17C2×C4⋊Dic139C2211yescharacteristic
18C2×C4⋊Dic139C2211yescharacteristic
19C2×C4⋊Dic139C2211yescharacteristic
20C2×Dic139⋊C4C2211yescharacteristic
21C2×Dic139⋊C4C2211yescharacteristic
22C2×Dic139⋊C4C2211yescharacteristic
23C2×Dic139⋊C4C2211yescharacteristic
24C2×Dic139⋊C4C2211yescharacteristic
25C2×(C2×D139)⋊C4C2211yescharacteristic
26C2×(C2×D139)⋊C4C2211yescharacteristic
27C2×(C2×D139)⋊C4C2211yescharacteristic
28C2×(C2×D139)⋊C4C2211yescharacteristic
29C2×(C2×D139)⋊C4C2211yescharacteristic
30C2×(C2×D139)⋊C4C2211yescharacteristic
31C2×(C2×D139)⋊C4C2211yescharacteristic
32C2×C4×Dic139C2211yescharacteristic
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
46#95×C139C2211yescharacteristic
47#95×C139C2211yescharacteristic
48#95×C139C2211yescharacteristic
49#95×C139C2211yescharacteristic
50#95×C139C2211yescharacteristic
51C23×D139C2311yescharacteristic
52C2×Dic278—41no—
53C2×Dic278—41no—
54C2×Dic278—41no—
55C22×Dic139C2311yescharacteristic
56C22×Dic139C2311yescharacteristic
57C22×Dic139C2311yescharacteristic
58C22×Dic139C2311yescharacteristic
59C22×Dic139C2311yescharacteristic
60C22×Dic139C2311yescharacteristic
61C22×Dic139C2311yescharacteristic
62C4⋊Dic139—22no—
63C4⋊Dic139—41no—
64C4⋊Dic139—41no—
65Dic139⋊C4—22no—
66Dic139⋊C4—41no—
67Dic139⋊C4—41no—
68Dic139⋊C4—41no—
69Dic139⋊C4—41no—
70(C2×D139)⋊C4—22no—
71(C2×D139)⋊C4—41no—
72(C2×D139)⋊C4—41no—
73(C2×D139)⋊C4—41no—
74(C2×D139)⋊C4—41no—
75(C2×D139)⋊C4—41no—
76(C2×D139)⋊C4—41no—
77C4×Dic139—41no—
78C22×C4×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—
87C22×D139—21no—
88C22×D139—21no—
89C22×D139—21no—
90C22×D139—21no—
91C22×D139—21no—
92C22×D139—21no—
93C22×D139—21no—
94Dic278—44no—
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—21no—
115C2×Dic139#4112yes—
116C23×C139C2411yescharacteristic
117C2×C4×C139—21no—
118C2×C4×C139—21no—
119C2×C4×C139—21no—
120C2×C4×C139—21no—
121C2×C4×C139—21no—
122C2×C4×C139—21no—
123C2×C4×C139—21no—
124C2×C4×C139—21no—
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—
138C22×C139C2×#4111yescharacteristic
139C22×C139H(5,𝔽2)11yescharacteristic
140C22×C139H(5,𝔽2)11yescharacteristic
141C22×C139H(5,𝔽2)11yescharacteristic
142C22×C1392−1+411yescharacteristic
143C22×C1392−1+411yescharacteristic
144C22×C1392−1+411yescharacteristic
145C2×D139—41no—
146C2×D139—41no—
147C2×D139—41no—
148C2×D139—41no—
149C2×D139—41no—
150C2×D139—41no—
151C2×D139—41no—
152C4×C139—41no—
153C4×C139—41no—
154C4×C139—41no—
155C4×C139—41no—
156C4×C139—41no—
157C4×C139—41no—
158C4×C139—41no—
159Dic139—22no—
160Dic139—41no—
161Dic139—41no—
162Dic139—41no—
163Dic139—41no—
164Dic139—41no—
165Dic139—41no—
166C2×C139#53911yescharacteristic
167C2×C139#54211yescharacteristic
168C2×C139#54211yescharacteristic
169C2×C139#56011yescharacteristic
170C2×C139#56311yescharacteristic
171C2×C139#56311yescharacteristic
172C2×C139#56311yescharacteristic
173D139—81no—
174C139#283811yescharacteristic, complemented, Sylow
175#2838—1391nomaximal, Sylow
176#401—1391no—
177#400—1391no—
178#400D13911yescharacteristic, complemented
179#399—1391no—
180#398—1391no—
181#397—1391no—
182#397—1391no—
183#397—1391no—
184#396—1391no—
185#395—1391no—
186#395—1391no—
187#393—1391no—
188#389—1391no—
189#388—1391no—
190#387—1391no—
191C22×Q8—1391no—
192C2×C4⋊C4—1391no—
193C2×C4⋊C4—1391no—
194C2×C4⋊C4—1391no—
195C2×C4⋊C4—1391no—
196C2×C4⋊C4—1391no—
197C2×C4⋊C4—1391no—
198C2×C4⋊C4—1391no—
199C2×C4⋊C4—1391no—
200C2×C4⋊C4C2×D13911yescharacteristic
201C2×C4⋊C4C2×D13911yescharacteristic
202C2×C22⋊C4—1391no—
203C2×C22⋊C4—1391no—
204C2×C22⋊C4—1391no—
205C2×C22⋊C4—1391no—
206C2×C22⋊C4—1391no—
207C2×C22⋊C4—1391no—
208C2×C22⋊C4—1391no—
209C2×C42—1391no—
210#95—1391no—
211#95—1391no—
212#95—1391no—
213#95—1391no—
214#95—1391no—
215#95—1391no—
216#95—1391no—
217#95—1391no—
218#95—1391no—
219#95—1391no—
220#95—1391no—
221#95C2×D13911yescharacteristic
222#95C2×D13911yescharacteristic
223#95C2×D13911yescharacteristic
224#95C2×D13911yescharacteristic
225#95C2×D13911yescharacteristic
226C24—1391no—
227C2×Q8—5561no—
228C2×Q8—5561no—
229C2×Q8—5561no—
230C22×C4—1391no—
231C22×C4—1391no—
232C22×C4—1391no—
233C22×C4—1391no—
234C22×C4—1391no—
235C22×C4—1391no—
236C22×C4—1391no—
237C22×C4C22×D13911yescharacteristic
238C22×C4C22×D13911yescharacteristic
239C22×C4C22×D13911yescharacteristic
240C22×C4C22×D13911yescharacteristic
241C22×C4C22×D13911yescharacteristic
242C22×C4C22×D13911yescharacteristic
243C22×C4C22×D13911yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—2782no—
247C4⋊C4—2782no—
248C4⋊C4—5561no—
249C4⋊C4—5561no—
250C4⋊C4—5561no—
251C4⋊C4—5561no—
252C4⋊C4—5561no—
253C4⋊C4—5561no—
254C22⋊C4—2782no—
255C22⋊C4—5561no—
256C22⋊C4—5561no—
257C22⋊C4—5561no—
258C22⋊C4—5561no—
259C22⋊C4—5561no—
260C22⋊C4—5561no—
261C42—5561no—
262C23—2781no—
263C23—2781no—
264C23—2781no—
265C23—2781no—
266C23—2781no—
267C23—2781no—
268C23—2781no—
269C23C23×D13911yescharacteristic
270Q8—5564no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
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—2781no—
293C2×C4—2781no—
294C2×C4—2781no—
295C2×C4—2781no—
296C2×C4—2781no—
297C2×C4—2781no—
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—1392no—
313C22—5561no—
314C22—5561no—
315C22—5561no—
316C22—5561no—
317C22—5561no—
318C22—5561no—
319C22—5561no—
320C22#41×D13911yescharacteristic
321C22#1798488711yescharacteristic
322C22#1798488811yescharacteristic
323C22#1798488811yescharacteristic
324C22#1798488911yescharacteristic
325C22#1798488911yescharacteristic
326C22#1798489011yescharacteristic
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2782no—
335C4—5561no—
336C4—5561no—
337C4—5561no—
338C4—5561no—
339C4—5561no—
340C4—5561no—
341C2—11121no—
342C2#2258155111yescharacteristic
343C2#2258156711yescharacteristic
344C2#2258156911yescharacteristic
345C2#2258169311yescharacteristic
346C2#2258170411yescharacteristic
347C2#2258170511yescharacteristic
348C2#2258170711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#400×C139C2
prime radicalC23×D139C23
hypercenter#400D139
hypocenterC139#2838
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C139⋊#401C2semidirect
2. #22580895C2semidirect
4. #22580883C2semidirect
9. #22580874C2semidirect
10. #22580873C2semidirect
12. #22580850C2semidirect
14. #22580836C2semidirect
15. #400×C139C2semidirect
174. C139#2838semidirect
178. #400D139semidirect

Maximal subgroups

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

subgroupindex
C139⋊#4012
#225808952
#225808882
#225808832
#225808822
#225808802
#225808752
#225808742
#225808732
#225808662
#225808502
#225808452
#225808362
#400×C1392
#2838139