Finite Group Databasebeta

← #31809178

Subgroups — #31809178

Order 17792.

476 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×#17984837C211yesmaximal, characteristic
2#22580849C211yesmaximal, characteristic, complemented
3#22580845C211yesmaximal, characteristic
4#22580844C211yesmaximal, characteristic
5#22580843C211yesmaximal, characteristic
6#22580839C211yesmaximal, characteristic, complemented
7#22580838C211yesmaximal, characteristic, complemented
8#22580834C211yesmaximal, characteristic, complemented
9#22580824C211yesmaximal, characteristic
10#22580824C211yesmaximal, characteristic
11#22580818C211yesmaximal, characteristic, complemented
12C4×Dic139⋊C4C211yesmaximal, characteristic, complemented
13#22580804C211yesmaximal, characteristic, complemented
14#22580800C211yesmaximal, characteristic
15#389×C139C211yesmaximal, characteristic, complemented
16C22×C4×D139C2211yescharacteristic
17#17984837C418yescomplemented
18C2×C4⋊Dic139C2211yescharacteristic
19C2×C4⋊Dic139C2211yescharacteristic
20C2×Dic139⋊C4C2211yescharacteristic
21C2×Dic139⋊C4C2211yescharacteristic
22C2×Dic139⋊C4C2211yescharacteristic
23C2×Dic139⋊C4C2211yescharacteristic
24C2×(C2×D139)⋊C4C2211yescharacteristic
25C2×(C2×D139)⋊C4C2211yescharacteristic
26C2×(C2×D139)⋊C4C2211yescharacteristic
27C2×(C2×D139)⋊C4C2211yescharacteristic
28C2×(C2×D139)⋊C4C2211yescharacteristic
29C2×(C2×D139)⋊C4C2211yescharacteristic
30C2×C4×Dic139C2211yescharacteristic
31C2×C4×Dic139C2211yescharacteristic
32C2×C4×Dic139C2211yescharacteristic
33C2×C4×Dic139C2211yescharacteristic
34C2×C4×Dic139C2211yescharacteristic
35C139⋊#95C2211yescharacteristic
36C139⋊#95C2211yescharacteristic
37C139⋊#95C2211yescharacteristic
38C139⋊#95C2211yescharacteristic
39C139⋊#95C2211yescharacteristic
40C139⋊#95C2211yescharacteristic
41C139⋊#95C2211yescharacteristic
42C139⋊#95C2211yescharacteristic
43C139⋊#95C2211yescharacteristic
44C139⋊#95C2211yescharacteristic
45C2×C4⋊C4×C139C2211yescharacteristic
46C2×C4⋊C4×C139C2211yescharacteristic
47C2×C4⋊C4×C139C2211yescharacteristic
48C2×C4⋊C4×C139C2211yescharacteristic
49C2×C42×C139C2211yescharacteristic
50#95×C139C2211yescharacteristic
51#95×C139C2211yescharacteristic
52C23×D139C2311yescharacteristic
53C22×Dic139C2311yescharacteristic
54C22×Dic139C2311yescharacteristic
55C22×Dic139C2311yescharacteristic
56C22×Dic139C2311yescharacteristic
57C22×Dic139C2311yescharacteristic
58C22×Dic139C2311yescharacteristic
59C22×Dic139C2311yescharacteristic
60C2×C4×D139—22no—
61C2×C4×D139—41no—
62C2×C4×D139—41no—
63C4⋊Dic139—41no—
64C4⋊Dic139C2×C414yescomplemented
65Dic139⋊C4—22no—
66Dic139⋊C4—22no—
67Dic139⋊C4—22no—
68Dic139⋊C4C2×C414yescomplemented
69(C2×D139)⋊C4—22no—
70(C2×D139)⋊C4—41no—
71(C2×D139)⋊C4—41no—
72(C2×D139)⋊C4C2×C414yes—
73(C2×D139)⋊C4C2×C414yes—
74(C2×D139)⋊C4C2×C414yes—
75C4×Dic139—22no—
76C4×Dic139—41no—
77C4×Dic139—41no—
78C4×Dic139—41no—
79C4×Dic139C2×C414yescomplemented
80C22×C4×C139C2311yescharacteristic
81C22×C4×C139C2311yescharacteristic
82C22×C4×C139C2311yescharacteristic
83C22×C4×C139C2311yescharacteristic
84C22×C4×C139C2311yescharacteristic
85C22×C4×C139C2311yescharacteristic
86C22×C4×C139C2311yescharacteristic
87C4⋊C4×C139—41no—
88C4⋊C4×C139—41no—
89C4⋊C4×C139—41no—
90C4⋊C4×C139C2×C414yescomplemented
91C42×C139—41no—
92C22×D139—21no—
93C22×D139—21no—
94C22×D139—21no—
95C22×D139—21no—
96C22×D139—21no—
97C22×D139—21no—
98C22×D139C22×C412yes—
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—21no—
116C2×Dic139C22×C412yes—
117C2×Dic139C22×C412yes—
118C2×Dic139C22×C412yes—
119C2×Dic139#4112yes—
120C4×D139—44no—
121C23×C139C2411yescharacteristic
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—
138C2×C4×C139—21no—
139C2×C4×C139C22×C412yes—
140C2×C4×C139C22×C412yes—
141C2×C4×C139C22×C412yes—
142C2×C4×C139#4112yes—
143C22×C139C23×C411yescharacteristic
144C22×C139C2×#4111yescharacteristic
145C22×C139C2×#4111yescharacteristic
146C22×C139H(5,𝔽2)11yescharacteristic
147C22×C139H(5,𝔽2)11yescharacteristic
148C22×C1392−1+411yescharacteristic
149C22×C1392−1+411yescharacteristic
150C2×D139—22no—
151C2×D139—22no—
152C2×D139—22no—
153C2×D139—41no—
154C2×D139—41no—
155C2×D139—41no—
156C2×D139—41no—
157C4×C139—22no—
158C4×C139—22no—
159C4×C139—22no—
160C4×C139—22no—
161C4×C139—41no—
162C4×C139—41no—
163C4×C139—41no—
164Dic139—22no—
165Dic139—22no—
166Dic139—22no—
167Dic139—22no—
168Dic139—41no—
169Dic139—41no—
170Dic139—41no—
171C2×C139C4×#4111yescharacteristic
172C2×C139#52011yescharacteristic
173C2×C139#52011yescharacteristic
174C2×C139#53811yescharacteristic
175C2×C139#53911yescharacteristic
176C2×C139#54111yescharacteristic
177C2×C139#54211yescharacteristic
178D139—42no—
179C139#233411yescharacteristic, complemented, Sylow
180#2334—1391nomaximal, Sylow
181C2×#126—1391no—
182#389—1391no—
183#389D13911yescharacteristic, complemented
184#388—1391no—
185#388—1391no—
186#388—1391no—
187#387—1391no—
188#387—1391no—
189#387—1391no—
190#385—1391no—
191#385—1391no—
192#382—1391no—
193C4×C4⋊C4—1391no—
194C4×C4⋊C4—1391no—
195C4×C22⋊C4—1391no—
196C23×C4—1391no—
197#126—1398no—
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⋊C4C2×D13911yescharacteristic
205C2×C4⋊C4C2×D13911yescharacteristic
206C2×C4⋊C4C2×D13911yescharacteristic
207C2×C4⋊C4C2×D13911yescharacteristic
208C2×C22⋊C4—1391no—
209C2×C22⋊C4—1391no—
210C2×C22⋊C4—1391no—
211C2×C22⋊C4—1391no—
212C2×C22⋊C4—1391no—
213C2×C22⋊C4—1391no—
214C2×C42—1391no—
215C2×C42—1391no—
216C2×C42—1391no—
217C2×C42—1391no—
218C2×C42—1391no—
219C2×C42C2×D13911yescharacteristic
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
231#95C2×D13911yescharacteristic
232C24—1391no—
233C22×C4—2782no—
234C22×C4—5561no—
235C22×C4—5561no—
236C22×C4—1391no—
237C22×C4—1391no—
238C22×C4—1391no—
239C22×C4—1391no—
240C22×C4—1391no—
241C22×C4—1391no—
242C22×C4—1391no—
243C22×C4C22×D13911yescharacteristic
244C22×C4C22×D13911yescharacteristic
245C22×C4C22×D13911yescharacteristic
246C22×C4C22×D13911yescharacteristic
247C22×C4C22×D13911yescharacteristic
248C22×C4C22×D13911yescharacteristic
249C22×C4C22×D13911yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—2782no—
254C4⋊C4—2782no—
255C4⋊C4—2782no—
256C4⋊C4—5561no—
257C4⋊C4—1394no—
258C4⋊C4—1394no—
259C4⋊C4C4×D13914yescomplemented
260C22⋊C4—2782no—
261C22⋊C4—5561no—
262C22⋊C4—5561no—
263C22⋊C4—1394no—
264C22⋊C4—1394no—
265C22⋊C4—1394no—
266C42—41no—
267C42—2782no—
268C42—5561no—
269C42—5561no—
270C42—5561no—
271C42—1394no—
272C23—2781no—
273C23—2781no—
274C23—2781no—
275C23—2781no—
276C23—2781no—
277C23—2781no—
278C23—1392no—
279C23C23×D13911yescharacteristic
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—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—2781no—
313C2×C4—2781no—
314C2×C4—5564no—
315C2×C4—1392no—
316C2×C4—1392no—
317C2×C4—1392no—
318C2×C4—1392no—
319C2×C4C2×C4×D13912yes—
320C2×C4C2×C4×D13912yes—
321C2×C4C2×C4×D13912yes—
322C2×C4#1455578612yes—
323C22—2782no—
324C22—2782no—
325C22—2782no—
326C22—5561no—
327C22—5561no—
328C22—5561no—
329C22—5561no—
330C22C22×C4×D13911yescharacteristic
331C22#41×D13911yescharacteristic
332C22C2×#1455578611yescharacteristic
333C22#1798488711yescharacteristic
334C22#1798488711yescharacteristic
335C22#1798488911yescharacteristic
336C22#1798489011yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2782no—
345C4—2782no—
346C4—2782no—
347C4—2782no—
348C4—5561no—
349C4—5561no—
350C4—5561no—
351C2—5562no—
352C2C4×#1455578611yescharacteristic
353C2#2258143211yescharacteristic
354C2#2258143411yescharacteristic
355C2#2258153511yescharacteristic
356C2#2258155211yescharacteristic
357C2#2258156211yescharacteristic
358C2#2258157711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutatorC22×C139C23×C4
Fitting#389×C139C2
socle, cosocleC23×C139C24
prime radicalC23×D139C23
hypercenter#389D139
hypocenterC139#2334
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #22580849C2semidirect
6. #22580839C2semidirect
7. #22580838C2semidirect
8. #22580834C2semidirect
11. #22580818C2semidirect
12. C4×Dic139⋊C4C2semidirect
13. #22580804C2semidirect
15. #389×C139C2semidirect
17. #17984837C4semidirect
64. C4⋊Dic139C2×C4semidirect
68. Dic139⋊C4C2×C4semidirect
79. C4×Dic139C2×C4semidirect
90. C4⋊C4×C139C2×C4semidirect
179. C139#2334semidirect
183. #389D139semidirect
259. C4⋊C4C4×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848372
#225808492
#225808452
#225808442
#225808432
#225808392
#225808382
#225808342
#225808242
#225808182
C4×Dic139⋊C42
#225808042
#225808002
#389×C1392
#2334139