Finite Group Databasebeta

← #31809259

Subgroups — #31809259

Order 17792.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984800C211yesmaximal, characteristic
2#22580839C211yesmaximal, characteristic, complemented
3#22580838C211yesmaximal, characteristic, complemented
4#22580836C211yesmaximal, characteristic, complemented
5#22580827C211yesmaximal, characteristic
6#22580824C211yesmaximal, characteristic
7#22580820C211yesmaximal, characteristic, complemented
8#22580817C211yesmaximal, characteristic, complemented
9#22580815C211yesmaximal, characteristic
10C4⋊C4×Dic139C211yesmaximal, characteristic, complemented
11C4×(C2×D139)⋊C4C211yesmaximal, characteristic
12#22580800C211yesmaximal, characteristic
13#22580799C211yesmaximal, characteristic, complemented
14#95×D139C211yesmaximal, characteristic
15#387×C139C211yesmaximal, characteristic, complemented
16C22×C4×D139C2211yescharacteristic
17C22×C4×D139C2211yescharacteristic
18C22×C4×D139C2211yescharacteristic
19#17984800C418yescomplemented
20C2×C4⋊Dic139C2211yescharacteristic
21C2×C4⋊Dic139C2211yescharacteristic
22C2×Dic139⋊C4C2211yescharacteristic
23C2×Dic139⋊C4C2211yescharacteristic
24C2×(C2×D139)⋊C4C2211yescharacteristic
25C2×(C2×D139)⋊C4C2211yescharacteristic
26C2×(C2×D139)⋊C4C2211yescharacteristic
27C2×(C2×D139)⋊C4C2211yescharacteristic
28C2×C4×Dic139C2211yescharacteristic
29C2×C4×Dic139C2211yescharacteristic
30C2×C4×Dic139C2211yescharacteristic
31C2×C4×Dic139C2211yescharacteristic
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
44C139⋊#95C2211yescharacteristic
45C2×C4⋊C4×C139C2211yescharacteristic
46C2×C4⋊C4×C139C2211yescharacteristic
47C2×C42×C139C2211yescharacteristic
48#95×C139C2211yescharacteristic
49#95×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—22no—
62C2×C4×D139—22no—
63C2×C4×D139—22no—
64C2×C4×D139—22no—
65C2×C4×D139—22no—
66C2×C4×D139—41no—
67C2×C4×D139—41no—
68C2×C4×D139C2×C414yes—
69C4⋊Dic139—22no—
70C4⋊Dic139C2×C414yescomplemented
71Dic139⋊C4—41no—
72Dic139⋊C4—41no—
73(C2×D139)⋊C4—22no—
74(C2×D139)⋊C4—22no—
75(C2×D139)⋊C4C2×C414yes—
76(C2×D139)⋊C4C2×C414yes—
77C4×Dic139—22no—
78C4×Dic139—41no—
79C4×Dic139—41no—
80C4×Dic139C2×C414yescomplemented
81C4×Dic139C2×C414yescomplemented
82C22×C4×C139C2311yescharacteristic
83C22×C4×C139C2311yescharacteristic
84C22×C4×C139C2311yescharacteristic
85C22×C4×C139C2311yescharacteristic
86C22×C4×C139C2311yescharacteristic
87C22×C4×C139C2311yescharacteristic
88C22×C4×C139C2311yescharacteristic
89C4⋊C4×C139—22no—
90C4⋊C4×C139C2×C414yescomplemented
91C42×C139—22no—
92C22×D139—21no—
93C22×D139—21no—
94C22×D139—21no—
95C22×D139—21no—
96C22×D139C22×C412yes—
97C22×D139#4112yes—
98C22×D139#4112yes—
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—28no—
121C4×D139—44no—
122C4×D139—44no—
123C23×C139C2411yescharacteristic
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×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139C22×C412yes—
142C2×C4×C139C22×C412yes—
143C2×C4×C139C22×C412yes—
144C2×C4×C139#4112yes—
145C22×C139C23×C411yescharacteristic
146C22×C139C2×#4111yescharacteristic
147C22×C139C2×#4111yescharacteristic
148C22×C139C2×#4111yescharacteristic
149C22×C139C2×#4111yescharacteristic
150C22×C139H(5,𝔽2)11yescharacteristic
151C22×C1392−1+411yescharacteristic
152C2×D139—22no—
153C2×D139—22no—
154C2×D139—22no—
155C2×D139—22no—
156C2×D139—22no—
157C2×D139—22no—
158C2×D139#11714yes—
159C4×C139—22no—
160C4×C139—22no—
161C4×C139—22no—
162C4×C139—22no—
163C4×C139—41no—
164C4×C139—41no—
165C4×C139—41no—
166Dic139—22no—
167Dic139—22no—
168Dic139—22no—
169Dic139—22no—
170Dic139—41no—
171Dic139—41no—
172Dic139—41no—
173C2×C139C2×#11711yescharacteristic
174C2×C139C4×#4111yescharacteristic
175C2×C139#52011yescharacteristic
176C2×C139#55111yescharacteristic
177C2×C139#55111yescharacteristic
178C2×C139#55211yescharacteristic
179C2×C139#55211yescharacteristic
180D139—24no—
181C139#234311yescharacteristic, complemented, Sylow
182#2343—1391nomaximal, Sylow
183C2×#117—1391no—
184#387—1391no—
185#387—1391no—
186#387—1391no—
187#387D13911yescharacteristic, complemented
188#385—1391no—
189#385—1391no—
190#383—1391no—
191#382—1391no—
192#381—1391no—
193C4×C4⋊C4—1391no—
194C4×C22⋊C4—1391no—
195C4×C22⋊C4—1391no—
196#376—1391no—
197C2×#95—1391no—
198C23×C4—1391no—
199C23×C4—1391no—
200C23×C4—1391no—
201#117—1398no—
202C2×C4⋊C4—1391no—
203C2×C4⋊C4—1391no—
204C2×C4⋊C4—1391no—
205C2×C4⋊C4—1391no—
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×C42—1391no—
213C2×C42—1391no—
214C2×C42—1391no—
215C2×C42—1391no—
216C2×C42—1391no—
217C2×C42C2×D13911yescharacteristic
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
231#95C2×D13911yescharacteristic
232#95C2×D13911yescharacteristic
233#95C2×D13911yescharacteristic
234C24—1391no—
235C22×C4—2782no—
236C22×C4—2782no—
237C22×C4—2782no—
238C22×C4—2782no—
239C22×C4—2782no—
240C22×C4—2782no—
241C22×C4—5561no—
242C22×C4—5561no—
243C22×C4—1391no—
244C22×C4—1391no—
245C22×C4—1391no—
246C22×C4—1391no—
247C22×C4—1391no—
248C22×C4—1391no—
249C22×C4—1391no—
250C22×C4—1394no—
251C22×C4C22×D13911yescharacteristic
252C22×C4C22×D13911yescharacteristic
253C22×C4C22×D13911yescharacteristic
254C22×C4C22×D13911yescharacteristic
255C22×C4C22×D13911yescharacteristic
256C22×C4C22×D13911yescharacteristic
257C22×C4C22×D13911yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—2782no—
260C4⋊C4—5561no—
261C4⋊C4—5561no—
262C4⋊C4—1394no—
263C4⋊C4C4×D13914yescomplemented
264C22⋊C4—2782no—
265C22⋊C4—2782no—
266C22⋊C4—1394no—
267C22⋊C4—1394no—
268C42—22no—
269C42—2782no—
270C42—5561no—
271C42—5561no—
272C42—1394no—
273C42—1394no—
274C23—2781no—
275C23—2781no—
276C23—2781no—
277C23—2781no—
278C23—1392no—
279C23—1392no—
280C23—1392no—
281C23C23×D13911yescharacteristic
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—2788no—
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—5564no—
318C2×C4—5564no—
319C2×C4—1392no—
320C2×C4—1392no—
321C2×C4—1392no—
322C2×C4—1392no—
323C2×C4C2×C4×D13912yes—
324C2×C4C2×C4×D13912yes—
325C2×C4C2×C4×D13912yes—
326C2×C4#1455578412yes—
327C22—2782no—
328C22—2782no—
329C22—2782no—
330C22—2782no—
331C22—2782no—
332C22—2782no—
333C22—1394no—
334C22C22×C4×D13911yescharacteristic
335C22#41×D13911yescharacteristic
336C22#41×D13911yescharacteristic
337C22#41×D13911yescharacteristic
338C22C2×#1455578411yescharacteristic
339C22#1798488811yescharacteristic
340C22#1798489011yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2782no—
349C4—2782no—
350C4—2782no—
351C4—2782no—
352C4—5561no—
353C4—5561no—
354C4—5561no—
355C2—2784no—
356C2#117×D13911yescharacteristic
357C2C4×#1455578411yescharacteristic
358C2#2258143511yescharacteristic
359C2#2258162611yescharacteristic
360C2#2258162811yescharacteristic
361C2#2258163511yescharacteristic
362C2#2258163711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutatorC22×C139C23×C4
Fitting#387×C139C2
socle, cosocleC23×C139C24
prime radicalC23×D139C23
hypercenter#387D139
hypocenterC139#2343
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #22580839C2semidirect
3. #22580838C2semidirect
4. #22580836C2semidirect
7. #22580820C2semidirect
8. #22580817C2semidirect
10. C4⋊C4×Dic139C2semidirect
13. #22580799C2semidirect
15. #387×C139C2semidirect
19. #17984800C4semidirect
70. C4⋊Dic139C2×C4semidirect
80. C4×Dic139C2×C4semidirect
81. C4×Dic139C2×C4semidirect
90. C4⋊C4×C139C2×C4semidirect
181. C139#2343semidirect
187. #387D139semidirect
263. C4⋊C4C4×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848002
#225808392
#225808382
#225808362
#225808272
#225808242
#225808202
#225808172
#225808152
C4⋊C4×Dic1392
C4×(C2×D139)⋊C42
#225808002
#225807992
#95×D1392
#387×C1392
#2343139