Finite Group Databasebeta

← #31814663

Subgroups — #31814663

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#22580890C211yesmaximal, characteristic
3#22580887C211yesmaximal, characteristic, complemented
4#22580886C211yesmaximal, characteristic, complemented
5#22580886C211yesmaximal, characteristic, complemented
6#22580885C211yesmaximal, characteristic, complemented
7#22580877C211yesmaximal, characteristic
8#22580875C211yesmaximal, characteristic
9#22580874C211yesmaximal, characteristic, complemented
10#22580874C211yesmaximal, characteristic, complemented
11#22580866C211yesmaximal, characteristic
12#22580815C211yesmaximal, characteristic
13#22580812C211yesmaximal, characteristic
14#22580810C211yesmaximal, characteristic
15#400×C139C211yesmaximal, characteristic, complemented
16C22×Dic278C2211yescharacteristic
17C22×C4×D139C2211yescharacteristic
18C2×C4⋊Dic139C2211yescharacteristic
19C2×C4⋊Dic139C2211yescharacteristic
20C2×C4⋊Dic139C2211yescharacteristic
21C2×C4⋊Dic139C2211yescharacteristic
22C2×C4⋊Dic139C2211yescharacteristic
23C2×Dic139⋊C4C2211yescharacteristic
24C2×Dic139⋊C4C2211yescharacteristic
25C2×Dic139⋊C4C2211yescharacteristic
26C2×Dic139⋊C4C2211yescharacteristic
27C2×Dic139⋊C4C2211yescharacteristic
28C2×Dic139⋊C4C2211yescharacteristic
29C2×(C2×D139)⋊C4C2211yescharacteristic
30C2×(C2×D139)⋊C4C2211yescharacteristic
31C2×(C2×D139)⋊C4C2211yescharacteristic
32C2×(C2×D139)⋊C4C2211yescharacteristic
33C2×(C2×D139)⋊C4C2211yescharacteristic
34C2×(C2×D139)⋊C4C2211yescharacteristic
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
62C2×C4×D139—41no—
63C2×C4×D139—41no—
64C2×C4×D139Q814yescomplemented
65C4⋊Dic139—41no—
66C4⋊Dic139—41no—
67C4⋊Dic139—41no—
68C4⋊Dic139—41no—
69C4⋊Dic139—41no—
70Dic139⋊C4—41no—
71Dic139⋊C4—41no—
72Dic139⋊C4—41no—
73Dic139⋊C4—41no—
74Dic139⋊C4—41no—
75Dic139⋊C4—41no—
76(C2×D139)⋊C4—41no—
77(C2×D139)⋊C4—41no—
78(C2×D139)⋊C4—41no—
79(C2×D139)⋊C4—41no—
80(C2×D139)⋊C4—41no—
81(C2×D139)⋊C4—41no—
82C22×C4×C139C2311yescharacteristic
83C22×C4×C139C2311yescharacteristic
84C22×C4×C139C2311yescharacteristic
85C22×C4×C139C2311yescharacteristic
86C22×C4×C139C2311yescharacteristic
87C22×C4×C139C2311yescharacteristic
88C22×C4×C139C2311yescharacteristic
89C4⋊C4×C139—41no—
90C4⋊C4×C139—41no—
91C22×D139—21no—
92C22×D139—21no—
93C22×D139—21no—
94C22×D139—21no—
95C22×D139—21no—
96C22×D139—21no—
97C22×D139C2×Q812yes—
98Dic278—44no—
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×Dic139—21no—
117C2×Dic139—21no—
118C2×Dic139—21no—
119C2×Dic139C2×Q812yes—
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×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139C2×Q812yes—
143C22×C139C22×Q811yescharacteristic
144C22×C139H(5,𝔽2)11yescharacteristic
145C22×C139H(5,𝔽2)11yescharacteristic
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—41no—
159C4×C139—41no—
160C4×C139—41no—
161C4×C139—41no—
162C4×C139—41no—
163C4×C139—41no—
164Dic139—22no—
165Dic139—41no—
166Dic139—41no—
167Dic139—41no—
168Dic139—41no—
169Dic139—41no—
170Dic139—41no—
171C2×C139#54311yescharacteristic
172C2×C139#54411yescharacteristic
173C2×C139#54411yescharacteristic
174C2×C139#56011yescharacteristic
175C2×C139#56211yescharacteristic
176C2×C139#56211yescharacteristic
177C2×C139#56311yescharacteristic
178D139—42no—
179C139#284111yescharacteristic, complemented, Sylow
180#2841—1391nomaximal, Sylow
181#400—1391no—
182#400D13911yescharacteristic, complemented
183#399—1391no—
184#398—1391no—
185#398—1391no—
186#398—1391no—
187#398—1391no—
188#396—1391no—
189#396—1391no—
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⋊C4—1391no—
209C2×C4⋊C4C2×D13911yescharacteristic
210C2×C4⋊C4C2×D13911yescharacteristic
211C2×C22⋊C4—1391no—
212C2×C22⋊C4—1391no—
213C2×C22⋊C4—1391no—
214C2×C22⋊C4—1391no—
215C2×C22⋊C4—1391no—
216C2×C22⋊C4—1391no—
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#95C2×D13911yescharacteristic
227#95C2×D13911yescharacteristic
228#95C2×D13911yescharacteristic
229#95C2×D13911yescharacteristic
230#95C2×D13911yescharacteristic
231C24—1391no—
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—1394no—
245C22×C4C22×D13911yescharacteristic
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—5561no—
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—5561no—
266C22⋊C4—5561no—
267C22⋊C4—5561no—
268C22⋊C4—5561no—
269C22⋊C4—5561no—
270C22⋊C4—5561no—
271C23—2781no—
272C23—2781no—
273C23—2781no—
274C23—2781no—
275C23—2781no—
276C23—2781no—
277C23—1392no—
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—21no—
299C2×C4—21no—
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×C4Q8×D13912yes—
323C22—2782no—
324C22—2782no—
325C22—2782no—
326C22—5561no—
327C22—5561no—
328C22—5561no—
329C22—5561no—
330C22C2×Q8×D13911yescharacteristic
331C22#1798488711yescharacteristic
332C22#1798488811yescharacteristic
333C22#1798488811yescharacteristic
334C22#1798488811yescharacteristic
335C22#1798488911yescharacteristic
336C22#1798488911yescharacteristic
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2782no—
345C4—5561no—
346C4—5561no—
347C4—5561no—
348C4—5561no—
349C4—5561no—
350C4—5561no—
351C2—5562no—
352C2#2258157811yescharacteristic
353C2#2258158311yescharacteristic
354C2#2258158311yescharacteristic
355C2#2258169411yescharacteristic
356C2#2258169711yescharacteristic
357C2#2258170011yescharacteristic
358C2#2258170511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#400×C139C2
prime radicalC23×D139C23
hypercenter#400D139
hypocenterC139#2841
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #22580894C2semidirect
3. #22580887C2semidirect
4. #22580886C2semidirect
5. #22580886C2semidirect
6. #22580885C2semidirect
9. #22580874C2semidirect
10. #22580874C2semidirect
15. #400×C139C2semidirect
64. C2×C4×D139Q8semidirect
179. C139#2841semidirect
182. #400D139semidirect

Maximal subgroups

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

subgroupindex
#225808942
#225808902
#225808872
#225808862
#225808852
#225808772
#225808752
#225808742
#225808662
#225808152
#225808122
#225808102
#400×C1392
#2841139