Finite Group Databasebeta

← C2×D137⋊#99 #31797382

Subgroups — C2×D137⋊#99 #31797382

Order 17536.

1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊#10587739C212yesmaximal, complemented
2C2×#17984147C212yesmaximal, complemented
3D137⋊#99C218yesmaximal, direct product factor
4C2×#17984146C212yesmaximal, complemented
5C22×D4×D137C211yesmaximal, characteristic
6C23×#10587739—22no—
7C2×C22⋊#10587739—22no—
8C2×C22⋊#10587739—24no—
9C2×C22⋊#10587739C2214yescomplemented
10C2×C22⋊#10587739C2218yescomplemented
11#17984147C2218yescomplemented
12#17984146C2218yescomplemented
13C24×D137C411yescharacteristic, complemented
14C24×D137C2211yescharacteristic
15C22×D548C2211yescharacteristic
16C22×C22⋊D137C411yescharacteristic, complemented
17C22×C22⋊D137C2211yescharacteristic
18C2×D4×D137—22no—
19C2×D4×D137—22no—
20C2×D4×D137—24no—
21C2×D4×D137C414yescomplemented
22C2×D4×D137C2214yes—
23C22×C4×D137C411yescharacteristic, complemented
24C22×D4×C137C411yescharacteristic, complemented
25C22×#10587739—28no—
26C22×#10587739—24no—
27C22×#10587739—48no—
28C22⋊#10587739—28no—
29C22⋊#10587739—24no—
30C22⋊#10587739C2318yescomplemented
31C23×D137—22no—
32C23×D137—21no—
33C23×D137—21no—
34C23×D137—44no—
35C23×D137—44no—
36C23×D137C2×C411yescharacteristic
37C23×D137C2×C412yes—
38C23×D137C2×C411yescharacteristic, complemented
39C23×D137C2×C414yescomplemented
40C23×D137D412yes—
41C23×D137D412yes—
42C23×D137D414yes—
43C23×D137C2312yes—
44C23×D137C2311yescharacteristic
45C2×D548—22no—
46C2×D548—22no—
47C2×D548C2×C412yescomplemented
48C2×D548C2312yes—
49C2×C22⋊D137—22no—
50C2×C22⋊D137—22no—
51C2×C22⋊D137—22no—
52C2×C22⋊D137—22no—
53C2×C22⋊D137C2×C414yescomplemented
54C2×C22⋊D137C2×C412yescomplemented
55C2×C22⋊D137C2312yes—
56D4×D137—28no—
57D4×D137—28no—
58D4×D137—28no—
59D4×D137—28no—
60C22×Dic137C2×C411yescharacteristic, complemented
61C2×C4×D137—22no—
62C2×C4×D137—21no—
63C2×C4×D137—21no—
64C2×C4×D137C2×C414yescomplemented
65C24×C137C2×C411yescharacteristic
66C24×C137C2×C411yescharacteristic, complemented
67C2×D4×C137—22no—
68C2×D4×C137—22no—
69C2×D4×C137C2×C414yescomplemented
70C22×C4×C137C2×C411yescharacteristic, complemented
71C2×#10587739—28no—
72C2×#10587739—48no—
73C2×#10587739—416no—
74C22×D137—24no—
75C22×D137—28no—
76C22×D137—21no—
77C22×D137—21no—
78C22×D137—24no—
79C22×D137—24no—
80C22×D137—44no—
81C22×D137—48no—
82C22×D137—44no—
83C22×D137—44no—
84C22×D137—42no—
85C22×D137—44no—
86C22×D137—48no—
87C22×D137—48no—
88C22×D137—44no—
89C22×D137—42no—
90C22×D137C22⋊C412yes—
91C22×D137C22⋊C411yescharacteristic
92C22×D137C22⋊C414yes—
93C22×D137C22⋊C414yes—
94C22×D137C22⋊C411yescharacteristic
95C22×D137C22×C412yes—
96C22×D137C22×C411yescharacteristic
97C22×D137C22×C412yescomplemented
98C22×D137C2×D414yes—
99C22×D137C2×D412yes—
100C22×D137C2×D414yes—
101C22×D137C2×D412yes—
102C22×D137C2411yescharacteristic
103D548—24no—
104D548—24no—
105C22⋊D137—28no—
106C22⋊D137—24no—
107C22⋊D137—24no—
108C2×Dic137—21no—
109C2×Dic137—21no—
110C2×Dic137C22×C412yescomplemented
111C4×D137—24no—
112C4×D137—24no—
113C23×C137—21no—
114C23×C137—21no—
115C23×C137—42no—
116C23×C137—42no—
117C23×C137C22⋊C412yes—
118C23×C137C22⋊C412yes—
119C23×C137C22×C411yescharacteristic
120C23×C137C22×C412yes—
121C23×C137C22×C412yescomplemented
122D4×C137—28no—
123C2×C4×C137—21no—
124C2×C4×C137—21no—
125C2×C4×C137C22×C412yescomplemented
126C22×C137—22no—
127C22×C137—24no—
128C22×C137—22no—
129C22×C137—42no—
130C22×C137—42no—
131C22×C137—42no—
132C22×C137—42no—
133C22×C137—42no—
134C22×C137C2×C22⋊C411yescharacteristic
135C22×C137C2×C22⋊C414yes—
136C22×C137C2×C22⋊C411yescharacteristic
137C22×C137C23×C411yescharacteristic
138C2×D137—22no—
139C2×D137—24no—
140C2×D137—24no—
141C2×D137—24no—
142C2×D137—28no—
143C2×D137—28no—
144C2×D137—22no—
145C2×D137—44no—
146C2×D137—41no—
147C2×D137—44no—
148C2×D137—42no—
149C2×D137—41no—
150C2×D137—48no—
151C2×D137—42no—
152C2×D137—42no—
153C2×D137—48no—
154C2×D137—42no—
155C2×D137#9914yescomplemented
156C2×D137C2×C22⋊C412yes—
157C2×D137C2×C22⋊C412yes—
158C2×D137C2×C22⋊C412yes—
159C2×D137C22×D412yes—
160#10587739—48no—
161C4×C137—22no—
162Dic137—22no—
163C2×C137—21no—
164C2×C137—21no—
165C2×C137—24no—
166C2×C137—42no—
167C2×C137C2×#9912yescomplemented
168C2×C137C22×C22⋊C411yescharacteristic
169D137—22no—
170D137—22no—
171D137—22no—
172D137—42no—
173D137C2×#9914yescomplemented
174C137C22×#9911yescharacteristic, complemented, Sylow
175C22×#99—1371nomaximal, Sylow
176C23×D4—1371no—
177C22×C22⋊C4—1372no—
178C2×#99—1372no—
179C2×#99—1378no—
180C2×#99—1372no—
181C25—1371no—
182C25—1371no—
183C22×D4—2742no—
184C22×D4—2744no—
185C22×D4—2742no—
186C22×D4—1371no—
187C22×D4—1371no—
188C22×D4—1374no—
189C22×D4—1374no—
190C22×D4—1371no—
191C22×D4#1058773911yescharacteristic, complemented
192C23×C4—2742no—
193C23×C4—1371no—
194C2×C22⋊C4—2744no—
195C2×C22⋊C4—2742no—
196C2×C22⋊C4—1374no—
197C2×C22⋊C4—1378no—
198#99—1378no—
199#99—1378no—
200C24—2742no—
201C24—2741no—
202C24—2741no—
203C24—5484no—
204C24—5484no—
205C24—1372no—
206C24—1371no—
207C24—1371no—
208C24—1374no—
209C24—1372no—
210C24—1374no—
211C24—1371no—
212C24—1372no—
213C24—1372no—
214C24C2×#1058773911yescharacteristic
215C24C2×#1058773911yescharacteristic, complemented
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—2742no—
219C2×D4—2742no—
220C2×D4—2748no—
221C2×D4—2748no—
222C2×D4—2748no—
223C2×D4—2748no—
224C2×D4—2742no—
225C2×D4—2742no—
226C2×D4—2742no—
227C2×D4—2742no—
228C2×D4—1374no—
229C2×D4—1372no—
230C2×D4—1372no—
231C2×D4—1372no—
232C2×D4—1372no—
233C2×D4C2×#1058773914yescomplemented
234C22×C4—2742no—
235C22×C4—2741no—
236C22×C4—2741no—
237C22×C4—2748no—
238C22×C4—2744no—
239C22×C4—5488no—
240C22×C4—1371no—
241C22×C4—1374no—
242C22×C4C2×#1058773911yescharacteristic, complemented
243C22⋊C4—2748no—
244C22⋊C4—2744no—
245C22⋊C4—1378no—
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—2748no—
251C23—2744no—
252C23—2744no—
253C23—2744no—
254C23—2741no—
255C23—2741no—
256C23—5482no—
257C23—5484no—
258C23—5482no—
259C23—5488no—
260C23—5484no—
261C23—5484no—
262C23—5488no—
263C23—5488no—
264C23—5484no—
265C23—5484no—
266C23—1374no—
267C23—1372no—
268C23—1374no—
269C23—1372no—
270C23—1371no—
271C23—1372no—
272C23—1372no—
273C23—1374no—
274C23—1372no—
275C23—1374no—
276C23—1371no—
277C23—1371no—
278C23—1371no—
279C23C22⋊#1058773912yes—
280C23C22⋊#1058773912yes—
281C23C22×#1058773911yescharacteristic
282C23C22×#1058773912yes—
283C23C22×#1058773912yescomplemented
284D4—28no—
285D4—2744no—
286D4—2744no—
287D4—2744no—
288D4—2744no—
289D4—2748no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—2744no—
293C2×C4—2744no—
294C2×C4—2741no—
295C2×C4—2741no—
296C2×C4—2748no—
297C2×C4—54816no—
298C2×C4—5488no—
299C2×C4—1372no—
300C2×C4C22×#1058773912yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—2748no—
310C22—2744no—
311C22—2744no—
312C22—2748no—
313C22—2744no—
314C22—2742no—
315C22—2742no—
316C22—5482no—
317C22—5481no—
318C22—5481no—
319C22—5484no—
320C22—5484no—
321C22—5482no—
322C22—5482no—
323C22—5488no—
324C22—5488no—
325C22—5482no—
326C22—1372no—
327C22—1372no—
328C22—1372no—
329C22—1372no—
330C22—1374no—
331C22C2×C22⋊#1058773911yescharacteristic
332C22C2×C22⋊#1058773914yes—
333C22C2×C22⋊#1058773911yescharacteristic
334C22C23×#1058773911yescharacteristic
335C4—22no—
336C4—2742no—
337C4—5488no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—2742no—
343C2—2742no—
344C2—2742no—
345C2—5482no—
346C2—1374no—
347C2D137⋊#9912yesdirect product factor
348C2C22×C22⋊#1058773911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10587739
commutatorC22×C137C23×C4
FrattiniC22C23×#10587739
FittingC22×D4×C137C4
socleC22×C137C2×C22⋊C4
prime radicalC22×D4×D137C2
cosocleC22×D137C24
hypercenterC22×D4#10587739
hypocenterC137C22×#99
LCSG ▷ C22×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#10587739C2semidirect
2. C2×#17984147C2semidirect
3. D137⋊#99C2direct (N × H)
4. C2×#17984146C2semidirect
9. C2×C22⋊#10587739C22semidirect
10. C2×C22⋊#10587739C22semidirect
11. #17984147C22semidirect
12. #17984146C22semidirect
13. C24×D137C4semidirect
16. C22×C22⋊D137C4semidirect
21. C2×D4×D137C4semidirect
23. C22×C4×D137C4semidirect
24. C22×D4×C137C4semidirect
30. C22⋊#10587739C23semidirect
38. C23×D137C2×C4semidirect
39. C23×D137C2×C4semidirect
47. C2×D548C2×C4semidirect
53. C2×C22⋊D137C2×C4semidirect
54. C2×C22⋊D137C2×C4semidirect
60. C22×Dic137C2×C4semidirect
64. C2×C4×D137C2×C4semidirect
66. C24×C137C2×C4semidirect
69. C2×D4×C137C2×C4semidirect
70. C22×C4×C137C2×C4semidirect
97. C22×D137C22×C4semidirect
110. C2×Dic137C22×C4semidirect
121. C23×C137C22×C4semidirect
125. C2×C4×C137C22×C4semidirect
155. C2×D137#99semidirect
167. C2×C137C2×#99semidirect
173. D137C2×#99semidirect
174. C137C22×#99semidirect
191. C22×D4#10587739semidirect
215. C24C2×#10587739semidirect
233. C2×D4C2×#10587739semidirect
242. C22×C4C2×#10587739semidirect
283. C23C22×#10587739semidirect
300. C2×C4C22×#10587739semidirect
347. C2D137⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#105877392
C2×#179841472
D137⋊#992
C2×#179841462
C22×D4×D1372
C22×#99137