Finite Group Databasebeta

← C2×D101⋊#99 #27187725

Subgroups — C2×D101⋊#99 #27187725

Order 12928.

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⋊#87938C212yesmaximal, complemented
2C2×#15692314C212yesmaximal, complemented
3D101⋊#99C218yesmaximal, direct product factor
4C2×#15692313C212yesmaximal, complemented
5C22×D4×D101C211yesmaximal, characteristic
6C23×#87938—22no—
7C2×C22⋊#87938—24no—
8C2×C22⋊#87938—22no—
9C2×C22⋊#87938C2214yescomplemented
10C2×C22⋊#87938C2218yescomplemented
11#15692314C2218yescomplemented
12#15692313C2218yescomplemented
13C24×D101C411yescharacteristic, complemented
14C24×D101C2211yescharacteristic
15C22×D404C2211yescharacteristic
16C22×C22⋊D101C411yescharacteristic, complemented
17C22×C22⋊D101C2211yescharacteristic
18C2×D4×D101—22no—
19C2×D4×D101—22no—
20C2×D4×D101—24no—
21C2×D4×D101C414yescomplemented
22C2×D4×D101C2214yes—
23C22×C4×D101C411yescharacteristic, complemented
24C22×D4×C101C411yescharacteristic, complemented
25C22×#87938—28no—
26C22×#87938—24no—
27C22×#87938—48no—
28C22⋊#87938—28no—
29C22⋊#87938—24no—
30C22⋊#87938C2318yescomplemented
31C23×D101—22no—
32C23×D101—21no—
33C23×D101—21no—
34C23×D101—44no—
35C23×D101—44no—
36C23×D101C2×C411yescharacteristic
37C23×D101C2×C412yes—
38C23×D101C2×C414yescomplemented
39C23×D101C2×C411yescharacteristic, complemented
40C23×D101D412yes—
41C23×D101D414yes—
42C23×D101D412yes—
43C23×D101C2312yes—
44C23×D101C2311yescharacteristic
45C2×D404—22no—
46C2×D404—22no—
47C2×D404C2×C412yescomplemented
48C2×D404C2312yes—
49C2×C22⋊D101—22no—
50C2×C22⋊D101—22no—
51C2×C22⋊D101—22no—
52C2×C22⋊D101—22no—
53C2×C22⋊D101C2×C412yescomplemented
54C2×C22⋊D101C2×C414yescomplemented
55C2×C22⋊D101C2312yes—
56D4×D101—28no—
57D4×D101—28no—
58D4×D101—28no—
59D4×D101—28no—
60C22×Dic101C2×C411yescharacteristic, complemented
61C2×C4×D101—22no—
62C2×C4×D101—21no—
63C2×C4×D101—21no—
64C2×C4×D101C2×C414yescomplemented
65C24×C101C2×C411yescharacteristic
66C24×C101C2×C411yescharacteristic, complemented
67C2×D4×C101—22no—
68C2×D4×C101—22no—
69C2×D4×C101C2×C414yescomplemented
70C22×C4×C101C2×C411yescharacteristic, complemented
71C23×C101—21no—
72C23×C101—21no—
73C23×C101—42no—
74C23×C101—42no—
75C23×C101C22⋊C412yes—
76C23×C101C22⋊C412yes—
77C23×C101C22×C411yescharacteristic
78C23×C101C22×C412yes—
79C23×C101C22×C412yescomplemented
80C22×D101—24no—
81C22×D101—28no—
82C22×D101—21no—
83C22×D101—21no—
84C22×D101—24no—
85C22×D101—24no—
86C22×D101—44no—
87C22×D101—48no—
88C22×D101—44no—
89C22×D101—44no—
90C22×D101—42no—
91C22×D101—44no—
92C22×D101—48no—
93C22×D101—48no—
94C22×D101—44no—
95C22×D101—42no—
96C22×D101C22⋊C412yes—
97C22×D101C22⋊C411yescharacteristic
98C22×D101C22⋊C414yes—
99C22×D101C22⋊C414yes—
100C22×D101C22⋊C411yescharacteristic
101C22×D101C22×C412yes—
102C22×D101C22×C411yescharacteristic
103C22×D101C22×C412yescomplemented
104C22×D101C2×D414yes—
105C22×D101C2×D412yes—
106C22×D101C2×D414yes—
107C22×D101C2×D412yes—
108C22×D101C2411yescharacteristic
109C2×#87938—28no—
110C2×#87938—48no—
111C2×#87938—416no—
112D4×C101—28no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101C22×C412yescomplemented
116C22⋊D101—28no—
117C22⋊D101—24no—
118C22⋊D101—24no—
119C2×Dic101—21no—
120C2×Dic101—21no—
121C2×Dic101C22×C412yescomplemented
122D404—24no—
123D404—24no—
124C4×D101—24no—
125C4×D101—24no—
126C22×C101—22no—
127C22×C101—24no—
128C22×C101—22no—
129C22×C101—42no—
130C22×C101—42no—
131C22×C101—42no—
132C22×C101—42no—
133C22×C101—42no—
134C22×C101C2×C22⋊C411yescharacteristic
135C22×C101C2×C22⋊C414yes—
136C22×C101C2×C22⋊C411yescharacteristic
137C22×C101C23×C411yescharacteristic
138C2×D101—24no—
139C2×D101—22no—
140C2×D101—28no—
141C2×D101—24no—
142C2×D101—24no—
143C2×D101—28no—
144C2×D101—22no—
145C2×D101—44no—
146C2×D101—41no—
147C2×D101—44no—
148C2×D101—42no—
149C2×D101—41no—
150C2×D101—48no—
151C2×D101—42no—
152C2×D101—42no—
153C2×D101—48no—
154C2×D101—42no—
155C2×D101#9914yescomplemented
156C2×D101C2×C22⋊C412yes—
157C2×D101C2×C22⋊C412yes—
158C2×D101C2×C22⋊C412yes—
159C2×D101C22×D412yes—
160#87938—48no—
161C4×C101—22no—
162Dic101—22no—
163C2×C101—21no—
164C2×C101—21no—
165C2×C101—24no—
166C2×C101—42no—
167C2×C101C2×#9912yescomplemented
168C2×C101C22×C22⋊C411yescharacteristic
169D101—22no—
170D101—22no—
171D101—22no—
172D101—42no—
173D101C2×#9914yescomplemented
174C22×#99—1011nomaximal, Sylow
175C101C22×#9911yescharacteristic, complemented, Sylow
176C23×D4—1011no—
177C22×C22⋊C4—1012no—
178C2×#99—1012no—
179C2×#99—1018no—
180C2×#99—1012no—
181C25—1011no—
182C25—1011no—
183C22×D4—1011no—
184C22×D4—1011no—
185C22×D4—1014no—
186C22×D4—1014no—
187C22×D4—1011no—
188C22×D4—2024no—
189C22×D4—2022no—
190C22×D4—2022no—
191C22×D4#8793811yescharacteristic, complemented
192C23×C4—1011no—
193C23×C4—2022no—
194C2×C22⋊C4—1014no—
195C2×C22⋊C4—1018no—
196C2×C22⋊C4—2024no—
197C2×C22⋊C4—2022no—
198#99—1018no—
199#99—1018no—
200C24—1012no—
201C24—1014no—
202C24—1012no—
203C24—1011no—
204C24—1012no—
205C24—1012no—
206C24—1011no—
207C24—1011no—
208C24—1014no—
209C24—4044no—
210C24—4044no—
211C24—2022no—
212C24—2021no—
213C24—2021no—
214C24C2×#8793811yescharacteristic
215C24C2×#8793811yescharacteristic, complemented
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—1014no—
219C2×D4—1012no—
220C2×D4—1012no—
221C2×D4—1012no—
222C2×D4—1012no—
223C2×D4—2022no—
224C2×D4—2022no—
225C2×D4—2028no—
226C2×D4—2028no—
227C2×D4—2028no—
228C2×D4—2028no—
229C2×D4—2022no—
230C2×D4—2022no—
231C2×D4—2022no—
232C2×D4—2022no—
233C2×D4C2×#8793814yescomplemented
234C22×C4—1011no—
235C22×C4—1014no—
236C22×C4—4048no—
237C22×C4—2022no—
238C22×C4—2021no—
239C22×C4—2021no—
240C22×C4—2028no—
241C22×C4—2024no—
242C22×C4C2×#8793811yescharacteristic, complemented
243C22⋊C4—1018no—
244C22⋊C4—2028no—
245C22⋊C4—2024no—
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—1011no—
251C23—1014no—
252C23—1012no—
253C23—1014no—
254C23—1011no—
255C23—1011no—
256C23—1014no—
257C23—1012no—
258C23—1014no—
259C23—1012no—
260C23—1011no—
261C23—1012no—
262C23—1012no—
263C23—4042no—
264C23—4042no—
265C23—4044no—
266C23—4044no—
267C23—4048no—
268C23—4044no—
269C23—4048no—
270C23—4048no—
271C23—4044no—
272C23—4044no—
273C23—2024no—
274C23—2024no—
275C23—2028no—
276C23—2024no—
277C23—2021no—
278C23—2021no—
279C23C22⋊#8793812yes—
280C23C22⋊#8793812yes—
281C23C22×#8793811yescharacteristic
282C23C22×#8793812yes—
283C23C22×#8793812yescomplemented
284D4—28no—
285D4—2024no—
286D4—2024no—
287D4—2024no—
288D4—2024no—
289D4—2028no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—1012no—
293C2×C4—40416no—
294C2×C4—4048no—
295C2×C4—2024no—
296C2×C4—2024no—
297C2×C4—2028no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4C22×#8793812yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—1014no—
310C22—1012no—
311C22—1012no—
312C22—1012no—
313C22—1012no—
314C22—4042no—
315C22—4042no—
316C22—4042no—
317C22—4041no—
318C22—4041no—
319C22—4044no—
320C22—4044no—
321C22—4048no—
322C22—4048no—
323C22—4042no—
324C22—2028no—
325C22—2024no—
326C22—2024no—
327C22—2028no—
328C22—2022no—
329C22—2024no—
330C22—2022no—
331C22C2×C22⋊#8793811yescharacteristic
332C22C2×C22⋊#8793814yes—
333C22C2×C22⋊#8793811yescharacteristic
334C22C23×#8793811yescharacteristic
335C4—22no—
336C4—4048no—
337C4—2022no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—1014no—
343C2—4042no—
344C2—2022no—
345C2—2022no—
346C2—2022no—
347C2D101⋊#9912yesdirect product factor
348C2C22×C22⋊#8793811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC22×C101C23×C4
FrattiniC22C23×#87938
FittingC22×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D4×D101C2
cosocleC22×D101C24
hypercenterC22×D4#87938
hypocenterC101C22×#99
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#87938C2semidirect
2. C2×#15692314C2semidirect
3. D101⋊#99C2direct (N × H)
4. C2×#15692313C2semidirect
9. C2×C22⋊#87938C22semidirect
10. C2×C22⋊#87938C22semidirect
11. #15692314C22semidirect
12. #15692313C22semidirect
13. C24×D101C4semidirect
16. C22×C22⋊D101C4semidirect
21. C2×D4×D101C4semidirect
23. C22×C4×D101C4semidirect
24. C22×D4×C101C4semidirect
30. C22⋊#87938C23semidirect
38. C23×D101C2×C4semidirect
39. C23×D101C2×C4semidirect
47. C2×D404C2×C4semidirect
53. C2×C22⋊D101C2×C4semidirect
54. C2×C22⋊D101C2×C4semidirect
60. C22×Dic101C2×C4semidirect
64. C2×C4×D101C2×C4semidirect
66. C24×C101C2×C4semidirect
69. C2×D4×C101C2×C4semidirect
70. C22×C4×C101C2×C4semidirect
79. C23×C101C22×C4semidirect
103. C22×D101C22×C4semidirect
115. C2×C4×C101C22×C4semidirect
121. C2×Dic101C22×C4semidirect
155. C2×D101#99semidirect
167. C2×C101C2×#99semidirect
173. D101C2×#99semidirect
175. C101C22×#99semidirect
191. C22×D4#87938semidirect
215. C24C2×#87938semidirect
233. C2×D4C2×#87938semidirect
242. C22×C4C2×#87938semidirect
283. C23C22×#87938semidirect
300. C2×C4C22×#87938semidirect
347. C2D101⋊#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⋊#879382
C2×#156923142
D101⋊#992
C2×#156923132
C22×D4×D1012
C22×#99101