Finite Group Databasebeta

← C2×D109⋊#99 #28379625

Subgroups — C2×D109⋊#99 #28379625

Order 13952.

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⋊#89137C212yesmaximal, complemented
2C2×#16812758C212yesmaximal, complemented
3D109⋊#99C218yesmaximal, direct product factor
4C2×#16812757C212yesmaximal, complemented
5C22×D4×D109C211yesmaximal, characteristic
6C23×#89137—22no—
7C2×C22⋊#89137—24no—
8C2×C22⋊#89137—22no—
9C2×C22⋊#89137C2214yescomplemented
10C2×C22⋊#89137C2218yescomplemented
11#16812758C2218yescomplemented
12#16812757C2218yescomplemented
13C24×D109C411yescharacteristic, complemented
14C24×D109C2211yescharacteristic
15C22×D436C2211yescharacteristic
16C22×C22⋊D109C411yescharacteristic, complemented
17C22×C22⋊D109C2211yescharacteristic
18C2×D4×D109—22no—
19C2×D4×D109—22no—
20C2×D4×D109—24no—
21C2×D4×D109C414yescomplemented
22C2×D4×D109C2214yes—
23C22×C4×D109C411yescharacteristic, complemented
24C22×D4×C109C411yescharacteristic, complemented
25C22×#89137—28no—
26C22×#89137—24no—
27C22×#89137—48no—
28C22⋊#89137—28no—
29C22⋊#89137—24no—
30C22⋊#89137C2318yescomplemented
31C23×D109—22no—
32C23×D109—21no—
33C23×D109—21no—
34C23×D109—44no—
35C23×D109—44no—
36C23×D109C2×C411yescharacteristic
37C23×D109C2×C412yes—
38C23×D109C2×C414yescomplemented
39C23×D109C2×C411yescharacteristic, complemented
40C23×D109D412yes—
41C23×D109D414yes—
42C23×D109D412yes—
43C23×D109C2312yes—
44C23×D109C2311yescharacteristic
45C2×D436—22no—
46C2×D436—22no—
47C2×D436C2×C412yescomplemented
48C2×D436C2312yes—
49C2×C22⋊D109—22no—
50C2×C22⋊D109—22no—
51C2×C22⋊D109—22no—
52C2×C22⋊D109—22no—
53C2×C22⋊D109C2×C412yescomplemented
54C2×C22⋊D109C2×C414yescomplemented
55C2×C22⋊D109C2312yes—
56D4×D109—28no—
57D4×D109—28no—
58D4×D109—28no—
59D4×D109—28no—
60C22×Dic109C2×C411yescharacteristic, complemented
61C2×C4×D109—22no—
62C2×C4×D109—21no—
63C2×C4×D109—21no—
64C2×C4×D109C2×C414yescomplemented
65C24×C109C2×C411yescharacteristic
66C24×C109C2×C411yescharacteristic, complemented
67C2×D4×C109—22no—
68C2×D4×C109—22no—
69C2×D4×C109C2×C414yescomplemented
70C22×C4×C109C2×C411yescharacteristic, complemented
71C23×C109—21no—
72C23×C109—21no—
73C23×C109—42no—
74C23×C109—42no—
75C23×C109C22⋊C412yes—
76C23×C109C22⋊C412yes—
77C23×C109C22×C411yescharacteristic
78C23×C109C22×C412yes—
79C23×C109C22×C412yescomplemented
80C22×D109—24no—
81C22×D109—28no—
82C22×D109—21no—
83C22×D109—21no—
84C22×D109—24no—
85C22×D109—24no—
86C22×D109—44no—
87C22×D109—48no—
88C22×D109—44no—
89C22×D109—44no—
90C22×D109—42no—
91C22×D109—44no—
92C22×D109—48no—
93C22×D109—48no—
94C22×D109—44no—
95C22×D109—42no—
96C22×D109C22⋊C412yes—
97C22×D109C22⋊C411yescharacteristic
98C22×D109C22⋊C414yes—
99C22×D109C22⋊C414yes—
100C22×D109C22⋊C411yescharacteristic
101C22×D109C22×C412yes—
102C22×D109C22×C411yescharacteristic
103C22×D109C22×C412yescomplemented
104C22×D109C2×D414yes—
105C22×D109C2×D412yes—
106C22×D109C2×D414yes—
107C22×D109C2×D412yes—
108C22×D109C2411yescharacteristic
109C2×#89137—28no—
110C2×#89137—48no—
111C2×#89137—416no—
112D4×C109—28no—
113C2×C4×C109—21no—
114C2×C4×C109—21no—
115C2×C4×C109C22×C412yescomplemented
116C22⋊D109—28no—
117C22⋊D109—24no—
118C22⋊D109—24no—
119C2×Dic109—21no—
120C2×Dic109—21no—
121C2×Dic109C22×C412yescomplemented
122D436—24no—
123D436—24no—
124C4×D109—24no—
125C4×D109—24no—
126C22×C109—22no—
127C22×C109—24no—
128C22×C109—22no—
129C22×C109—42no—
130C22×C109—42no—
131C22×C109—42no—
132C22×C109—42no—
133C22×C109—42no—
134C22×C109C2×C22⋊C411yescharacteristic
135C22×C109C2×C22⋊C414yes—
136C22×C109C2×C22⋊C411yescharacteristic
137C22×C109C23×C411yescharacteristic
138C2×D109—24no—
139C2×D109—22no—
140C2×D109—28no—
141C2×D109—24no—
142C2×D109—24no—
143C2×D109—28no—
144C2×D109—22no—
145C2×D109—44no—
146C2×D109—41no—
147C2×D109—44no—
148C2×D109—42no—
149C2×D109—41no—
150C2×D109—48no—
151C2×D109—42no—
152C2×D109—42no—
153C2×D109—48no—
154C2×D109—42no—
155C2×D109#9914yescomplemented
156C2×D109C2×C22⋊C412yes—
157C2×D109C2×C22⋊C412yes—
158C2×D109C2×C22⋊C412yes—
159C2×D109C22×D412yes—
160#89137—48no—
161C4×C109—22no—
162Dic109—22no—
163C2×C109—21no—
164C2×C109—21no—
165C2×C109—24no—
166C2×C109—42no—
167C2×C109C2×#9912yescomplemented
168C2×C109C22×C22⋊C411yescharacteristic
169D109—22no—
170D109—22no—
171D109—22no—
172D109—42no—
173D109C2×#9914yescomplemented
174C22×#99—1091nomaximal, Sylow
175C109C22×#9911yescharacteristic, complemented, Sylow
176C23×D4—1091no—
177C22×C22⋊C4—1092no—
178C2×#99—1092no—
179C2×#99—1098no—
180C2×#99—1092no—
181C25—1091no—
182C25—1091no—
183C22×D4—1091no—
184C22×D4—1091no—
185C22×D4—1094no—
186C22×D4—1094no—
187C22×D4—1091no—
188C22×D4—2184no—
189C22×D4—2182no—
190C22×D4—2182no—
191C22×D4#8913711yescharacteristic, complemented
192C23×C4—1091no—
193C23×C4—2182no—
194C2×C22⋊C4—1094no—
195C2×C22⋊C4—1098no—
196C2×C22⋊C4—2184no—
197C2×C22⋊C4—2182no—
198#99—1098no—
199#99—1098no—
200C24—1092no—
201C24—1094no—
202C24—1092no—
203C24—1091no—
204C24—1092no—
205C24—1092no—
206C24—1091no—
207C24—1091no—
208C24—1094no—
209C24—4364no—
210C24—4364no—
211C24—2182no—
212C24—2181no—
213C24—2181no—
214C24C2×#8913711yescharacteristic
215C24C2×#8913711yescharacteristic, complemented
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—1094no—
219C2×D4—1092no—
220C2×D4—1092no—
221C2×D4—1092no—
222C2×D4—1092no—
223C2×D4—2182no—
224C2×D4—2182no—
225C2×D4—2188no—
226C2×D4—2188no—
227C2×D4—2188no—
228C2×D4—2188no—
229C2×D4—2182no—
230C2×D4—2182no—
231C2×D4—2182no—
232C2×D4—2182no—
233C2×D4C2×#8913714yescomplemented
234C22×C4—1091no—
235C22×C4—1094no—
236C22×C4—4368no—
237C22×C4—2182no—
238C22×C4—2181no—
239C22×C4—2181no—
240C22×C4—2188no—
241C22×C4—2184no—
242C22×C4C2×#8913711yescharacteristic, complemented
243C22⋊C4—1098no—
244C22⋊C4—2188no—
245C22⋊C4—2184no—
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—1091no—
251C23—1094no—
252C23—1092no—
253C23—1094no—
254C23—1091no—
255C23—1091no—
256C23—1094no—
257C23—1092no—
258C23—1094no—
259C23—1092no—
260C23—1091no—
261C23—1092no—
262C23—1092no—
263C23—4362no—
264C23—4362no—
265C23—4364no—
266C23—4364no—
267C23—4368no—
268C23—4364no—
269C23—4368no—
270C23—4368no—
271C23—4364no—
272C23—4364no—
273C23—2184no—
274C23—2184no—
275C23—2188no—
276C23—2184no—
277C23—2181no—
278C23—2181no—
279C23C22⋊#8913712yes—
280C23C22⋊#8913712yes—
281C23C22×#8913711yescharacteristic
282C23C22×#8913712yes—
283C23C22×#8913712yescomplemented
284D4—28no—
285D4—2184no—
286D4—2184no—
287D4—2184no—
288D4—2184no—
289D4—2188no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—1092no—
293C2×C4—43616no—
294C2×C4—4368no—
295C2×C4—2184no—
296C2×C4—2184no—
297C2×C4—2188no—
298C2×C4—2181no—
299C2×C4—2181no—
300C2×C4C22×#8913712yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—1094no—
310C22—1092no—
311C22—1092no—
312C22—1092no—
313C22—1092no—
314C22—4362no—
315C22—4362no—
316C22—4362no—
317C22—4361no—
318C22—4361no—
319C22—4364no—
320C22—4364no—
321C22—4368no—
322C22—4368no—
323C22—4362no—
324C22—2188no—
325C22—2184no—
326C22—2184no—
327C22—2188no—
328C22—2182no—
329C22—2184no—
330C22—2182no—
331C22C2×C22⋊#8913711yescharacteristic
332C22C2×C22⋊#8913714yes—
333C22C2×C22⋊#8913711yescharacteristic
334C22C23×#8913711yescharacteristic
335C4—22no—
336C4—4368no—
337C4—2182no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—1094no—
343C2—4362no—
344C2—2182no—
345C2—2182no—
346C2—2182no—
347C2D109⋊#9912yesdirect product factor
348C2C22×C22⋊#8913711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC22×C109C23×C4
FrattiniC22C23×#89137
FittingC22×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D4×D109C2
cosocleC22×D109C24
hypercenterC22×D4#89137
hypocenterC109C22×#99
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#89137C2semidirect
2. C2×#16812758C2semidirect
3. D109⋊#99C2direct (N × H)
4. C2×#16812757C2semidirect
9. C2×C22⋊#89137C22semidirect
10. C2×C22⋊#89137C22semidirect
11. #16812758C22semidirect
12. #16812757C22semidirect
13. C24×D109C4semidirect
16. C22×C22⋊D109C4semidirect
21. C2×D4×D109C4semidirect
23. C22×C4×D109C4semidirect
24. C22×D4×C109C4semidirect
30. C22⋊#89137C23semidirect
38. C23×D109C2×C4semidirect
39. C23×D109C2×C4semidirect
47. C2×D436C2×C4semidirect
53. C2×C22⋊D109C2×C4semidirect
54. C2×C22⋊D109C2×C4semidirect
60. C22×Dic109C2×C4semidirect
64. C2×C4×D109C2×C4semidirect
66. C24×C109C2×C4semidirect
69. C2×D4×C109C2×C4semidirect
70. C22×C4×C109C2×C4semidirect
79. C23×C109C22×C4semidirect
103. C22×D109C22×C4semidirect
115. C2×C4×C109C22×C4semidirect
121. C2×Dic109C22×C4semidirect
155. C2×D109#99semidirect
167. C2×C109C2×#99semidirect
173. D109C2×#99semidirect
175. C109C22×#99semidirect
191. C22×D4#89137semidirect
215. C24C2×#89137semidirect
233. C2×D4C2×#89137semidirect
242. C22×C4C2×#89137semidirect
283. C23C22×#89137semidirect
300. C2×C4C22×#89137semidirect
347. C2D109⋊#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⋊#891372
C2×#168127582
D109⋊#992
C2×#168127572
C22×D4×D1092
C22×#99109