Finite Group Databasebeta

← C2×#20295171 #28372233

Subgroups — C2×#20295171 #28372233

Order 13952.

812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13182016C211yesmaximal, characteristic, complemented
2C22×#13182014C211yesmaximal, characteristic, complemented
3C2×#16812673C211yesmaximal, characteristic, complemented
4#20295171C218yesmaximal, direct product factor
5C2×#16812623C211yesmaximal, characteristic, complemented
6C2×#16812620C211yesmaximal, characteristic, complemented
7C2×C22⋊#11724784C211yesmaximal, characteristic, complemented
8C22×#41×C109C211yesmaximal, characteristic, complemented
9C22×D436C2211yescharacteristic
10C22×C22⋊D109—21no—
11C2×#13182016—24no—
12C2×#13182016C2214yescomplemented
13C2×#13182014—24no—
14C2×#13182014C2214yescomplemented
15C22×#11724784C2211yescharacteristic
16C22×#11724784C2211yescharacteristic
17#16812673—22no—
18#16812673C2214yescomplemented
19C2×C4⋊Dic109C2211yescharacteristic
20C2×#13182006—21no—
21#16812623C2214yescomplemented
22#16812620C2214yescomplemented
23C22⋊#11724784C2214yescomplemented
24C2×#41×C109—24no—
25C2×#41×C109—24no—
26C2×#41×C109—22no—
27C2×#41×C109C2214yescomplemented
28C22×Q8×C109C2211yescharacteristic
29C22×D4×C109—21no—
30C22×D4×C109C2211yescharacteristic
31C23×C4×C109—21no—
32C23×C4×C109C2211yescharacteristic
33C23×D109—21no—
34C2×D436—22no—
35C2×D436—22no—
36C2×D436—21no—
37C2×D436C2312yes—
38C2×C22⋊D109—24no—
39C2×C22⋊D109—44no—
40C22×Dic109—21no—
41#13182016—28no—
42#13182014—28no—
43C2×#11724784—22no—
44C2×#11724784—22no—
45C2×#11724784C2312yes—
46C2×#11724784C2312yes—
47C4⋊Dic109—21no—
48C4⋊Dic109C2312yes—
49#13182006—24no—
50C24×C109—21no—
51C24×C109D411yescharacteristic
52#41×C109—216no—
53#41×C109—28no—
54#41×C109—28no—
55C2×Q8×C109—22no—
56C2×Q8×C109—21no—
57C2×Q8×C109D414yescomplemented
58C2×Q8×C109C2312yes—
59C2×D4×C109—28no—
60C2×D4×C109—24no—
61C2×D4×C109—21no—
62C2×D4×C109—22no—
63C2×D4×C109D414yescomplemented
64C2×D4×C109C2312yes—
65C22×C4×C109—28no—
66C22×C4×C109—21no—
67C22×C4×C109—24no—
68C22×C4×C109—22no—
69C22×C4×C109—22no—
70C22×C4×C109D411yescharacteristic
71C22×C4×C109D412yes—
72C22×C4×C109C2312yes—
73C22×C4×C109C2311yescharacteristic
74C23×C109—22no—
75C23×C109—24no—
76C23×C109—22no—
77C23×C109—22no—
78C23×C109—22no—
79C23×C109—42no—
80C23×C109—42no—
81C23×C109C2×D412yes—
82C23×C109C2×D411yescharacteristic
83C22×D109—22no—
84C22×D109—42no—
85C22×D109—42no—
86C22×D109—42no—
87Q8×C109—24no—
88Q8×C109—22no—
89Q8×C109C2×D414yescomplemented
90D4×C109—216no—
91D4×C109—24no—
92D4×C109—22no—
93D4×C109C2×D414yescomplemented
94C2×C4×C109—216no—
95C2×C4×C109—22no—
96C2×C4×C109—24no—
97C2×C4×C109—22no—
98C2×C4×C109—24no—
99C2×C4×C109—22no—
100C2×C4×C109—22no—
101C2×C4×C109C2×D412yes—
102C2×C4×C109C2×D411yescharacteristic
103C2×C4×C109C2×D412yes—
104C2×C4×C109C2×D412yes—
105C2×C4×C109C2411yescharacteristic
106C22⋊D109—48no—
107C2×Dic109—22no—
108C2×Dic109—42no—
109D436—22no—
110D436—22no—
111D436—42no—
112#11724784—22no—
113#11724784—22no—
114C22×C109—22no—
115C22×C109—24no—
116C22×C109—22no—
117C22×C109—22no—
118C22×C109—42no—
119C22×C109—42no—
120C22×C109—44no—
121C22×C109—48no—
122C22×C109#12012yes—
123C22×C109#13512yes—
124C22×C109AGL(1,ℤ/8)12yes—
125C22×C109C22×D411yescharacteristic
126C2×D109—42no—
127C2×D109—42no—
128C2×D109—42no—
129C2×D109—84no—
130C4×C109—22no—
131C4×C109—24no—
132C4×C109#12012yes—
133C4×C109C22×D411yescharacteristic
134C4×C109C22×D411yescharacteristic
135Dic109—42no—
136C2×C109—42no—
137C2×C109—44no—
138C2×C109#44914yescomplemented
139C2×C109C2×#12011yescharacteristic
140C2×C109C2×#13511yescharacteristic
141C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
142D109—82no—
143C2×#449—1091nomaximal, Sylow
144C109C2×#44911yescharacteristic, complemented, Sylow
145C22×#41D10911yescharacteristic, complemented
146C22×SD16—1091no—
147C22×D8—1091no—
148C2×#121—1091no—
149#449—1098no—
150C2×#103—1091no—
151C2×#102—1091no—
152C2×C22⋊C8—1091no—
153C2×#41—24no—
154C2×#41—24no—
155C2×#41—22no—
156C2×#41C2×D10914yescomplemented
157C22×Q8C2×D10911yescharacteristic
158C22×D4—21no—
159C22×D4—1091no—
160C22×D4—2181no—
161C22×D4C2×D10911yescharacteristic
162C23×C4—21no—
163C23×C4C2×D10911yescharacteristic
164C2×SD16—1094no—
165C2×SD16—2184no—
166C2×D8—1094no—
167C2×D8—2184no—
168C22×C8—1091no—
169C22×C8—1091no—
170#121—1094no—
171#121—2182no—
172C2×C4⋊C4—1091no—
173C2×C22⋊C4—2181no—
174#103—1094no—
175#102—1094no—
176C22⋊C8—1094no—
177C24—21no—
178C24—2181no—
179C24C22⋊D10911yescharacteristic
180#41—216no—
181#41—28no—
182#41—28no—
183C2×Q8—22no—
184C2×Q8—21no—
185C2×Q8C22⋊D10914yescomplemented
186C2×Q8C22×D10912yes—
187C2×D4—28no—
188C2×D4—24no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—1092no—
192C2×D4—4364no—
193C2×D4—2184no—
194C2×D4—2181no—
195C2×D4—2182no—
196C2×D4—2182no—
197C2×D4C22⋊D10914yescomplemented
198C2×D4C22×D10912yes—
199C22×C4—28no—
200C22×C4—21no—
201C22×C4—24no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—2181no—
205C22×C4C22⋊D10912yes—
206C22×C4C22⋊D10911yescharacteristic
207C22×C4C22×D10912yes—
208C22×C4C22×D10911yescharacteristic
209SD16—2188no—
210D8—2188no—
211C2×C8—1092no—
212C2×C8—1092no—
213C2×C8—2182no—
214C2×C8—2182no—
215C4⋊C4—1092no—
216C4⋊C4—2181no—
217C22⋊C4—2184no—
218C23—22no—
219C23—24no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—4362no—
226C23—4362no—
227C23—4362no—
228C23—2182no—
229C23C2×C22⋊D10912yes—
230C23C2×C22⋊D10911yescharacteristic
231Q8—24no—
232Q8—22no—
233Q8C2×C22⋊D10914yescomplemented
234D4—216no—
235D4—24no—
236D4—22no—
237D4—4368no—
238D4—4362no—
239D4—2182no—
240D4—2182no—
241D4C2×C22⋊D10914yescomplemented
242C2×C4—216no—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—4362no—
250C2×C4—2182no—
251C2×C4C2×C22⋊D10912yes—
252C2×C4C2×C22⋊D10911yescharacteristic
253C2×C4C2×C22⋊D10912yes—
254C2×C4C2×C22⋊D10912yes—
255C2×C4C23×D10911yescharacteristic
256C8—2182no—
257C8—2182no—
258C22—22no—
259C22—24no—
260C22—22no—
261C22—22no—
262C22—44no—
263C22—48no—
264C22—42no—
265C22—42no—
266C22—8724no—
267C22—4362no—
268C22—4362no—
269C22—4362no—
270C22#1681266812yes—
271C22#1681271912yes—
272C22#1681272412yes—
273C22C22×C22⋊D10911yescharacteristic
274C4—22no—
275C4—24no—
276C4—4362no—
277C4#1681266812yes—
278C4C22×C22⋊D10911yescharacteristic
279C4C22×C22⋊D10911yescharacteristic
280C2—42no—
281C2—44no—
282C2—8722no—
283C2#2029517114yesdirect product factor
284C2C2×#1681266811yescharacteristic
285C2C2×#1681271911yescharacteristic
286C2C2×#1681272411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC22×#41×C109C2
socleC23×C109C2×D4
hypercenterC22×#41D109
hypocenterC109C2×#449
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#13182016C2semidirect
2. C22×#13182014C2semidirect
3. C2×#16812673C2semidirect
4. #20295171C2direct (N × H)
5. C2×#16812623C2semidirect
6. C2×#16812620C2semidirect
7. C2×C22⋊#11724784C2semidirect
8. C22×#41×C109C2semidirect
12. C2×#13182016C22semidirect
14. C2×#13182014C22semidirect
18. #16812673C22semidirect
21. #16812623C22semidirect
22. #16812620C22semidirect
23. C22⋊#11724784C22semidirect
27. C2×#41×C109C22semidirect
57. C2×Q8×C109D4semidirect
63. C2×D4×C109D4semidirect
89. Q8×C109C2×D4semidirect
93. D4×C109C2×D4semidirect
138. C2×C109#449semidirect
144. C109C2×#449semidirect
145. C22×#41D109semidirect
156. C2×#41C2×D109semidirect
185. C2×Q8C22⋊D109semidirect
197. C2×D4C22⋊D109semidirect
233. Q8C2×C22⋊D109semidirect
241. D4C2×C22⋊D109semidirect
283. C2#20295171direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131820162
C22×#131820142
C2×#168126732
#202951712
C2×#168126232
C2×#168126202
C2×C22⋊#117247842
C22×#41×C1092
C2×#449109