Finite Group Databasebeta

← C2×#31770796 #46820274

Subgroups — C2×#31770796 #46820274

Order 34432.

794 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#22575498C211yesmaximal, characteristic
2C2×#22575437C212yesmaximal, complemented
3C2×#22575434C211yesmaximal, characteristic, complemented
4#31770796C218yesmaximal, direct product factor
5C2×#22575367C212yesmaximal, complemented
6C2×#99×C269C211yesmaximal, characteristic, complemented
7#22575498—24no—
8#22575498—22no—
9#22575498C2214yes—
10C2×#16864402—21no—
11C2×#16864401—22no—
12C22×C22⋊D269—21no—
13C22×C22⋊D269C2212yes—
14C2×D4×D269—22no—
15C23×Dic269C2211yescharacteristic, complemented
16#22575437—24no—
17#22575437C2218yescomplemented
18#22575434—22no—
19#22575434C2214yescomplemented
20C2×C4⋊Dic269—22no—
21C2×#16864381—21no—
22C2×C22⋊Dic269—21no—
23C2×C22⋊Dic269C2211yescharacteristic, complemented
24C2×#16864379—22no—
25#22575367C2218yescomplemented
26C22×D4×C269C2211yescharacteristic
27C2×C22⋊C4×C269C2212yescomplemented
28#99×C269C2214yescomplemented
29C23×D269—21no—
30C23×D269D412yes—
31#16864402—24no—
32#16864402—24no—
33#16864401—28no—
34#16864401—28no—
35C2×Dic538—21no—
36C2×D1076—21no—
37C2×C22⋊D269—22no—
38C2×C22⋊D269—24no—
39C2×C22⋊D269—22no—
40C2×C22⋊D269—22no—
41C2×C22⋊D269—24no—
42C2×C22⋊D269—22no—
43C2×C22⋊D269—22no—
44C2×C22⋊D269D414yes—
45C2×C22⋊D269C2314yes—
46D4×D269—28no—
47D4×D269—28no—
48C22×Dic269—21no—
49C22×Dic269—22no—
50C22×Dic269—21no—
51C22×Dic269—21no—
52C22×Dic269—21no—
53C22×Dic269—22no—
54C22×Dic269D412yes—
55C22×Dic269C2312yescomplemented
56C2×C4×D269—22no—
57C4⋊Dic269—28no—
58#16864381—24no—
59C22⋊Dic269—24no—
60C22⋊Dic269—21no—
61C22⋊Dic269C2312yescomplemented
62#16864379—28no—
63C24×C269D411yescharacteristic
64C24×C269C2311yescharacteristic
65C2×D4×C269—22no—
66C2×D4×C269—22no—
67C2×D4×C269D412yes—
68C2×D4×C269C2312yes—
69C22×C4×C269—22no—
70C22×C4×C269D411yescharacteristic
71C22⋊C4×C269—22no—
72C22⋊C4×C269C2314yescomplemented
73C22×D269—22no—
74C22×D269—24no—
75C22×D269—22no—
76C22×D269—44no—
77C22×D269—82no—
78C22×D269C2×D414yes—
79Dic538—24no—
80D1076—24no—
81C22⋊D269—28no—
82C22⋊D269—24no—
83C22⋊D269—24no—
84C22⋊D269—24no—
85C22⋊D269—24no—
86C2×Dic269—24no—
87C2×Dic269—22no—
88C2×Dic269—22no—
89C2×Dic269—24no—
90C2×Dic269—22no—
91C2×Dic269—22no—
92C2×Dic269—42no—
93C2×Dic269—41no—
94C2×Dic269—42no—
95C2×Dic269—41no—
96C2×Dic269C2×D414yes—
97C4×D269—28no—
98C23×C269—21no—
99C23×C269—21no—
100C23×C269—42no—
101C23×C269—42no—
102C23×C269C2×D412yes—
103C23×C269C2×D412yes—
104C23×C269C2×D411yescharacteristic
105C23×C269C2×D412yes—
106C23×C269C2×D411yescharacteristic
107C23×C269C2411yescharacteristic
108D4×C269—24no—
109D4×C269—24no—
110C2×C4×C269—21no—
111C2×C4×C269—21no—
112C2×C4×C269—24no—
113C2×C4×C269—44no—
114C2×C4×C269C2×D412yes—
115C22×C269—24no—
116C22×C269—22no—
117C22×C269—22no—
118C22×C269—42no—
119C22×C269—41no—
120C22×C269—41no—
121C22×C269—42no—
122C22×C269—42no—
123C22×C269—81no—
124C22×C269#12011yescharacteristic
125C22×C269#12012yes—
126C22×C269#12011yescharacteristic
127C22×C269C22×D412yes—
128C22×C269C22×D411yescharacteristic
129C2×D269—24no—
130C2×D269—44no—
131C2×D269—44no—
132C2×D269—82no—
133C2×D269—84no—
134C4×C269—22no—
135C4×C269—44no—
136Dic269—24no—
137Dic269—42no—
138Dic269—42no—
139C2×C269—21no—
140C2×C269—22no—
141C2×C269—22no—
142C2×C269—21no—
143C2×C269—42no—
144C2×C269#45812yescomplemented
145C2×C269C2×#12011yescharacteristic
146D269—44no—
147C269C2×#45811yescharacteristic, complemented, Sylow
148C2×#458—2691nomaximal, Sylow
149C2×H(5,𝔽2)—2691no—
150C2×#123—2691no—
151C2×#123—2692no—
152#458—2698no—
153C2×#99—2692no—
154C2×#99D26911yescharacteristic, complemented
155H(5,𝔽2)—2694no—
156H(5,𝔽2)—5384no—
157H(5,𝔽2)—5382no—
158C2×#41—5382no—
159C2×#41—5381no—
160C22×D4—2692no—
161C22×D4—5382no—
162C22×D4—5381no—
163C22×D4C2×D26911yescharacteristic
164C23×C4—2691no—
165#123—2694no—
166#123—2698no—
167#123—5384no—
168#123—5382no—
169C2×C4⋊C4—5382no—
170C2×C4⋊C4—5381no—
171C2×C22⋊C4—2691no—
172C2×C22⋊C4—5382no—
173C2×C22⋊C4—5381no—
174C2×C22⋊C4C2×D26912yescomplemented
175#99—2698no—
176#99C2×D26914yescomplemented
177C24—2692no—
178C24—5381no—
179C24D107611yescharacteristic
180C24C22×D26911yescharacteristic
181#41—5384no—
182#41—5388no—
183#41—5388no—
184#41—5384no—
185C2×Q8—5381no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—2694no—
189C2×D4—2694no—
190C2×D4—5381no—
191C2×D4—5388no—
192C2×D4—5388no—
193C2×D4—5382no—
194C2×D4—5384no—
195C2×D4—5382no—
196C2×D4—5382no—
197C2×D4—5382no—
198C2×D4—5382no—
199C2×D4—5384no—
200C2×D4D107612yes—
201C2×D4C22×D26912yes—
202C22×C4—22no—
203C22×C4—2692no—
204C22×C4—2692no—
205C22×C4—5382no—
206C22×C4—5381no—
207C22×C4—5382no—
208C22×C4—5382no—
209C22×C4—5381no—
210C22×C4—5381no—
211C22×C4—5381no—
212C22×C4D107611yescharacteristic
213C4⋊C4—5388no—
214C4⋊C4—5384no—
215C22⋊C4—22no—
216C22⋊C4—2692no—
217C22⋊C4—5388no—
218C22⋊C4—5381no—
219C22⋊C4—5384no—
220C22⋊C4C22×D26914yescomplemented
221C23—21no—
222C23—21no—
223C23—42no—
224C23—42no—
225C23—2694no—
226C23—5384no—
227C23—5382no—
228C23—5382no—
229C23—10764no—
230C23—21522no—
231C23D4×D26912yes—
232C23D4×D26912yes—
233C23C2×D107611yescharacteristic
234C23C2×D107612yes—
235C23C2×D107611yescharacteristic
236C23C23×D26911yescharacteristic
237Q8—5384no—
238D4—24no—
239D4—24no—
240D4—5384no—
241D4—5388no—
242D4—5384no—
243D4—5384no—
244D4—5384no—
245D4—5384no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—24no—
249C2×C4—44no—
250C2×C4—2694no—
251C2×C4—5388no—
252C2×C4—5384no—
253C2×C4—5382no—
254C2×C4—5382no—
255C2×C4—5384no—
256C2×C4—5382no—
257C2×C4—5382no—
258C2×C4—10762no—
259C2×C4—10761no—
260C2×C4—10762no—
261C2×C4—10761no—
262C2×C4C2×D107612yes—
263C22—24no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—42no—
270C22—42no—
271C22—81no—
272C22—5384no—
273C22—10764no—
274C22—10764no—
275C22—21522no—
276C22—21524no—
277C22#2257542311yescharacteristic
278C22#2257542312yes—
279C22#2257542311yescharacteristic
280C22C2×D4×D26912yes—
281C22C22×D107611yescharacteristic
282C4—22no—
283C4—44no—
284C4—5384no—
285C4—10762no—
286C4—10762no—
287C2—22no—
288C2—21no—
289C2—21no—
290C2—22no—
291C2—42no—
292C2—10764no—
293C2#3177079612yesdirect product factor
294C2C2×#2257542311yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC23×C269C24
FrattiniC23C23×D269
FittingC2×#99×C269C2
socleC22×C269#120
prime radicalC2×#22575498C2
hypercenterC2×#99D269
hypocenterC269C2×#458
LCSG ▷ C23×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#22575437C2semidirect
3. C2×#22575434C2semidirect
4. #31770796C2direct (N × H)
5. C2×#22575367C2semidirect
6. C2×#99×C269C2semidirect
15. C23×Dic269C22semidirect
17. #22575437C22semidirect
19. #22575434C22semidirect
23. C2×C22⋊Dic269C22semidirect
25. #22575367C22semidirect
27. C2×C22⋊C4×C269C22semidirect
28. #99×C269C22semidirect
55. C22×Dic269C23semidirect
61. C22⋊Dic269C23semidirect
72. C22⋊C4×C269C23semidirect
144. C2×C269#458semidirect
147. C269C2×#458semidirect
154. C2×#99D269semidirect
174. C2×C22⋊C4C2×D269semidirect
176. #99C2×D269semidirect
220. C22⋊C4C22×D269semidirect
293. C2#31770796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225754982
C2×#225754372
C2×#225754342
#317707962
C2×#225753672
C2×#99×C2692
C2×#458269