Finite Group Databasebeta

← C2×#31770793 #46820270

Subgroups — C2×#31770793 #46820270

Order 34432.

1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1018 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, complemented
2C2×#22575423C212yesmaximal, complemented
3C2×#22575421C211yesmaximal, characteristic, complemented
4#31770793C218yesmaximal, direct product factor
5C2×#22575367C212yesmaximal, complemented
6C2×#99×C269C211yesmaximal, characteristic, complemented
7C24×D269C2211yescharacteristic, complemented
8#22575498—24no—
9#22575498—22no—
10#22575498C2214yescomplemented
11C2×#16864402—21no—
12C2×#16864401—22no—
13C22×D1076—22no—
14C22×C22⋊D269—21no—
15C22×C22⋊D269—21no—
16C22×C22⋊D269C2212yes—
17C2×D4×D269—22no—
18#22575423—24no—
19#22575423C2218yescomplemented
20#22575421—22no—
21#22575421C2214yescomplemented
22C2×C22⋊Dic269C2211yescharacteristic, complemented
23C2×#16864379—22no—
24C2×#16864379—21no—
25#22575367C2218yescomplemented
26C22×D4×C269C2211yescharacteristic
27C2×C22⋊C4×C269C2212yescomplemented
28#99×C269C2214yescomplemented
29C23×D269—21no—
30C23×D269—21no—
31C23×D269—22no—
32C23×D269—21no—
33C23×D269—22no—
34C23×D269—44no—
35C23×D269D412yescomplemented
36C23×D269C2312yescomplemented
37#16864402—24no—
38#16864402—24no—
39#16864401—28no—
40#16864401—28no—
41C2×Dic538—21no—
42C2×D1076—21no—
43C2×D1076—28no—
44C2×D1076—48no—
45C2×C22⋊D269—22no—
46C2×C22⋊D269—24no—
47C2×C22⋊D269—22no—
48C2×C22⋊D269—22no—
49C2×C22⋊D269—22no—
50C2×C22⋊D269—22no—
51C2×C22⋊D269—24no—
52C2×C22⋊D269—24no—
53C2×C22⋊D269—44no—
54C2×C22⋊D269D414yescomplemented
55C2×C22⋊D269C2314yes—
56D4×D269—28no—
57D4×D269—28no—
58C22×Dic269—21no—
59C22×Dic269—21no—
60C22×Dic269D412yescomplemented
61C2×C4×D269—22no—
62C22⋊Dic269—21no—
63C22⋊Dic269C2312yescomplemented
64#16864379—28no—
65#16864379—24no—
66C24×C269D411yescharacteristic, complemented
67C24×C269C2311yescharacteristic
68C2×D4×C269—22no—
69C2×D4×C269—22no—
70C2×D4×C269D412yescomplemented
71C2×D4×C269C2312yes—
72C22×C4×C269—22no—
73C22×C4×C269D411yescharacteristic, complemented
74C22⋊C4×C269—22no—
75C22⋊C4×C269C2314yescomplemented
76C22×D269—24no—
77C22×D269—28no—
78C22×D269—22no—
79C22×D269—22no—
80C22×D269—24no—
81C22×D269—24no—
82C22×D269—22no—
83C22×D269—44no—
84C22×D269—44no—
85C22×D269—48no—
86C22×D269—44no—
87C22×D269—42no—
88C22×D269—41no—
89C22×D269—42no—
90C22×D269—41no—
91C22×D269—44no—
92C22×D269—82no—
93C22×D269C2×D414yescomplemented
94Dic538—24no—
95D1076—24no—
96D1076—416no—
97C22⋊D269—28no—
98C22⋊D269—24no—
99C22⋊D269—24no—
100C22⋊D269—24no—
101C22⋊D269—24no—
102C22⋊D269—48no—
103C2×Dic269—24no—
104C2×Dic269—22no—
105C2×Dic269—22no—
106C2×Dic269—22no—
107C2×Dic269—42no—
108C2×Dic269C2×D414yescomplemented
109C4×D269—28no—
110C23×C269—21no—
111C23×C269—21no—
112C23×C269—42no—
113C23×C269—42no—
114C23×C269C2×D412yes—
115C23×C269C2×D412yes—
116C23×C269C2×D411yescharacteristic
117C23×C269C2×D411yescharacteristic
118C23×C269C2×D412yescomplemented
119C23×C269C2411yescharacteristic
120D4×C269—24no—
121D4×C269—24no—
122C2×C4×C269—21no—
123C2×C4×C269—21no—
124C2×C4×C269—24no—
125C2×C4×C269—44no—
126C2×C4×C269C2×D412yescomplemented
127C22×C269—24no—
128C22×C269—22no—
129C22×C269—22no—
130C22×C269—42no—
131C22×C269—41no—
132C22×C269—41no—
133C22×C269—42no—
134C22×C269—42no—
135C22×C269—81no—
136C22×C269#12011yescharacteristic
137C22×C269#12012yes—
138C22×C269#12011yescharacteristic
139C22×C269C22×D412yes—
140C22×C269C22×D411yescharacteristic
141C2×D269—24no—
142C2×D269—28no—
143C2×D269—24no—
144C2×D269—42no—
145C2×D269—44no—
146C2×D269—48no—
147C2×D269—44no—
148C2×D269—42no—
149C2×D269—44no—
150C2×D269—44no—
151C2×D269—44no—
152C2×D269—82no—
153C2×D269—84no—
154C4×C269—22no—
155C4×C269—44no—
156Dic269—24no—
157Dic269—42no—
158C2×C269—21no—
159C2×C269—22no—
160C2×C269—22no—
161C2×C269—21no—
162C2×C269—42no—
163C2×C269B(4,𝔽2)12yescomplemented
164C2×C269C2×#12011yescharacteristic
165D269—44no—
166D269—44no—
167C269C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
168C2×B(4,𝔽2)—2691nomaximal, Sylow
169C2×H(5,𝔽2)—2691no—
170C2×#120—2691no—
171C2×#120—2692no—
172B(4,𝔽2)—2698no—
173C2×#99—2692no—
174C2×#99D26911yescharacteristic, complemented
175C25—2691no—
176H(5,𝔽2)—2694no—
177H(5,𝔽2)—5384no—
178H(5,𝔽2)—5382no—
179C2×#41—5382no—
180C2×#41—5381no—
181C22×D4—2692no—
182C22×D4—5382no—
183C22×D4—5382no—
184C22×D4—5381no—
185C22×D4—5381no—
186C22×D4C2×D26911yescharacteristic
187#120—2694no—
188#120—2698no—
189#120—5384no—
190#120—5382no—
191C2×C22⋊C4—2691no—
192C2×C22⋊C4—5382no—
193C2×C22⋊C4—5381no—
194C2×C22⋊C4C2×D26912yescomplemented
195#99—2698no—
196#99C2×D26914yescomplemented
197C24—2692no—
198C24—2692no—
199C24—5381no—
200C24—5382no—
201C24—5381no—
202C24—5382no—
203C24—5381no—
204C24—10764no—
205C24D107611yescharacteristic, complemented
206C24C22×D26911yescharacteristic
207#41—5384no—
208#41—5388no—
209#41—5388no—
210#41—5384no—
211C2×Q8—5381no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—2694no—
215C2×D4—2694no—
216C2×D4—5381no—
217C2×D4—5388no—
218C2×D4—5388no—
219C2×D4—5388no—
220C2×D4—5382no—
221C2×D4—5384no—
222C2×D4—5382no—
223C2×D4—5382no—
224C2×D4—5382no—
225C2×D4—5382no—
226C2×D4—5384no—
227C2×D4—5384no—
228C2×D4—10768no—
229C2×D4—10764no—
230C2×D4D107612yescomplemented
231C2×D4C22×D26912yes—
232C22×C4—22no—
233C22×C4—2692no—
234C22×C4—5382no—
235C22×C4—5381no—
236C22×C4—5381no—
237C22×C4D107611yescharacteristic, complemented
238C22⋊C4—22no—
239C22⋊C4—2692no—
240C22⋊C4—5388no—
241C22⋊C4—5381no—
242C22⋊C4—5384no—
243C22⋊C4C22×D26914yescomplemented
244C23—21no—
245C23—21no—
246C23—42no—
247C23—42no—
248C23—2694no—
249C23—5388no—
250C23—5384no—
251C23—5384no—
252C23—5382no—
253C23—5384no—
254C23—5382no—
255C23—5382no—
256C23—10764no—
257C23—10762no—
258C23—10764no—
259C23—10764no—
260C23—10768no—
261C23—10764no—
262C23—10761no—
263C23—10762no—
264C23—10761no—
265C23—21522no—
266C23D4×D26912yes—
267C23D4×D26912yes—
268C23C2×D107611yescharacteristic
269C23C2×D107611yescharacteristic
270C23C2×D107612yescomplemented
271C23C23×D26911yescharacteristic
272Q8—5384no—
273D4—24no—
274D4—24no—
275D4—5384no—
276D4—5388no—
277D4—5384no—
278D4—5384no—
279D4—5384no—
280D4—5384no—
281D4—107616no—
282D4—10768no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—2694no—
288C2×C4—5388no—
289C2×C4—5384no—
290C2×C4—5382no—
291C2×C4—5382no—
292C2×C4—5382no—
293C2×C4—10762no—
294C2×C4C2×D107612yescomplemented
295C22—24no—
296C22—22no—
297C22—22no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—5388no—
305C22—5384no—
306C22—5384no—
307C22—10764no—
308C22—10764no—
309C22—10762no—
310C22—10764no—
311C22—10768no—
312C22—10764no—
313C22—10764no—
314C22—10762no—
315C22—21522no—
316C22—21524no—
317C22#2257542311yescharacteristic
318C22#2257542312yes—
319C22#2257542311yescharacteristic
320C22C2×D4×D26912yes—
321C22C22×D107611yescharacteristic
322C4—22no—
323C4—44no—
324C4—5384no—
325C4—10762no—
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—42no—
331C2—10764no—
332C2—10764no—
333C2#3177079312yesdirect product factor
334C2C2×#2257542311yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC23×C269C24
FrattiniC23C23×D269
FittingC2×#99×C269C2
socleC22×C269#120
hypercenterC2×#99D269
hypocenterC269C2×B(4,𝔽2)
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
1. C2×#22575498C2semidirect
2. C2×#22575423C2semidirect
3. C2×#22575421C2semidirect
4. #31770793C2direct (N × H)
5. C2×#22575367C2semidirect
6. C2×#99×C269C2semidirect
7. C24×D269C22semidirect
10. #22575498C22semidirect
19. #22575423C22semidirect
21. #22575421C22semidirect
22. C2×C22⋊Dic269C22semidirect
25. #22575367C22semidirect
27. C2×C22⋊C4×C269C22semidirect
28. #99×C269C22semidirect
35. C23×D269D4semidirect
36. C23×D269C23semidirect
54. C2×C22⋊D269D4semidirect
60. C22×Dic269D4semidirect
63. C22⋊Dic269C23semidirect
66. C24×C269D4semidirect
70. C2×D4×C269D4semidirect
73. C22×C4×C269D4semidirect
75. C22⋊C4×C269C23semidirect
93. C22×D269C2×D4semidirect
108. C2×Dic269C2×D4semidirect
118. C23×C269C2×D4semidirect
126. C2×C4×C269C2×D4semidirect
163. C2×C269B(4,𝔽2)semidirect
167. C269C2×B(4,𝔽2)semidirect
174. C2×#99D269semidirect
194. C2×C22⋊C4C2×D269semidirect
196. #99C2×D269semidirect
205. C24D1076semidirect
230. C2×D4D1076semidirect
237. C22×C4D1076semidirect
243. C22⋊C4C22×D269semidirect
270. C23C2×D1076semidirect
294. C2×C4C2×D1076semidirect
333. C2#31770793direct (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×#225754232
C2×#225754212
#317707932
C2×#225753672
C2×#99×C2692
C2×B(4,𝔽2)269