Finite Group Databasebeta

← C2×#26011679 #36362948

Subgroups — C2×#26011679 #36362948

Order 22144.

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×#19149724C211yesmaximal, characteristic, complemented
2C2×#19149649C212yesmaximal, complemented
3C2×#19149647C211yesmaximal, characteristic, complemented
4#26011679C218yesmaximal, direct product factor
5C2×#19149593C212yesmaximal, complemented
6C2×#99×C173C211yesmaximal, characteristic, complemented
7C24×D173C2211yescharacteristic, complemented
8#19149724—22no—
9#19149724—24no—
10#19149724C2214yescomplemented
11C2×#14583826—21no—
12C2×#14583825—22no—
13C22×D692—22no—
14C22×C22⋊D173—21no—
15C22×C22⋊D173—21no—
16C22×C22⋊D173C2212yes—
17C2×D4×D173—22no—
18#19149649—24no—
19#19149649C2218yescomplemented
20#19149647—22no—
21#19149647C2214yescomplemented
22C2×C22⋊Dic173C2211yescharacteristic, complemented
23C2×#14583803—21no—
24C2×#14583803—22no—
25#19149593C2218yescomplemented
26C22×D4×C173C2211yescharacteristic
27C2×C22⋊C4×C173C2212yescomplemented
28#99×C173C2214yescomplemented
29C23×D173—21no—
30C23×D173—21no—
31C23×D173—22no—
32C23×D173—21no—
33C23×D173—22no—
34C23×D173—44no—
35C23×D173D412yescomplemented
36C23×D173C2312yescomplemented
37#14583826—24no—
38#14583826—24no—
39#14583825—28no—
40#14583825—28no—
41C2×Dic346—21no—
42C2×D692—21no—
43C2×D692—28no—
44C2×D692—48no—
45C2×C22⋊D173—22no—
46C2×C22⋊D173—24no—
47C2×C22⋊D173—22no—
48C2×C22⋊D173—22no—
49C2×C22⋊D173—22no—
50C2×C22⋊D173—22no—
51C2×C22⋊D173—24no—
52C2×C22⋊D173—24no—
53C2×C22⋊D173—44no—
54C2×C22⋊D173D414yescomplemented
55C2×C22⋊D173C2314yes—
56D4×D173—28no—
57D4×D173—28no—
58C22×Dic173—21no—
59C22×Dic173—21no—
60C22×Dic173D412yescomplemented
61C2×C4×D173—22no—
62C22⋊Dic173—21no—
63C22⋊Dic173C2312yescomplemented
64#14583803—28no—
65#14583803—24no—
66C24×C173D411yescharacteristic, complemented
67C24×C173C2311yescharacteristic
68C2×D4×C173—22no—
69C2×D4×C173—22no—
70C2×D4×C173D412yescomplemented
71C2×D4×C173C2312yes—
72C22×C4×C173—22no—
73C22×C4×C173D411yescharacteristic, complemented
74C22⋊C4×C173—22no—
75C22⋊C4×C173C2314yescomplemented
76C22×D173—24no—
77C22×D173—28no—
78C22×D173—22no—
79C22×D173—22no—
80C22×D173—24no—
81C22×D173—24no—
82C22×D173—22no—
83C22×D173—44no—
84C22×D173—44no—
85C22×D173—48no—
86C22×D173—44no—
87C22×D173—42no—
88C22×D173—41no—
89C22×D173—42no—
90C22×D173—41no—
91C22×D173—44no—
92C22×D173—82no—
93C22×D173C2×D414yescomplemented
94Dic346—24no—
95D692—24no—
96D692—416no—
97C22⋊D173—28no—
98C22⋊D173—24no—
99C22⋊D173—24no—
100C22⋊D173—24no—
101C22⋊D173—24no—
102C22⋊D173—48no—
103C2×Dic173—24no—
104C2×Dic173—22no—
105C2×Dic173—22no—
106C2×Dic173—22no—
107C2×Dic173—42no—
108C2×Dic173C2×D414yescomplemented
109C4×D173—28no—
110C23×C173—21no—
111C23×C173—21no—
112C23×C173—42no—
113C23×C173—42no—
114C23×C173C2×D412yes—
115C23×C173C2×D412yes—
116C23×C173C2×D411yescharacteristic
117C23×C173C2×D411yescharacteristic
118C23×C173C2×D412yescomplemented
119C23×C173C2411yescharacteristic
120D4×C173—24no—
121D4×C173—24no—
122C2×C4×C173—21no—
123C2×C4×C173—21no—
124C2×C4×C173—24no—
125C2×C4×C173—44no—
126C2×C4×C173C2×D412yescomplemented
127C22×C173—24no—
128C22×C173—22no—
129C22×C173—22no—
130C22×C173—41no—
131C22×C173—42no—
132C22×C173—41no—
133C22×C173—42no—
134C22×C173—42no—
135C22×C173—81no—
136C22×C173#12011yescharacteristic
137C22×C173#12012yes—
138C22×C173#12011yescharacteristic
139C22×C173C22×D412yes—
140C22×C173C22×D411yescharacteristic
141C2×D173—24no—
142C2×D173—28no—
143C2×D173—24no—
144C2×D173—42no—
145C2×D173—44no—
146C2×D173—48no—
147C2×D173—44no—
148C2×D173—42no—
149C2×D173—44no—
150C2×D173—44no—
151C2×D173—44no—
152C2×D173—82no—
153C2×D173—84no—
154C4×C173—22no—
155C4×C173—44no—
156Dic173—24no—
157Dic173—42no—
158C2×C173—21no—
159C2×C173—22no—
160C2×C173—22no—
161C2×C173—21no—
162C2×C173—42no—
163C2×C173B(4,𝔽2)12yescomplemented
164C2×C173C2×#12011yescharacteristic
165D173—44no—
166D173—44no—
167C173C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
168C2×B(4,𝔽2)—1731nomaximal, Sylow
169C2×H(5,𝔽2)—1731no—
170C2×#120—1731no—
171C2×#120—1732no—
172B(4,𝔽2)—1738no—
173C2×#99—1732no—
174C2×#99D17311yescharacteristic, complemented
175C25—1731no—
176H(5,𝔽2)—3464no—
177H(5,𝔽2)—3462no—
178H(5,𝔽2)—1734no—
179C2×#41—3462no—
180C2×#41—3461no—
181C22×D4—3462no—
182C22×D4—3462no—
183C22×D4—3461no—
184C22×D4—3461no—
185C22×D4—1732no—
186C22×D4C2×D17311yescharacteristic
187#120—3464no—
188#120—3462no—
189#120—1734no—
190#120—1738no—
191C2×C22⋊C4—3462no—
192C2×C22⋊C4—3461no—
193C2×C22⋊C4—1731no—
194C2×C22⋊C4C2×D17312yescomplemented
195#99—1738no—
196#99C2×D17314yescomplemented
197C24—3461no—
198C24—3462no—
199C24—3461no—
200C24—3462no—
201C24—3461no—
202C24—1732no—
203C24—1732no—
204C24—6924no—
205C24D69211yescharacteristic, complemented
206C24C22×D17311yescharacteristic
207#41—3464no—
208#41—3468no—
209#41—3468no—
210#41—3464no—
211C2×Q8—3461no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—3461no—
215C2×D4—3468no—
216C2×D4—3468no—
217C2×D4—3468no—
218C2×D4—3462no—
219C2×D4—3464no—
220C2×D4—3462no—
221C2×D4—3462no—
222C2×D4—3462no—
223C2×D4—3462no—
224C2×D4—3464no—
225C2×D4—3464no—
226C2×D4—1734no—
227C2×D4—1734no—
228C2×D4—6928no—
229C2×D4—6924no—
230C2×D4D69212yescomplemented
231C2×D4C22×D17312yes—
232C22×C4—22no—
233C22×C4—3462no—
234C22×C4—3461no—
235C22×C4—3461no—
236C22×C4—1732no—
237C22×C4D69211yescharacteristic, complemented
238C22⋊C4—22no—
239C22⋊C4—3468no—
240C22⋊C4—3461no—
241C22⋊C4—3464no—
242C22⋊C4—1732no—
243C22⋊C4C22×D17314yescomplemented
244C23—21no—
245C23—21no—
246C23—42no—
247C23—42no—
248C23—3464no—
249C23—3468no—
250C23—3464no—
251C23—3462no—
252C23—3462no—
253C23—3464no—
254C23—3462no—
255C23—13842no—
256C23—1734no—
257C23—6924no—
258C23—6924no—
259C23—6922no—
260C23—6924no—
261C23—6928no—
262C23—6924no—
263C23—6921no—
264C23—6922no—
265C23—6921no—
266C23D4×D17312yes—
267C23D4×D17312yes—
268C23C2×D69211yescharacteristic
269C23C2×D69211yescharacteristic
270C23C2×D69212yescomplemented
271C23C23×D17311yescharacteristic
272Q8—3464no—
273D4—24no—
274D4—24no—
275D4—3464no—
276D4—3468no—
277D4—3464no—
278D4—3464no—
279D4—3464no—
280D4—3464no—
281D4—69216no—
282D4—6928no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—3468no—
288C2×C4—3464no—
289C2×C4—3462no—
290C2×C4—3462no—
291C2×C4—3462no—
292C2×C4—1734no—
293C2×C4—6922no—
294C2×C4C2×D69212yescomplemented
295C22—24no—
296C22—22no—
297C22—22no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—3468no—
305C22—3464no—
306C22—3464no—
307C22—13842no—
308C22—13844no—
309C22—6924no—
310C22—6924no—
311C22—6922no—
312C22—6924no—
313C22—6928no—
314C22—6924no—
315C22—6924no—
316C22—6922no—
317C22#1914964911yescharacteristic
318C22#1914964912yes—
319C22#1914964911yescharacteristic
320C22C2×D4×D17312yes—
321C22C22×D69211yescharacteristic
322C4—22no—
323C4—44no—
324C4—3464no—
325C4—6922no—
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—42no—
331C2—6924no—
332C2—6924no—
333C2#2601167912yesdirect product factor
334C2C2×#1914964911yescharacteristic
subgroupG/H
centerC22#19149649
commutator, cosocleC23×C173C24
FrattiniC23C23×D173
FittingC2×#99×C173C2
socleC22×C173#120
hypercenterC2×#99D173
hypocenterC173C2×B(4,𝔽2)
LCSG ▷ C23×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#19149724C2semidirect
2. C2×#19149649C2semidirect
3. C2×#19149647C2semidirect
4. #26011679C2direct (N × H)
5. C2×#19149593C2semidirect
6. C2×#99×C173C2semidirect
7. C24×D173C22semidirect
10. #19149724C22semidirect
19. #19149649C22semidirect
21. #19149647C22semidirect
22. C2×C22⋊Dic173C22semidirect
25. #19149593C22semidirect
27. C2×C22⋊C4×C173C22semidirect
28. #99×C173C22semidirect
35. C23×D173D4semidirect
36. C23×D173C23semidirect
54. C2×C22⋊D173D4semidirect
60. C22×Dic173D4semidirect
63. C22⋊Dic173C23semidirect
66. C24×C173D4semidirect
70. C2×D4×C173D4semidirect
73. C22×C4×C173D4semidirect
75. C22⋊C4×C173C23semidirect
93. C22×D173C2×D4semidirect
108. C2×Dic173C2×D4semidirect
118. C23×C173C2×D4semidirect
126. C2×C4×C173C2×D4semidirect
163. C2×C173B(4,𝔽2)semidirect
167. C173C2×B(4,𝔽2)semidirect
174. C2×#99D173semidirect
194. C2×C22⋊C4C2×D173semidirect
196. #99C2×D173semidirect
205. C24D692semidirect
230. C2×D4D692semidirect
237. C22×C4D692semidirect
243. C22⋊C4C22×D173semidirect
270. C23C2×D692semidirect
294. C2×C4C2×D692semidirect
333. C2#26011679direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191497242
C2×#191496492
C2×#191496472
#260116792
C2×#191495932
C2×#99×C1732
C2×B(4,𝔽2)173