Finite Group Databasebeta

← C2×#22626495 #34031074

Subgroups — C2×#22626495 #34031074

Order 18688.

3342 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11924037C212yesmaximal
2#22626495C2116yesmaximal, direct product factor
3C2×#17989551C218yesmaximal, complemented
4C2×C4×#11924037C214yesmaximal, complemented
5C22×#14556547C211yesmaximal, characteristic
6C22×#11924037C4132yescomplemented
7C22×#11924037C2214yes—
8C22×#11924037C2214yes—
9C22×#11924037C22116yes—
10C23×#10596833C2214yes—
11#17989551C22164yescomplemented
12C4×#11924037C22132yescomplemented
13C2×#14556646C2218yescomplemented
14C2×C4×#10596833C2218yescomplemented
15C24×Dic73C2211yescharacteristic
16C2×#14556547C414yes—
17C2×#14556547C418yes—
18C2×#14556547C2214yes—
19C2×#14556547C2218yes—
20C22×#11924007C412yes—
21C22×C22⋊Dic73C411yescharacteristic
22C22×C4×Dic73C2212yes—
23C22×C22⋊C4×C73C411yescharacteristic
24C2×#11924037C2×C4132yes—
25C2×#11924037C2×C4132yescomplemented
26C2×#11924037C2×C41128yescomplemented
27C2×#11924037C23116yes—
28C2×#11924037C23116yes—
29C22×#10596833C2×C4132yescomplemented
30C22×#10596833C2318yes—
31C22×#10596833C23116yes—
32#14556646C23132yescomplemented
33C4×#10596833C23132yescomplemented
34C23×Dic73C2×C4116yes—
35C23×Dic73C2×C412yes—
36C23×Dic73C2×C411yescharacteristic
37C23×Dic73C2×C412yes—
38C23×Dic73C2×C414yes—
39C23×Dic73C2312yes—
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2314yes—
42#14556547C2×C4116yes—
43#14556547C2×C4132yes—
44#14556547C23116yes—
45C2×#11924007C2×C418yes—
46C2×#11924007C2×C4116yes—
47C2×C22⋊Dic73C2×C414yes—
48C2×C22⋊Dic73C2×C418yes—
49C2×C4×Dic73C2×C414yes—
50C2×C4×Dic73C2×C418yes—
51C2×C4×Dic73C2314yes—
52C2×C4×Dic73C2318yes—
53C25×C73C2×C411yescharacteristic
54C23×C4×C73C2×C412yes—
55C2×C22⋊C4×C73C2×C414yes—
56C2×C22⋊C4×C73C2×C418yes—
57#11924037C22×C4164yes—
58#11924037C22×C4164yescomplemented
59C2×#10596833C22×C4132yes—
60C2×#10596833C22×C4164yescomplemented
61C2×#10596833C24116yes—
62C22×Dic73—44no—
63C22×Dic73C4218yes—
64C22×Dic73C42116yes—
65C22×Dic73C42132yes—
66C22×Dic73C22×C414yes—
67C22×Dic73C22×C418yes—
68C22×Dic73C22×C412yes—
69C22×Dic73C22×C411yescharacteristic
70C22×Dic73C22×C414yes—
71C22×Dic73C22×C412yes—
72C22×Dic73C22×C414yes—
73C22×Dic73C22×C418yes—
74C22×Dic73C22×C418yes—
75C22×Dic73C22×C418yes—
76C22×Dic73C22×C418yes—
77C22×Dic73C22×C4132yes—
78C22×Dic73C2411yescharacteristic
79C22×Dic73C2414yes—
80C22×Dic73C2412yes—
81#11924007C22×C4132yes—
82C22⋊Dic73C22×C4116yes—
83C4×Dic73C22×C418yes—
84C4×Dic73C22×C4116yes—
85C4×Dic73C2418yes—
86C24×C73—44no—
87C24×C73C4218yes—
88C24×C73C22×C412yes—
89C24×C73C22×C411yescharacteristic
90C24×C73C22×C414yes—
91C22×C4×C73—44no—
92C22×C4×C73C22×C414yes—
93C22×C4×C73C22×C418yes—
94C22⋊C4×C73C22×C4116yes—
95C23×C73—24no—
96C23×C73—28no—
97C23×C73—416no—
98C23×C73—48no—
99C23×C73C2×C4218yes—
100C23×C73C2×C4214yes—
101C23×C73C2×C42116yes—
102C23×C73C23×C414yes—
103C23×C73C23×C412yes—
104C23×C73C23×C411yescharacteristic
105C2×C4×C73—28no—
106C2×C4×C73—48no—
107C2×C4×C73C23×C418yes—
108C2×Dic73—28no—
109C2×Dic73—48no—
110C2×Dic73C2×C4218yes—
111C2×Dic73C2×C42116yes—
112C2×Dic73C2×C42116yes—
113C2×Dic73C2×C42132yes—
114C2×Dic73C2×C4214yes—
115C2×Dic73C2×C4218yes—
116C2×Dic73C23×C418yes—
117C2×Dic73C23×C414yes—
118C2×Dic73C23×C418yes—
119C2×Dic73C23×C418yes—
120C2×Dic73C23×C418yes—
121C2×Dic73C23×C411yescharacteristic
122C2×Dic73C23×C412yes—
123C2×Dic73C23×C414yes—
124C2×Dic73C2511yescharacteristic
125#10596833C23×C4132yes—
126C22×C73—28no—
127C22×C73—216no—
128C22×C73—24no—
129C22×C73—28no—
130C22×C73—416no—
131C22×C73C22×C4218yes—
132C22×C73C22×C4214yes—
133C22×C73C22×C4212yes—
134C22×C73#56814yes—
135C22×C73C24×C411yescharacteristic
136C4×C73—28no—
137Dic73—28no—
138Dic73C22×C4212yes—
139Dic73C22×C4218yes—
140Dic73C22×C4214yes—
141Dic73C24×C412yes—
142C2×#2873—731nomaximal, Sylow
143C2×C73—24no—
144C2×C73—28no—
145C2×C73#287314yescomplemented
146C2×C73C23×C4211yescharacteristic
147C2×C73C2×#56812yes—
148C23×M16—732no—
149C22×#117—731no—
150#2873—7316no—
151C2×#405—738no—
152C2×C4×M16—734no—
153C73C2×#287311yescharacteristic, complemented, Sylow
154C24×C4—731no—
155C22×M16—7332no—
156C22×M16—734no—
157C22×M16—734no—
158C22×M16—7316no—
159C23×C8—734no—
160C2×#117—734no—
161C2×#117—738no—
162C2×#117—738no—
163C2×#117—734no—
164C22×C4⋊C4—732no—
165C22×C22⋊C4—731no—
166C22×C22⋊C4#6440811yescharacteristic
167C22×C42—732no—
168#405—7364no—
169C4×M16—7332no—
170C2×#97—738no—
171C2×C4×C8—738no—
172C25C2×#6440811yescharacteristic
173C23×C4—732no—
174C23×C4—7316no—
175C23×C4—731no—
176C23×C4—732no—
177C23×C4—734no—
178C23×C4—734no—
179C23×C4—732no—
180C23×C4—731no—
181C23×C4C2×#6440812yes—
182C2×M16—7332no—
183C2×M16—7332no—
184C2×M16—73128no—
185C2×M16—7316no—
186C2×M16—7316no—
187C22×C8—7332no—
188C22×C8—738no—
189C22×C8—7316no—
190#117—7316no—
191#117—7332no—
192#117—7316no—
193C2×C4⋊C4—7316no—
194C2×C4⋊C4—738no—
195C2×C22⋊C4—738no—
196C2×C22⋊C4—734no—
197C2×C22⋊C4C2×#6440814yes—
198C2×C22⋊C4C2×#6440818yes—
199C2×C42—738no—
200C2×C42—734no—
201C2×C42—734no—
202C2×C42—738no—
203#97—7332no—
204C4×C8—7332no—
205C24—44no—
206C24C4×#6440818yes—
207C24C22×#6440812yes—
208C24C22×#6440811yescharacteristic
209C24C22×#6440814yes—
210C22×C4—44no—
211C22×C4—2924no—
212C22×C4—738no—
213C22×C4—732no—
214C22×C4—734no—
215C22×C4—734no—
216C22×C4—738no—
217C22×C4—732no—
218C22×C4—734no—
219C22×C4—731no—
220C22×C4—732no—
221C22×C4—731no—
222C22×C4—738no—
223C22×C4—7316no—
224C22×C4—7332no—
225C22×C4—738no—
226C22×C4—738no—
227C22×C4—738no—
228C22×C4—7332no—
229C22×C4—734no—
230C22×C4C22×#6440814yes—
231C22×C4C22×#6440818yes—
232M16—7364no—
233M16—7364no—
234C2×C8—7332no—
235C2×C8—7364no—
236C2×C8—7316no—
237C4⋊C4—7332no—
238C22⋊C4—7316no—
239C22⋊C4C22×#64408116yes—
240C42—738no—
241C42—7316no—
242C42—738no—
243C23—24no—
244C23—28no—
245C23—416no—
246C23—48no—
247C23C2×C4×#6440818yes—
248C23C2×C4×#6440814yes—
249C23C2×C4×#64408116yes—
250C23C23×#6440814yes—
251C23C23×#6440812yes—
252C23C23×#6440811yescharacteristic
253C2×C4—28no—
254C2×C4—48no—
255C2×C4—2928no—
256C2×C4—738no—
257C2×C4—734no—
258C2×C4—738no—
259C2×C4—738no—
260C2×C4—738no—
261C2×C4—7316no—
262C2×C4—7316no—
263C2×C4—7332no—
264C2×C4—734no—
265C2×C4—738no—
266C2×C4—731no—
267C2×C4—731no—
268C2×C4—732no—
269C2×C4—734no—
270C2×C4—738no—
271C2×C4—1468no—
272C2×C4C23×#6440818yes—
273C8—7332no—
274C22—24no—
275C22—28no—
276C22—28no—
277C22—216no—
278C22—416no—
279C22C22×C4×#6440818yes—
280C22C22×C4×#6440814yes—
281C22C22×C4×#6440812yes—
282C22#1798966514yes—
283C22C24×#6440811yescharacteristic
284C4—28no—
285C4—732no—
286C4—732no—
287C4—738no—
288C4—734no—
289C4—1468no—
290C2—24no—
291C2—28no—
292C2#2262649514yesdirect product factor
293C2C23×C4×#6440811yescharacteristic
294C2C2×#1798966512yes—
subgroupG/H
centerC23C23×#64408
commutatorC2×C73C23×C42
FrattiniC22C24×#64408
FittingC22×C22⋊C4×C73C4
socleC23×C73C23×C4
prime radicalC25×C73C2×C4
cosocleC2×Dic73C25
hypercenterC22×C22⋊C4#64408
hypocenterC73C2×#2873
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #22626495C2direct (N × H)
3. C2×#17989551C2semidirect
4. C2×C4×#11924037C2semidirect
6. C22×#11924037C4semidirect
11. #17989551C22semidirect
12. C4×#11924037C22semidirect
13. C2×#14556646C22semidirect
14. C2×C4×#10596833C22semidirect
25. C2×#11924037C2×C4semidirect
26. C2×#11924037C2×C4semidirect
29. C22×#10596833C2×C4semidirect
32. #14556646C23semidirect
33. C4×#10596833C23semidirect
58. #11924037C22×C4semidirect
60. C2×#10596833C22×C4semidirect
145. C2×C73#2873semidirect
153. C73C2×#2873semidirect
292. C2#22626495direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#119240372
#226264952
C2×#179895512
C2×C4×#119240372
C22×#145565472
C2×#287373