Finite Group Databasebeta

← C2×#22625484 #34017978

Subgroups — C2×#22625484 #34017978

Order 18688.

834 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989603C211yesmaximal, characteristic
2C22×C4⋊#10596833C211yesmaximal, characteristic
3#22625484C218yesmaximal, direct product factor
4C2×#17989451C212yesmaximal, complemented
5C2×#17989449C212yesmaximal, complemented
6C2×M16×Dic73C211yesmaximal, characteristic
7C23×#10596833—21no—
8#17989603—22no—
9#17989603C2214yes—
10C2×C4⋊#10596833—21no—
11C2×C4⋊#10596833—22no—
12C2×C4⋊#10596833C2212yes—
13C2×C4⋊#10596833C2214yes—
14C2×C4⋊#10596833C2211yescharacteristic
15C2×C4⋊#10596833C2211yescharacteristic
16C2×C22⋊#10596833—21no—
17C2×C4×#10596833—21no—
18#17989451C2218yescomplemented
19#17989449C2218yescomplemented
20C22×#11924012C411yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22M16×Dic73C414yes—
23M16×Dic73C2214yes—
24C2×#14556501C412yes—
25C2×C8×Dic73C2212yes—
26C22×M16×C73C411yescharacteristic
27C22×#10596833—24no—
28C22×#10596833—22no—
29C22×#10596833—21no—
30C22×#10596833—21no—
31C22×#10596833—44no—
32C4⋊#10596833—24no—
33C4⋊#10596833—22no—
34C4⋊#10596833—21no—
35C4⋊#10596833—21no—
36C4⋊#10596833C2312yes—
37C4⋊#10596833C2314yes—
38C4⋊#10596833C2312yes—
39C22⋊#10596833—24no—
40C4×#10596833—24no—
41C23×Dic73D411yescharacteristic
42C23×Dic73Q811yescharacteristic
43C2×#11924012C818yescomplemented
44C2×#11924012C2×C414yes—
45C22×#10596831C2×C412yes—
46C2×C4×Dic73C2×C411yescharacteristic
47C2×C4×Dic73C2×C412yes—
48C2×C4×Dic73D411yescharacteristic
49C2×C4×Dic73D412yes—
50C2×C4×Dic73Q811yescharacteristic
51C2×C4×Dic73Q812yes—
52C2×C4×Dic73C2311yescharacteristic
53C2×C4×Dic73C2312yes—
54#14556501C2×C418yes—
55C8×Dic73C2×C414yes—
56C8×Dic73C2314yes—
57C23×C4×C73C2×C411yescharacteristic
58C2×M16×C73—24no—
59C2×M16×C73C2×C414yes—
60C22×C8×C73C2×C412yes—
61C2×#10596833—24no—
62C2×#10596833—22no—
63C2×#10596833—22no—
64C2×#10596833—48no—
65C2×#10596833—42no—
66C2×#10596833—44no—
67C2×#10596833—42no—
68C22×Dic73—22no—
69C22×Dic73—22no—
70C22×Dic73—42no—
71C22×Dic73C4⋊C411yescharacteristic
72C22×Dic73C4⋊C412yes—
73C22×Dic73C4⋊C411yescharacteristic
74C22×Dic73C4⋊C412yes—
75C22×Dic73C2×D412yes—
76C22×Dic73C2×D411yescharacteristic
77C22×Dic73C2×Q811yescharacteristic
78C22×Dic73C2×Q812yes—
79#11924012C2×C8116yescomplemented
80C2×#10596831C2×C818yescomplemented
81C2×#10596831C22×C414yes—
82C4×Dic73C4⋊C412yes—
83C4×Dic73C4⋊C412yes—
84C4×Dic73C4⋊C412yes—
85C4×Dic73C22×C411yescharacteristic
86C4×Dic73C22×C412yes—
87C4×Dic73C2×D412yes—
88C4×Dic73C2×D411yescharacteristic
89C4×Dic73C2×Q812yes—
90C4×Dic73C2×Q811yescharacteristic
91C4×Dic73C2411yescharacteristic
92C24×C73C4⋊C411yescharacteristic
93C22×C4×C73C4⋊C412yes—
94C22×C4×C73C4⋊C411yescharacteristic
95C22×C4×C73C2×C814yes—
96C22×C4×C73M1614yes—
97C22×C4×C73C22×C411yescharacteristic
98C22×C4×C73C22×C412yes—
99M16×C73—28no—
100C2×C8×C73—24no—
101C2×C8×C73C22×C414yes—
102C23×C73—22no—
103C23×C73—22no—
104C23×C73C4⋊C814yes—
105C23×C73C2×C4⋊C412yes—
106C23×C73C2×C4⋊C411yescharacteristic
107C2×C4×C73C4⋊C818yes—
108C2×C4×C73C4⋊C814yes—
109C2×C4×C73C2×C4⋊C411yescharacteristic
110C2×C4×C73C2×C4⋊C412yes—
111C2×C4×C73C22×C812yes—
112C2×C4×C73C22×C814yes—
113C2×C4×C73C2×M1612yes—
114C2×C4×C73C2×M1614yes—
115C2×C4×C73C23×C411yescharacteristic
116C2×Dic73—22no—
117C2×Dic73—22no—
118C2×Dic73—22no—
119C2×Dic73—22no—
120C2×Dic73—22no—
121C2×Dic73—24no—
122C2×Dic73—42no—
123C2×Dic73—42no—
124C2×Dic73C2×C4⋊C411yescharacteristic
125C2×Dic73C2×C4⋊C412yes—
126C2×Dic73C2×C4⋊C412yes—
127C2×Dic73C2×C4⋊C411yescharacteristic
128C2×Dic73AGL(1,ℤ/8)12yes—
129C2×Dic73#13712yes—
130C2×Dic73C22×D411yescharacteristic
131C2×Dic73C22×Q811yescharacteristic
132#10596833—42no—
133#10596833—44no—
134#10596833—42no—
135C8×C73—24no—
136#10596831C22×C818yescomplemented
137C22×C73—28no—
138C22×C73—22no—
139C22×C73—22no—
140C22×C73C2×C4⋊C814yes—
141C22×C73C2×C4⋊C812yes—
142C22×C73#42812yes—
143C22×C73#43012yes—
144C22×C73C22×C4⋊C411yescharacteristic
145C4×C73C2×C4⋊C812yes—
146C4×C73C2×C4⋊C814yes—
147C4×C73C23×C811yescharacteristic
148C4×C73C22×M1611yescharacteristic
149Dic73—22no—
150Dic73—22no—
151Dic73—21no—
152Dic73—21no—
153Dic73#42812yes—
154Dic73C2×AGL(1,ℤ/8)11yescharacteristic
155Dic73C2×#13711yescharacteristic
156C2×#1565—731nomaximal, Sylow
157C2×C73—24no—
158C2×C73#156514yescomplemented
159C2×C73C22×C4⋊C811yescharacteristic
160C2×C73C2×#42811yescharacteristic
161C2×C73C2×#43011yescharacteristic
162C2×#431—731no—
163C22×C4⋊C8—731no—
164C2×C4×M16—731no—
165#1565—738no—
166C2×#335—732no—
167C2×#334—732no—
168C73C2×#156511yescharacteristic, complemented, Sylow
169C22×M16—731no—
170C22×M16#6440811yescharacteristic
171C23×C8—1461no—
172C22×C42—731no—
173#431—734no—
174#431—1462no—
175C2×C4⋊C8—731no—
176C2×C4⋊C8—732no—
177C2×C4⋊C8—731no—
178C2×C4⋊C8—734no—
179C2×C4⋊C8—1461no—
180C2×C4⋊C8—1462no—
181C2×C22⋊C8—1461no—
182C4×M16—734no—
183C4×M16—734no—
184C2×#97—732no—
185C2×C4×C8—732no—
186C2×C4×C8—1461no—
187#335—738no—
188#334—738no—
189C23×C4—731no—
190C23×C4—731no—
191C23×C4C2×#6440811yescharacteristic
192C2×M16—24no—
193C2×M16—738no—
194C2×M16—734no—
195C2×M16C2×#6440814yes—
196C22×C8—2924no—
197C22×C8—732no—
198C22×C8—1462no—
199C22×C8—1464no—
200C22×C8—1461no—
201C22×C8—1461no—
202C22×C8C2×#6440812yes—
203C2×C42—731no—
204C2×C42—732no—
205C2×C42—732no—
206C2×C42—731no—
207C2×C42—731no—
208C2×C42—732no—
209C2×C42—731no—
210C2×C42—732no—
211C4⋊C8—732no—
212C4⋊C8—734no—
213C4⋊C8—732no—
214C4⋊C8—1464no—
215C4⋊C8—1462no—
216C4⋊C8—1461no—
217C4⋊C8—1461no—
218C22⋊C8—1464no—
219#97—738no—
220C4×C8—734no—
221C4×C8—734no—
222C4×C8—1464no—
223C24C4⋊#6440811yescharacteristic
224C22×C4—2922no—
225C22×C4—732no—
226C22×C4—732no—
227C22×C4—731no—
228C22×C4—732no—
229C22×C4—732no—
230C22×C4—731no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—1462no—
234C22×C4—1462no—
235C22×C4C4⋊#6440812yes—
236C22×C4C4⋊#6440811yescharacteristic
237C22×C4#1192403614yes—
238C22×C4#1192403714yes—
239C22×C4C22×#6440812yes—
240C22×C4C22×#6440811yescharacteristic
241M16—28no—
242M16—7316no—
243C2×C8—24no—
244C2×C8—2924no—
245C2×C8—2922no—
246C2×C8—2922no—
247C2×C8—2928no—
248C2×C8—738no—
249C2×C8—734no—
250C2×C8—1462no—
251C2×C8—1462no—
252C2×C8—1464no—
253C2×C8C22×#6440814yes—
254C42—731no—
255C42—732no—
256C42—731no—
257C42—732no—
258C42—732no—
259C42—732no—
260C42—732no—
261C42—731no—
262C42—731no—
263C42—732no—
264C23—22no—
265C23—22no—
266C23#1455665814yes—
267C23C2×C4⋊#6440812yes—
268C23C2×C4⋊#6440811yescharacteristic
269C2×C4—2922no—
270C2×C4—2922no—
271C2×C4—731no—
272C2×C4—731no—
273C2×C4—732no—
274C2×C4—732no—
275C2×C4—732no—
276C2×C4—731no—
277C2×C4—732no—
278C2×C4—731no—
279C2×C4—1462no—
280C2×C4—1462no—
281C2×C4—1464no—
282C2×C4—1462no—
283C2×C4—1462no—
284C2×C4—1462no—
285C2×C4#1455665818yes—
286C2×C4#1455665814yes—
287C2×C4C2×C4⋊#6440812yes—
288C2×C4C2×C4⋊#6440811yescharacteristic
289C2×C4C2×#1192403612yes—
290C2×C4C2×#1192403614yes—
291C2×C4C2×#1192403712yes—
292C2×C4C2×#1192403714yes—
293C2×C4C23×#6440811yescharacteristic
294C8—24no—
295C8—2924no—
296C8—2922no—
297C8—2922no—
298C8—738no—
299C22—22no—
300C22—22no—
301C22—28no—
302C22C2×#1455665814yes—
303C22C2×#1455665812yes—
304C22#1798959812yes—
305C22#1798960212yes—
306C22C22×C4⋊#6440811yescharacteristic
307C4—731no—
308C4—731no—
309C4—732no—
310C4—1462no—
311C4—1461no—
312C4—1462no—
313C4—1461no—
314C4C2×#1455665812yes—
315C4C2×#1455665814yes—
316C4C22×#1192403611yescharacteristic
317C4C22×#1192403711yescharacteristic
318C2—24no—
319C2#2262548414yesdirect product factor
320C2C22×#1455665811yescharacteristic
321C2C2×#1798959811yescharacteristic
322C2C2×#1798960211yescharacteristic
subgroupG/H
centerC23C2×C4⋊#64408
commutatorC4×C73C23×C8
FrattiniC2×C4C23×#64408
FittingC22×M16×C73C4
socleC23×C73C2×C4⋊C4
prime radicalC24×C73C4⋊C4
cosocleC4×Dic73C24
hypercenterC22×M16#64408
hypocenterC73C2×#1565
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #22625484C2direct (N × H)
4. C2×#17989451C2semidirect
5. C2×#17989449C2semidirect
18. #17989451C22semidirect
19. #17989449C22semidirect
43. C2×#11924012C8semidirect
79. #11924012C2×C8semidirect
80. C2×#10596831C2×C8semidirect
136. #10596831C22×C8semidirect
158. C2×C73#1565semidirect
168. C73C2×#1565semidirect
319. C2#22625484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896032
C22×C4⋊#105968332
#226254842
C2×#179894512
C2×#179894492
C2×M16×Dic732
C2×#156573