Finite Group Databasebeta

← C2×#22625483 #34017977

Subgroups — C2×#22625483 #34017977

Order 18688.

834 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989606C211yesmaximal, characteristic
2C2×#17989588C211yesmaximal, characteristic
3#22625483C218yesmaximal, direct product factor
4C2×#17989451C211yesmaximal, characteristic, complemented
5C2×#17989450C211yesmaximal, characteristic, complemented
6C2×#17989449C211yesmaximal, characteristic, complemented
7C2×#17989448C211yesmaximal, characteristic, complemented
8C2×#17988539C211yesmaximal, characteristic
9C22×#11924036—21no—
10#17989606—22no—
11#17989606C2214yes—
12C2×#14556658—21no—
13#17989588—22no—
14#17989588C2214yes—
15C2×C4⋊#10596833C2211yescharacteristic
16C2×C4⋊#10596833C2211yescharacteristic
17C2×C4⋊#10596833C2211yescharacteristic
18C2×C4⋊#10596833C2211yescharacteristic
19C2×#14556648—21no—
20C2×C4×#10596833—21no—
21#17989451C2214yescomplemented
22#17989450C2214yescomplemented
23#17989449C2214yescomplemented
24#17989448C2214yescomplemented
25C22×#11924011C411yescharacteristic
26C22×#11924011C411yescharacteristic
27C2×C42×D73C2211yescharacteristic
28#17988539C414yes—
29#17988539C2214yes—
30C2×#14556502C411yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33C2×#97×C73C411yescharacteristic
34C2×#11924036—24no—
35C2×#11924036—44no—
36C22×#10596833—21no—
37C22×#10596833—21no—
38C22×#10596833—21no—
39C22×#10596833—21no—
40#14556658—24no—
41C4⋊#10596833—21no—
42C4⋊#10596833—21no—
43C4⋊#10596833—21no—
44C4⋊#10596833—21no—
45C4⋊#10596833C2312yes—
46C4⋊#10596833C2312yes—
47C4⋊#10596833C2312yes—
48C4⋊#10596833C2312yes—
49#14556648—24no—
50C4×#10596833—24no—
51C22×C4×D73C2×C411yescharacteristic
52C22×C4×D73D411yescharacteristic
53C22×C4×D73Q811yescharacteristic
54C2×#11924011—24no—
55C2×#11924011C818yescomplemented
56C2×#11924011C2×C414yes—
57C2×#11924011C2×C414yes—
58C22×#10596831C2×C411yescharacteristic
59C22×#10596831C2×C411yescharacteristic
60C2×C4×Dic73D411yescharacteristic
61C2×C4×Dic73Q811yescharacteristic
62C2×C4×Dic73C2311yescharacteristic
63C42×D73C2×C412yes—
64C42×D73D412yes—
65C42×D73Q812yes—
66C42×D73C2312yes—
67#14556502C2×C414yes—
68C8×Dic73C2×C412yes—
69C8×Dic73C2×C412yes—
70C8×Dic73C2312yes—
71C8×Dic73C2312yes—
72C22×C8×C73C2×C411yescharacteristic
73C22×C8×C73C2×C411yescharacteristic
74C2×C42×C73C2×C411yescharacteristic
75#97×C73C2×C414yes—
76#11924036—48no—
77C2×#10596833—22no—
78C2×#10596833—22no—
79C2×#10596833—22no—
80C2×#10596833—22no—
81C2×#10596833—42no—
82C2×#10596833—42no—
83C2×#10596833—42no—
84C2×#10596833—42no—
85C23×D73C4⋊C411yescharacteristic
86C22×Dic73C4⋊C411yescharacteristic
87C22×Dic73C2×D411yescharacteristic
88C22×Dic73C2×Q811yescharacteristic
89C2×C4×D73—22no—
90C2×C4×D73—22no—
91C2×C4×D73—42no—
92C2×C4×D73C4⋊C412yes—
93C2×C4×D73C4⋊C412yes—
94C2×C4×D73C4⋊C412yes—
95C2×C4×D73C2×C814yes—
96C2×C4×D73M1614yes—
97C2×C4×D73C22×C412yes—
98C2×C4×D73C2×D412yes—
99C2×C4×D73C2×Q812yes—
100#11924011—28no—
101#11924011C2×C8116yescomplemented
102C2×#10596831—22no—
103C2×#10596831C2×C814yescomplemented
104C2×#10596831C22×C412yes—
105C2×#10596831C22×C412yes—
106C4×Dic73C4⋊C412yes—
107C4×Dic73C4⋊C412yes—
108C4×Dic73C22×C411yescharacteristic
109C4×Dic73C2×D411yescharacteristic
110C4×Dic73C2×D412yes—
111C4×Dic73C2×Q811yescharacteristic
112C4×Dic73C2×Q812yes—
113C4×Dic73C2411yescharacteristic
114C22×C4×C73C4⋊C411yescharacteristic
115C22×C4×C73C4⋊C411yescharacteristic
116C22×C4×C73C22×C411yescharacteristic
117C2×C8×C73—22no—
118C2×C8×C73C2×C814yescomplemented
119C2×C8×C73C22×C412yes—
120C2×C8×C73C22×C412yes—
121C42×C73C4⋊C412yes—
122C42×C73C22×C412yes—
123C23×C73C2×C4⋊C411yescharacteristic
124C22×D73—22no—
125C22×D73—22no—
126C22×D73C4⋊C814yes—
127C22×D73C2×C4⋊C412yes—
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73C2×C4⋊C412yes—
131C2×C4×C73C2×C4⋊C412yes—
132C2×C4×C73C2×C4⋊C411yescharacteristic
133C2×C4×C73C22×C812yes—
134C2×C4×C73C2×M1612yes—
135C2×C4×C73C23×C411yescharacteristic
136C2×Dic73—22no—
137C2×Dic73C4⋊C814yes—
138C2×Dic73C2×C4⋊C411yescharacteristic
139C2×Dic73C2×C4⋊C412yes—
140C2×Dic73C2×C4⋊C411yescharacteristic
141C2×Dic73AGL(1,ℤ/8)12yes—
142C2×Dic73#13712yes—
143C2×Dic73C22×D411yescharacteristic
144C2×Dic73C22×Q811yescharacteristic
145C4×D73—22no—
146C4×D73—22no—
147C4×D73—24no—
148C4×D73—42no—
149C4×D73—42no—
150C4×D73C4⋊C818yes—
151C4×D73C22×C814yes—
152C4×D73C2×M1614yes—
153#10596833—42no—
154#10596833—42no—
155#10596833—42no—
156#10596833—42no—
157C8×C73—22no—
158C8×C73C22×C814yescomplemented
159#10596831—22no—
160#10596831C22×C814yescomplemented
161C22×C73C2×C4⋊C812yes—
162C22×C73#42812yes—
163C22×C73#43012yes—
164C22×C73C22×C4⋊C411yescharacteristic
165C2×D73—28no—
166C2×D73—22no—
167C2×D73—22no—
168C2×D73C2×C4⋊C814yes—
169C4×C73—22no—
170C4×C73—22no—
171C4×C73C2×C4⋊C812yes—
172C4×C73C23×C811yescharacteristic
173C4×C73C22×M1611yescharacteristic
174Dic73—21no—
175Dic73—21no—
176Dic73C2×C4⋊C814yes—
177Dic73#42812yes—
178Dic73C2×AGL(1,ℤ/8)11yescharacteristic
179Dic73C2×#13711yescharacteristic
180C2×#1565—731nomaximal, Sylow
181C2×C73#156514yescomplemented
182C2×C73C22×C4⋊C811yescharacteristic
183C2×C73C2×#42811yescharacteristic
184C2×C73C2×#43011yescharacteristic
185D73—24no—
186C2×#431—731no—
187C22×C4⋊C8—731no—
188C2×C4×M16—731no—
189#1565—738no—
190C2×#335—731no—
191C2×#335—731no—
192C2×#334—731no—
193C2×#334—731no—
194C73C2×#156511yescharacteristic, complemented, Sylow
195C22×M16—731no—
196C22×M16—731no—
197C23×C8—1461no—
198C22×C42—731no—
199#431—734no—
200#431—1462no—
201C2×C4⋊C8—731no—
202C2×C4⋊C8—731no—
203C2×C4⋊C8—731no—
204C2×C4⋊C8—731no—
205C2×C4⋊C8—734no—
206C2×C4⋊C8—1462no—
207C2×C4⋊C8—1461no—
208C2×C22⋊C8—1461no—
209C4×M16—734no—
210C4×M16—734no—
211C2×#97—731no—
212C2×#97#6440811yescharacteristic
213C2×C4×C8—731no—
214C2×C4×C8—731no—
215C2×C4×C8—1461no—
216#335—734no—
217#335—734no—
218#334—734no—
219#334—734no—
220C23×C4—731no—
221C23×C4—731no—
222C23×C4—731no—
223C2×M16—738no—
224C2×M16—734no—
225C2×M16—734no—
226C2×M16—1464no—
227C22×C8—2924no—
228C22×C8—731no—
229C22×C8—731no—
230C22×C8—1461no—
231C22×C8—1461no—
232C22×C8—1461no—
233C22×C8—1461no—
234C22×C8—1464no—
235C22×C8C2×#6440811yescharacteristic
236C22×C8C2×#6440811yescharacteristic
237C2×C42—731no—
238C2×C42—731no—
239C2×C42—731no—
240C2×C42—732no—
241C2×C42—732no—
242C2×C42—732no—
243C2×C42—732no—
244C2×C42C2×#6440811yescharacteristic
245C4⋊C8—732no—
246C4⋊C8—732no—
247C4⋊C8—732no—
248C4⋊C8—732no—
249C4⋊C8—1461no—
250C4⋊C8—1461no—
251C4⋊C8—1464no—
252C4⋊C8—1461no—
253C4⋊C8—1461no—
254C22⋊C8—1464no—
255#97—734no—
256#97C2×#6440814yes—
257C4×C8—732no—
258C4×C8—732no—
259C4×C8—732no—
260C4×C8—732no—
261C4×C8—1464no—
262C24—731no—
263C22×C4—2922no—
264C22×C4—732no—
265C22×C4—732no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—734no—
269C22×C4—734no—
270C22×C4—732no—
271C22×C4—732no—
272C22×C4—731no—
273C22×C4—732no—
274C22×C4—732no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4C4⋊#6440811yescharacteristic
278C22×C4C4⋊#6440811yescharacteristic
279C22×C4C22×#6440811yescharacteristic
280M16—7316no—
281M16—1468no—
282C2×C8—22no—
283C2×C8—2922no—
284C2×C8—2922no—
285C2×C8—2922no—
286C2×C8—2922no—
287C2×C8—2928no—
288C2×C8—734no—
289C2×C8—732no—
290C2×C8—732no—
291C2×C8—1462no—
292C2×C8—1462no—
293C2×C8—1462no—
294C2×C8—1462no—
295C2×C8—1462no—
296C2×C8#1192403614yescomplemented
297C2×C8C22×#6440812yes—
298C2×C8C22×#6440812yes—
299C42—731no—
300C42—731no—
301C42—732no—
302C42—732no—
303C42—732no—
304C42—731no—
305C42—732no—
306C42—731no—
307C42C4⋊#6440812yes—
308C42C22×#6440812yes—
309C23—732no—
310C23—734no—
311C23—1462no—
312C23—1462no—
313C23C2×C4⋊#6440811yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—2922no—
317C2×C4—2922no—
318C2×C4—731no—
319C2×C4—732no—
320C2×C4—731no—
321C2×C4—734no—
322C2×C4—732no—
323C2×C4—732no—
324C2×C4—734no—
325C2×C4—734no—
326C2×C4—738no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—1462no—
330C2×C4—1462no—
331C2×C4—1464no—
332C2×C4—1462no—
333C2×C4C2×C4⋊#6440812yes—
334C2×C4C2×C4⋊#6440812yes—
335C2×C4C2×C4⋊#6440811yescharacteristic
336C2×C4C2×#1192403612yes—
337C2×C4D73⋊M1612yes—
338C2×C4C23×#6440811yescharacteristic
339C8—22no—
340C8—2922no—
341C8—2922no—
342C8—2922no—
343C8—2922no—
344C8—734no—
345C8—1462no—
346C8C2×#1192403614yescomplemented
347C22—734no—
348C22—1462no—
349C22—1462no—
350C22—1468no—
351C22#1798958812yes—
352C22#1798959812yes—
353C22#1798960212yes—
354C22C22×C4⋊#6440811yescharacteristic
355C4—22no—
356C4—22no—
357C4—734no—
358C4—731no—
359C4—731no—
360C4—732no—
361C4—1461no—
362C4—1461no—
363C4#1798958812yes—
364C4C22×#1192403611yescharacteristic
365C4C2×D73⋊M1611yescharacteristic
366C2—1464no—
367C2#2262548314yesdirect product factor
368C2C2×#1798958811yescharacteristic
369C2C2×#1798959811yescharacteristic
370C2C2×#1798960211yescharacteristic
subgroupG/H
centerC23C2×C4⋊#64408
commutatorC4×C73C23×C8
FrattiniC2×C4C23×#64408
FittingC2×#97×C73C4
socleC23×C73C2×C4⋊C4
prime radicalC23×D73C4⋊C4
cosocleC4×Dic73C24
hypercenterC2×#97#64408
hypocenterC73C2×#1565
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. #22625483C2direct (N × H)
4. C2×#17989451C2semidirect
5. C2×#17989450C2semidirect
6. C2×#17989449C2semidirect
7. C2×#17989448C2semidirect
21. #17989451C22semidirect
22. #17989450C22semidirect
23. #17989449C22semidirect
24. #17989448C22semidirect
55. C2×#11924011C8semidirect
101. #11924011C2×C8semidirect
103. C2×#10596831C2×C8semidirect
118. C2×C8×C73C2×C8semidirect
158. C8×C73C22×C8semidirect
160. #10596831C22×C8semidirect
181. C2×C73#1565semidirect
194. C73C2×#1565semidirect
296. C2×C8#11924036semidirect
346. C8C2×#11924036semidirect
367. C2#22625483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896062
C2×#179895882
#226254832
C2×#179894512
C2×#179894502
C2×#179894492
C2×#179894482
C2×#179885392
C2×#156573