Finite Group Databasebeta

← C2×#22625495 #34018010

Subgroups — C2×#22625495 #34018010

Order 18688.

758 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×#17989608C211yesmaximal, characteristic
2C2×#17989590C211yesmaximal, characteristic
3#22625495C218yesmaximal, direct product factor
4C2×#17989451C211yesmaximal, characteristic, complemented
5C2×#17989450C211yesmaximal, characteristic, complemented
6C2×#17989449C211yesmaximal, characteristic, complemented
7C2×#17989448C211yesmaximal, characteristic, complemented
8C2×M16×Dic73C211yesmaximal, characteristic
9C22×#11924037—21no—
10#17989608—22no—
11#17989608C2214yes—
12#17989590—22no—
13#17989590C2214yes—
14C2×#14556658—21no—
15C2×C4⋊#10596833C2211yescharacteristic
16C2×C4⋊#10596833C2211yescharacteristic
17C2×C4⋊#10596833C2211yescharacteristic
18C2×C4⋊#10596833C2211yescharacteristic
19C2×C22⋊#10596833—21no—
20C2×#14556646—21no—
21#17989451C2214yescomplemented
22#17989450C2214yescomplemented
23#17989449C2214yescomplemented
24#17989448C2214yescomplemented
25C22×#11924012C411yescharacteristic
26C22×C4×Dic73C2211yescharacteristic
27M16×Dic73C414yes—
28M16×Dic73C2214yes—
29C2×#14556501C411yescharacteristic
30C2×#14556501C411yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33C22×M16×C73C411yescharacteristic
34C2×#11924037—24no—
35C2×#11924037—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—
49C22⋊#10596833—24no—
50#14556646—24no—
51C23×Dic73D411yescharacteristic
52C23×Dic73Q811yescharacteristic
53C2×#11924012—24no—
54C2×#11924012C2×C414yes—
55C22×#10596831C2×C411yescharacteristic
56C22×#10596831C2×C411yescharacteristic
57C2×C4×Dic73C2×C411yescharacteristic
58C2×C4×Dic73C2×C412yes—
59C2×C4×Dic73D411yescharacteristic
60C2×C4×Dic73D412yes—
61C2×C4×Dic73Q811yescharacteristic
62C2×C4×Dic73Q812yes—
63C2×C4×Dic73C2311yescharacteristic
64C2×C4×Dic73C2312yes—
65#14556501C2×C414yes—
66#14556501C2×C414yes—
67C8×Dic73C2×C412yes—
68C8×Dic73C2×C412yes—
69C8×Dic73C2312yes—
70C8×Dic73C2312yes—
71C23×C4×C73C2×C411yescharacteristic
72C2×M16×C73—24no—
73C2×M16×C73C2×C414yes—
74C22×C8×C73C2×C411yescharacteristic
75C22×C8×C73C2×C411yescharacteristic
76#11924037—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—
85C22×Dic73—22no—
86C22×Dic73—22no—
87C22×Dic73—42no—
88C22×Dic73C4⋊C411yescharacteristic
89C22×Dic73C4⋊C412yes—
90C22×Dic73C4⋊C411yescharacteristic
91C22×Dic73C4⋊C412yes—
92C22×Dic73C2×D412yes—
93C22×Dic73C2×D411yescharacteristic
94C22×Dic73C2×Q811yescharacteristic
95C22×Dic73C2×Q812yes—
96#11924012—28no—
97C2×#10596831—22no—
98C2×#10596831M1614yescomplemented
99C2×#10596831C22×C412yes—
100C2×#10596831C22×C412yes—
101C4×Dic73C4⋊C412yes—
102C4×Dic73C4⋊C412yes—
103C4×Dic73C4⋊C412yes—
104C4×Dic73C22×C411yescharacteristic
105C4×Dic73C22×C412yes—
106C4×Dic73C2×D412yes—
107C4×Dic73C2×D411yescharacteristic
108C4×Dic73C2×Q812yes—
109C4×Dic73C2×Q811yescharacteristic
110C4×Dic73C2411yescharacteristic
111C24×C73C4⋊C411yescharacteristic
112C22×C4×C73—22no—
113C22×C4×C73—22no—
114C22×C4×C73C4⋊C412yes—
115C22×C4×C73C4⋊C411yescharacteristic
116C22×C4×C73C22×C412yes—
117C22×C4×C73C22×C411yescharacteristic
118M16×C73—28no—
119C2×C8×C73—22no—
120C2×C8×C73M1614yescomplemented
121C2×C8×C73C22×C412yes—
122C2×C8×C73C22×C412yes—
123C23×C73—22no—
124C23×C73—22no—
125C23×C73—22no—
126C23×C73C2×C4⋊C412yes—
127C23×C73C2×C4⋊C411yescharacteristic
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—22no—
131C2×C4×C73—24no—
132C2×C4×C73C2×C4⋊C412yes—
133C2×C4×C73C2×C4⋊C411yescharacteristic
134C2×C4×C73C2×M1612yes—
135C2×C4×C73C2×M1612yes—
136C2×C4×C73C23×C411yescharacteristic
137C2×Dic73—22no—
138C2×Dic73—22no—
139C2×Dic73—22no—
140C2×Dic73—22no—
141C2×Dic73—22no—
142C2×Dic73—24no—
143C2×Dic73—42no—
144C2×Dic73—42no—
145C2×Dic73C2×C4⋊C411yescharacteristic
146C2×Dic73C2×C4⋊C412yes—
147C2×Dic73C2×C4⋊C412yes—
148C2×Dic73C2×C4⋊C411yescharacteristic
149C2×Dic73AGL(1,ℤ/8)12yes—
150C2×Dic73#13712yes—
151C2×Dic73C22×D411yescharacteristic
152C2×Dic73C22×Q811yescharacteristic
153#10596833—42no—
154#10596833—42no—
155#10596833—42no—
156#10596833—42no—
157C8×C73—22no—
158C8×C73C2×M1614yescomplemented
159#10596831—22no—
160#10596831C2×M1614yescomplemented
161C22×C73—22no—
162C22×C73—22no—
163C22×C73—22no—
164C22×C73—44no—
165C22×C73#42312yes—
166C22×C73#42812yes—
167C22×C73#43012yes—
168C22×C73C22×C4⋊C411yescharacteristic
169C4×C73—22no—
170C4×C73#42312yes—
171C4×C73C22×M1611yescharacteristic
172C4×C73C22×M1611yescharacteristic
173Dic73—22no—
174Dic73—22no—
175Dic73—21no—
176Dic73—21no—
177Dic73#42812yes—
178Dic73C2×AGL(1,ℤ/8)11yescharacteristic
179Dic73C2×#13711yescharacteristic
180C2×#1569—731nomaximal, Sylow
181C2×C73—42no—
182C2×C73#156914yescomplemented
183C2×C73C2×#42311yescharacteristic
184C2×C73C2×#42811yescharacteristic
185C2×C73C2×#43011yescharacteristic
186C2×#432—731no—
187C2×#423—731no—
188C2×C4×M16—731no—
189#1569—738no—
190C2×#335—731no—
191C2×#335—731no—
192C2×#334—731no—
193C2×#334—731no—
194C73C2×#156911yescharacteristic, complemented, Sylow
195C22×M16—731no—
196C22×M16—1461no—
197C22×M16#6440811yescharacteristic
198C22×C42—731no—
199#432—734no—
200#432—1462no—
201#423—734no—
202#423—1462no—
203C2×C4⋊C8—731no—
204C2×C4⋊C8—731no—
205C2×C4⋊C8—731no—
206C2×C4⋊C8—731no—
207C2×C4⋊C8—1461no—
208C2×C22⋊C8—1461no—
209C4×M16—734no—
210C4×M16—734no—
211C2×#97—731no—
212C2×#97—731no—
213C2×#97—1461no—
214C2×C4×C8—731no—
215C2×C4×C8—731no—
216#335—734no—
217#335—734no—
218#334—734no—
219#334—734no—
220C23×C4—731no—
221C23×C4—731no—
222C23×C4C2×#6440811yescharacteristic
223C2×M16—24no—
224C2×M16—2924no—
225C2×M16—734no—
226C2×M16—1464no—
227C2×M16—1464no—
228C2×M16C2×#6440814yes—
229C22×C8—731no—
230C22×C8—731no—
231C22×C8—1461no—
232C22×C8—1461no—
233C22×C8—1461no—
234C22×C8—1461no—
235C22×C8C2×#6440811yescharacteristic
236C22×C8C2×#6440811yescharacteristic
237C2×C42—731no—
238C2×C42—732no—
239C2×C42—732no—
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—732no—
243C2×C42—731no—
244C2×C42—732no—
245C4⋊C8—732no—
246C4⋊C8—732no—
247C4⋊C8—732no—
248C4⋊C8—732no—
249C4⋊C8—1461no—
250C4⋊C8—1461no—
251C4⋊C8—1461no—
252C4⋊C8—1461no—
253C4⋊C8—1464no—
254C22⋊C8—1464no—
255#97—734no—
256#97—734no—
257#97—1464no—
258C4×C8—732no—
259C4×C8—732no—
260C4×C8—732no—
261C4×C8—732no—
262C24C4⋊#6440811yescharacteristic
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—2922no—
266C22×C4—732no—
267C22×C4—732no—
268C22×C4—731no—
269C22×C4—732no—
270C22×C4—732no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—1462no—
275C22×C4—1462no—
276C22×C4C4⋊#6440812yes—
277C22×C4C4⋊#6440811yescharacteristic
278C22×C4C22×#6440812yes—
279C22×C4C22×#6440811yescharacteristic
280M16—28no—
281M16—2928no—
282M16—1468no—
283C2×C8—22no—
284C2×C8—2922no—
285C2×C8—2922no—
286C2×C8—2922no—
287C2×C8—2922no—
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#1192403714yescomplemented
297C2×C8C22×#6440812yes—
298C2×C8C22×#6440812yes—
299C42—731no—
300C42—732no—
301C42—731no—
302C42—732no—
303C42—732no—
304C42—732no—
305C42—732no—
306C42—731no—
307C42—731no—
308C42—732no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23C2×C4⋊#6440812yes—
313C23C2×C4⋊#6440811yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—2922no—
319C2×C4—2922no—
320C2×C4—731no—
321C2×C4—731no—
322C2×C4—732no—
323C2×C4—732no—
324C2×C4—732no—
325C2×C4—731no—
326C2×C4—732no—
327C2×C4—731no—
328C2×C4—1462no—
329C2×C4—1462no—
330C2×C4—1464no—
331C2×C4—1462no—
332C2×C4—1462no—
333C2×C4—1462no—
334C2×C4C2×C4⋊#6440812yes—
335C2×C4C2×C4⋊#6440811yescharacteristic
336C2×C4C2×#1192403712yes—
337C2×C4D73⋊M1612yes—
338C2×C4C23×#6440811yescharacteristic
339C8—22no—
340C8—2922no—
341C8—2922no—
342C8—2922no—
343C8—2922no—
344C8—734no—
345C8—1462no—
346C8C2×#1192403714yescomplemented
347C22—22no—
348C22—22no—
349C22—22no—
350C22—44no—
351C22#1798959012yes—
352C22#1798959812yes—
353C22#1798960212yes—
354C22C22×C4⋊#6440811yescharacteristic
355C4—22no—
356C4—731no—
357C4—731no—
358C4—732no—
359C4—1462no—
360C4—1461no—
361C4—1462no—
362C4—1461no—
363C4#1798959012yes—
364C4C22×#1192403711yescharacteristic
365C4C2×D73⋊M1611yescharacteristic
366C2—42no—
367C2#2262549514yesdirect product factor
368C2C2×#1798959011yescharacteristic
369C2C2×#1798959811yescharacteristic
370C2C2×#1798960211yescharacteristic
subgroupG/H
centerC23C2×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC22×M16×C73C4
socleC23×C73C2×C4⋊C4
prime radicalC24×C73C4⋊C4
cosocleC4×Dic73C24
hypercenterC22×M16#64408
hypocenterC73C2×#1569
LCSG ▷ C2×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. #22625495C2direct (N × H)
4. C2×#17989451C2semidirect
5. C2×#17989450C2semidirect
6. C2×#17989449C2semidirect
7. C2×#17989448C2semidirect
21. #17989451C22semidirect
22. #17989450C22semidirect
23. #17989449C22semidirect
24. #17989448C22semidirect
98. C2×#10596831M16semidirect
120. C2×C8×C73M16semidirect
158. C8×C73C2×M16semidirect
160. #10596831C2×M16semidirect
182. C2×C73#1569semidirect
194. C73C2×#1569semidirect
296. C2×C8#11924037semidirect
346. C8C2×#11924037semidirect
367. C2#22625495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896082
C2×#179895902
#226254952
C2×#179894512
C2×#179894502
C2×#179894492
C2×#179894482
C2×M16×Dic732
C2×#156973