Finite Group Databasebeta

← C2×#22622569 #33965544

Subgroups — C2×#22622569 #33965544

Order 18688.

2058 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D292C211yesmaximal, characteristic
2#22622569C2116yesmaximal, direct product factor
3C2×#17988937C213yesmaximal, complemented
4C2×#17988872C213yesmaximal, complemented
5C2×#17988789C213yesmaximal
6C2×Q8×#10596831C211yesmaximal, characteristic, complemented
7C2×C4×#11924015C213yesmaximal
8C2×#557×C73C211yesmaximal, characteristic, complemented
9C22×Q8×D73—21no—
10C22×#11924015C2213yes—
11Q8×D292—24no—
12Q8×D292C2218yes—
13C2×#14556591C2213yes—
14C2×#14556571—23no—
15C2×C4×D292C2213yes—
16#17988937C22124yescomplemented
17#17988872C22124yescomplemented
18#17988789C22124yes—
19Q8×#10596831C2218yescomplemented
20C4×#11924015C22124yes—
21C2×#14556522C2213yes—
22C2×C4⋊#10596831C2213yes—
23C2×#14556515C2216yes—
24C2×#14556515C2213yes—
25C2×#14556511C2211yescharacteristic
26C2×C4×#10596831C2213yes—
27#557×C73—24no—
28#557×C73C2218yescomplemented
29C2×C4⋊Q8×C73C2213yes—
30C2×#125×C73—23no—
31C2×C4×Q8×C73—21no—
32C2×C4×Q8×C73C2213yes—
33C2×C4×Q8×C73C2211yescharacteristic
34C22×Dic146—23no—
35C2×Q8×D73—28no—
36C2×Q8×D73—48no—
37C22×D292C2311yescharacteristic
38C22×C4×D73—23no—
39C2×#11924015—212no—
40C2×#11924015C23112yes—
41C22×#10596831C2313yes—
42C22×#10596831C2311yescharacteristic
43#14556591—26no—
44#14556591C23112yes—
45#14556571—224no—
46C4×D292—26no—
47C4×D292C23112yes—
48C2×C4⋊Dic73—23no—
49C2×C4⋊Dic73C2313yes—
50C2×#11924005—23no—
51#14556522C23112yes—
52C4⋊#10596831C23112yes—
53#14556515C23124yes—
54#14556515C23112yes—
55#14556511C2314yes—
56C4×#10596831C23112yes—
57C22×Q8×C73D411yescharacteristic
58C22×Q8×C73C2313yes—
59C4⋊Q8×C73—26no—
60C4⋊Q8×C73C23112yes—
61#125×C73—224no—
62C4×Q8×C73—28no—
63C4×Q8×C73—26no—
64C4×Q8×C73D414yes—
65C4×Q8×C73C23112yes—
66C4×Q8×C73C2314yes—
67C2×C4⋊C4×C73—23no—
68C2×C4⋊C4×C73—23no—
69C2×C4⋊C4×C73—23no—
70C2×C4⋊C4×C73D413yes—
71C2×C4⋊C4×C73C2311yescharacteristic
72C2×C42×C73—23no—
73C2×C42×C73C2313yes—
74C23×D73—21no—
75C2×Dic146—212no—
76C2×Dic146—412no—
77Q8×D73—432no—
78C2×D292—21no—
79C2×D292—22no—
80C2×D292#4114yes—
81C2×D292C2412yes—
82C22×Dic73—23no—
83C2×C4×D73—212no—
84C2×C4×D73—412no—
85#11924015—224no—
86C2×#10596831—26no—
87C2×#10596831—22no—
88C2×#10596831C2412yes—
89C2×#10596831C2416yes—
90C4⋊Dic73—212no—
91C4⋊Dic73—23no—
92C4⋊Dic73C2416yes—
93#11924005—212no—
94C2×Q8×C73—23no—
95C2×Q8×C73—26no—
96C2×Q8×C73—26no—
97C2×Q8×C73SD1618yescomplemented
98C2×Q8×C73C2×D414yes—
99C2×Q8×C73C2416yes—
100C22×C4×C73—21no—
101C22×C4×C73—23no—
102C22×C4×C73C2×D413yes—
103C22×C4×C73C2×D413yes—
104C22×C4×C73C2411yescharacteristic
105C4⋊C4×C73—212no—
106C4⋊C4×C73—212no—
107C4⋊C4×C73—212no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2×D4112yes—
110C4⋊C4×C73C2412yes—
111C42×C73—212no—
112C42×C73C2×D416yes—
113C42×C73C2416yes—
114C23×C73C22×D411yescharacteristic
115C22×D73—24no—
116C22×D73—22no—
117C22×D73—42no—
118C22×D73—42no—
119Q8×C73—26no—
120Q8×C73—26no—
121Q8×C73—46no—
122Q8×C73C2×SD16116yescomplemented
123C2×C4×C73—26no—
124C2×C4×C73—22no—
125C2×C4×C73—26no—
126C2×C4×C73—46no—
127C2×C4×C73—42no—
128C2×C4×C73C2×SD16112yes—
129C2×C4×C73C22×D416yes—
130C2×C4×C73C22×D411yescharacteristic
131C2×C4×C73C22×D416yes—
132C2×C4×C73C2×#4112yes—
133C2×C4×C732−1+412yes—
134C2×C4×C73C2511yescharacteristic
135C2×Dic73—26no—
136C2×Dic73—46no—
137D292—24no—
138D292—22no—
139D292C2×#4114yes—
140C4×D73—424no—
141Dic146—424no—
142#10596831—26no—
143#10596831—22no—
144C22×C73#54812yes—
145C22×C73C22×SD1612yes—
146C22×C73#57812yes—
147C22×C73C23×D411yescharacteristic
148C2×D73—24no—
149C2×D73—48no—
150C2×D73—42no—
151C2×D73—42no—
152C4×C73—26no—
153C4×C73—46no—
154C4×C73—42no—
155C4×C73#54812yes—
156C4×C73C22×SD16112yes—
157C4×C73C22×#4111yescharacteristic
158C4×C73C2×2−1+411yescharacteristic
159Dic73—46no—
160C2×#3359—731nomaximal, Sylow
161C2×C73#335914yescomplemented
162C2×C73C2×#54811yescharacteristic
163C2×C73C23×SD1611yescharacteristic
164C2×C73C2×#57811yescharacteristic
165D73—44no—
166C2×#557D7311yescharacteristic, complemented
167C2×D4×Q8—731no—
168#3359—7316no—
169C2×#487—733no—
170C2×#475—733no—
171C2×#461—733no—
172C2×C8×Q8—731no—
173C2×C4×SD16—733no—
174C73C2×#335911yescharacteristic, complemented, Sylow
175C23×Q8—1461no—
176C22×SD16—733no—
177#557—24no—
178#557C2×D7318yescomplemented
179D4×Q8—738no—
180D4×Q8—1464no—
181C2×C4⋊Q8—733no—
182C2×C4⋊Q8C2×D7313yes—
183C2×#125—23no—
184C2×C22⋊Q8—1463no—
185C2×C4×Q8—21no—
186C2×C4×Q8C2×D7313yes—
187C2×C4×Q8C2×D7311yescharacteristic
188C2×C4×D4—733no—
189#487—7324no—
190#475—7324no—
191#461—7324no—
192C8×Q8—738no—
193C4×SD16—7324no—
194C2×#106—733no—
195C2×C4⋊C8—733no—
196C2×#103—736no—
197C2×#103—733no—
198C2×#102—731no—
199C2×C4×C8—733no—
200C22×Q8—2928no—
201C22×Q8—1468no—
202C22×Q8—1463no—
203C22×Q8C22⋊D7311yescharacteristic
204C22×Q8C22×D7313yes—
205C22×D4—731no—
206C23×C4—1463no—
207C2×SD16—7312no—
208C2×SD16—14612no—
209C22×C8—733no—
210C22×C8—731no—
211C4⋊Q8—26no—
212C4⋊Q8—7312no—
213C4⋊Q8—1466no—
214C4⋊Q8C22×D73112yes—
215#125—224no—
216C22⋊Q8—14624no—
217C4×Q8—28no—
218C4×Q8—26no—
219C4×Q8C22⋊D7314yes—
220C4×Q8C22×D73112yes—
221C4×Q8C22×D7314yes—
222C4×D4—7312no—
223C4×D4—1466no—
224C2×C4⋊C4—23no—
225C2×C4⋊C4—23no—
226C2×C4⋊C4—23no—
227C2×C4⋊C4—733no—
228C2×C4⋊C4—1463no—
229C2×C4⋊C4C22⋊D7313yes—
230C2×C4⋊C4C22×D7311yescharacteristic
231C2×C22⋊C4—1463no—
232C2×C42—23no—
233C2×C42C22×D7313yes—
234#106—7312no—
235C4⋊C8—7312no—
236#103—7312no—
237#103—7324no—
238#102—734no—
239C4×C8—7312no—
240C24—1461no—
241C2×Q8—23no—
242C2×Q8—26no—
243C2×Q8—26no—
244C2×Q8—29232no—
245C2×Q8—29212no—
246C2×Q8—14612no—
247C2×Q8#1192401518yescomplemented
248C2×Q8C2×C22⋊D7314yes—
249C2×Q8C23×D7316yes—
250C2×D4—734no—
251C2×D4—732no—
252C2×D4—1461no—
253C2×D4—1462no—
254C22×C4—21no—
255C22×C4—23no—
256C22×C4—29212no—
257C22×C4—1463no—
258C22×C4—14612no—
259C22×C4C2×C22⋊D7313yes—
260C22×C4C2×C22⋊D7313yes—
261C22×C4C23×D7311yescharacteristic
262SD16—14624no—
263C2×C8—732no—
264C2×C8—736no—
265C2×C8—1466no—
266C2×C8—1462no—
267C4⋊C4—212no—
268C4⋊C4—212no—
269C4⋊C4—212no—
270C4⋊C4—21no—
271C4⋊C4—736no—
272C4⋊C4—1463no—
273C4⋊C4—14612no—
274C4⋊C4C2×C22⋊D73112yes—
275C4⋊C4C23×D7312yes—
276C22⋊C4—14612no—
277C42—212no—
278C42C2×C22⋊D7316yes—
279C42C23×D7316yes—
280C23—2922no—
281C23—2922no—
282C23—1462no—
283C23—1464no—
284C23C22×C22⋊D7311yescharacteristic
285Q8—26no—
286Q8—26no—
287Q8—46no—
288Q8—29224no—
289Q8C2×#11924015116yescomplemented
290D4—734no—
291D4—1462no—
292D4—1464no—
293C2×C4—26no—
294C2×C4—22no—
295C2×C4—26no—
296C2×C4—42no—
297C2×C4—46no—
298C2×C4—2926no—
299C2×C4—29224no—
300C2×C4—1466no—
301C2×C4C2×#11924015112yes—
302C2×C4C22×C22⋊D7316yes—
303C2×C4C22×C22⋊D7311yescharacteristic
304C2×C4C22×C22⋊D7316yes—
305C2×C4#41×D7312yes—
306C2×C4#1455663812yes—
307C2×C4C24×D7311yescharacteristic
308C8—1466no—
309C8—1462no—
310C22—2928no—
311C22—2922no—
312C22—2922no—
313C22—1464no—
314C22#1798924412yes—
315C22C22×#1192401512yes—
316C22#1798940212yes—
317C22C23×C22⋊D7311yescharacteristic
318C4—26no—
319C4—46no—
320C4—42no—
321C4—2926no—
322C4#1798924412yes—
323C4C22×#11924015112yes—
324C4C2×#41×D7311yescharacteristic
325C4C2×#1455663811yescharacteristic
326C2—2924no—
327C2#2262256914yesdirect product factor
328C2C2×#1798924411yescharacteristic
329C2C23×#1192401511yescharacteristic
330C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#557×C73C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenterC2×#557D73
hypocenterC73C2×#3359
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #22622569C2direct (N × H)
3. C2×#17988937C2semidirect
4. C2×#17988872C2semidirect
6. C2×Q8×#10596831C2semidirect
8. C2×#557×C73C2semidirect
16. #17988937C22semidirect
17. #17988872C22semidirect
19. Q8×#10596831C22semidirect
28. #557×C73C22semidirect
97. C2×Q8×C73SD16semidirect
122. Q8×C73C2×SD16semidirect
161. C2×C73#3359semidirect
166. C2×#557D73semidirect
174. C73C2×#3359semidirect
178. #557C2×D73semidirect
247. C2×Q8#11924015semidirect
289. Q8C2×#11924015semidirect
327. C2#22622569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D2922
#226225692
C2×#179889372
C2×#179888722
C2×#179887892
C2×Q8×#105968312
C2×C4×#119240152
C2×#557×C732
C2×#335973