Finite Group Databasebeta

← C2×#22622573 #33965548

Subgroups — C2×#22622573 #33965548

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×#17989316C211yesmaximal, characteristic, complemented
2#22622573C2116yesmaximal, direct product factor
3C2×#17988939C213yesmaximal, complemented
4C2×#17988869C213yesmaximal, complemented
5C2×#17988792C213yesmaximal
6C2×Q8×#10596831C211yesmaximal, characteristic, complemented
7C2×C4×#11924016C213yesmaximal
8C2×D4×Q8×C73C211yesmaximal, characteristic
9C22×#11924016C2213yes—
10#17989316—24no—
11#17989316C2218yescomplemented
12C2×#14556591C2213yes—
13C2×#14556582—23no—
14C2×Q8×Dic73—21no—
15C2×C4×Dic146C2213yes—
16#17988939C22124yescomplemented
17#17988869C22124yescomplemented
18#17988792C22124yes—
19Q8×#10596831C2218yescomplemented
20C4×#11924016C22124yes—
21C2×#14556522C2213yes—
22C2×C4⋊#10596831C2213yes—
23C2×#14556514C2216yes—
24C2×#14556514C2213yes—
25C2×#14556512C2211yescharacteristic
26C2×C4×#10596831C2213yes—
27C23×Q8×C73—21no—
28D4×Q8×C73—24no—
29D4×Q8×C73C2218yes—
30C2×C4⋊Q8×C73C2213yes—
31C2×C22⋊Q8×C73—23no—
32C2×C4×Q8×C73C2211yescharacteristic
33C2×C4×D4×C73C2213yes—
34C22×Dic146C2313yes—
35C2×#11924016—212no—
36C2×#11924016C23112yes—
37C22×#10596831C2313yes—
38C22×#10596831C2311yescharacteristic
39#14556591—26no—
40#14556591C23112yes—
41#14556582—224no—
42Q8×Dic73—28no—
43C4×Dic146—26no—
44C4×Dic146C23112yes—
45C2×C4⋊Dic73—23no—
46C2×C4⋊Dic73—23no—
47C2×C4⋊Dic73C2311yescharacteristic
48C2×#11924007—23no—
49C2×C4×Dic73—23no—
50#14556522C23112yes—
51C4⋊#10596831C23112yes—
52#14556514C23124yes—
53#14556514C23112yes—
54#14556512C2314yes—
55C4×#10596831C23112yes—
56C22×Q8×C73—28no—
57C22×Q8×C73—23no—
58C22×Q8×C73—48no—
59C22×Q8×C73D411yescharacteristic
60C22×D4×C73C2311yescharacteristic
61C23×C4×C73—23no—
62C4⋊Q8×C73—26no—
63C4⋊Q8×C73C23112yes—
64C22⋊Q8×C73—224no—
65C4×Q8×C73D414yes—
66C4×Q8×C73C2314yes—
67C4×D4×C73—26no—
68C4×D4×C73C23112yes—
69C2×C4⋊C4×C73—23no—
70C2×C4⋊C4×C73D413yes—
71C2×C4⋊C4×C73C2313yes—
72C2×C22⋊C4×C73—23no—
73C2×C42×C73C2313yes—
74C2×Dic146—26no—
75C2×Dic146—26no—
76C2×Dic146—23no—
77C2×Dic146C2416yes—
78C22×Dic73—21no—
79C22×Dic73—23no—
80#11924016—224no—
81C2×#10596831—26no—
82C2×#10596831—22no—
83C2×#10596831C2412yes—
84C2×#10596831C2416yes—
85C4⋊Dic73—212no—
86C4⋊Dic73—212no—
87C4⋊Dic73—21no—
88C4⋊Dic73C2412yes—
89#11924007—212no—
90C4×Dic73—212no—
91C24×C73—21no—
92C2×Q8×C73—212no—
93C2×Q8×C73—432no—
94C2×Q8×C73—412no—
95C2×Q8×C73SD1618yescomplemented
96C2×Q8×C73C2×D414yes—
97C2×D4×C73—21no—
98C2×D4×C73—22no—
99C2×D4×C73#4114yes—
100C2×D4×C73C2412yes—
101C22×C4×C73—23no—
102C22×C4×C73—212no—
103C22×C4×C73—412no—
104C22×C4×C73C2×D413yes—
105C22×C4×C73C2×D413yes—
106C22×C4×C73C2411yescharacteristic
107C4⋊C4×C73—212no—
108C4⋊C4×C73—23no—
109C4⋊C4×C73C2×D4112yes—
110C4⋊C4×C73C2416yes—
111C22⋊C4×C73—212no—
112C42×C73C2×D416yes—
113C42×C73C2416yes—
114C23×C73—24no—
115C23×C73—22no—
116C23×C73—42no—
117C23×C73—42no—
118C23×C73C22×D411yescharacteristic
119Q8×C73—424no—
120Q8×C73C2×SD16116yescomplemented
121D4×C73—24no—
122D4×C73—22no—
123D4×C73C2×#4114yes—
124C2×C4×C73—26no—
125C2×C4×C73—26no—
126C2×C4×C73—46no—
127C2×C4×C73—424no—
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—22no—
136C2×Dic73—26no—
137C2×Dic73—46no—
138C2×Dic73—42no—
139Dic146—26no—
140Dic146—26no—
141Dic146—46no—
142#10596831—26no—
143#10596831—22no—
144C22×C73—24no—
145C22×C73—48no—
146C22×C73—42no—
147C22×C73—42no—
148C22×C73#54812yes—
149C22×C73C22×SD1612yes—
150C22×C73#57812yes—
151C22×C73C23×D411yescharacteristic
152C4×C73—26no—
153C4×C73—46no—
154C4×C73#54812yes—
155C4×C73C22×SD16112yes—
156C4×C73C22×#4111yescharacteristic
157C4×C73C2×2−1+411yescharacteristic
158Dic73—46no—
159Dic73—42no—
160C2×#3359—731nomaximal, Sylow
161C2×C73—44no—
162C2×C73#335914yescomplemented
163C2×C73C2×#54811yescharacteristic
164C2×C73C23×SD1611yescharacteristic
165C2×C73C2×#57811yescharacteristic
166C2×#557—731no—
167C2×D4×Q8D7311yescharacteristic
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—21no—
176C22×SD16—733no—
177#557—738no—
178#557—1464no—
179D4×Q8—24no—
180D4×Q8C2×D7318yes—
181C2×C4⋊Q8—733no—
182C2×C4⋊Q8C2×D7313yes—
183C2×#125—1463no—
184C2×C22⋊Q8—23no—
185C2×C4×Q8—733no—
186C2×C4×Q8—1461no—
187C2×C4×Q8C2×D7311yescharacteristic
188C2×C4×D4C2×D7313yes—
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—28no—
201C22×Q8—23no—
202C22×Q8—48no—
203C22×Q8—733no—
204C22×Q8C22⋊D7311yescharacteristic
205C22×D4C22×D7311yescharacteristic
206C23×C4—23no—
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—14624no—
216C22⋊Q8—224no—
217C4×Q8—7312no—
218C4×Q8—1468no—
219C4×Q8—1466no—
220C4×Q8C22⋊D7314yes—
221C4×Q8C22×D7314yes—
222C4×D4—26no—
223C4×D4C22×D73112yes—
224C2×C4⋊C4—23no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—1463no—
227C2×C4⋊C4—1463no—
228C2×C4⋊C4—1463no—
229C2×C4⋊C4C22⋊D7313yes—
230C2×C4⋊C4C22×D7313yes—
231C2×C22⋊C4—23no—
232C2×C42—1463no—
233C2×C42C22×D7313yes—
234#106—7312no—
235C4⋊C8—7312no—
236#103—7312no—
237#103—7324no—
238#102—734no—
239C4×C8—7312no—
240C24—21no—
241C2×Q8—212no—
242C2×Q8—432no—
243C2×Q8—412no—
244C2×Q8—736no—
245C2×Q8—1466no—
246C2×Q8—1466no—
247C2×Q8—1463no—
248C2×Q8#1192401618yescomplemented
249C2×Q8C2×C22⋊D7314yes—
250C2×D4—21no—
251C2×D4—22no—
252C2×D4#1192402914yes—
253C2×D4C23×D7312yes—
254C22×C4—23no—
255C22×C4—212no—
256C22×C4—412no—
257C22×C4—1461no—
258C22×C4—1463no—
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—23no—
269C4⋊C4—732no—
270C4⋊C4—14612no—
271C4⋊C4—1461no—
272C4⋊C4—14612no—
273C4⋊C4—14612no—
274C4⋊C4C2×C22⋊D73112yes—
275C4⋊C4C23×D7316yes—
276C22⋊C4—212no—
277C42—14612no—
278C42C2×C22⋊D7316yes—
279C42C23×D7316yes—
280C23—22no—
281C23—24no—
282C23—42no—
283C23—42no—
284C23C22×C22⋊D7311yescharacteristic
285Q8—424no—
286Q8—2926no—
287Q8—1466no—
288Q8—1466no—
289Q8C2×#11924016116yescomplemented
290D4—22no—
291D4—24no—
292D4C2×#1192402914yes—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—46no—
296C2×C4—424no—
297C2×C4—2922no—
298C2×C4—2926no—
299C2×C4—1462no—
300C2×C4—1466no—
301C2×C4C2×#11924016112yes—
302C2×C4C22×C22⋊D7316yes—
303C2×C4C22×C22⋊D7311yescharacteristic
304C2×C4C22×C22⋊D7316yes—
305C2×C4C2×#1192402912yes—
306C2×C4#1455663912yes—
307C2×C4C24×D7311yescharacteristic
308C8—1466no—
309C8—1462no—
310C22—24no—
311C22—48no—
312C22—42no—
313C22—42no—
314C22#1798924812yes—
315C22C22×#1192401612yes—
316C22#1798940212yes—
317C22C23×C22⋊D7311yescharacteristic
318C4—26no—
319C4—46no—
320C4—2926no—
321C4—2922no—
322C4#1798924812yes—
323C4C22×#11924016112yes—
324C4C22×#1192402911yescharacteristic
325C4C2×#1455663911yescharacteristic
326C2—44no—
327C2#2262257314yesdirect product factor
328C2C2×#1798924811yescharacteristic
329C2C23×#1192401611yescharacteristic
330C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×D4×Q8×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenterC2×D4×Q8D73
hypocenterC73C2×#3359
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#17989316C2semidirect
2. #22622573C2direct (N × H)
3. C2×#17988939C2semidirect
4. C2×#17988869C2semidirect
6. C2×Q8×#10596831C2semidirect
11. #17989316C22semidirect
16. #17988939C22semidirect
17. #17988869C22semidirect
19. Q8×#10596831C22semidirect
95. C2×Q8×C73SD16semidirect
120. Q8×C73C2×SD16semidirect
162. C2×C73#3359semidirect
174. C73C2×#3359semidirect
248. C2×Q8#11924016semidirect
289. Q8C2×#11924016semidirect
327. C2#22622573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893162
#226225732
C2×#179889392
C2×#179888692
C2×#179887922
C2×Q8×#105968312
C2×C4×#119240162
C2×D4×Q8×C732
C2×#335973