Finite Group Databasebeta

← C2×#22622603 #33965581

Subgroups — C2×#22622603 #33965581

Order 18688.

2174 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic146C211yesmaximal, characteristic, complemented
2C2×#17989259C211yesmaximal, characteristic
3#22622603C2116yesmaximal, direct product factor
4C2×#17988934C213yesmaximal, complemented
5C2×#17988878C213yesmaximal, complemented
6C2×#17988788C213yesmaximal, complemented
7C2×C4×#11924017C213yesmaximal, complemented
8C2×C8×Q8×C73C211yesmaximal, characteristic, complemented
9C22×#11924029—21no—
10C22×#11924017C2213yes—
11Q8×Dic146—24no—
12Q8×Dic146C2218yescomplemented
13#17989259—24no—
14#17989259C2218yes—
15C2×#14556591C2213yes—
16C2×#14556590—23no—
17C2×#14556588C2213yes—
18C2×#14556566—23no—
19C2×Q8×Dic73—21no—
20C2×C4×Dic146C2213yes—
21C2×C4×D292C2213yes—
22#17988934C22124yescomplemented
23#17988878C22124yescomplemented
24#17988788C22124yescomplemented
25C4×#11924017C22124yescomplemented
26C2×#14556523C2213yes—
27C2×#14556516C2211yescharacteristic
28C2×#14556513C2216yes—
29C2×#14556513C2213yes—
30C2×C4×Q8×C73C2211yescharacteristic
31C8×Q8×C73C2218yescomplemented
32C2×C4⋊C8×C73C2213yes—
33C2×C4×C8×C73C2213yes—
34C2×#11924029—28no—
35C2×#11924029—48no—
36C22×Dic146—23no—
37C22×Dic146C2311yescharacteristic
38C22×D292—23no—
39C22×D292—23no—
40C22×D292C2313yes—
41C22×C4×D73—23no—
42C2×#11924017—212no—
43C2×#11924017C23112yes—
44#14556591—26no—
45#14556591C23112yes—
46#14556590—224no—
47#14556588—26no—
48#14556588C23112yes—
49#14556566—224no—
50Q8×Dic73—28no—
51C4×Dic146—26no—
52C4×Dic146C23112yes—
53C4×D292—26no—
54C4×D292C23112yes—
55C2×C4⋊Dic73—23no—
56C2×C4⋊Dic73C2311yescharacteristic
57C2×C4⋊Dic73C2313yes—
58C2×#11924007—23no—
59C2×#11924005—23no—
60C2×C4×Dic73—23no—
61#14556523C23112yes—
62#14556516C2314yes—
63#14556513C23124yes—
64#14556513C23112yes—
65C22×Q8×C73D411yescharacteristic
66C22×C8×C73C2313yes—
67C22×C8×C73C2311yescharacteristic
68C4×Q8×C73D414yes—
69C4×Q8×C73C2314yes—
70C2×C4⋊C4×C73D413yes—
71C2×C42×C73C2313yes—
72C4⋊C8×C73C23112yes—
73C4×C8×C73C23112yes—
74C23×D73—23no—
75#11924029—432no—
76C2×Dic146—21no—
77C2×Dic146—22no—
78C2×Dic146—212no—
79C2×Dic146—86no—
80C2×Dic146#4114yescomplemented
81C2×Dic146C2412yes—
82C2×D292—26no—
83C2×D292—26no—
84C2×D292—23no—
85C2×D292—212no—
86C2×D292—212no—
87C2×D292—412no—
88C2×D292—86no—
89C2×D292C2416yes—
90C22×Dic73—21no—
91C22×Dic73—23no—
92C22×Dic73—21no—
93C2×C4×D73—212no—
94C2×C4×D73—412no—
95#11924017—224no—
96C4⋊Dic73—212no—
97C4⋊Dic73—21no—
98C4⋊Dic73—23no—
99C4⋊Dic73C2416yes—
100C4⋊Dic73C2412yes—
101#11924007—212no—
102#11924005—212no—
103C4×Dic73—212no—
104C2×Q8×C73SD1618yescomplemented
105C2×Q8×C73C2×D414yes—
106C22×C4×C73C2×D413yes—
107C22×C4×C73C2×D413yes—
108C22×C4×C73C2411yescharacteristic
109C2×C8×C73—26no—
110C2×C8×C73—22no—
111C2×C8×C73C2412yes—
112C2×C8×C73C2416yes—
113C4⋊C4×C73C2×D4112yes—
114C42×C73C2×D416yes—
115C42×C73C2416yes—
116C23×C73C22×D411yescharacteristic
117C22×D73—26no—
118C22×D73—46no—
119C22×D73—46no—
120C22×D73—46no—
121Q8×C73C2×SD16116yescomplemented
122C2×C4×C73—26no—
123C2×C4×C73C2×SD16112yes—
124C2×C4×C73C22×D416yes—
125C2×C4×C73C22×D411yescharacteristic
126C2×C4×C73C22×D416yes—
127C2×C4×C73C2×#4112yes—
128C2×C4×C732−1+412yes—
129C2×C4×C73C2511yescharacteristic
130C2×Dic73—24no—
131C2×Dic73—22no—
132C2×Dic73—26no—
133C2×Dic73—22no—
134C2×Dic73—42no—
135C2×Dic73—46no—
136D292—26no—
137D292—26no—
138D292—46no—
139D292—424no—
140D292—812no—
141C4×D73—424no—
142Dic146—24no—
143Dic146—22no—
144Dic146—812no—
145Dic146C2×#4114yescomplemented
146C8×C73—26no—
147C8×C73—22no—
148C22×C73#54812yes—
149C22×C73C22×SD1612yes—
150C22×C73#57612yes—
151C22×C73C23×D411yescharacteristic
152C2×D73—46no—
153C2×D73—46no—
154C2×D73—46no—
155C2×D73—812no—
156C4×C73—26no—
157C4×C73#54812yes—
158C4×C73C22×SD16112yes—
159C4×C73C22×#4111yescharacteristic
160C4×C73C2×2−1+411yescharacteristic
161Dic73—24no—
162Dic73—42no—
163Dic73—46no—
164C2×#3362—731nomaximal, Sylow
165C2×C73#336214yescomplemented
166C2×C73C2×#54811yescharacteristic
167C2×C73C23×SD1611yescharacteristic
168C2×C73C2×#57611yescharacteristic
169D73—86no—
170C2×Q82—731no—
171C2×#550—731no—
172#3362—7316no—
173C2×#486—733no—
174C2×#476—733no—
175C2×#460—733no—
176C2×C8×Q8D7311yescharacteristic, complemented
177C2×C4×SD16—733no—
178C73C2×#336211yescharacteristic, complemented, Sylow
179C22×#41—1461no—
180C22×SD16—733no—
181Q82—738no—
182Q82—1464no—
183#550—738no—
184#550—1464no—
185C2×C4⋊Q8—733no—
186C2×C4⋊Q8—1463no—
187C2×#127—733no—
188C2×#121—1463no—
189C2×C4×Q8—733no—
190C2×C4×Q8—1461no—
191C2×C4×Q8C2×D7311yescharacteristic
192C2×C4×D4—733no—
193#486—7324no—
194#476—7324no—
195#460—7324no—
196C8×Q8C2×D7318yescomplemented
197C4×SD16—7324no—
198C2×#106—733no—
199C2×C4⋊C8C2×D7313yes—
200C2×#103—731no—
201C2×#102—733no—
202C2×#102—736no—
203C2×C4×C8C2×D7313yes—
204C2×#41—2928no—
205C2×#41—1468no—
206C22×Q8—731no—
207C22×Q8—1463no—
208C22×Q8D29211yescharacteristic
209C22×D4—733no—
210C22×D4—1463no—
211C22×D4—1463no—
212C23×C4—1463no—
213C2×SD16—7312no—
214C2×SD16—14612no—
215C22×C8C22×D7313yes—
216C22×C8C22×D7311yescharacteristic
217C4⋊Q8—7312no—
218C4⋊Q8—14624no—
219C4⋊Q8—1466no—
220#127—7312no—
221#127—1466no—
222#121—14624no—
223C4×Q8—7312no—
224C4×Q8—1468no—
225C4×Q8—1466no—
226C4×Q8D29214yes—
227C4×Q8C22×D7314yes—
228C4×D4—7312no—
229C4×D4—1466no—
230C2×C4⋊C4—731no—
231C2×C4⋊C4—733no—
232C2×C4⋊C4—1463no—
233C2×C4⋊C4—1463no—
234C2×C4⋊C4D29213yes—
235C2×C22⋊C4—1463no—
236C2×C42—1463no—
237C2×C42C22×D7313yes—
238#106—7312no—
239C4⋊C8C22×D73112yes—
240#103—734no—
241#102—7312no—
242#102—7324no—
243C4×C8C22×D73112yes—
244C24—1463no—
245#41—29232no—
246C2×Q8—5846no—
247C2×Q8—734no—
248C2×Q8—732no—
249C2×Q8—14612no—
250C2×Q8—1461no—
251C2×Q8—1462no—
252C2×Q8#1192401718yescomplemented
253C2×Q8C2×D29214yes—
254C2×D4—29212no—
255C2×D4—5846no—
256C2×D4—736no—
257C2×D4—1463no—
258C2×D4—14612no—
259C2×D4—14612no—
260C2×D4—1466no—
261C2×D4—1466no—
262C22×C4—29212no—
263C22×C4—1463no—
264C22×C4—1461no—
265C22×C4—14612no—
266C22×C4—1461no—
267C22×C4C2×D29213yes—
268C22×C4C2×D29213yes—
269C22×C4C23×D7311yescharacteristic
270SD16—14624no—
271C2×C8—26no—
272C2×C8—22no—
273C2×C8C23×D7312yes—
274C2×C8C23×D7316yes—
275C4⋊C4—736no—
276C4⋊C4—732no—
277C4⋊C4—14612no—
278C4⋊C4—1461no—
279C4⋊C4—1463no—
280C4⋊C4—14612no—
281C4⋊C4C2×D292112yes—
282C22⋊C4—14612no—
283C42—14612no—
284C42C2×D29216yes—
285C42C23×D7316yes—
286C23—2926no—
287C23—2926no—
288C23—2926no—
289C23—1466no—
290C23C22×D29211yescharacteristic
291Q8—58412no—
292Q8—734no—
293Q8—1462no—
294Q8—1464no—
295Q8C2×#11924017116yescomplemented
296D4—2926no—
297D4—29224no—
298D4—58412no—
299D4—1466no—
300D4—1466no—
301C2×C4—26no—
302C2×C4—2926no—
303C2×C4—2922no—
304C2×C4—29224no—
305C2×C4—1466no—
306C2×C4—1462no—
307C2×C4—1462no—
308C2×C4—1464no—
309C2×C4C2×#11924017112yes—
310C2×C4C22×D29216yes—
311C2×C4C22×D29211yescharacteristic
312C2×C4C22×D29216yes—
313C2×C4#41×D7312yes—
314C2×C4#1455663912yes—
315C2×C4C24×D7311yescharacteristic
316C8—26no—
317C8—22no—
318C22—2926no—
319C22—2926no—
320C22—2926no—
321C22—58412no—
322C22#1798924912yes—
323C22C22×#1192401712yes—
324C22#1798939212yes—
325C22C23×D29211yescharacteristic
326C4—26no—
327C4—2922no—
328C4—2926no—
329C4—1464no—
330C4#1798924912yes—
331C4C22×#11924017112yes—
332C4C2×#41×D7311yescharacteristic
333C4C2×#1455663911yescharacteristic
334C2—5846no—
335C2#2262260314yesdirect product factor
336C2C2×#1798924911yescharacteristic
337C2C23×#1192401711yescharacteristic
338C2C2×#1798939211yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C8×Q8×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989259C2
hypercenterC2×C8×Q8D73
hypocenterC73C2×#3362
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic146C2semidirect
3. #22622603C2direct (N × H)
4. C2×#17988934C2semidirect
5. C2×#17988878C2semidirect
6. C2×#17988788C2semidirect
7. C2×C4×#11924017C2semidirect
8. C2×C8×Q8×C73C2semidirect
12. Q8×Dic146C22semidirect
22. #17988934C22semidirect
23. #17988878C22semidirect
24. #17988788C22semidirect
25. C4×#11924017C22semidirect
31. C8×Q8×C73C22semidirect
80. C2×Dic146#41semidirect
104. C2×Q8×C73SD16semidirect
121. Q8×C73C2×SD16semidirect
145. Dic146C2×#41semidirect
165. C2×C73#3362semidirect
176. C2×C8×Q8D73semidirect
178. C73C2×#3362semidirect
196. C8×Q8C2×D73semidirect
252. C2×Q8#11924017semidirect
295. Q8C2×#11924017semidirect
335. C2#22622603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1462
C2×#179892592
#226226032
C2×#179889342
C2×#179888782
C2×#179887882
C2×C4×#119240172
C2×C8×Q8×C732
C2×#336273