Finite Group Databasebeta

← C2×#22622913 #33966886

Subgroups — C2×#22622913 #33966886

Order 18688.

2238 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×#17989316C211yesmaximal, characteristic, complemented
2C2×#17989259C211yesmaximal, characteristic
3#22622913C2116yesmaximal, direct product factor
4C2×#17988960C213yesmaximal, complemented
5C2×#17988788C213yesmaximal, complemented
6C2×#17988793C213yesmaximal, complemented
7C2×C4×#11924017C213yesmaximal, complemented
8C2×C8×Q8×C73C211yesmaximal, characteristic, complemented
9C22×#11924029—21no—
10C22×#11924017C2213yes—
11C22×#11924017C2216yes—
12#17989316—24no—
13#17989316C2218yescomplemented
14#17989259—24no—
15#17989259C2218yes—
16C2×#14556591C2213yes—
17C2×#14556588C2213yes—
18C2×#14556582—23no—
19C2×#14556566—23no—
20C2×Q8×Dic73—21no—
21C2×C4×Dic146C2213yes—
22C2×C4×D292C2213yes—
23#17988960C22124yescomplemented
24#17988793C22124yescomplemented
25#17988788C22124yescomplemented
26C4×#11924017C22124yescomplemented
27C2×#14556523C2211yescharacteristic
28C2×#14556516C2213yes—
29C2×#14556513C2213yes—
30C2×C4×Q8×C73C2211yescharacteristic
31C8×Q8×C73C2218yescomplemented
32C2×C4⋊C8×C73C2213yes—
33C2×C4×C8×C73C2213yes—
34C2×#11924029—28no—
35C2×#11924029—48no—
36C22×Dic146C2313yes—
37C22×D292—23no—
38C22×D292—23no—
39C22×D292C2313yes—
40C22×C4×D73—23no—
41C2×#11924017—212no—
42C2×#11924017—412no—
43C2×#11924017C23112yes—
44C2×#11924017C23124yes—
45#14556591—26no—
46#14556591C23112yes—
47#14556588—26no—
48#14556588C23112yes—
49#14556582—224no—
50#14556566—224no—
51Q8×Dic73—28no—
52C4×Dic146—26no—
53C4×Dic146C23112yes—
54C4×D292—26no—
55C4×D292C23112yes—
56C2×C4⋊Dic73—23no—
57C2×C4⋊Dic73—23no—
58C2×C4⋊Dic73C2311yescharacteristic
59C2×C4⋊Dic73C2311yescharacteristic
60C2×#11924007—23no—
61C2×#11924005—23no—
62C2×C4×Dic73—23no—
63#14556523C2314yes—
64#14556516C23112yes—
65#14556513C23112yes—
66C22×Q8×C73D411yescharacteristic
67C22×C8×C73C2313yes—
68C22×C8×C73C2311yescharacteristic
69C4×Q8×C73D414yes—
70C4×Q8×C73C2314yes—
71C2×C4⋊C4×C73D413yes—
72C2×C42×C73C2313yes—
73C4⋊C8×C73C23112yes—
74C4×C8×C73C23112yes—
75C23×D73—23no—
76#11924029—432no—
77C2×Dic146—26no—
78C2×Dic146—26no—
79C2×Dic146—23no—
80C2×Dic146C2416yes—
81C2×D292—26no—
82C2×D292—26no—
83C2×D292—23no—
84C2×D292—212no—
85C2×D292—212no—
86C2×D292—412no—
87C2×D292—86no—
88C2×D292C2416yes—
89C22×Dic73—21no—
90C22×Dic73—23no—
91C22×Dic73—21no—
92C2×C4×D73—212no—
93C2×C4×D73—412no—
94#11924017—224no—
95#11924017—424no—
96C4⋊Dic73—212no—
97C4⋊Dic73—212no—
98C4⋊Dic73—21no—
99C4⋊Dic73—21no—
100C4⋊Dic73C2412yes—
101C4⋊Dic73C2412yes—
102#11924007—212no—
103#11924005—212no—
104C4×Dic73—212no—
105C2×Q8×C73SD1618yescomplemented
106C2×Q8×C73C2×D414yes—
107C22×C4×C73C2×D413yes—
108C22×C4×C73C2×D413yes—
109C22×C4×C73C2411yescharacteristic
110C2×C8×C73—26no—
111C2×C8×C73#4114yescomplemented
112C2×C8×C73C2416yes—
113C2×C8×C73C2412yes—
114C4⋊C4×C73C2×D4112yes—
115C42×C73C2×D416yes—
116C42×C73C2416yes—
117C23×C73C22×D411yescharacteristic
118C22×D73—26no—
119C22×D73—46no—
120C22×D73—46no—
121C22×D73—46no—
122Q8×C73C2×SD16116yescomplemented
123C2×C4×C73—26no—
124C2×C4×C73C2×SD16112yes—
125C2×C4×C73C22×D416yes—
126C2×C4×C73C22×D411yescharacteristic
127C2×C4×C73C22×D416yes—
128C2×C4×C73C2×#4112yes—
129C2×C4×C73H(5,𝔽2)12yes—
130C2×C4×C73C2511yescharacteristic
131C2×Dic73—22no—
132C2×Dic73—26no—
133C2×Dic73—22no—
134C2×Dic73—46no—
135C2×Dic73—42no—
136C2×Dic73—42no—
137D292—26no—
138D292—26no—
139D292—46no—
140D292—424no—
141D292—812no—
142C4×D73—424no—
143Dic146—26no—
144Dic146—26no—
145Dic146—46no—
146C8×C73—26no—
147C8×C73C2×#4114yescomplemented
148C22×C73#55012yes—
149C22×C73C22×SD1612yes—
150C22×C73#57712yes—
151C22×C73C23×D411yescharacteristic
152C2×D73—46no—
153C2×D73—46no—
154C2×D73—46no—
155C2×D73—812no—
156C4×C73—26no—
157C4×C73#55012yes—
158C4×C73C22×SD16112yes—
159C4×C73C22×#4111yescharacteristic
160C4×C73C2×H(5,𝔽2)11yescharacteristic
161Dic73—46no—
162Dic73—42no—
163Dic73—42no—
164C2×#3392—731nomaximal, Sylow
165C2×C73#339214yescomplemented
166C2×C73C2×#55011yescharacteristic
167C2×C73C23×SD1611yescharacteristic
168C2×C73C2×#57711yescharacteristic
169D73—86no—
170C2×#557—731no—
171C2×#550—731no—
172#3392—7316no—
173C2×#492—733no—
174C2×#460—733no—
175C2×#461—733no—
176C2×C8×Q8D7311yescharacteristic, complemented
177C2×C4×SD16—733no—
178C73C2×#339211yescharacteristic, complemented, Sylow
179C22×#41—1461no—
180C22×SD16—736no—
181C22×SD16—733no—
182#557—738no—
183#557—1464no—
184#550—738no—
185#550—1464no—
186C2×C4⋊Q8—733no—
187C2×#127—733no—
188C2×#125—1463no—
189C2×#121—1463no—
190C2×C4×Q8—733no—
191C2×C4×Q8—1461no—
192C2×C4×Q8C2×D7311yescharacteristic
193C2×C4×D4—733no—
194#492—7324no—
195#461—7324no—
196#460—7324no—
197C8×Q8C2×D7318yescomplemented
198C4×SD16—7324no—
199C2×#106—731no—
200C2×C4⋊C8C2×D7313yes—
201C2×#103—733no—
202C2×#102—733no—
203C2×C4×C8C2×D7313yes—
204C2×#41—2928no—
205C2×#41—1468no—
206C22×Q8—733no—
207C22×Q8D29211yescharacteristic
208C22×D4—733no—
209C22×D4—1463no—
210C22×D4—1463no—
211C23×C4—1463no—
212C2×SD16—29212no—
213C2×SD16—7324no—
214C2×SD16—7312no—
215C2×SD16—14612no—
216C22×C8C22×D7313yes—
217C22×C8C22×D7311yescharacteristic
218C4⋊Q8—7312no—
219C4⋊Q8—1466no—
220#127—7312no—
221#127—1466no—
222#125—14624no—
223#121—14624no—
224C4×Q8—7312no—
225C4×Q8—1468no—
226C4×Q8—1466no—
227C4×Q8D29214yes—
228C4×Q8C22×D7314yes—
229C4×D4—7312no—
230C4×D4—1466no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—1463no—
234C2×C4⋊C4—1463no—
235C2×C4⋊C4—1463no—
236C2×C4⋊C4D29213yes—
237C2×C22⋊C4—1463no—
238C2×C42—1463no—
239C2×C42C22×D7313yes—
240#106—734no—
241C4⋊C8C22×D73112yes—
242#103—7312no—
243#102—7312no—
244C4×C8C22×D73112yes—
245C24—1463no—
246#41—29232no—
247C2×Q8—736no—
248C2×Q8—1466no—
249C2×Q8—1466no—
250C2×Q8—1463no—
251C2×Q8#1192401718yescomplemented
252C2×Q8C2×D29214yes—
253C2×D4—29212no—
254C2×D4—5846no—
255C2×D4—736no—
256C2×D4—1463no—
257C2×D4—14612no—
258C2×D4—14612no—
259C2×D4—1466no—
260C2×D4—1466no—
261C22×C4—29212no—
262C22×C4—1461no—
263C22×C4—1463no—
264C22×C4—1461no—
265C22×C4—14612no—
266C22×C4C2×D29213yes—
267C22×C4C2×D29213yes—
268C22×C4C23×D7311yescharacteristic
269SD16—29224no—
270SD16—14624no—
271C2×C8—26no—
272C2×C8#1192402914yescomplemented
273C2×C8C23×D7316yes—
274C2×C8C23×D7312yes—
275C4⋊C4—732no—
276C4⋊C4—732no—
277C4⋊C4—14612no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—14612no—
281C4⋊C4—14612no—
282C4⋊C4C2×D292112yes—
283C22⋊C4—14612no—
284C42—14612no—
285C42C2×D29216yes—
286C42C23×D7316yes—
287C23—2926no—
288C23—2926no—
289C23—2926no—
290C23—1466no—
291C23C22×D29211yescharacteristic
292Q8—2926no—
293Q8—1466no—
294Q8—1466no—
295Q8C2×#11924017116yescomplemented
296D4—2926no—
297D4—29224no—
298D4—58412no—
299D4—1466no—
300D4—1466no—
301C2×C4—26no—
302C2×C4—2922no—
303C2×C4—2926no—
304C2×C4—2922no—
305C2×C4—29224no—
306C2×C4—1462no—
307C2×C4—1466no—
308C2×C4—1462no—
309C2×C4C2×#11924017112yes—
310C2×C4C22×D29216yes—
311C2×C4C22×D29211yescharacteristic
312C2×C4C22×D29216yes—
313C2×C4C2×#1192402912yes—
314C2×C4#1455663712yes—
315C2×C4C24×D7311yescharacteristic
316C8—26no—
317C8C2×#1192402914yescomplemented
318C22—2926no—
319C22—2926no—
320C22—2926no—
321C22—58412no—
322C22#1798925912yes—
323C22C22×#1192401712yes—
324C22#1798939912yes—
325C22C23×D29211yescharacteristic
326C4—26no—
327C4—2922no—
328C4—2926no—
329C4—2922no—
330C4#1798925912yes—
331C4C22×#11924017112yes—
332C4C22×#1192402911yescharacteristic
333C4C2×#1455663711yescharacteristic
334C2—5846no—
335C2#2262291314yesdirect product factor
336C2C2×#1798925911yescharacteristic
337C2C23×#1192401711yescharacteristic
338C2C2×#1798939911yescharacteristic
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×#3392
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×#17989316C2semidirect
3. #22622913C2direct (N × H)
4. C2×#17988960C2semidirect
5. C2×#17988788C2semidirect
6. C2×#17988793C2semidirect
7. C2×C4×#11924017C2semidirect
8. C2×C8×Q8×C73C2semidirect
13. #17989316C22semidirect
23. #17988960C22semidirect
24. #17988793C22semidirect
25. #17988788C22semidirect
26. C4×#11924017C22semidirect
31. C8×Q8×C73C22semidirect
105. C2×Q8×C73SD16semidirect
111. C2×C8×C73#41semidirect
122. Q8×C73C2×SD16semidirect
147. C8×C73C2×#41semidirect
165. C2×C73#3392semidirect
176. C2×C8×Q8D73semidirect
178. C73C2×#3392semidirect
197. C8×Q8C2×D73semidirect
251. C2×Q8#11924017semidirect
272. C2×C8#11924029semidirect
295. Q8C2×#11924017semidirect
317. C8C2×#11924029semidirect
335. C2#22622913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893162
C2×#179892592
#226229132
C2×#179889602
C2×#179887882
C2×#179887932
C2×C4×#119240172
C2×C8×Q8×C732
C2×#339273