Finite Group Databasebeta

← C2×#22618950 #33950485

Subgroups — C2×#22618950 #33950485

Order 18688.

2230 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11924029C211yesmaximal, characteristic
2#22618950C2116yesmaximal, direct product factor
3C2×Q8×#10596831C211yesmaximal, characteristic, complemented
4C2×#17988666C213yesmaximal, complemented
5C2×#17988664C213yesmaximal, complemented
6C2×#17988643C213yesmaximal, complemented
7C2×C4×#11924011C213yesmaximal, complemented
8C2×C8×Q8×C73C211yesmaximal, characteristic, complemented
9C22×#11924029C411yescharacteristic
10C22×#11924011C2213yes—
11C22×#11924011C2213yes—
12C4×#11924029C418yes—
13C4×#11924029C2218yes—
14C2×Q8×Dic73C411yescharacteristic
15C2×C4×D292C2213yes—
16C2×#14556553C413yes—
17C2×#14556549C413yes—
18C2×C42×D73C2213yes—
19Q8×#10596831C2218yescomplemented
20#17988666C22124yescomplemented
21#17988664C22124yescomplemented
22#17988643C22124yescomplemented
23C2×C4⋊#10596831C2213yes—
24C2×#14556503C2216yes—
25C4×#11924011C22124yescomplemented
26C2×#14556501C2213yes—
27C2×#14556501C2211yescharacteristic
28C2×C4×#10596831C2213yes—
29C2×C4×Q8×C73C2211yescharacteristic
30C8×Q8×C73C2218yescomplemented
31C2×C4⋊C8×C73C2213yes—
32C2×C4×C8×C73C2213yes—
33C2×#11924029—28no—
34C2×#11924029C2×C418yes—
35C22×D292C2×C413yes—
36C22×C4×D73C2×C413yes—
37C22×C4×D73C2×C413yes—
38C22×C4×D73C2313yes—
39C2×#11924011—212no—
40C2×#11924011—212no—
41C2×#11924011C23112yes—
42C2×#11924011C23112yes—
43C22×#10596831C2313yes—
44C22×#10596831C2311yescharacteristic
45Q8×Dic73C2×C418yes—
46C4×D292C2×C4112yes—
47C4×D292C23112yes—
48#14556553C2×C4124yes—
49#14556549C2×C4124yes—
50C2×C4⋊Dic73C2×C413yes—
51C2×#11924005C2×C416yes—
52C2×C4×Dic73C2×C413yes—
53C2×C4×Dic73C2×C413yes—
54C2×C4×Dic73C2311yescharacteristic
55C42×D73C2×C4112yes—
56C42×D73C23112yes—
57C4⋊#10596831C23112yes—
58#14556503C23124yes—
59#14556501C23112yes—
60#14556501C2314yes—
61C4×#10596831C23112yes—
62C22×Q8×C73C2×C411yescharacteristic
63C22×C8×C73C2313yes—
64C22×C8×C73C2311yescharacteristic
65C4×Q8×C73C2×C414yes—
66C4×Q8×C73C2314yes—
67C2×C4⋊C4×C73C2×C413yes—
68C2×C42×C73C2313yes—
69C4⋊C8×C73C23112yes—
70C4×C8×C73C23112yes—
71C23×D73C22×C413yes—
72#11924029—232no—
73C2×D292—212no—
74C2×D292C22×C4112yes—
75C22×Dic73C22×C411yescharacteristic
76C22×Dic73C22×C411yescharacteristic
77C22×Dic73C22×C413yes—
78C2×C4×D73—212no—
79C2×C4×D73—26no—
80C2×C4×D73—26no—
81C2×C4×D73—46no—
82C2×C4×D73C22×C416yes—
83C2×C4×D73C22×C4112yes—
84C2×C4×D73C22×C4112yes—
85C2×C4×D73C2416yes—
86#11924011—224no—
87#11924011—224no—
88C2×#10596831—26no—
89C2×#10596831#4114yescomplemented
90C2×#10596831C2416yes—
91C2×#10596831C2412yes—
92C4⋊Dic73C22×C4112yes—
93#11924005C22×C4124yes—
94C4×Dic73C22×C412yes—
95C4×Dic73C22×C4112yes—
96C4×Dic73C22×C4112yes—
97C4×Dic73C2412yes—
98C2×Q8×C73M1618yescomplemented
99C2×Q8×C73C22×C414yes—
100C22×C4×C73C22×C413yes—
101C22×C4×C73C22×C413yes—
102C22×C4×C73C2411yescharacteristic
103C2×C8×C73—26no—
104C2×C8×C73#4114yescomplemented
105C2×C8×C73C2416yes—
106C2×C8×C73C2412yes—
107C4⋊C4×C73C22×C4112yes—
108C42×C73C22×C416yes—
109C42×C73C2416yes—
110C23×C73C23×C411yescharacteristic
111C22×D73—26no—
112C22×D73—26no—
113C22×D73—26no—
114C22×D73C23×C416yes—
115Q8×C73C2×M16116yescomplemented
116C2×C4×C73—26no—
117C2×C4×C73C2×M16112yes—
118C2×C4×C73C23×C416yes—
119C2×C4×C73C23×C411yescharacteristic
120C2×C4×C73C23×C416yes—
121C2×C4×C73C2×#4112yes—
122C2×C4×C73C2×#4112yes—
123C2×C4×C73C2511yescharacteristic
124C2×Dic73—26no—
125C2×Dic73—22no—
126C2×Dic73—22no—
127C2×Dic73C23×C412yes—
128C2×Dic73C23×C412yes—
129C2×Dic73C23×C416yes—
130D292—224no—
131C4×D73—212no—
132C4×D73—224no—
133C4×D73—26no—
134C4×D73—26no—
135C4×D73—412no—
136C8×C73—26no—
137C8×C73C2×#4114yescomplemented
138#10596831—26no—
139#10596831C2×#4114yescomplemented
140C22×C73C4×#4112yes—
141C22×C73C22×M1612yes—
142C22×C73#56812yes—
143C22×C73C24×C411yescharacteristic
144C2×D73—26no—
145C2×D73—26no—
146C2×D73—26no—
147C2×D73—412no—
148C4×C73—26no—
149C4×C73C4×#4112yes—
150C4×C73C22×M16112yes—
151C4×C73C22×#4111yescharacteristic
152C4×C73C22×#4111yescharacteristic
153Dic73—26no—
154Dic73—22no—
155Dic73—22no—
156C2×#2971—731nomaximal, Sylow
157C2×C73#297114yescomplemented
158C2×C73C2×C4×#4111yescharacteristic
159C2×C73C23×M1611yescharacteristic
160C2×C73C2×#56811yescharacteristic
161D73—46no—
162C2×C4×#41—731no—
163#2971—7316no—
164C2×C8×Q8—731no—
165C2×C8×Q8D7311yescharacteristic, complemented
166C2×#436—733no—
167C2×#436—733no—
168C2×#432—733no—
169C2×C4×M16—733no—
170C73C2×#297111yescharacteristic, complemented, Sylow
171C22×#41—731no—
172C22×M16—733no—
173C22×M16—733no—
174C4×#41—738no—
175C4×#41—738no—
176C2×C4×Q8—731no—
177C2×C4×Q8C2×D7311yescharacteristic
178C2×C4×D4—733no—
179C2×C4×D4—733no—
180C2×#117—733no—
181C22×C42—733no—
182C8×Q8—738no—
183C8×Q8C2×D7318yescomplemented
184#436—7324no—
185#436—7324no—
186#432—7324no—
187C2×C4⋊C8—733no—
188C2×C4⋊C8C2×D7313yes—
189C2×C22⋊C8—736no—
190C4×M16—7324no—
191C2×#97—731no—
192C2×#97—733no—
193C2×C4×C8—733no—
194C2×C4×C8C2×D7313yes—
195C2×#41—738no—
196C2×#41—1468no—
197C22×Q8C4×D7311yescharacteristic
198C22×D4—733no—
199C23×C4—733no—
200C23×C4—733no—
201C23×C4—733no—
202C2×M16—7312no—
203C2×M16—7312no—
204C2×M16—14612no—
205C2×M16—14612no—
206C22×C8—731no—
207C22×C8—733no—
208C22×C8C22×D7313yes—
209C22×C8C22×D7311yescharacteristic
210C4×Q8—738no—
211C4×Q8C4×D7314yes—
212C4×Q8C22×D7314yes—
213C4×D4—7324no—
214C4×D4—7312no—
215C4×D4—7312no—
216#117—7324no—
217C2×C4⋊C4—733no—
218C2×C4⋊C4C4×D7313yes—
219C2×C22⋊C4—736no—
220C2×C42—733no—
221C2×C42—733no—
222C2×C42—731no—
223C2×C42—7312no—
224C2×C42—7312no—
225C2×C42C22×D7313yes—
226C4⋊C8—7312no—
227C4⋊C8C22×D73112yes—
228C22⋊C8—7324no—
229#97—734no—
230#97—7312no—
231C4×C8—7312no—
232C4×C8C22×D73112yes—
233C24—733no—
234#41—14632no—
235C2×Q8#1192401118yescomplemented
236C2×Q8C2×C4×D7314yes—
237C2×D4—7312no—
238C2×D4—14612no—
239C22×C4—2926no—
240C22×C4—7312no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—733no—
244C22×C4—7312no—
245C22×C4—736no—
246C22×C4—736no—
247C22×C4—14612no—
248C22×C4—1466no—
249C22×C4—1466no—
250C22×C4C2×C4×D7313yes—
251C22×C4C2×C4×D7313yes—
252C22×C4C23×D7311yescharacteristic
253M16—14624no—
254M16—14624no—
255C2×C8—26no—
256C2×C8—734no—
257C2×C8—732no—
258C2×C8—736no—
259C2×C8—1466no—
260C2×C8#1192402914yescomplemented
261C2×C8C23×D7316yes—
262C2×C8C23×D7312yes—
263C4⋊C4—7312no—
264C4⋊C4C2×C4×D73112yes—
265C22⋊C4—7324no—
266C42—732no—
267C42—7312no—
268C42—7312no—
269C42—732no—
270C42C2×C4×D7316yes—
271C42C23×D7316yes—
272C23—736no—
273C23—1466no—
274C23—1466no—
275C23—1466no—
276C23C22×C4×D7311yescharacteristic
277Q8C2×#11924011116yescomplemented
278D4—14624no—
279C2×C4—26no—
280C2×C4—29212no—
281C2×C4—732no—
282C2×C4—732no—
283C2×C4—736no—
284C2×C4—1466no—
285C2×C4—1462no—
286C2×C4—1462no—
287C2×C4—1466no—
288C2×C4—1466no—
289C2×C4—14612no—
290C2×C4—14624no—
291C2×C4C2×#11924011112yes—
292C2×C4C22×C4×D7316yes—
293C2×C4C22×C4×D7311yescharacteristic
294C2×C4C22×C4×D7316yes—
295C2×C4#41×D7312yes—
296C2×C4C2×#1192402912yes—
297C2×C4C24×D7311yescharacteristic
298C8—26no—
299C8—734no—
300C8—1466no—
301C8C2×#1192402914yescomplemented
302C22—29212no—
303C22—1466no—
304C22—1466no—
305C22—1466no—
306C22C4×#1192402912yes—
307C22C22×#1192401112yes—
308C22#1798935212yes—
309C22C23×C4×D7311yescharacteristic
310C4—26no—
311C4—1462no—
312C4—1462no—
313C4—1466no—
314C4C4×#1192402912yes—
315C4C22×#11924011112yes—
316C4C2×#41×D7311yescharacteristic
317C4C22×#1192402911yescharacteristic
318C2—2926no—
319C2#2261895014yesdirect product factor
320C2C2×C4×#1192402911yescharacteristic
321C2C23×#1192401111yescharacteristic
322C2C2×#1798935211yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC2×C4C24×D73
FittingC2×C8×Q8×C73C2
socleC23×C73C23×C4
prime radicalC22×#11924029C4
cosocleC2×C4×C73C25
hypercenterC2×C8×Q8D73
hypocenterC73C2×#2971
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #22618950C2direct (N × H)
3. C2×Q8×#10596831C2semidirect
4. C2×#17988666C2semidirect
5. C2×#17988664C2semidirect
6. C2×#17988643C2semidirect
7. C2×C4×#11924011C2semidirect
8. C2×C8×Q8×C73C2semidirect
19. Q8×#10596831C22semidirect
20. #17988666C22semidirect
21. #17988664C22semidirect
22. #17988643C22semidirect
25. C4×#11924011C22semidirect
30. C8×Q8×C73C22semidirect
89. C2×#10596831#41semidirect
98. C2×Q8×C73M16semidirect
104. C2×C8×C73#41semidirect
115. Q8×C73C2×M16semidirect
137. C8×C73C2×#41semidirect
139. #10596831C2×#41semidirect
157. C2×C73#2971semidirect
165. C2×C8×Q8D73semidirect
170. C73C2×#2971semidirect
183. C8×Q8C2×D73semidirect
235. C2×Q8#11924011semidirect
260. C2×C8#11924029semidirect
277. Q8C2×#11924011semidirect
301. C8C2×#11924029semidirect
319. C2#22618950direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#119240292
#226189502
C2×Q8×#105968312
C2×#179886662
C2×#179886642
C2×#179886432
C2×C4×#119240112
C2×C8×Q8×C732
C2×#297173