Finite Group Databasebeta

← C2×#22618493 #33949604

Subgroups — C2×#22618493 #33949604

Order 18688.

2830 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D73C212yesmaximal
2C22×#14556548C211yesmaximal, characteristic
3#22618493C2116yesmaximal, direct product factor
4C2×#17988612C218yesmaximal, complemented
5C2×#17988611C211yesmaximal, characteristic, complemented
6C2×#17988610C212yesmaximal, complemented
7C2×#423×C73C211yesmaximal, characteristic, complemented
8C23×C4×D73C2211yescharacteristic
9C22×#11924012C2212yes—
10C22×#11924011C2214yes—
11C2×M16×D73—216no—
12C2×M16×D73C22116yes—
13C22×C8×D73C2214yes—
14C2×#14556548C414yes—
15C2×#14556548C418yes—
16C2×#14556548C2214yes—
17C2×#14556548C2218yes—
18C22×#11924007C412yes—
19C22×#11924005C412yes—
20C22×C4×Dic73C2211yescharacteristic
21#17988612C22164yescomplemented
22#17988611C2218yescomplemented
23#17988610C22116yescomplemented
24C2×C4⋊#10596831C2214yescomplemented
25C2×#14556520C2218yescomplemented
26C22×M16×C73C2212yes—
27C22×C42×C73C2211yescharacteristic
28#423×C73C2218yescomplemented
29C2×C4⋊C8×C73C2214yescomplemented
30C24×D73C2×C411yescharacteristic
31C23×Dic73C2×C412yes—
32C23×Dic73C2×C411yescharacteristic
33C22×C4×D73C2×C412yes—
34C22×C4×D73C2×C414yes—
35C22×C4×D73D418yes—
36C22×C4×D73Q818yes—
37C22×C4×D73C2312yes—
38C22×C4×D73C2314yes—
39C2×#11924012—28no—
40C2×#11924012C2318yes—
41C2×#11924011—216no—
42C2×#11924011C23116yes—
43M16×D73—264no—
44C22×#10596831C2314yes—
45C2×C8×D73—216no—
46C2×C8×D73C23116yes—
47#14556548C2×C4116yes—
48#14556548C2×C4132yes—
49#14556548C23116yes—
50C2×#11924007C2×C418yes—
51C2×#11924007C2×C4116yes—
52C2×#11924005C2×C418yes—
53C2×#11924005C2×C4116yes—
54C2×C4×Dic73C2×C412yes—
55C2×C4×Dic73C2×C414yes—
56C2×C4×Dic73C2314yes—
57C2×C4×Dic73C2312yes—
58C4⋊#10596831C23116yescomplemented
59#14556520C23132yescomplemented
60C23×C4×C73C2×C412yes—
61C23×C4×C73C2311yescharacteristic
62C2×M16×C73—28no—
63C2×M16×C73C2318yes—
64C22×C8×C73C2314yes—
65C2×C42×C73C2×C412yes—
66C2×C42×C73C2×C414yes—
67C2×C42×C73C2312yes—
68C2×C42×C73C2314yes—
69C4⋊C8×C73C23116yescomplemented
70C23×D73—44no—
71C23×D73C4⋊C418yes—
72C23×D73C22×C412yes—
73C23×D73C22×C414yes—
74C22×Dic73—44no—
75C22×Dic73C4⋊C418yes—
76C22×Dic73C22×C414yes—
77C22×Dic73C22×C418yes—
78C22×Dic73C22×C414yes—
79C22×Dic73C22×C412yes—
80C2×C4×D73C4⋊C4116yes—
81C2×C4×D73C4⋊C4132yes—
82C2×C4×D73C22×C414yes—
83C2×C4×D73C22×C418yes—
84C2×C4×D73C2×D418yes—
85C2×C4×D73C2×D4116yes—
86C2×C4×D73C2×Q818yes—
87C2×C4×D73C2×Q8116yes—
88C2×C4×D73C2414yes—
89#11924012—216no—
90#11924011—232no—
91C2×#10596831—28no—
92C2×#10596831C2418yes—
93C8×D73—232no—
94#11924007C22×C4132yes—
95#11924005C22×C4132yes—
96C4×Dic73C22×C418yes—
97C4×Dic73C22×C414yes—
98C4×Dic73C2414yes—
99C24×C73C22×C411yescharacteristic
100C22×C4×C73—44no—
101C22×C4×C73C22×C414yes—
102C22×C4×C73C22×C418yes—
103C22×C4×C73C22×C412yes—
104C22×C4×C73C22×C411yescharacteristic
105C22×C4×C73C2×D414yes—
106C22×C4×C73C2×Q814yes—
107C22×C4×C73C2412yes—
108C22×C4×C73C2411yescharacteristic
109M16×C73—216no—
110C2×C8×C73—28no—
111C2×C8×C73C2418yes—
112C42×C73C22×C414yes—
113C42×C73C22×C418yes—
114C42×C73C2414yes—
115C23×C73—24no—
116C23×C73C2×C4⋊C414yes—
117C23×C73C23×C412yes—
118C23×C73C23×C411yescharacteristic
119C22×D73—28no—
120C22×D73—416no—
121C22×D73—48no—
122C22×D73C2×C4⋊C418yes—
123C22×D73C2×C4⋊C4116yes—
124C22×D73C23×C414yes—
125C2×C4×C73—28no—
126C2×C4×C73—48no—
127C2×C4×C73C2×C4⋊C418yes—
128C2×C4×C73C2×C4⋊C414yes—
129C2×C4×C73C23×C418yes—
130C2×C4×C73C23×C412yes—
131C2×C4×C73C23×C411yescharacteristic
132C2×C4×C73C22×D412yes—
133C2×C4×C73C22×D414yes—
134C2×C4×C73C22×Q814yes—
135C2×C4×C73C22×Q812yes—
136C2×C4×C73C2511yescharacteristic
137C2×Dic73—28no—
138C2×Dic73—48no—
139C2×Dic73C2×C4⋊C4116yes—
140C2×Dic73C2×C4⋊C418yes—
141C2×Dic73C23×C418yes—
142C2×Dic73C23×C414yes—
143C4×D73C2×C4⋊C4116yes—
144C4×D73C2×C4⋊C4132yes—
145C4×D73C22×D418yes—
146C4×D73C22×Q818yes—
147C8×C73—28no—
148#10596831—28no—
149C22×C73—28no—
150C22×C73—24no—
151C22×C73C22×C4⋊C414yes—
152C22×C73C22×C4⋊C412yes—
153C22×C73#56814yes—
154C22×C73C24×C411yescharacteristic
155C2×D73—216no—
156C2×D73—28no—
157C2×D73—416no—
158C2×D73C22×C4⋊C418yes—
159C4×C73—28no—
160C4×C73C22×C4⋊C412yes—
161C4×C73C22×C4⋊C414yes—
162C4×C73C23×D411yescharacteristic
163C4×C73C23×Q811yescharacteristic
164Dic73—28no—
165Dic73C22×C4⋊C418yes—
166C2×#2905—731nomaximal, Sylow
167C2×C73—24no—
168C2×C73#290514yescomplemented
169C2×C73C23×C4⋊C411yescharacteristic
170C2×C73C2×#56812yes—
171D73—28no—
172C23×M16—732no—
173C22×#117—731no—
174#2905—7316no—
175C2×#424—738no—
176C2×#423—731no—
177C2×#423—732no—
178C2×#423D7311yescharacteristic, complemented
179C73C2×#290511yescharacteristic, complemented, Sylow
180C24×C4—731no—
181C22×M16—732no—
182C22×M16—7316no—
183C22×M16—734no—
184C22×M16—14616no—
185C22×M16C2×D7312yes—
186C23×C8—734no—
187C2×#117—738no—
188C2×#117—734no—
189C2×#117—734no—
190C2×#117—738no—
191C22×C4⋊C4—732no—
192C22×C22⋊C4—732no—
193C22×C42—731no—
194C22×C42C2×D7311yescharacteristic
195#424—7364no—
196#423—7316no—
197#423—738no—
198#423C2×D7318yescomplemented
199C2×C4⋊C8—738no—
200C2×C4⋊C8—734no—
201C2×C4⋊C8C2×D7314yescomplemented
202C25—731no—
203C23×C4—732no—
204C23×C4—731no—
205C23×C4—734no—
206C23×C4—732no—
207C23×C4—738no—
208C23×C4—738no—
209C23×C4—734no—
210C23×C4—732no—
211C23×C4C4×D7312yes—
212C23×C4C22×D7311yescharacteristic
213C2×M16—28no—
214C2×M16—738no—
215C2×M16—7316no—
216C2×M16—14616no—
217C2×M16—14664no—
218C2×M16—1468no—
219C2×M16C22×D7318yes—
220C22×C8—734no—
221C22×C8—7316no—
222C22×C8—14616no—
223C22×C8C22×D7314yes—
224#117—7316no—
225#117—7332no—
226#117—7316no—
227C2×C4⋊C4—7316no—
228C2×C4⋊C4—738no—
229C2×C22⋊C4—7316no—
230C2×C22⋊C4—738no—
231C2×C42—734no—
232C2×C42—732no—
233C2×C42—734no—
234C2×C42—732no—
235C2×C42C4×D7312yes—
236C2×C42C4×D7314yes—
237C2×C42C22×D7314yes—
238C2×C42C22×D7312yes—
239C4⋊C8—7332no—
240C4⋊C8—7316no—
241C4⋊C8C22×D73116yescomplemented
242C24—2924no—
243C24—738no—
244C24—734no—
245C24—732no—
246C24C2×C4×D7311yescharacteristic
247C22×C4—44no—
248C22×C4—2924no—
249C22×C4—738no—
250C22×C4—738no—
251C22×C4—734no—
252C22×C4—732no—
253C22×C4—7332no—
254C22×C4—7316no—
255C22×C4—738no—
256C22×C4—734no—
257C22×C4—738no—
258C22×C4—7316no—
259C22×C4—7316no—
260C22×C4—738no—
261C22×C4—734no—
262C22×C4—734no—
263C22×C4C2×C4×D7314yes—
264C22×C4C2×C4×D7318yes—
265C22×C4C2×C4×D7311yescharacteristic
266C22×C4C2×C4×D7312yes—
267C22×C4D4×D7314yes—
268C22×C4Q8×D7314yes—
269C22×C4C23×D7312yes—
270C22×C4C23×D7311yescharacteristic
271M16—216no—
272M16—14632no—
273M16—14616no—
274C2×C8—28no—
275C2×C8—738no—
276C2×C8—14632no—
277C2×C8—1468no—
278C2×C8C23×D7318yes—
279C4⋊C4—7332no—
280C22⋊C4—7332no—
281C42—738no—
282C42—734no—
283C42—734no—
284C42C2×C4×D7318yes—
285C42C2×C4×D7314yes—
286C42C23×D7314yes—
287C23—24no—
288C23—29216no—
289C23—2928no—
290C23—7316no—
291C23—734no—
292C23—738no—
293C23—1468no—
294C23C4⋊C4×D7314yes—
295C23C22×C4×D7312yes—
296C23C22×C4×D7311yescharacteristic
297C2×C4—28no—
298C2×C4—48no—
299C2×C4—2928no—
300C2×C4—734no—
301C2×C4—7316no—
302C2×C4—738no—
303C2×C4—738no—
304C2×C4—738no—
305C2×C4—7316no—
306C2×C4—7332no—
307C2×C4—738no—
308C2×C4—1468no—
309C2×C4C4⋊C4×D7318yes—
310C2×C4C4⋊C4×D7314yes—
311C2×C4C22×C4×D7318yes—
312C2×C4C22×C4×D7312yes—
313C2×C4C22×C4×D7311yescharacteristic
314C2×C4C2×D4×D7312yes—
315C2×C4C2×D4×D7314yes—
316C2×C4C2×Q8×D7314yes—
317C2×C4C2×Q8×D7312yes—
318C2×C4C24×D7311yescharacteristic
319C8—28no—
320C8—1468no—
321C22—28no—
322C22—24no—
323C22—29216no—
324C22—738no—
325C22—14616no—
326C22—1468no—
327C22C2×C4⋊C4×D7314yes—
328C22C2×C4⋊C4×D7312yes—
329C22#1798935314yes—
330C22C23×C4×D7311yescharacteristic
331C4—28no—
332C4—738no—
333C4—1468no—
334C4C2×C4⋊C4×D7314yes—
335C4C2×C4⋊C4×D7312yes—
336C4C22×D4×D7311yescharacteristic
337C4C22×Q8×D7311yescharacteristic
338C2—24no—
339C2—1468no—
340C2#2261849314yesdirect product factor
341C2C22×C4⋊C4×D7311yescharacteristic
342C2C2×#1798935312yes—
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC2×C4C24×D73
FittingC2×#423×C73C2
socleC23×C73C23×C4
prime radicalC24×D73C2×C4
cosocleC2×C4×C73C25
hypercenterC2×#423D73
hypocenterC73C2×#2905
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
3. #22618493C2direct (N × H)
4. C2×#17988612C2semidirect
5. C2×#17988611C2semidirect
6. C2×#17988610C2semidirect
7. C2×#423×C73C2semidirect
21. #17988612C22semidirect
22. #17988611C22semidirect
23. #17988610C22semidirect
24. C2×C4⋊#10596831C22semidirect
25. C2×#14556520C22semidirect
28. #423×C73C22semidirect
29. C2×C4⋊C8×C73C22semidirect
58. C4⋊#10596831C23semidirect
59. #14556520C23semidirect
69. C4⋊C8×C73C23semidirect
168. C2×C73#2905semidirect
178. C2×#423D73semidirect
179. C73C2×#2905semidirect
198. #423C2×D73semidirect
201. C2×C4⋊C8C2×D73semidirect
241. C4⋊C8C22×D73semidirect
340. C2#22618493direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×D732
C22×#145565482
#226184932
C2×#179886122
C2×#179886112
C2×#179886102
C2×#423×C732
C2×#290573