Finite Group Databasebeta

← C2×#22618782 #33950111

Subgroups — C2×#22618782 #33950111

Order 18688.

3086 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
1C23×D584C211yesmaximal, characteristic
2C2×#17989061C212yesmaximal, complemented
3#22618782C2116yesmaximal, direct product factor
4C2×#17988698C214yesmaximal, complemented
5C2×#17988669C214yesmaximal, complemented
6C2×#17988591C212yesmaximal, complemented
7C2×#17988542C211yesmaximal, characteristic, complemented
8C2×#427×C73C211yesmaximal, characteristic, complemented
9C23×D292C2212yes—
10C22×D584C4116yescomplemented
11C22×D584C2212yes—
12C22×D584C2212yes—
13C22×D584C2218yes—
14C22×#11924012C2211yescharacteristic
15#17989061—28no—
16#17989061C22116yescomplemented
17C2×C4×D292—24no—
18C2×#14556553C2218yescomplemented
19C2×#14556550C2211yescharacteristic
20C2×C22⋊C4×D73—24no—
21#17988698C22132yescomplemented
22#17988669C22132yescomplemented
23#17988591C22116yescomplemented
24C2×#14556511C2218yescomplemented
25#17988542C2218yescomplemented
26C2×#14556501C2212yescomplemented
27C2×C8×Dic73C2212yescomplemented
28C23×C8×C73C2211yescharacteristic
29C2×#117×C73C2212yes—
30#427×C73C2218yescomplemented
31C2×#107×C73C2212yescomplemented
32C2×#106×C73C2212yescomplemented
33C24×D73—22no—
34C22×D292—22no—
35C22×D292—24no—
36C22×D292—28no—
37C22×D292C2×C4116yescomplemented
38C22×D292C2314yes—
39C22×D292C2318yes—
40C22×C4×D73—28no—
41C2×D584C2×C4116yescomplemented
42C2×D584C2×C4116yescomplemented
43C2×D584C2×C4164yescomplemented
44C2×D584C2318yes—
45C2×D584C2318yes—
46C2×#11924012—24no—
47C2×#11924012C2314yes—
48C22×#10596831C2312yes—
49C4×D292—232no—
50#14556553—216no—
51#14556553C23132yescomplemented
52#14556550D414yes—
53#14556550C2314yes—
54C2×C4⋊Dic73D412yes—
55C2×C22⋊Dic73D412yes—
56C2×#11924005—28no—
57C22⋊C4×D73—232no—
58C2×C4×Dic73C2312yes—
59#14556511C23132yescomplemented
60#14556501C2318yescomplemented
61C8×Dic73C2318yescomplemented
62C23×C4×C73C2311yescharacteristic
63C22×C8×C73C2×C418yescomplemented
64C22×C8×C73C2311yescharacteristic
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2314yes—
67#117×C73—24no—
68#117×C73C2318yes—
69C2×C4⋊C4×C73C2314yes—
70C2×C22⋊C4×C73—22no—
71C2×C42×C73—22no—
72#107×C73C2318yescomplemented
73#106×C73C2318yescomplemented
74C23×D73—24no—
75C23×D73—216no—
76C23×D73—28no—
77C23×D73—88no—
78C2×D292—232no—
79C2×D292—216no—
80C2×D292—24no—
81C2×D292—28no—
82C2×D292—28no—
83C2×D292—216no—
84C2×D292C22×C4116yes—
85C2×D292C22×C4132yescomplemented
86C2×D292C2418yes—
87C22×Dic73C2×D414yes—
88C2×C4×D73—232no—
89C2×C4×D73—816no—
90D584C22×C4132yescomplemented
91D584C22×C4132yescomplemented
92#11924012—28no—
93C2×#10596831—24no—
94C2×#10596831C2414yes—
95C4⋊Dic73C2×D418yes—
96C22⋊Dic73C2×D418yes—
97#11924005—232no—
98C4×Dic73C2×D414yes—
99C4×Dic73C2414yes—
100C24×C73C2×D411yescharacteristic
101C22×C4×C73—24no—
102C22×C4×C73C22×C414yes—
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73C2×D412yes—
105C22×C4×C73#4114yes—
106C22×C4×C73C2411yescharacteristic
107C22×C4×C73C2412yes—
108C2×C8×C73C22×C414yes—
109C2×C8×C73C22×C414yes—
110C2×C8×C73C22×C4116yescomplemented
111C2×C8×C73C2412yes—
112C2×C8×C73C2412yes—
113C4⋊C4×C73—24no—
114C4⋊C4×C73C2418yes—
115C22⋊C4×C73—28no—
116C42×C73—28no—
117C23×C73—24no—
118C23×C73C4×D414yes—
119C23×C73C22×D412yes—
120C23×C73C22×D411yescharacteristic
121C22×D73—216no—
122C22×D73—28no—
123C22×D73—232no—
124C22×D73—416no—
125C22×D73—832no—
126C22×D73—816no—
127C2×C4×C73—28no—
128C2×C4×C73—48no—
129C2×C4×C73C4×D418yes—
130C2×C4×C73C4×D414yes—
131C2×C4×C73C23×C412yes—
132C2×C4×C73C23×C414yes—
133C2×C4×C73C22×D412yes—
134C2×C4×C73C22×D411yescharacteristic
135C2×C4×C73C2×#4112yes—
136C2×C4×C73C2×#4114yes—
137C2×C4×C73C2511yescharacteristic
138C2×Dic73—28no—
139C2×Dic73C22×D418yes—
140D292—216no—
141D292—232no—
142D292—28no—
143D292C23×C4116yes—
144C4×D73—832no—
145C8×C73C23×C414yes—
146C8×C73C23×C414yes—
147#10596831—24no—
148C22×C73—28no—
149C22×C73—24no—
150C22×C73C2×C4×D414yes—
151C22×C73C2×C4×D412yes—
152C22×C73#57614yes—
153C22×C73C23×D411yescharacteristic
154C2×D73—216no—
155C2×D73—432no—
156C2×D73—416no—
157C2×D73—832no—
158C4×C73—48no—
159C4×C73C2×C4×D412yes—
160C4×C73C2×C4×D414yes—
161C4×C73C24×C411yescharacteristic
162C4×C73C22×#4111yescharacteristic
163Dic73—28no—
164C2×#2948—731nomaximal, Sylow
165C2×C73—24no—
166C2×C73#294814yescomplemented
167C2×C73C22×C4×D411yescharacteristic
168C2×C73C2×#57612yes—
169D73—416no—
170C23×D8—731no—
171C2×#518—732no—
172#2948—7316no—
173C2×#442—734no—
174C2×C4×D8—734no—
175C2×#427D7311yescharacteristic, complemented
176C2×#418—732no—
177C2×#405—731no—
178C73C2×#294811yescharacteristic, complemented, Sylow
179C23×D4—732no—
180C22×D8—7316no—
181C22×D8—732no—
182C22×D8—732no—
183C22×D8—738no—
184C22×M16—731no—
185C23×C8C2×D7311yescharacteristic
186#518—7316no—
187#518—1468no—
188C2×C4×D4—738no—
189C2×C4×D4—1464no—
190C2×#117—731no—
191C2×#117C2×D7312yes—
192C22×C22⋊C4—1464no—
193#442—7332no—
194C4×D8—7332no—
195#427C2×D7318yescomplemented
196C2×#107C2×D7312yescomplemented
197C2×#106C2×D7312yescomplemented
198#418—7316no—
199C2×#102—738no—
200#405—738no—
201C2×#97—732no—
202C2×C4×C8—732no—
203C25—1462no—
204C22×D4—7316no—
205C22×D4—734no—
206C22×D4—738no—
207C22×D4—1462no—
208C22×D4—1464no—
209C22×D4—1468no—
210C23×C4—1468no—
211C23×C4C22×D7311yescharacteristic
212C2×D8—7316no—
213C2×D8—7316no—
214C2×D8—7364no—
215C2×D8—738no—
216C2×D8—738no—
217C2×M16—734no—
218C2×M16—1464no—
219C22×C8—732no—
220C22×C8C4×D7318yescomplemented
221C22×C8C22×D7311yescharacteristic
222C22×C8C22×D7311yescharacteristic
223C22×C8C22×D7314yes—
224C4×D4—7332no—
225C4×D4—14632no—
226C4×D4—14616no—
227#117—24no—
228#117—734no—
229#117—734no—
230#117C22×D7318yes—
231C2×C4⋊C4—732no—
232C2×C4⋊C4C22×D7314yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—732no—
235C2×C22⋊C4—14632no—
236C2×C22⋊C4—1468no—
237C2×C42—22no—
238C2×C42—732no—
239#107C22×D7318yescomplemented
240#106C22×D7318yescomplemented
241#102—7332no—
242#97—738no—
243C4×C8—738no—
244C24—5848no—
245C24—1464no—
246C24—14616no—
247C24—1468no—
248C24D4×D7311yescharacteristic
249C2×D4—7316no—
250C2×D4—7332no—
251C2×D4—738no—
252C2×D4—14616no—
253C2×D4—14632no—
254C2×D4—1468no—
255C2×D4—1464no—
256C2×D4—1468no—
257C2×D4—14616no—
258C22×C4—24no—
259C22×C4—58416no—
260C22×C4—734no—
261C22×C4—14632no—
262C22×C4C2×C4×D7314yes—
263C22×C4D4×D7312yes—
264C22×C4D4×D7311yescharacteristic
265C22×C4#1192402914yes—
266C22×C4C23×D7312yes—
267C22×C4C23×D7311yescharacteristic
268D8—7332no—
269D8—7332no—
270M16—1468no—
271C2×C8—734no—
272C2×C8—1464no—
273C2×C8C2×C4×D7314yes—
274C2×C8C2×C4×D7314yes—
275C2×C8C2×C4×D73116yescomplemented
276C2×C8C23×D7312yes—
277C2×C8C23×D7312yes—
278C4⋊C4—24no—
279C4⋊C4—738no—
280C4⋊C4C23×D7318yes—
281C22⋊C4—28no—
282C22⋊C4—738no—
283C22⋊C4—14632no—
284C42—28no—
285C42—734no—
286C42—734no—
287C23—24no—
288C23—29216no—
289C23—58432no—
290C23—58416no—
291C23—1468no—
292C23—14616no—
293C23—14632no—
294C23#1455655314yes—
295C23C2×D4×D7312yes—
296C23C2×D4×D7311yescharacteristic
297D4—7316no—
298D4—1468no—
299D4—14616no—
300D4—14632no—
301C2×C4—28no—
302C2×C4—48no—
303C2×C4—58432no—
304C2×C4—738no—
305C2×C4—1468no—
306C2×C4#1455655318yes—
307C2×C4#1455655314yes—
308C2×C4C22×C4×D7312yes—
309C2×C4C22×C4×D7314yes—
310C2×C4C2×D4×D7312yes—
311C2×C4C2×D4×D7311yescharacteristic
312C2×C4C2×#1192402912yes—
313C2×C4C2×#1192402914yes—
314C2×C4C24×D7311yescharacteristic
315C8—1464no—
316C8C22×C4×D7314yes—
317C8C22×C4×D7314yes—
318C22—28no—
319C22—24no—
320C22—29232no—
321C22—29216no—
322C22—58432no—
323C22—14616no—
324C22C2×#1455655314yes—
325C22C2×#1455655312yes—
326C22#1798938914yes—
327C22C22×D4×D7311yescharacteristic
328C4—48no—
329C4—1468no—
330C4C2×#1455655312yes—
331C4C2×#1455655314yes—
332C4C23×C4×D7311yescharacteristic
333C4C22×#1192402911yescharacteristic
334C2—24no—
335C2—29216no—
336C2#2261878214yesdirect product factor
337C2C22×#1455655311yescharacteristic
338C2C2×#1798938912yes—
subgroupG/H
centerC23C2×D4×D73
commutatorC4×C73C24×C4
FrattiniC2×C4C24×D73
FittingC2×#427×C73C2
socleC23×C73C22×D4
prime radicalC23×D584C2
cosocleC2×C4×C73C25
hypercenterC2×#427D73
hypocenterC73C2×#2948
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#17989061C2semidirect
3. #22618782C2direct (N × H)
4. C2×#17988698C2semidirect
5. C2×#17988669C2semidirect
6. C2×#17988591C2semidirect
7. C2×#17988542C2semidirect
8. C2×#427×C73C2semidirect
10. C22×D584C4semidirect
16. #17989061C22semidirect
18. C2×#14556553C22semidirect
21. #17988698C22semidirect
22. #17988669C22semidirect
23. #17988591C22semidirect
24. C2×#14556511C22semidirect
25. #17988542C22semidirect
26. C2×#14556501C22semidirect
27. C2×C8×Dic73C22semidirect
30. #427×C73C22semidirect
31. C2×#107×C73C22semidirect
32. C2×#106×C73C22semidirect
37. C22×D292C2×C4semidirect
41. C2×D584C2×C4semidirect
42. C2×D584C2×C4semidirect
43. C2×D584C2×C4semidirect
51. #14556553C23semidirect
59. #14556511C23semidirect
60. #14556501C23semidirect
61. C8×Dic73C23semidirect
63. C22×C8×C73C2×C4semidirect
72. #107×C73C23semidirect
73. #106×C73C23semidirect
85. C2×D292C22×C4semidirect
90. D584C22×C4semidirect
91. D584C22×C4semidirect
110. C2×C8×C73C22×C4semidirect
166. C2×C73#2948semidirect
175. C2×#427D73semidirect
178. C73C2×#2948semidirect
195. #427C2×D73semidirect
196. C2×#107C2×D73semidirect
197. C2×#106C2×D73semidirect
220. C22×C8C4×D73semidirect
239. #107C22×D73semidirect
240. #106C22×D73semidirect
275. C2×C8C2×C4×D73semidirect
336. C2#22618782direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D5842
C2×#179890612
#226187822
C2×#179886982
C2×#179886692
C2×#179885912
C2×#179885422
C2×#427×C732
C2×#294873