Finite Group Databasebeta

← C2×#22626279 #34030088

Subgroups — C2×#22626279 #34030088

Order 18688.

658 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556661C211yesmaximal, characteristic
2C2×#17989597C211yesmaximal, characteristic
3#22626279C218yesmaximal, direct product factor
4C2×#17989512C212yesmaximal, complemented
5C2×#17989511C212yesmaximal, complemented
6C2×M32×D73C211yesmaximal, characteristic
7C22×#11924038—21no—
8C2×#14556670—21no—
9C2×#14556661—21no—
10C2×#14556661—22no—
11C2×#14556661C2212yes—
12C2×#14556661C2214yes—
13#17989597—22no—
14#17989597C2214yes—
15C2×#14556660—21no—
16C2×#14556659C2211yescharacteristic
17C2×#14556659C2211yescharacteristic
18#17989512C2218yescomplemented
19#17989511C2218yescomplemented
20C22×C8×D73C2211yescharacteristic
21C2×#14556531C411yescharacteristic, complemented
22C2×#14556530C2212yes—
23M32×D73C414yescomplemented
24M32×D73C2214yes—
25C2×C16×D73C412yescomplemented
26C2×M32×C73C411yescharacteristic, complemented
27C2×#11924038—22no—
28C2×#11924038—24no—
29C2×#11924038—41no—
30C2×#11924038—42no—
31C22×#10596833—41no—
32#14556670—24no—
33#14556670—42no—
34C2×C4⋊#64408—21no—
35C2×C4⋊#64408—21no—
36C2×C22⋊#64408—41no—
37C2×C4×#64408—41no—
38#14556661—22no—
39#14556661—24no—
40#14556661C2314yes—
41#14556660—24no—
42#14556659—21no—
43#14556659—21no—
44#14556659C2312yes—
45#14556659C2312yes—
46C22×C4×D73D411yescharacteristic
47C22×#10596831Q811yescharacteristic
48C2×C8×D73C2×C411yescharacteristic
49C2×C8×D73C2×C412yes—
50C2×C8×D73D411yescharacteristic
51C2×C8×D73D412yes—
52C2×C8×D73Q811yescharacteristic
53C2×C8×D73Q812yes—
54C2×C8×D73C2312yes—
55C2×C8×D73C2311yescharacteristic
56#14556531C2×C414yescomplemented
57#14556530C2×C414yes—
58#14556530C2314yes—
59C2×#11924003C2×C412yes—
60C16×D73C2×C418yescomplemented
61C22×C8×C73C2×C411yescharacteristic
62M32×C73C2×C414yescomplemented
63C2×C16×C73C2×C412yes—
64C22×#64408—41no—
65C22×#64408—41no—
66#11924038—24no—
67#11924038—42no—
68#11924038—44no—
69C2×#10596833—44no—
70C2×#10596833—42no—
71C4⋊#64408—22no—
72C4⋊#64408—22no—
73C4⋊#64408—41no—
74C4⋊#64408—41no—
75C22⋊#64408—44no—
76C4×#64408—44no—
77C23×D73SD1611yescharacteristic
78C22×Dic73SD1611yescharacteristic
79C2×C4×D73C4⋊C411yescharacteristic
80C2×C4×D73C4⋊C412yes—
81C2×C4×D73SD1611yescharacteristic
82C2×C4×D73SD1612yes—
83C2×C4×D73SD1611yescharacteristic
84C2×C4×D73SD1612yes—
85C2×C4×D73C2×D411yescharacteristic
86C2×C4×D73C2×D412yes—
87C2×#10596831C4⋊C411yescharacteristic
88C2×#10596831C4⋊C412yes—
89C2×#10596831C2×Q812yes—
90C2×#10596831C2×Q811yescharacteristic
91C8×D73C4⋊C412yes—
92C8×D73C4⋊C412yes—
93C8×D73C4⋊C412yes—
94C8×D73C22×C412yes—
95C8×D73C22×C411yescharacteristic
96C8×D73C2×D411yescharacteristic
97C8×D73C2×D412yes—
98C8×D73C2×Q812yes—
99C8×D73C2×Q811yescharacteristic
100C8×D73C2411yescharacteristic
101#11924003C22×C414yes—
102C22×C4×C73C4⋊C411yescharacteristic
103C2×C8×C73C4⋊C411yescharacteristic
104C2×C8×C73C4⋊C412yes—
105C2×C8×C73C22×C411yescharacteristic
106C2×C8×C73C22×C412yes—
107C16×C73C22×C414yes—
108C23×C73#10611yescharacteristic
109C22×D73—42no—
110C22×D73#10611yescharacteristic
111C22×D73#10612yes—
112C22×D73C2×SD1611yescharacteristic
113C22×D73C2×SD1612yes—
114C2×#64408—42no—
115C2×#64408—42no—
116C2×#64408—82no—
117C2×#64408—82no—
118C2×C4×C73#10612yes—
119C2×C4×C73#10611yescharacteristic
120C2×C4×C73C2×C4⋊C412yes—
121C2×C4×C73C2×C4⋊C411yescharacteristic
122C2×Dic73#10612yes—
123C2×Dic73#10611yescharacteristic
124C2×Dic73C2×SD1612yes—
125C2×Dic73C2×SD1611yescharacteristic
126C4×D73#10612yes—
127C4×D73#10612yes—
128C4×D73#10612yes—
129C4×D73C2×C4⋊C412yes—
130C4×D73C2×C4⋊C411yescharacteristic
131C4×D73C2×SD1611yescharacteristic
132C4×D73C2×SD1612yes—
133C4×D73C2×SD1612yes—
134C4×D73C2×SD1611yescharacteristic
135C4×D73C22×D411yescharacteristic
136#10596833—44no—
137C8×C73C2×C4⋊C411yescharacteristic
138C8×C73C2×C4⋊C412yes—
139C8×C73C23×C411yescharacteristic
140#10596831C2×C4⋊C412yes—
141#10596831C2×C4⋊C411yescharacteristic
142#10596831C22×Q811yescharacteristic
143C22×C73—22no—
144C22×C73C2×#10612yes—
145C22×C73C2×#10611yescharacteristic
146C2×D73—22no—
147C2×D73—22no—
148C2×D73—42no—
149C2×D73—42no—
150C2×D73C2×#10612yes—
151C2×D73C2×#10611yescharacteristic
152C2×D73C22×SD1611yescharacteristic
153#64408—82no—
154#64408—82no—
155C4×C73C2×#10612yes—
156C4×C73C2×#10611yescharacteristic
157C4×C73C22×C4⋊C411yescharacteristic
158Dic73C2×#10612yes—
159Dic73C2×#10611yescharacteristic
160Dic73C22×SD1611yescharacteristic
161C2×#2155—731nomaximal, Sylow
162C2×C73—22no—
163C2×C73#215512yescomplemented
164C2×C73C22×#10611yescharacteristic
165D73—21no—
166D73—21no—
167D73—22no—
168C22×M32—731no—
169C22×#108—731no—
170C2×#427—731no—
171#2155—738no—
172C2×#365—732no—
173C2×#365—732no—
174C73C2×#215511yescharacteristic, complemented, Sylow
175C22×M16—1461no—
176C23×C8—731no—
177C2×#117—1461no—
178C2×M32—731no—
179C2×M32—734no—
180C2×M32—734no—
181C2×M32—732no—
182C2×M32#6440811yescharacteristic, complemented
183C22×C16—732no—
184C2×#108—732no—
185C2×#108—734no—
186C2×#108—1461no—
187C2×#108—1462no—
188#427—734no—
189#427—1462no—
190C2×#107—1461no—
191C2×#106—731no—
192C2×#106—731no—
193#365—738no—
194#365—738no—
195C23×C4—731no—
196C2×M16—2922no—
197C2×M16—2921no—
198C2×M16—1462no—
199C2×M16—1464no—
200C22×C8—2921no—
201C22×C8—731no—
202C22×C8—731no—
203C22×C8—732no—
204C22×C8—732no—
205C22×C8—731no—
206C22×C8—731no—
207C22×C8—732no—
208C22×C8—731no—
209C22×C8—732no—
210C22×C8C2×#6440811yescharacteristic
211#117—2922no—
212#117—1464no—
213C2×C4⋊C4—1461no—
214C2×C4⋊C4—1461no—
215C2×C22⋊C4—2921no—
216C2×C42—2921no—
217M32—734no—
218M32—734no—
219M32—734no—
220M32C2×#6440814yescomplemented
221C2×C16—732no—
222C2×C16—738no—
223C2×C16C2×#6440812yes—
224#108—734no—
225#108—1462no—
226#108—1464no—
227#107—1464no—
228#106—732no—
229#106—732no—
230#106—1461no—
231#106—1461no—
232C24—731no—
233C22×C4—2921no—
234C22×C4—2921no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—732no—
238C22×C4—732no—
239C22×C4—731no—
240C22×C4—732no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—732no—
244C22×C4C4⋊#6440811yescharacteristic
245M16—2922no—
246M16—2924no—
247M16—1464no—
248C2×C8—2924no—
249C2×C8—2922no—
250C2×C8—732no—
251C2×C8—731no—
252C2×C8—732no—
253C2×C8—731no—
254C2×C8—732no—
255C2×C8—731no—
256C2×C8—731no—
257C2×C8—732no—
258C2×C8—732no—
259C2×C8—732no—
260C2×C8—731no—
261C2×C8—732no—
262C2×C8—731no—
263C2×C8—732no—
264C2×C8C4⋊#6440812yes—
265C2×C8C4⋊#6440811yescharacteristic
266C2×C8C22×#6440811yescharacteristic
267C2×C8C22×#6440812yes—
268C4⋊C4—2921no—
269C4⋊C4—2921no—
270C4⋊C4—1462no—
271C4⋊C4—1462no—
272C22⋊C4—2924no—
273C42—2924no—
274C16—734no—
275C16C22×#6440814yes—
276C23—2922no—
277C23—732no—
278C23—732no—
279C23—731no—
280C23—731no—
281C23#1455665911yescharacteristic
282C2×C4—2922no—
283C2×C4—2922no—
284C2×C4—5842no—
285C2×C4—5842no—
286C2×C4—732no—
287C2×C4—732no—
288C2×C4—731no—
289C2×C4—731no—
290C2×C4—731no—
291C2×C4—732no—
292C2×C4—731no—
293C2×C4—732no—
294C2×C4—731no—
295C2×C4—731no—
296C2×C4—732no—
297C2×C4—732no—
298C2×C4—732no—
299C2×C4—732no—
300C2×C4#1455665912yes—
301C2×C4#1455665911yescharacteristic
302C2×C4C2×C4⋊#6440812yes—
303C2×C4C2×C4⋊#6440811yescharacteristic
304C8—2924no—
305C8—732no—
306C8—731no—
307C8—731no—
308C8C2×C4⋊#6440811yescharacteristic
309C8C2×C4⋊#6440812yes—
310C8C23×#6440811yescharacteristic
311C22—22no—
312C22—2922no—
313C22—2922no—
314C22—731no—
315C22—732no—
316C22—731no—
317C22—1462no—
318C22—1462no—
319C22C2×#1455665912yes—
320C22C2×#1455665911yescharacteristic
321C4—5842no—
322C4—5842no—
323C4—731no—
324C4—732no—
325C4—731no—
326C4C2×#1455665912yes—
327C4C2×#1455665911yescharacteristic
328C4C22×C4⋊#6440811yescharacteristic
329C2—22no—
330C2—1461no—
331C2—1461no—
332C2—1462no—
333C2#2262627912yesdirect product factor
334C2C22×#1455665911yescharacteristic
subgroupG/H
centerC22C2×#14556659
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×M32×C73C4
socleC22×C73C2×#106
prime radicalC23×D73SD16
cosocleC8×D73C24
hypercenterC2×M32#64408
hypocenterC73C2×#2155
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
3. #22626279C2direct (N × H)
4. C2×#17989512C2semidirect
5. C2×#17989511C2semidirect
18. #17989512C22semidirect
19. #17989511C22semidirect
21. C2×#14556531C4semidirect
23. M32×D73C4semidirect
25. C2×C16×D73C4semidirect
26. C2×M32×C73C4semidirect
56. #14556531C2×C4semidirect
60. C16×D73C2×C4semidirect
62. M32×C73C2×C4semidirect
163. C2×C73#2155semidirect
174. C73C2×#2155semidirect
182. C2×M32#64408semidirect
220. M32C2×#64408semidirect
333. C2#22626279direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566612
C2×#179895972
#226262792
C2×#179895122
C2×#179895112
C2×M32×D732
C2×#215573