Finite Group Databasebeta

← C2×#22626278 #34030086

Subgroups — C2×#22626278 #34030086

Order 18688.

658 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D73⋊#108C211yesmaximal, characteristic
2C2×#17989597C211yesmaximal, characteristic
3#22626278C218yesmaximal, direct product factor
4C2×#17989512C212yesmaximal, complemented
5C2×#17989511C212yesmaximal, complemented
6C22×#14556530C211yesmaximal, characteristic
7C2×D73⋊M16—21no—
8C2×#14556670—21no—
9C2×#14556662—21no—
10D73⋊#108—22no—
11D73⋊#108C2214yes—
12C2×#14556661C2212yes—
13#17989597—22no—
14#17989597C2214yes—
15C2×#14556660—21no—
16C2×#14556659C2212yes—
17#17989512C2218yescomplemented
18#17989511C2218yescomplemented
19C22×C8×D73C2211yescharacteristic
20C2×#14556530C411yescharacteristic, complemented
21C2×#14556530C411yescharacteristic, complemented
22C2×#14556530C414yescomplemented
23C2×#14556530C2211yescharacteristic
24C2×#14556530C2211yescharacteristic
25C2×#14556530C2214yes—
26C22×#11924003C411yescharacteristic, complemented
27C22×C16×C73C411yescharacteristic, complemented
28C2×#11924038—22no—
29D73⋊M16—24no—
30D73⋊M16—42no—
31C2×#11924037—41no—
32C2×#11924036—41no—
33#14556670—24no—
34#14556670—42no—
35C2×C4⋊#64408—22no—
36C2×C22⋊#64408—41no—
37C2×C4×#64408—41no—
38#14556662—24no—
39#14556661—22no—
40#14556661C2314yes—
41#14556660—24no—
42#14556659—22no—
43#14556659C2314yes—
44C22×C4×D73D411yescharacteristic
45C22×#10596831Q811yescharacteristic
46C2×C8×D73C2×C411yescharacteristic
47C2×C8×D73C2×C412yes—
48C2×C8×D73D411yescharacteristic
49C2×C8×D73D412yes—
50C2×C8×D73Q811yescharacteristic
51C2×C8×D73Q812yes—
52C2×C8×D73C2311yescharacteristic
53C2×C8×D73C2312yes—
54#14556530C2×C412yes—
55#14556530C2×C412yes—
56#14556530C2×C414yescomplemented
57#14556530C2×C414yescomplemented
58#14556530C2312yes—
59#14556530C2312yes—
60C2×#11924003C2×C411yescharacteristic
61C2×#11924003C2×C411yescharacteristic
62C2×#11924003C2×C414yescomplemented
63C22×C8×C73C2×C411yescharacteristic
64C2×C16×C73C2×C411yescharacteristic
65C2×C16×C73C2×C411yescharacteristic
66C2×C16×C73C2×C414yescomplemented
67C22×#64408—42no—
68#11924038—24no—
69#11924038—42no—
70#11924037—44no—
71#11924036—44no—
72C2×#10596833—42no—
73C4⋊#64408—24no—
74C4⋊#64408—42no—
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×D412yes—
86C2×C4×D73C2×D411yescharacteristic
87C2×#10596831C4⋊C411yescharacteristic
88C2×#10596831C4⋊C412yes—
89C2×#10596831C2×Q811yescharacteristic
90C2×#10596831C2×Q812yes—
91C8×D73C4⋊C412yes—
92C8×D73C4⋊C412yes—
93C8×D73C4⋊C412yes—
94C8×D73C22×C411yescharacteristic
95C8×D73C22×C412yes—
96C8×D73C2×D411yescharacteristic
97C8×D73C2×D412yes—
98C8×D73C2×Q811yescharacteristic
99C8×D73C2×Q812yes—
100C8×D73C2411yescharacteristic
101#11924003C22×C412yes—
102#11924003C22×C412yes—
103C22×C4×C73C4⋊C411yescharacteristic
104C2×C8×C73C4⋊C411yescharacteristic
105C2×C8×C73C4⋊C412yes—
106C2×C8×C73C22×C411yescharacteristic
107C2×C8×C73C22×C412yes—
108C16×C73C22×C412yes—
109C16×C73C22×C412yes—
110C23×C73#10611yescharacteristic
111C22×D73—42no—
112C22×D73#10611yescharacteristic
113C22×D73#10612yes—
114C22×D73C2×SD1611yescharacteristic
115C22×D73C2×SD1612yes—
116C2×#64408—44no—
117C2×#64408—84no—
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×SD1611yescharacteristic
125C2×Dic73C2×SD1612yes—
126C4×D73#10612yes—
127C4×D73#10612yes—
128C4×D73#10612yes—
129C4×D73C2×C4⋊C411yescharacteristic
130C4×D73C2×C4⋊C412yes—
131C4×D73C2×SD1612yes—
132C4×D73C2×SD1611yescharacteristic
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⋊C411yescharacteristic
141#10596831C2×C4⋊C412yes—
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—84no—
154C4×C73C2×#10611yescharacteristic
155C4×C73C2×#10612yes—
156C4×C73C22×C4⋊C411yescharacteristic
157Dic73C2×#10612yes—
158Dic73C2×#10611yescharacteristic
159Dic73C22×SD1611yescharacteristic
160C2×#2155—731nomaximal, Sylow
161C2×C73—22no—
162C2×C73#215512yescomplemented
163C2×C73C22×#10611yescharacteristic
164D73—21no—
165D73—21no—
166D73—22no—
167C22×M32—731no—
168C22×#108—731no—
169C2×#427—731no—
170#2155—738no—
171C2×#365—732no—
172C2×#365—732no—
173C73C2×#215511yescharacteristic, complemented, Sylow
174C22×M16—1461no—
175C23×C8—731no—
176C2×#117—1461no—
177C2×M32—731no—
178C2×M32—731no—
179C2×M32—731no—
180C2×M32—731no—
181C2×M32—734no—
182C2×M32—734no—
183C22×C16—731no—
184C22×C16#6440811yescharacteristic, complemented
185C2×#108—732no—
186C2×#108—734no—
187C2×#108—1462no—
188C2×#108—1461no—
189#427—734no—
190#427—1462no—
191C2×#107—1461no—
192C2×#106—732no—
193#365—738no—
194#365—738no—
195C23×C4—731no—
196C2×M16—2921no—
197C2×M16—2922no—
198C2×M16—1464no—
199C2×M16—1462no—
200C22×C8—2921no—
201C22×C8—731no—
202C22×C8—731no—
203C22×C8—732no—
204C22×C8—731no—
205C22×C8—732no—
206C22×C8—731no—
207C22×C8—732no—
208C22×C8—731no—
209C22×C8—732no—
210C22×C8C2×#6440811yescharacteristic
211#117—2922no—
212#117—1464no—
213C2×C4⋊C4—1462no—
214C2×C22⋊C4—2921no—
215C2×C42—2921no—
216M32—732no—
217M32—732no—
218M32—732no—
219M32—732no—
220M32—734no—
221M32—734no—
222C2×C16—731no—
223C2×C16—731no—
224C2×C16—734no—
225C2×C16C2×#6440811yescharacteristic
226C2×C16C2×#6440811yescharacteristic
227C2×C16C2×#6440814yescomplemented
228#108—734no—
229#108—1462no—
230#108—1464no—
231#107—1464no—
232#106—734no—
233#106—1462no—
234C24—731no—
235C22×C4—2922no—
236C22×C4—731no—
237C22×C4—732no—
238C22×C4—732no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—732no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4—732no—
245C22×C4C4⋊#6440811yescharacteristic
246M16—2924no—
247M16—2922no—
248M16—1464no—
249C2×C8—2922no—
250C2×C8—2924no—
251C2×C8—731no—
252C2×C8—732no—
253C2×C8—731no—
254C2×C8—732no—
255C2×C8—731no—
256C2×C8—732no—
257C2×C8—731no—
258C2×C8—732no—
259C2×C8—732no—
260C2×C8—732no—
261C2×C8—731no—
262C2×C8—732no—
263C2×C8—731no—
264C2×C8—732no—
265C2×C8C4⋊#6440811yescharacteristic
266C2×C8C4⋊#6440812yes—
267C2×C8C22×#6440811yescharacteristic
268C2×C8C22×#6440812yes—
269C4⋊C4—2922no—
270C4⋊C4—1464no—
271C22⋊C4—2924no—
272C42—2924no—
273C16—732no—
274C16—732no—
275C16C22×#6440812yes—
276C16C22×#6440812yes—
277C23—2922no—
278C23—732no—
279C23—732no—
280C23—731no—
281C23—731no—
282C23#1455665911yescharacteristic
283C2×C4—2924no—
284C2×C4—5844no—
285C2×C4—731no—
286C2×C4—732no—
287C2×C4—732no—
288C2×C4—731no—
289C2×C4—731no—
290C2×C4—731no—
291C2×C4—732no—
292C2×C4—732no—
293C2×C4—731no—
294C2×C4—732no—
295C2×C4—731no—
296C2×C4—732no—
297C2×C4—732no—
298C2×C4—732no—
299C2×C4#1455665912yes—
300C2×C4#1455665911yescharacteristic
301C2×C4C2×C4⋊#6440811yescharacteristic
302C2×C4C2×C4⋊#6440812yes—
303C8—2924no—
304C8—731no—
305C8—732no—
306C8—731no—
307C8C2×C4⋊#6440811yescharacteristic
308C8C2×C4⋊#6440812yes—
309C8C23×#6440811yescharacteristic
310C22—22no—
311C22—2922no—
312C22—2922no—
313C22—731no—
314C22—732no—
315C22—731no—
316C22—1462no—
317C22—1462no—
318C22C2×#1455665912yes—
319C22C2×#1455665911yescharacteristic
320C4—5844no—
321C4—731no—
322C4—731no—
323C4—732no—
324C4C2×#1455665911yescharacteristic
325C4C2×#1455665912yes—
326C4C22×C4⋊#6440811yescharacteristic
327C2—22no—
328C2—1461no—
329C2—1461no—
330C2—1462no—
331C2#2262627812yesdirect product factor
332C2C22×#1455665911yescharacteristic
subgroupG/H
centerC2×C4#14556659
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC22×C16×C73C4
socleC22×C73C2×#106
prime radicalC23×D73SD16
cosocleC8×D73C24
hypercenterC22×C16#64408
hypocenterC73C2×#2155
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
3. #22626278C2direct (N × H)
4. C2×#17989512C2semidirect
5. C2×#17989511C2semidirect
17. #17989512C22semidirect
18. #17989511C22semidirect
20. C2×#14556530C4semidirect
21. C2×#14556530C4semidirect
22. C2×#14556530C4semidirect
26. C22×#11924003C4semidirect
27. C22×C16×C73C4semidirect
56. #14556530C2×C4semidirect
57. #14556530C2×C4semidirect
62. C2×#11924003C2×C4semidirect
66. C2×C16×C73C2×C4semidirect
162. C2×C73#2155semidirect
173. C73C2×#2155semidirect
184. C22×C16#64408semidirect
227. C2×C16C2×#64408semidirect
331. C2#22626278direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D73⋊#1082
C2×#179895972
#226262782
C2×#179895122
C2×#179895112
C22×#145565302
C2×#215573