Finite Group Databasebeta

← C2×#22625868 #34021334

Subgroups — C2×#22625868 #34021334

Order 18688.

1182 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556660C212yesmaximal
2C22×#14556659C212yesmaximal
3C2×#17989531C212yesmaximal
4#22625868C218yesmaximal, direct product factor
5C2×C4×C8×D73C211yesmaximal, characteristic
6C22×C4⋊#64408C2214yes—
7C2×#14556660—28no—
8C2×#14556660C2218yes—
9C2×#14556659—28no—
10C2×#14556659C2218yes—
11#17989531—24no—
12#17989531C2218yes—
13C2×(C2×#64408)⋊C4—24no—
14C22×C8×D73C2211yescharacteristic
15C22×C8×D73C2211yescharacteristic
16C2×C42×D73C2211yescharacteristic
17C2×C4×#10596831C411yescharacteristic, complemented
18C2×C8×Dic73C411yescharacteristic, complemented
19C2×C8×Dic73C411yescharacteristic, complemented
20C4×C8×D73C414yescomplemented
21C4×C8×D73C2214yes—
22C2×C4×C8×C73C411yescharacteristic, complemented
23C23×#64408—24no—
24C2×C4⋊#64408—28no—
25C2×C4⋊#64408—28no—
26C2×C4⋊#64408—24no—
27C2×C4⋊#64408C2318yes—
28#14556660—216no—
29#14556659—216no—
30(C2×#64408)⋊C4—216no—
31C22×C4×D73D412yes—
32C22×C4×D73C2311yescharacteristic
33C22×#10596831C2×C411yescharacteristic
34C22×#10596831C2×C411yescharacteristic
35C2×C8×D73C2×C412yes—
36C2×C8×D73C2×C412yes—
37C2×C8×D73D414yes—
38C2×C8×D73D414yes—
39C2×C8×D73Q814yes—
40C2×C8×D73Q814yes—
41C2×C8×D73C2312yes—
42C2×C8×D73C2312yes—
43C2×C4×Dic73C2×C411yescharacteristic
44C2×C4×Dic73Q812yes—
45C42×D73C2×C412yes—
46C42×D73D412yes—
47C42×D73Q812yes—
48C42×D73C2312yes—
49C4×#10596831C2×C414yescomplemented
50C8×Dic73C2×C414yescomplemented
51C8×Dic73C2×C414yescomplemented
52C22×C8×C73C2×C411yescharacteristic
53C22×C8×C73C2×C411yescharacteristic
54C2×C42×C73C2×C411yescharacteristic
55C4×C8×C73C2×C414yescomplemented
56C22×#64408—28no—
57C22×#64408—48no—
58C22×#64408—416no—
59C4⋊#64408—28no—
60C4⋊#64408—28no—
61C4⋊#64408—48no—
62C23×D73C2×D411yescharacteristic
63C22×Dic73C4⋊C412yes—
64C22×Dic73C2×Q811yescharacteristic
65C2×C4×D73—28no—
66C2×C4×D73C4⋊C414yes—
67C2×C4×D73C22×C411yescharacteristic
68C2×C4×D73C2×D414yes—
69C2×C4×D73C2×D412yes—
70C2×C4×D73C2×D412yes—
71C2×C4×D73C2×D411yescharacteristic
72C2×C4×D73C2×Q812yes—
73C2×C4×D73C2×Q812yes—
74C2×C4×D73C2×Q811yescharacteristic
75C2×C4×D73C2411yescharacteristic
76C2×#10596831C4⋊C414yes—
77C2×#10596831C4⋊C414yes—
78C2×#10596831C22×C412yes—
79C2×#10596831C22×C412yes—
80C8×D73C4⋊C418yes—
81C8×D73C4⋊C418yes—
82C8×D73C2×D414yes—
83C8×D73C2×D414yes—
84C8×D73C2×Q814yes—
85C8×D73C2×Q814yes—
86C4×Dic73C4⋊C414yes—
87C4×Dic73C4⋊C412yes—
88C4×Dic73C22×C412yes—
89C4×Dic73C2×Q814yes—
90C22×C4×C73C4⋊C412yes—
91C22×C4×C73C22×C411yescharacteristic
92C2×C8×C73C4⋊C414yes—
93C2×C8×C73C4⋊C414yes—
94C2×C8×C73C22×C412yes—
95C2×C8×C73C22×C412yes—
96C42×C73C4⋊C412yes—
97C42×C73C22×C412yes—
98C23×C73C2×C4⋊C411yescharacteristic
99C22×D73C2×C4⋊C411yescharacteristic
100C22×D73#12712yes—
101C22×D73C4⋊Q812yes—
102C22×D73#13518yes—
103C22×D73C22×D411yescharacteristic
104C2×#64408—48no—
105C2×#64408—416no—
106C2×#64408—816no—
107C2×C4×C73—24no—
108C2×C4×C73C2×C4⋊C414yes—
109C2×C4×C73C2×C4⋊C412yes—
110C2×C4×C73C2×C4⋊C412yes—
111C2×C4×C73C2×C4⋊C411yescharacteristic
112C2×C4×C73C23×C411yescharacteristic
113C2×Dic73—24no—
114C2×Dic73C2×C4⋊C414yes—
115C2×Dic73C2×C4⋊C411yescharacteristic
116C2×Dic73C4⋊Q812yes—
117C2×Dic73C4⋊Q812yes—
118C2×Dic73C22×Q811yescharacteristic
119C4×D73—28no—
120C4×D73—28no—
121C4×D73C2×C4⋊C412yes—
122C4×D73C2×C4⋊C412yes—
123C4×D73#12712yes—
124C4×D73C4⋊Q812yes—
125C4×D73C4⋊Q812yes—
126C4×D73C4⋊Q812yes—
127C4×D73C22×D411yescharacteristic
128C4×D73C22×D411yescharacteristic
129C4×D73C22×Q811yescharacteristic
130C4×D73C22×Q811yescharacteristic
131C8×C73C2×C4⋊C414yes—
132C8×C73C2×C4⋊C414yes—
133#10596831C2×C4⋊C414yes—
134#10596831C2×C4⋊C414yes—
135C22×C73#38412yes—
136C22×C73#42714yes—
137C22×C73C22×C4⋊C411yescharacteristic
138C2×D73#38412yes—
139C2×D73#42714yes—
140C2×D73#49518yes—
141C2×D73#49918yes—
142C2×D73C2×#12711yescharacteristic
143C2×D73C2×C4⋊Q811yescharacteristic
144C2×D73C2×#13514yes—
145#64408—88no—
146C4×C73—24no—
147C4×C73#38412yes—
148C4×C73C22×C4⋊C411yescharacteristic
149C4×C73C22×C4⋊C411yescharacteristic
150Dic73—24no—
151Dic73#38412yes—
152Dic73C2×C4⋊Q811yescharacteristic
153Dic73C2×C4⋊Q811yescharacteristic
154C2×#1846—731nomaximal, Sylow
155C2×C73#184614yescomplemented
156C2×C73C2×#38411yescharacteristic
157C2×C73C2×#42712yes—
158D73#184614yescomplemented
159D73C2×#49512yes—
160D73C2×#49912yes—
161C22×#107—732no—
162C22×#106—732no—
163C22×C4×C8—731no—
164C2×#382—732no—
165#1846—738no—
166C73C2×#184611yescharacteristic, complemented, Sylow
167C23×C8—731no—
168C23×C8—731no—
169C22×C4⋊C4—734no—
170C22×C42—731no—
171C2×#107—738no—
172C2×#107—1468no—
173C2×#106—738no—
174C2×#106—1468no—
175C2×C4×C8—731no—
176C2×C4×C8—731no—
177C2×C4×C8—731no—
178C2×C4×C8—734no—
179C2×C4×C8—734no—
180C2×C4×C8#6440811yescharacteristic, complemented
181#382—738no—
182#382—1464no—
183C2×#95—1464no—
184C23×C4—731no—
185C23×C4—732no—
186C23×C4—1464no—
187C22×C8—731no—
188C22×C8—731no—
189C22×C8—734no—
190C22×C8—734no—
191C22×C8—734no—
192C22×C8—734no—
193C22×C8—732no—
194C22×C8—732no—
195C22×C8—732no—
196C22×C8—732no—
197C22×C8C2×#6440811yescharacteristic
198C22×C8C2×#6440811yescharacteristic
199C2×C4⋊C4—738no—
200C2×C4⋊C4—1464no—
201C2×C4⋊C4—1468no—
202C2×C4⋊C4—1468no—
203C2×C42—732no—
204C2×C42—731no—
205C2×C42—732no—
206C2×C42—732no—
207C2×C42—732no—
208C2×C42—732no—
209C2×C42C2×#6440811yescharacteristic
210#107—14616no—
211#106—14616no—
212C4×C8—734no—
213C4×C8—734no—
214C4×C8—734no—
215C4×C8C2×#6440814yescomplemented
216#95—14616no—
217C24—731no—
218C22×C4—2928no—
219C22×C4—29216no—
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—731no—
223C22×C4—731no—
224C22×C4—732no—
225C22×C4—732no—
226C22×C4—731no—
227C22×C4—732no—
228C22×C4—732no—
229C22×C4—732no—
230C22×C4—734no—
231C22×C4—734no—
232C22×C4—1468no—
233C22×C4—1468no—
234C22×C4C4⋊#6440812yes—
235C22×C4C22×#6440811yescharacteristic
236C2×C8—732no—
237C2×C8—732no—
238C2×C8—734no—
239C2×C8—734no—
240C2×C8—738no—
241C2×C8—738no—
242C2×C8—734no—
243C2×C8—734no—
244C2×C8—734no—
245C2×C8—734no—
246C2×C8C4⋊#6440814yes—
247C2×C8C4⋊#6440814yes—
248C2×C8C22×#6440812yes—
249C2×C8C22×#6440812yes—
250C4⋊C4—2928no—
251C4⋊C4—1468no—
252C4⋊C4—1468no—
253C42—732no—
254C42—734no—
255C42—732no—
256C42—734no—
257C42C4⋊#6440812yes—
258C42C22×#6440812yes—
259C23—731no—
260C23—731no—
261C23—732no—
262C23—732no—
263C23—738no—
264C23C2×C4⋊#6440811yescharacteristic
265C2×C4—24no—
266C2×C4—2928no—
267C2×C4—29216no—
268C2×C4—58416no—
269C2×C4—731no—
270C2×C4—731no—
271C2×C4—732no—
272C2×C4—732no—
273C2×C4—731no—
274C2×C4—731no—
275C2×C4—732no—
276C2×C4—732no—
277C2×C4—731no—
278C2×C4—731no—
279C2×C4—732no—
280C2×C4—732no—
281C2×C4—732no—
282C2×C4—732no—
283C2×C4—734no—
284C2×C4—1468no—
285C2×C4—1468no—
286C2×C4—1464no—
287C2×C4C2×C4⋊#6440814yes—
288C2×C4C2×C4⋊#6440812yes—
289C2×C4C2×C4⋊#6440812yes—
290C2×C4C2×C4⋊#6440811yescharacteristic
291C2×C4C23×#6440811yescharacteristic
292C8—734no—
293C8—734no—
294C8C2×C4⋊#6440814yes—
295C8C2×C4⋊#6440814yes—
296C22—734no—
297C22—734no—
298C22—731no—
299C22—731no—
300C22—732no—
301C22—738no—
302C22—738no—
303C22#1798953312yes—
304C22#1798959714yes—
305C22C22×C4⋊#6440811yescharacteristic
306C4—24no—
307C4—5848no—
308C4—731no—
309C4—731no—
310C4—732no—
311C4—1464no—
312C4#1798953312yes—
313C4C22×C4⋊#6440811yescharacteristic
314C4C22×C4⋊#6440811yescharacteristic
315C2—732no—
316C2—734no—
317C2—732no—
318C2#2262586814yesdirect product factor
319C2C2×#1798953311yescharacteristic
320C2C2×#1798959712yes—
subgroupG/H
centerC23C2×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×C4×C8×C73C4
socleC23×C73C2×C4⋊C4
prime radicalC23×D73C2×D4
cosocleC2×C4×D73C24
hypercenterC2×C4×C8#64408
hypocenterC73C2×#1846
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
4. #22625868C2direct (N × H)
17. C2×C4×#10596831C4semidirect
18. C2×C8×Dic73C4semidirect
19. C2×C8×Dic73C4semidirect
20. C4×C8×D73C4semidirect
22. C2×C4×C8×C73C4semidirect
49. C4×#10596831C2×C4semidirect
50. C8×Dic73C2×C4semidirect
51. C8×Dic73C2×C4semidirect
55. C4×C8×C73C2×C4semidirect
155. C2×C73#1846semidirect
158. D73#1846semidirect
166. C73C2×#1846semidirect
180. C2×C4×C8#64408semidirect
215. C4×C8C2×#64408semidirect
318. C2#22625868direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566602
C22×#145566592
C2×#179895312
#226258682
C2×C4×C8×D732
C2×#184673