Finite Group Databasebeta

← C2×#21444902 #29655895

Subgroups — C2×#21444902 #29655895

Order 15616.

1190 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 219 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840136C211yesmaximal, characteristic, complemented
2C2×#16839957C212yesmaximal, complemented
3#21444902C218yesmaximal, direct product factor
4C2×#16839511C211yesmaximal, characteristic, complemented
5C2×D4⋊#92418C212yesmaximal, complemented
6C2×C61×#555C211yesmaximal, characteristic, complemented
7C22×#11758201—22no—
8C22×#11758199—22no—
9C2×#14519774C2211yescharacteristic
10#16840136—22no—
11#16840136C2214yescomplemented
12#16839957—24no—
13#16839957C2218yescomplemented
14C2×C4⋊#92418C2212yes—
15C2×#14519697—22no—
16C2×C4×#92418C2211yescharacteristic
17#16839511C2214yescomplemented
18D4⋊#92418C2218yescomplemented
19C61×#555—22no—
20C61×#555—24no—
21C61×#555C2214yescomplemented
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#124×C61—22no—
24C2×#121×C61—22no—
25C2×C4×D4×C61C2212yes—
26C2×#117×C61—22no—
27C22×D244—22no—
28C22×D244—21no—
29C2×#11758201—28no—
30C2×#11758201—48no—
31C2×#11758199—28no—
32C2×#11758199—48no—
33C22×#92418—21no—
34C22×#92418—22no—
35#14519774—22no—
36#14519774—21no—
37#14519774C2312yes—
38C4⋊#92418—22no—
39C4⋊#92418C2314yes—
40#14519697—28no—
41C4×#92418—21no—
42C4×#92418C2312yes—
43C22×Q8×C61D412yes—
44C22×D4×C61—22no—
45C22×D4×C61D412yes—
46C23×C4×C61—22no—
47C4⋊Q8×C61—22no—
48C4⋊Q8×C61D412yes—
49C4⋊Q8×C61C2312yes—
50#124×C61—28no—
51#124×C61—28no—
52#121×C61—28no—
53#121×C61—28no—
54C4×D4×C61—22no—
55C4×D4×C61—22no—
56C4×D4×C61D414yes—
57C4×D4×C61C2314yes—
58#117×C61—28no—
59#117×C61—28no—
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61D412yes—
62C2×C22⋊C4×C61—24no—
63C2×C22⋊C4×C61—22no—
64C2×C42×C61—22no—
65C2×C42×C61C2311yescharacteristic
66C24×C61—22no—
67C23×D61—41no—
68C2×Q8×C61—22no—
69C2×Q8×C61—44no—
70C2×Q8×C61C2×D414yes—
71C2×D4×C61—28no—
72C2×D4×C61—22no—
73C2×D4×C61—24no—
74C2×D4×C61—24no—
75C2×D4×C61—84no—
76C2×D4×C61C2×D414yes—
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—24no—
80C22×C4×C61—24no—
81C22×C4×C61—44no—
82C22×C4×C61—44no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D412yes—
85C2×D244—24no—
86C2×D244—22no—
87C2×D244—44no—
88C2×D244—44no—
89C2×D244—44no—
90C2×D244—41no—
91C2×D244—42no—
92C4⋊C4×C61—24no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—24no—
95C4⋊C4×C61C2×D414yes—
96C22⋊C4×C61—216no—
97C22⋊C4×C61—24no—
98C22⋊C4×C61—24no—
99C42×C61—28no—
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D412yes—
102C42×C61C2411yescharacteristic
103#11758201—416no—
104#11758199—416no—
105C2×#92418—24no—
106C2×#92418—22no—
107C2×#92418—24no—
108C2×#92418—44no—
109C23×C61—24no—
110C23×C61—44no—
111C23×C61—44no—
112C23×C61—44no—
113C23×C61#12011yescharacteristic
114C22×D61—42no—
115C22×D61—84no—
116C22×D61—82no—
117Q8×C61—44no—
118Q8×C61—82no—
119D4×C61—24no—
120D4×C61—24no—
121D4×C61—44no—
122D4×C61—88no—
123C2×C4×C61—22no—
124C2×C4×C61—24no—
125C2×C4×C61—24no—
126C2×C4×C61—44no—
127C2×C4×C61—44no—
128C2×C4×C61—44no—
129C2×C4×C61—44no—
130C2×C4×C61—48no—
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12012yes—
133C2×C4×C61#13514yes—
134C2×C4×C61AGL(1,ℤ/8)14yes—
135C2×C4×C61C22×D411yescharacteristic
136C2×C4×C61C22×D412yes—
137D244—44no—
138D244—44no—
139D244—44no—
140D244—82no—
141D244—84no—
142#92418—24no—
143#92418—44no—
144C2×#1624—611nomaximal, Sylow
145C22×C61—44no—
146C22×C61—44no—
147C22×C61—44no—
148C22×C61—88no—
149C22×C61#44914yes—
150C22×C61#45312yes—
151C22×C61C2×#12011yescharacteristic
152C2×D61—84no—
153C2×D61—82no—
154C2×D61—164no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—44no—
158C4×C61—44no—
159C4×C61#44914yes—
160C4×C61C2×#13512yes—
161C4×C61C2×AGL(1,ℤ/8)12yes—
162C2×#555D6111yescharacteristic, complemented
163C2×#492—611no—
164C2×#459—612no—
165#1624—618no—
166C2×#333—611no—
167C2×D4⋊C8—612no—
168C2×C61—84no—
169C2×C61#162414yescomplemented
170C2×C61C2×#44912yes—
171C2×C61C2×#45311yescharacteristic
172D61—162no—
173C22×SD16—1222no—
174C22×D8—1222no—
175#555—22no—
176#555—24no—
177#555C2×D6114yescomplemented
178C2×C4⋊Q8C2×D6111yescharacteristic
179C2×#127—611no—
180C2×#124—22no—
181C2×#121—22no—
182C2×C4×D4C2×D6112yes—
183C2×#117—22no—
184#492—614no—
185#492—1222no—
186#459—618no—
187#459—1224no—
188C2×C4⋊C8—612no—
189C2×#102—1222no—
190C2×C4×C8—611no—
191#333—614no—
192D4⋊C8—618no—
193C61C2×#162411yescharacteristic, complemented, Sylow
194C22×Q8C22⋊D6112yes—
195C22×D4—22no—
196C22×D4—1222no—
197C22×D4—1221no—
198C22×D4C22⋊D6112yes—
199C23×C4—22no—
200C2×SD16—1228no—
201C2×SD16—2448no—
202C2×D8—1228no—
203C2×D8—2448no—
204C22×C8—1221no—
205C22×C8—1222no—
206C4⋊Q8—22no—
207C4⋊Q8C22⋊D6112yes—
208C4⋊Q8C22×D6112yes—
209#127—612no—
210#127—1222no—
211#127—1221no—
212#124—28no—
213#124—28no—
214#121—28no—
215#121—28no—
216C4×D4—22no—
217C4×D4—22no—
218C4×D4C22⋊D6114yes—
219C4×D4C22×D6114yes—
220#117—28no—
221#117—28no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4C22⋊D6112yes—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—22no—
226C2×C42—22no—
227C2×C42C22×D6111yescharacteristic
228C4⋊C8—614no—
229C4⋊C8—1222no—
230#102—1228no—
231C4×C8—612no—
232C4×C8—1221no—
233C24—22no—
234C24—2441no—
235C2×Q8—22no—
236C2×Q8—44no—
237C2×Q8C2×C22⋊D6114yes—
238C2×D4—28no—
239C2×D4—22no—
240C2×D4—24no—
241C2×D4—24no—
242C2×D4—84no—
243C2×D4—1224no—
244C2×D4—1222no—
245C2×D4—2444no—
246C2×D4—2441no—
247C2×D4—2442no—
248C2×D4—2444no—
249C2×D4—2444no—
250C2×D4C2×C22⋊D6114yes—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—44no—
256C22×C4—44no—
257C22×C4C2×C22⋊D6111yescharacteristic
258C22×C4C2×C22⋊D6112yes—
259SD16—24416no—
260D8—24416no—
261C2×C8—1224no—
262C2×C8—1222no—
263C2×C8—1224no—
264C2×C8—2444no—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—22no—
268C4⋊C4C2×C22⋊D6114yes—
269C22⋊C4—216no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C42—28no—
273C42C2×C22⋊D6111yescharacteristic
274C42C2×C22⋊D6112yes—
275C42C23×D6111yescharacteristic
276C23—24no—
277C23—44no—
278C23—44no—
279C23—44no—
280C23—4884no—
281C23—4882no—
282C23—2442no—
283C23#1451974611yescharacteristic
284Q8—44no—
285Q8—82no—
286D4—24no—
287D4—24no—
288D4—44no—
289D4—88no—
290D4—4882no—
291D4—4884no—
292D4—2444no—
293D4—2444no—
294D4—2444no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—48no—
303C2×C4#1451974611yescharacteristic
304C2×C4#1451974612yes—
305C2×C4#1451979714yes—
306C2×C4#1451980214yes—
307C2×C4C22×C22⋊D6111yescharacteristic
308C2×C4C22×C22⋊D6112yes—
309C8—1224no—
310C8—2444no—
311C22—44no—
312C22—44no—
313C22—44no—
314C22—88no—
315C22—9764no—
316C22—4882no—
317C22—4884no—
318C22#1683990714yes—
319C22#1683993012yes—
320C22C2×#1451974611yescharacteristic
321C4—21no—
322C4—21no—
323C4—44no—
324C4—44no—
325C4#1683990714yes—
326C4C2×#1451979712yes—
327C4C2×#1451980212yes—
328C2—84no—
329C2—9762no—
330C2#2144490214yesdirect product factor
331C2C2×#1683990712yes—
332C2C2×#1683993011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#555C2
socleC23×C61#120
hypercenterC2×#555D61
hypocenterC61C2×#1624
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#16840136C2semidirect
2. C2×#16839957C2semidirect
3. #21444902C2direct (N × H)
4. C2×#16839511C2semidirect
5. C2×D4⋊#92418C2semidirect
6. C2×C61×#555C2semidirect
11. #16840136C22semidirect
13. #16839957C22semidirect
17. #16839511C22semidirect
18. D4⋊#92418C22semidirect
21. C61×#555C22semidirect
162. C2×#555D61semidirect
169. C2×C61#1624semidirect
177. #555C2×D61semidirect
193. C61C2×#1624semidirect
330. C2#21444902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401362
C2×#168399572
#214449022
C2×#168395112
C2×D4⋊#924182
C2×C61×#5552
C2×#162461