Finite Group Databasebeta

← #30602163

Subgroups — #30602163

Order 15616.

518 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 126 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
1#21461734C211yesmaximal, characteristic
2C4×#14519832C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#21448390C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519832—21no—
8C2×#14519832—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519776C411yescharacteristic
13C2×#14519742—21no—
14#16839666—21no—
15#16839660C411yescharacteristic
16#16839657—21no—
17#16839631C411yescharacteristic
18C4⋊C4×Dic61C2211yescharacteristic
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26#14519832—24no—
27#14519832—24no—
28C4×#92420—22no—
29C4×#92420Q814yescomplemented
30C22×Dic122—21no—
31#14519776—22no—
32#14519776—22no—
33#14519742—44no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×Dic122—24no—
68C2×Dic122—42no—
69C2×Dic122—42no—
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—24no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—22no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61M1612yes—
80C42×C61—22no—
81C4⋊Dic61—21no—
82C4⋊Dic61—22no—
83C4⋊Dic61M1612yes—
84#11758196—24no—
85#11758196—42no—
86#11758196—42no—
87#11758196—42no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—42no—
95C4×Dic61—42no—
96C4×Dic61C2×Q812yes—
97C4×Dic61#4112yes—
98C23×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61C4×Q812yes—
112C2×C4×C61C2×M1611yescharacteristic
113C2×C4×C61C2×M1611yescharacteristic
114C2×C4×C61#13112yes—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—22no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61#10412yes—
128C2×Dic61#10412yes—
129C2×Dic61C22⋊Q812yes—
130C2×Dic61#12411yescharacteristic
131C2×Dic61C4⋊Q811yescharacteristic
132C2×Dic61AGL(1,ℤ/8)12yes—
133C2×Dic61#13712yes—
134Dic122—48no—
135#92420—28no—
136#92420—82no—
137#9877—611nomaximal, Sylow
138C22×C61#39111yescharacteristic
139C22×C61#40711yescharacteristic
140C22×C61#40811yescharacteristic
141C22×C61#41811yescharacteristic
142C22×C61#41911yescharacteristic
143C22×C61C2×#10411yescharacteristic
144C22×C61C2×#10411yescharacteristic
145C4×C61—41no—
146C4×C61—41no—
147C4×C61—42no—
148C4×C61—81no—
149C4×C61#44612yes—
150C4×C61#44612yes—
151Dic61—22no—
152Dic61—22no—
153Dic61—22no—
154Dic61—42no—
155Dic61—81no—
156Dic61#48912yes—
157Dic61#50112yes—
158C4×C4⋊Q8—611no—
159#1831—611no—
160C4×#97—611no—
161#1279—612no—
162#1279—612no—
163C2×C61#148411yescharacteristic
164C2×C61#148511yescharacteristic
165C2×C61#149011yescharacteristic
166C2×C61#149111yescharacteristic
167C2×C61#198511yescharacteristic
168C2×C61#199311yescharacteristic
169C2×C61#199411yescharacteristic
170C2×C4⋊Q8—611no—
171C2×C4×Q8—1221no—
172C2×C4⋊C8—612no—
173C2×#97—1221no—
174C2×#97—1221no—
175C2×C4×C8—612no—
176#391—1221no—
177#389—611no—
178#389—1221no—
179#389#692311yescharacteristic
180#384—611no—
181C4×C4⋊C4—611no—
182C4×C4⋊C4—611no—
183C4×C4⋊C4—1221no—
184C43—611no—
185#336—1221no—
186#336—1221no—
187C61#987711yescharacteristic, complemented, Sylow
188C22×Q8—1221no—
189C22×C8—1222no—
190C22×C8—1222no—
191C4⋊Q8—1222no—
192C4⋊Q8—1222no—
193C4×Q8—2444no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4C2×#692311yescharacteristic
202C2×C4⋊C4C2×#692311yescharacteristic
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—1221no—
210C2×C42—1221no—
211C2×C42C2×#692311yescharacteristic
212C4⋊C8—1224no—
213#97—1224no—
214#97—1224no—
215C4×C8—614no—
216C4×C8—1222no—
217#95—21no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221C2×Q8—1224no—
222C2×Q8—2442no—
223C2×Q8—2442no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4C22⋊#692311yescharacteristic
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22×#692311yescharacteristic
235C2×C8—1224no—
236C2×C8—1224no—
237C2×C8—1224no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8—2442no—
241C4⋊C4—21no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—612no—
245C4⋊C4—1224no—
246C4⋊C4—1221no—
247C4⋊C4—1222no—
248C4⋊C4—2442no—
249C4⋊C4—2442no—
250C4⋊C4—2442no—
251C4⋊C4#1175821312yes—
252C42—22no—
253C42—612no—
254C42—612no—
255C42—1222no—
256C42—1222no—
257C42—1222no—
258C42—1222no—
259C42—1221no—
260C42—1221no—
261C42—2442no—
262C42—2442no—
263C23C2×C22⋊#692311yescharacteristic
264Q8—2448no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—612no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—612no—
283C2×C4—612no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1222no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4Q8×#692312yes—
297C2×C4D61⋊M1611yescharacteristic
298C2×C4C2×#1175821311yescharacteristic
299C2×C4#1451986412yes—
300C8—1228no—
301C8—4882no—
302C22(C2×#6923)⋊Q811yescharacteristic
303C22#1684073311yescharacteristic
304C22#1684073511yescharacteristic
305C22#1684075411yescharacteristic
306C22#1684075511yescharacteristic
307C22D61⋊#10411yescharacteristic
308C22D61⋊#10411yescharacteristic
309C4—41no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4—612no—
314C4—612no—
315C4—1222no—
316C4—1222no—
317C4—1222no—
318C4—4881no—
319C4—2442no—
320C4#1684081212yes—
321C4#1684081412yes—
322C2#2146113811yescharacteristic
323C2#2146114111yescharacteristic
324C2#2146115911yescharacteristic
325C2#2146116211yescharacteristic
326C2#2146199211yescharacteristic
327C2#2146200311yescharacteristic
328C2#2146200511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9877
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
29. C4×#92420Q8semidirect
187. C61#9877semidirect

Maximal subgroups

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

subgroupindex
#214617342
C4×#145198322
#214606552
#214483902
#987761