Finite Group Databasebeta

← #30601796

Subgroups — #30601796

Order 15616.

538 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461735C211yesmaximal, characteristic
2#21461604C211yesmaximal, characteristic
3C2×#16840622C214yesmaximal
4#21454215C211yesmaximal, characteristic
5C2×#14519844C2212yes—
6C2×#14519844C2212yes—
7C2×#14519832—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628—21no—
11#16840622—28no—
12C2×#14519777C411yescharacteristic
13C2×#14519775C412yes—
14C2×#14519775C2212yes—
15#16839631—21no—
16#16839631—21no—
17#16839631—21no—
18#16839631—21no—
19C42×Dic61C2211yescharacteristic
20C2×C4⋊Q8×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23#14519844—24no—
24#14519844—22no—
25#14519844D414yes—
26#14519832—42no—
27C22×Dic122C2×C412yes—
28#14519777—42no—
29#14519775—24no—
30#14519775—24no—
31#14519775—44no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×#11758196—22no—
37C2×#11758196—22no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44C22×Q8×C61C2×C412yes—
45C4⋊Q8×C61—42no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C42×C61C2×C411yescharacteristic
49C2×Q8×C61—24no—
50C2×Q8×C61—42no—
51C2×Q8×C61—42no—
52C22×C4×C61—22no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C2×Dic122—24no—
62C2×Dic122—42no—
63C2×Dic122—42no—
64C2×#92420—24no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—42no—
72C42×C61—22no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75#11758196—44no—
76#11758196—44no—
77#11758196—44no—
78#11758196—42no—
79#11758196—42no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61SD1612yes—
85C4×Dic61Q1612yes—
86C4×Dic61C2×D412yes—
87C4×Dic61#4112yes—
88C23×C61C2×C22⋊C411yescharacteristic
89Q8×C61—84no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61#10012yes—
100C2×C4×C61#10312yes—
101C2×C4×C61C4×D412yes—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61#10012yes—
110C2×Dic61#10312yes—
111C2×Dic61#12112yes—
112C2×Dic61#12411yescharacteristic
113C2×Dic61#12711yescharacteristic
114C2×Dic61C2×SD1611yescharacteristic
115C2×Dic61C2×Q1611yescharacteristic
116C2×Dic61#13712yes—
117C2×Dic61#13712yes—
118C2×Dic61#13712yes—
119Dic122—84no—
120#92420—44no—
121#92420—82no—
122#9702—611nomaximal, Sylow
123C22×C61#39011yescharacteristic
124C22×C61C2×#10011yescharacteristic
125C22×C61C2×#10011yescharacteristic
126C22×C61C2×#10311yescharacteristic
127C22×C61#41911yescharacteristic
128C22×C61#41911yescharacteristic
129C22×C61#41911yescharacteristic
130C4×C61—22no—
131C4×C61—22no—
132C4×C61—22no—
133C4×C61—82no—
134Dic61—22no—
135Dic61—22no—
136Dic61—82no—
137Dic61#46112yes—
138Dic61#46212yes—
139Dic61#49112yes—
140Dic61#49712yes—
141#2868—611no—
142#1831—611no—
143#1767—611no—
144C2×#333—614no—
145C2×C61#154811yescharacteristic
146C2×C61#154811yescharacteristic
147C2×C61#155811yescharacteristic
148C2×C61#155811yescharacteristic
149C2×C61#196011yescharacteristic
150C2×C61#196511yescharacteristic
151C2×C61#198111yescharacteristic
152C2×C4⋊Q8—612no—
153C2×C4⋊Q8—612no—
154C2×C4⋊Q8—611no—
155C2×C4⋊Q8#692311yescharacteristic
156C2×C4⋊C8—612no—
157C2×C4⋊C8—612no—
158C2×#97—1221no—
159#384—1221no—
160#384—1221no—
161#384—1221no—
162#384—1221no—
163C43—611no—
164#336—1221no—
165#336—1221no—
166#336—1221no—
167#333—1228no—
168C61#970211yescharacteristic, complemented, Sylow
169C22×Q8—612no—
170C22×Q8C2×#692312yes—
171C22×C8—1222no—
172C22×C8—1222no—
173C4⋊Q8—42no—
174C4⋊Q8—1224no—
175C4⋊Q8—1224no—
176C4⋊Q8—2442no—
177C4⋊Q8—2444no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—1222no—
181C2×C4⋊C4—1222no—
182C2×C4⋊C4—1222no—
183C2×C4⋊C4—1222no—
184C2×C4⋊C4—1221no—
185C2×C4⋊C4—1221no—
186C2×C42—611no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42C2×#692311yescharacteristic
193C4⋊C8—614no—
194C4⋊C8—1222no—
195C4⋊C8—1224no—
196#97—2442no—
197C2×Q8—24no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—1224no—
201C2×Q8—2442no—
202C2×Q8—2442no—
203C22×C4—22no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1222no—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22×#692311yescharacteristic
212C2×C8—1224no—
213C2×C8—2442no—
214C2×C8—2442no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—2442no—
221C4⋊C4—2444no—
222C4⋊C4—2442no—
223C4⋊C4—2442no—
224C4⋊C4—2444no—
225C4⋊C4—2444no—
226C4⋊C4—2442no—
227C42—22no—
228C42—612no—
229C42—612no—
230C42—612no—
231C42—612no—
232C42—1222no—
233C42—1222no—
234C42—1222no—
235C42—1222no—
236C23C2×C22⋊#692311yescharacteristic
237Q8—84no—
238Q8—4884no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—612no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—612no—
254C2×C4—612no—
255C2×C4—612no—
256C2×C4—612no—
257C2×C4—612no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—2442no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4#1451983712yes—
266C2×C4#1451984012yes—
267C2×C4D4×#692312yes—
268C8—4882no—
269C8—2444no—
270C22#1684071411yescharacteristic
271C22C2×#1451983711yescharacteristic
272C22D61⋊#10011yescharacteristic
273C22C2×#1451984011yescharacteristic
274C22#1684075511yescharacteristic
275C22#1684075511yescharacteristic
276C22#1684075511yescharacteristic
277C4—22no—
278C4—22no—
279C4—22no—
280C4—82no—
281C4—612no—
282C4—612no—
283C4—612no—
284C4—612no—
285C4—1222no—
286C4—1222no—
287C4—4882no—
288C2#2146133211yescharacteristic
289C2#2146133311yescharacteristic
290C2#2146135211yescharacteristic
291C2#2146135311yescharacteristic
292C2#2146195011yescharacteristic
293C2#2146196111yescharacteristic
294C2#2146198511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#9702
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
168. C61#9702semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214616042
C2×#168406222
#214542152
#970261