Finite Group Databasebeta

← #30604346

Subgroups — #30604346

Order 15616.

374 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461082C211yesmaximal, characteristic
2#21461062C211yesmaximal, characteristic
3#21460762C212yesmaximal
4#21460761C212yesmaximal
5#21451029C211yesmaximal, characteristic
6#16840782—21no—
7#16840778—21no—
8#16840607—21no—
9#16840607—21no—
10#16840607C2212yes—
11#16840607C2212yes—
12C2×#14519776C411yescharacteristic
13C2×Q8×Dic61C2211yescharacteristic
14#16839683—21no—
15#16839683—21no—
16#16839669C411yescharacteristic
17#16839659—21no—
18#16839659—21no—
19#16839632C2211yescharacteristic
20#16839631C2211yescharacteristic
21C4×#11758196C411yescharacteristic
22C61×#391C411yescharacteristic
23#14519844—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C22×Dic122—21no—
30#14519776—41no—
31#14519776—41no—
32Q8×Dic61—41no—
33Q8×Dic61—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61C2311yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56C2×Q8×C61—22no—
57C2×Q8×C61—22no—
58C2×Q8×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×Dic122—42no—
71C2×Dic122—81no—
72C2×Dic122—81no—
73C2×#92420—42no—
74C2×#92420—42no—
75C4⋊C4×C61—41no—
76C42×C61—22no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—81no—
82C4⋊Dic61—81no—
83#11758196—24no—
84#11758196—41no—
85#11758196—41no—
86#11758196—81no—
87#11758196—81no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—22no—
95C23×C61C2×C22⋊C411yescharacteristic
96Q8×C61—44no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61#10112yes—
111C2×C4×C61#13112yes—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#9911yescharacteristic
126C2×Dic61#9911yescharacteristic
127Dic122—84no—
128#92420—82no—
129#92420—82no—
130#11574—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61#40811yescharacteristic
134C22×C61C2×#9911yescharacteristic
135C22×C61C2×#10111yescharacteristic
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—42no—
139C4×C61—41no—
140C4×C61—81no—
141Dic61—21no—
142Dic61—42no—
143Dic61—41no—
144Dic61—41no—
145Dic61—41no—
146Dic61—81no—
147Dic61#35612yes—
148#2567—611no—
149#1467—611no—
150#1461—611no—
151#1325—612no—
152#1325—612no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61#147211yescharacteristic
156C2×C61#212811yescharacteristic
157C2×C61C2×#35611yescharacteristic
158C2×C4⋊Q8—611no—
159C2×C4×Q8—611no—
160#432—1221no—
161#431—1221no—
162#395—1221no—
163#395—1221no—
164#391—611no—
165#391#692311yescharacteristic
166#389—1221no—
167#389—1221no—
168#384—611no—
169#384—611no—
170C4×C4⋊C4—611no—
171#324—612no—
172#324—612no—
173#324—1221no—
174#324—1221no—
175C61#1157411yescharacteristic, complemented, Sylow
176C22×Q8—1221no—
177C22×Q8C2×#692311yescharacteristic
178C4⋊Q8—2441no—
179C4⋊Q8—2441no—
180C4×Q8—2441no—
181C4×Q8—2441no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4C2×#692311yescharacteristic
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42C2×#692311yescharacteristic
198C4⋊C8—2441no—
199C4⋊C8—2441no—
200C22⋊C8—1222no—
201C22⋊C8—1222no—
202#97—2441no—
203C4×C8—2441no—
204#95—21no—
205#95—21no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—41no—
212C2×Q8—4881no—
213C2×Q8—4881no—
214C2×Q8—2442no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4C22⋊#692311yescharacteristic
224C22×C4C22⋊#692311yescharacteristic
225C22×C4C22×#692311yescharacteristic
226C2×C8—2442no—
227C2×C8—2442no—
228C4⋊C4—41no—
229C4⋊C4—1224no—
230C4⋊C4—4881no—
231C4⋊C4—4881no—
232C4⋊C4—4881no—
233C4⋊C4—4881no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C42—22no—
241C42—1221no—
242C42—1221no—
243C42—1221no—
244C42—1221no—
245C42—1221no—
246C42—1221no—
247C42—1222no—
248C23C2×C22⋊#692311yescharacteristic
249Q8—44no—
250Q8—4884no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4#1451983812yes—
280C2×C4#1451986412yes—
281C8—4882no—
282C8—4882no—
283C22—21no—
284C22—21no—
285C22#1684073511yescharacteristic
286C22D61⋊#9911yescharacteristic
287C22C2×#1451983811yescharacteristic
288C4—22no—
289C4—22no—
290C4—42no—
291C4—41no—
292C4—81no—
293C4—612no—
294C4—1221no—
295C4—4881no—
296C4—2442no—
297C4—2441no—
298C4—2441no—
299C4—2441no—
300C2—21no—
301C2—21no—
302C2#2146109811yescharacteristic
303C2#2146209911yescharacteristic
304C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenter#391#6923
hypocenterC61#11574
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
175. C61#11574semidirect

Maximal subgroups

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

subgroupindex
#214610822
#214610622
#214607622
#214607612
#214510292
#1157461