Finite Group Databasebeta

← #30605490

Subgroups — #30605490

Order 15616.

372 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461686C211yesmaximal, characteristic
2#21461063C211yesmaximal, characteristic
3#21460819C212yesmaximal
4#21460818C212yesmaximal
5#21451182C211yesmaximal, characteristic
6#16840778—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519742C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14#16839700C2211yescharacteristic
15#16839683C2211yescharacteristic
16#16839682C411yescharacteristic
17#16839666—21no—
18#16839659—21no—
19#16839645—21no—
20#16839644—21no—
21#16839626C411yescharacteristic
22C61×#400C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29C4×#92420—41no—
30C22×Dic122C2×C411yescharacteristic
31C22×Dic122D411yescharacteristic
32#14519742—41no—
33#14519742—41no—
34#14519742—41no—
35#14519742—41no—
36C2×C4⋊Dic61—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196D411yescharacteristic
41C2×#11758196C2311yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122—42no—
72C2×Dic122SD1612yes—
73C2×Dic122Q1612yes—
74#11758217—42no—
75#11758217—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊Dic61—42no—
81#11758196—41no—
82#11758196—41no—
83#11758196—42no—
84#11758196—42no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—42no—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—42no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61#10312yes—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61#9911yescharacteristic
121C2×Dic61#9911yescharacteristic
122C2×Dic61#10312yes—
123C2×Dic61C2×SD1611yescharacteristic
124C2×Dic61C2×Q1611yescharacteristic
125Dic122—42no—
126Dic122—42no—
127Dic122—42no—
128Dic122—42no—
129#92420—82no—
130#92420—82no—
131#11905—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61C2×#9911yescharacteristic
135C22×C61C2×#10311yescharacteristic
136C22×C61#42111yescharacteristic
137C4×C61—22no—
138C4×C61—41no—
139C4×C61—41no—
140C4×C61—81no—
141C4×C61—81no—
142Dic61—21no—
143Dic61—21no—
144Dic61—21no—
145Dic61—22no—
146Dic61—21no—
147Dic61—41no—
148Dic61—42no—
149Dic61—81no—
150#2581—611no—
151#1801—611no—
152#1461—611no—
153#1354—612no—
154#1353—612no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61#152011yescharacteristic
158C2×C61#212011yescharacteristic
159C2×C61#213311yescharacteristic
160C2×C4×Q8—611no—
161C2×C4×Q8—611no—
162#431—1221no—
163#423—1221no—
164C2×#101—1221no—
165#400—611no—
166#400#692311yescharacteristic
167#395—611no—
168#395—611no—
169#391—1221no—
170#389—1221no—
171#387—1221no—
172#387—1221no—
173#382—611no—
174#343—612no—
175#324—612no—
176#324—1221no—
177C61#1190511yescharacteristic, complemented, Sylow
178C22×Q8—611no—
179C22×Q8—611no—
180C2×M16—1222no—
181C4×Q8—2441no—
182C4×Q8—2441no—
183C4×Q8—2441no—
184C4×Q8—2441no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4C2×#692311yescharacteristic
192C2×C4⋊C4C2×#692311yescharacteristic
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—1221no—
197C4⋊C8—2441no—
198C4⋊C8—2441no—
199C4⋊C8—2441no—
200#101—2442no—
201C22⋊C8—1222no—
202C4×C8—2441no—
203#95—21no—
204#95—21no—
205#95—611no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211#95C2×#692311yescharacteristic
212C2×Q8—612no—
213C2×Q8—612no—
214C2×Q8—2441no—
215C2×Q8—2441no—
216C2×Q8—2441no—
217C2×Q8—2442no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22⋊#692311yescharacteristic
228C22×C4C22×#692311yescharacteristic
229M16—2442no—
230M16—2442no—
231C2×C8—2442no—
232C2×C8—2442no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2442no—
240C4⋊C4—2442no—
241C4⋊C4—2442no—
242C42—1221no—
243C42—1221no—
244C42—1221no—
245C42—1221no—
246C42—1221no—
247C42—1221no—
248C42—2442no—
249C23C2×C22⋊#692311yescharacteristic
250Q8—2442no—
251Q8—2442no—
252Q8—2442no—
253Q8—2442no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—612no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1222no—
275C2×C4—1221no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4#1451984012yes—
284C8—4882no—
285C8—4882no—
286C22—21no—
287C22—21no—
288C22D61⋊#9911yescharacteristic
289C22C2×#1451984011yescharacteristic
290C22#1684075911yescharacteristic
291C4—22no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—1221no—
297C4—1222no—
298C4—1221no—
299C4—1221no—
300C4—1221no—
301C4—4881no—
302C4—2441no—
303C4—2442no—
304C2—21no—
305C2—21no—
306C2#2146125711yescharacteristic
307C2#2146207311yescharacteristic
308C2#2146211511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenter#400#6923
hypocenterC61#11905
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
177. C61#11905semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610632
#214608192
#214608182
#214511822
#1190561