Finite Group Databasebeta

← #30605165

Subgroups — #30605165

Order 15616.

434 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461719C211yesmaximal, characteristic
2#21461068C211yesmaximal, characteristic
3#21460818C212yesmaximal, complemented
4#21460817C212yesmaximal, complemented
5#400×D61C211yesmaximal, characteristic
6#16840734—21no—
7#16840733—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×C4⋊C4×D61C411yescharacteristic
13C2×C4⋊C4×D61C2211yescharacteristic
14#16839704—21no—
15#16839703—21no—
16#16839702C2211yescharacteristic
17#16839701C411yescharacteristic
18#16839700C2211yescharacteristic
19#95×D61—21no—
20#95×D61—21no—
21#95×D61C411yescharacteristic
22C61×#400C411yescharacteristic
23C2×#11758213—41no—
24C2×#11758217—22no—
25#14519834—41no—
26#14519834—41no—
27#14519834—41no—
28C22⋊#92420—22no—
29C22×C4×D61—21no—
30C22×C4×D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196D411yescharacteristic
38C2×#11758196C2311yescharacteristic
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C4⋊C4×D61—41no—
42C4⋊C4×D61—41no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53#95×C61—21no—
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56C23×D61C22⋊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×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—22no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—42no—
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61—44no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83#11758217—42no—
84#11758217—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87#11758213—82no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—42no—
95C23×C61C2×C22⋊C411yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—22no—
99C22×D61—22no—
100C22×D61#9911yescharacteristic
101C22×D61#9911yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—42no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#13712yes—
126C4×D61—42no—
127C4×D61—42no—
128C4×D61—42no—
129C4×D61—42no—
130C4×D61—42no—
131C4×D61—81no—
132C4×D61—84no—
133C4×D61—82no—
134C4×D61—82no—
135#92420—82no—
136#92420—82no—
137#11814—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61C2×#9911yescharacteristic
141C22×C61#41911yescharacteristic
142C22×C61#42111yescharacteristic
143C2×D61—24no—
144C2×D61—24no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—21no—
149C2×D61#35212yes—
150C2×D61#35512yes—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—81no—
155C4×C61—81no—
156Dic61—22no—
157Dic61—41no—
158Dic61—41no—
159Dic61—81no—
160Dic61—81no—
161C2×#400—611no—
162#1821—611no—
163#1463—611no—
164#1353—612no—
165#1353—612no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61#151111yescharacteristic
169C2×C61C2×#35211yescharacteristic
170C2×C61C2×#35511yescharacteristic
171D61—22no—
172D61—22no—
173C22×C4⋊C4—611no—
174C22×C4⋊C4—611no—
175#407—1221no—
176#407—1221no—
177#400—611no—
178#400—611no—
179#400—611no—
180#400—1221no—
181#400—1221no—
182#400#692311yescharacteristic
183C2×#95—611no—
184C2×#95—1221no—
185C2×#95—1221no—
186#343—612no—
187#343—1221no—
188#324—612no—
189#324—1221no—
190C61#1181411yescharacteristic, complemented, Sylow
191C23×C4—611no—
192C23×C4—611no—
193C23×C4—611no—
194C23×C4—1221no—
195C23×C4—1221no—
196C2×M16—1222no—
197C2×M16—2441no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—2441no—
204C2×C4⋊C4—2441no—
205C2×C4⋊C4—2441no—
206C2×C4⋊C4—2441no—
207C2×C4⋊C4C2×#692311yescharacteristic
208C2×C4⋊C4C2×#692311yescharacteristic
209C22⋊C8—1222no—
210C22⋊C8—2441no—
211C22⋊C8—2441no—
212C22⋊C8—2441no—
213#95—21no—
214#95—21no—
215#95—611no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95C2×#692311yescharacteristic
224C24—611no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—1222no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—2441no—
240C22×C4—2441no—
241C22×C4—2441no—
242C22×C4—2444no—
243C22×C4—2442no—
244C22×C4—2442no—
245C22×C4—2442no—
246C22×C4—2442no—
247C22×C4—2442no—
248C22×C4C22⋊#692311yescharacteristic
249C22×C4C22⋊#692311yescharacteristic
250C22×C4C22×#692311yescharacteristic
251M16—4882no—
252M16—2442no—
253M16—2442no—
254C2×C8—2442no—
255C2×C8—2442no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2442no—
263C23—611no—
264C23—611no—
265C23—1222no—
266C23—1222no—
267C23—1221no—
268C23—1221no—
269C23C2×C22⋊#692311yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—612no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—4881no—
288C2×C4—4882no—
289C2×C4—4884no—
290C2×C4—4882no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2442no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C8—4882no—
304C8—4882no—
305C22—21no—
306C22—21no—
307C22—612no—
308C22—612no—
309C22—1224no—
310C22—1224no—
311C22—1221no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22D61⋊#9911yescharacteristic
316C22#1684075511yescharacteristic
317C22#1684075911yescharacteristic
318C4—41no—
319C4—41no—
320C4—41no—
321C4—81no—
322C4—81no—
323C4—1222no—
324C4—4881no—
325C4—4881no—
326C4—2441no—
327C4—2441no—
328C2—21no—
329C2—21no—
330C2—1222no—
331C2—1222no—
332C2#2146122811yescharacteristic
333C2D61⋊#35211yescharacteristic
334C2D61⋊#35511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenter#400#6923
hypocenterC61#11814
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
3. #21460818C2semidirect
4. #21460817C2semidirect
190. C61#11814semidirect

Maximal subgroups

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

subgroupindex
#214617192
#214610682
#214608182
#214608172
#400×D612
#1181461