Finite Group Databasebeta

← #30601009

Subgroups — #30601009

Order 15616.

446 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462499C211yesmaximal, characteristic
2#21461281C212yesmaximal, complemented
3#21461071C211yesmaximal, characteristic
4#21460707C212yesmaximal, complemented
5#21451518C211yesmaximal, characteristic
6#16840786—24no—
7#16840783C2212yes—
8#16840765—21no—
9#16840732—21no—
10C4×#11758217C2212yes—
11#16840619—24no—
12#16840608—21no—
13#16840605—21no—
14C2×#14519768C2211yescharacteristic
15C2×#14519733C2211yescharacteristic
16#16839702C411yescharacteristic
17#16839698C411yescharacteristic
18#16839693C411yescharacteristic
19#16839659—21no—
20#16839655—21no—
21#16839644—21no—
22#16839634—21no—
23#16839607C2211yescharacteristic
24C61×#397C411yescharacteristic
25C2×#11758217—22no—
26#14519844—22no—
27C4⋊#92420—22no—
28C4⋊#92420—22no—
29C22⋊#92420—24no—
30C22⋊#92420—22no—
31#14519832—22no—
32#14519832D414yes—
33C4×#92420—22no—
34C23×Dic61D411yescharacteristic
35#14519768—22no—
36#14519768—22no—
37#14519733—22no—
38#14519733—22no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196C2×C411yescharacteristic
45C2×#11758196D411yescharacteristic
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61D411yescharacteristic
48C2×C4×Dic61—21no—
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2×C411yescharacteristic
59#95×C61—21no—
60#95×C61C2×C411yescharacteristic
61C24×C61C22⋊C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76#11758217—42no—
77#11758217—42no—
78C2×#92420—24no—
79C2×#92420—42no—
80C4⋊C4×C61—22no—
81C22⋊C4×C61—22no—
82C22⋊C4×C61—42no—
83C22⋊Dic61—22no—
84C22⋊Dic61—42no—
85C4⋊Dic61—22no—
86C4⋊Dic61—42no—
87#11758196—22no—
88#11758196—22no—
89#11758196—42no—
90#11758196—42no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—42no—
96C4×Dic61C2×D412yes—
97C4×Dic61#4112yes—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61C2×C22⋊C411yescharacteristic
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—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61C4×D412yes—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#12011yescharacteristic
131C2×Dic61#12112yes—
132C2×Dic61#12311yescharacteristic
133#92420—44no—
134#92420—82no—
135#9390—611nomaximal, Sylow
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—42no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61—81no—
143C22×C61#38611yescharacteristic
144C22×C61#42111yescharacteristic
145C22×C61#42111yescharacteristic
146C4×C61—22no—
147C4×C61—41no—
148C4×C61—81no—
149C4×C61—81no—
150Dic61—22no—
151Dic61—21no—
152Dic61—21no—
153Dic61—42no—
154Dic61—41no—
155Dic61—41no—
156Dic61—81no—
157#2921—611no—
158#2611—611no—
159#1528—612no—
160#1464—611no—
161#1300—612no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61—81no—
165C2×C61#188411yescharacteristic
166C2×C61#189711yescharacteristic
167C2×C61#191511yescharacteristic
168C2×#125—611no—
169C2×#117—611no—
170#433—1224no—
171#432—612no—
172#423—1221no—
173#407—1221no—
174C4×M16—612no—
175#400—611no—
176#399—611no—
177#398—611no—
178#397#692311yescharacteristic
179#389—1221no—
180#388—1221no—
181#387—1221no—
182#385—1221no—
183#376—611no—
184#330—1224no—
185#324—1221no—
186#323—1221no—
187C61#939011yescharacteristic, complemented, Sylow
188C23×C4—611no—
189C2×M16—1222no—
190#125—1222no—
191#125—1222no—
192#117—1222no—
193#117—1222no—
194C2×C4⋊C4—611no—
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×C22⋊C4—21no—
203C2×C22⋊C4—611no—
204C2×C22⋊C4—1221no—
205C2×C22⋊C4C2×#692311yescharacteristic
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—1221no—
209C4⋊C8—1222no—
210C4⋊C8—1222no—
211C4⋊C8—1222no—
212C22⋊C8—1224no—
213C22⋊C8—1222no—
214#97—614no—
215#97—1222no—
216C4×C8—1222no—
217#95—21no—
218#95—611no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95C2×#692311yescharacteristic
224C24C22⋊#692311yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—2441no—
236C22×C4—2441no—
237C22×C4C22⋊#692311yescharacteristic
238C22×C4C22×#692311yescharacteristic
239M16—2442no—
240M16—2442no—
241C2×C8—1224no—
242C2×C8—2442no—
243C4⋊C4—22no—
244C4⋊C4—1222no—
245C4⋊C4—1222no—
246C4⋊C4—1222no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C4⋊C4—2442no—
250C4⋊C4—2442no—
251C4⋊C4—2442no—
252C22⋊C4—22no—
253C22⋊C4—42no—
254C22⋊C4—1222no—
255C22⋊C4—2442no—
256C42—612no—
257C42—612no—
258C42—1221no—
259C42—1221no—
260C42—2442no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊#692311yescharacteristic
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—611no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1222no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—2441no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4D4×#692312yes—
296C8—4882no—
297C8—2444no—
298C22—21no—
299C22—21no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22#1684071011yescharacteristic
306C22#1684075911yescharacteristic
307C22#1684076011yescharacteristic
308C4—22no—
309C4—41no—
310C4—81no—
311C4—81no—
312C4—1222no—
313C4—1221no—
314C4—1221no—
315C4—4881no—
316C4—2442no—
317C4—2441no—
318C4—2441no—
319C2—21no—
320C2—21no—
321C2—81no—
322C2#2146182011yescharacteristic
323C2#2146183911yescharacteristic
324C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61#386
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#397#6923
hypocenterC61#9390
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #21461281C2semidirect
4. #21460707C2semidirect
187. C61#9390semidirect

Maximal subgroups

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

subgroupindex
#214624992
#214612812
#214610712
#214607072
#214515182
#939061