Finite Group Databasebeta

← #30599396

Subgroups — #30599396

Order 15616.

422 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461685C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460717C212yesmaximal
4#21460672C212yesmaximal
5#21448736C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519838—21no—
9#16840642—21no—
10#16840608—21no—
11#16840607—21no—
12C2×C4×Dic122C2211yescharacteristic
13C2×#14519742—21no—
14#16839659—21no—
15#16839659—21no—
16#16839658—21no—
17#16839626C411yescharacteristic
18#16839626C2211yescharacteristic
19C4×C4⋊Dic61C411yescharacteristic
20#16839613C411yescharacteristic
21#16839613C2211yescharacteristic
22C61×#382C411yescharacteristic
23C2×#11758217—22no—
24#14519844—22no—
25#14519844—22no—
26C4⋊#92420—22no—
27#14519838—42no—
28C22⋊#92420—22no—
29C4×#92420—22no—
30C22×Dic122D411yescharacteristic
31C4×Dic122—22no—
32C4×Dic122—22no—
33#14519742—42no—
34#14519742—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×#11758196D411yescharacteristic
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
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—22no—
69C2×Dic122—22no—
70C2×Dic122D812yes—
71C2×Dic122SD1612yes—
72#11758217—42no—
73#11758217—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—42no—
77C42×C61—21no—
78C42×C61—21no—
79C4⋊Dic61—22no—
80C4⋊Dic61—42no—
81#11758196—22no—
82#11758196—22no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86#11758196—41no—
87#11758196—41no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—42no—
91C4×Dic61—42no—
92C4×Dic61—41no—
93C4×Dic61—41no—
94C4×Dic61#4112yes—
95C4×Dic61#4112yes—
96C23×C61C2×C22⋊C411yescharacteristic
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61#10212yes—
109C2×C4×C61#11711yescharacteristic
110C2×C4×C61#11711yescharacteristic
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61#10212yes—
123C2×Dic61#12312yes—
124C2×Dic61#12312yes—
125C2×Dic61C2×D811yescharacteristic
126C2×Dic61C2×SD1611yescharacteristic
127C2×Dic61#13712yes—
128Dic122—24no—
129Dic122—24no—
130#92420—82no—
131#92420—82no—
132#8766—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#38111yescharacteristic
136C22×C61C2×#10211yescharacteristic
137C22×C61#41911yescharacteristic
138C4×C61—22no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—81no—
143C4×C61—81no—
144Dic61—22no—
145Dic61—22no—
146Dic61—42no—
147Dic61—41no—
148Dic61—81no—
149Dic61#48012yes—
150Dic61#48312yes—
151#2351—611no—
152#1801—611no—
153#1461—611no—
154#1303—612no—
155#1286—612no—
156C2×C61—21no—
157C2×C61—21no—
158C2×C61#182311yescharacteristic
159C2×C61#182711yescharacteristic
160C2×C61#183011yescharacteristic
161C2×C4×Q8—611no—
162C2×C4×Q8—1221no—
163#431—612no—
164#423—612no—
165C2×#101—1221no—
166#389—1221no—
167#389—1221no—
168#389—1221no—
169#382—611no—
170#382—611no—
171#382#692311yescharacteristic
172C4×C4⋊C4—611no—
173C4×C4⋊C4—611no—
174C4×C4⋊C4—611no—
175#343—1221no—
176#324—1221no—
177#324—1221no—
178C61#876611yescharacteristic, complemented, Sylow
179C22×Q8—611no—
180C2×M16—1222no—
181C4×Q8—1222no—
182C4×Q8—1222no—
183C4×Q8—2442no—
184C4×Q8—2442no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—1221no—
197C2×C42—1221no—
198C2×C42—1221no—
199C2×C42C2×#692311yescharacteristic
200C4⋊C8—1222no—
201C4⋊C8—1222no—
202C4⋊C8—1222no—
203#101—2442no—
204C22⋊C8—1222no—
205C4×C8—1222no—
206#95—21no—
207#95—611no—
208#95—611no—
209#95—1221no—
210#95—1221no—
211#95C2×#692311yescharacteristic
212#95C2×#692311yescharacteristic
213C2×Q8—612no—
214C2×Q8—612no—
215C2×Q8—1222no—
216C2×Q8—1222no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4C22⋊#692311yescharacteristic
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22×#692311yescharacteristic
228M16—2442no—
229M16—2442no—
230C2×C8—2442no—
231C2×C8—2442no—
232C4⋊C4—42no—
233C4⋊C4—1222no—
234C4⋊C4—1222no—
235C4⋊C4—1222no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2442no—
239C4⋊C4—2442no—
240C4⋊C4—2442no—
241C4⋊C4—2442no—
242C42—21no—
243C42—21no—
244C42—612no—
245C42—612no—
246C42—1221no—
247C42—1221no—
248C42—2441no—
249C42—2441no—
250C42—2442no—
251C42—2442no—
252C23C2×C22⋊#692311yescharacteristic
253Q8—1224no—
254Q8—1224no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—612no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—612no—
270C2×C4—612no—
271C2×C4—612no—
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#1451983912yes—
284C2×C4#1451985611yescharacteristic
285C2×C4#1451985611yescharacteristic
286C8—4882no—
287C8—4882no—
288C22—21no—
289C22—21no—
290C22#1684070511yescharacteristic
291C22C2×#1451983911yescharacteristic
292C22#1684075511yescharacteristic
293C4—22no—
294C4—21no—
295C4—21no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—612no—
300C4—612no—
301C4—1222no—
302C4—1222no—
303C4—4881no—
304C4—2442no—
305C4—2441no—
306C2—21no—
307C2—21no—
308C2#2146172211yescharacteristic
309C2#2146172911yescharacteristic
310C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#8766
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
178. C61#8766semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610612
#214607172
#214606722
#214487362
#876661