Finite Group Databasebeta

← #30604311

Subgroups — #30604311

Order 15616.

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

normal subgroups only

This group has 444 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#21461076C211yesmaximal, characteristic
2#21461056C211yesmaximal, characteristic
3#21460749C214yesmaximal, complemented
4#21450815C211yesmaximal, characteristic
5#16840733—21no—
6D61⋊(C22⋊C8)—21no—
7#16840607C2212yes—
8#16840607C2212yes—
9#16840606—21no—
10#16840606—21no—
11C2×#14519766C412yes—
12C2×C4×D244C2211yescharacteristic
13#16839688—21no—
14#16839688—21no—
15#16839669C2212yes—
16#16839619—21no—
17#16839619—21no—
18C4×C4⋊Dic61C411yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758213—41no—
21C2×D61⋊C8—41no—
22#14519834—41no—
23#14519834—41no—
24C22⋊#92420—22no—
25C22⋊#92420—22no—
26C22×D244C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29#14519766—44no—
30C4×D244—41no—
31C4×D244—41no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2311yescharacteristic
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×#11758198D411yescharacteristic
37C2×#11758198D411yescharacteristic
38C2×C4×Dic61C2×C412yes—
39#14519684—21no—
40#14519684—22no—
41#14519684—22no—
42C22×Q8×C61C2×C412yes—
43C4⋊Q8×C61—41no—
44C4⋊Q8×C61—41no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C42×C61C2×C411yescharacteristic
48C23×D61C22⋊C411yescharacteristic
49C23×D61C22⋊C411yescharacteristic
50C2×Q8×C61—24no—
51C2×Q8×C61—42no—
52C2×Q8×C61—42no—
53C22×C4×C61—22no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—22no—
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×D244—22no—
61C2×D244—22no—
62C2×D244—41no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—42no—
68C2×C4×D61—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71#11758213—82no—
72D61⋊C8—82no—
73C4⋊C4×C61—42no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C42×C61—21no—
77C42×C61—21no—
78#11758198—41no—
79#11758198—41no—
80#11758198—44no—
81#11758198—44no—
82C4⋊Dic61—41no—
83C4⋊Dic61—42no—
84C4×Dic61—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—41no—
92C22×D61—41no—
93C22×D61—41no—
94C22×D61—41no—
95C22×D61#10012yes—
96Q8×C61—84no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61#9911yescharacteristic
106C2×C4×C61#9911yescharacteristic
107C2×C4×C61#13112yes—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115D244—44no—
116C4×D61—42no—
117C4×D61—42no—
118C4×D61—81no—
119C4×D61—81no—
120#92420—82no—
121#92420—82no—
122#11564—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#40811yescharacteristic
126C22×C61C2×#9911yescharacteristic
127C22×C61C2×#10011yescharacteristic
128C2×D61—22no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—81no—
137C2×D61—81no—
138C4×C61—21no—
139C4×C61—22no—
140C4×C61—41no—
141C4×C61—82no—
142C4×C61#35412yes—
143Dic61—41no—
144Dic61—41no—
145Dic61—82no—
146#2547—611no—
147#1465—611no—
148#1459—611no—
149#1319—614no—
150C2×C61—21no—
151C2×C61—21no—
152C2×C61#147111yescharacteristic
153C2×C61C2×#35411yescharacteristic
154C2×C61#213511yescharacteristic
155D61—42no—
156D61—81no—
157C2×C4⋊Q8#692311yescharacteristic
158C2×#124—612no—
159C2×C4×D4—611no—
160#407—1221no—
161C2×C22⋊C8—1221no—
162#397—1221no—
163#397—1221no—
164#391—612no—
165#380—1221no—
166#380—1221no—
167C4×C4⋊C4—611no—
168#324—612no—
169#324—612no—
170#323—1221no—
171#323—1221no—
172C61#1156411yescharacteristic, complemented, Sylow
173C22×Q8C2×#692312yes—
174C22×D4—611no—
175C23×C4—611no—
176C23×C4—611no—
177C2×M16—2441no—
178C22×C8—2441no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181#124—2444no—
182C4×D4—2441no—
183C4×D4—2441no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—1221no—
188C2×C22⋊C4—611no—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—1222no—
191C2×C22⋊C4—1222no—
192C2×C42—612no—
193C2×C42C2×#692311yescharacteristic
194C22⋊C8—1222no—
195C22⋊C8—1222no—
196C22⋊C8—2441no—
197C22⋊C8—2441no—
198#95—1222no—
199#95—1222no—
200#95—1221no—
201C24—611no—
202C24—611no—
203C2×Q8—24no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—2441no—
209C22×C4—22no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1222no—
217C22×C4—2442no—
218C22×C4—2442no—
219C22×C4C22⋊#692311yescharacteristic
220C22×C4C22⋊#692311yescharacteristic
221C22×C4C22×#692311yescharacteristic
222M16—4882no—
223C2×C8—4882no—
224C2×C8—2442no—
225C2×C8—2442no—
226C4⋊C4—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—2441no—
230C4⋊C4—2442no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C22⋊C4—2444no—
234C22⋊C4—2444no—
235C42—21no—
236C42—21no—
237C42—2442no—
238C23—612no—
239C23—1221no—
240C23—1221no—
241C23—1221no—
242C23—1221no—
243C23—1221no—
244C23—2441no—
245C23—2441no—
246C23—2441no—
247C23—2441no—
248C23C2×C22⋊#692311yescharacteristic
249Q8—84no—
250D4—2444no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—4881no—
262C2×C4—4881no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4#1451983511yescharacteristic
271C2×C4#1451983511yescharacteristic
272C2×C4#1451986412yes—
273C8—4882no—
274C8—4882no—
275C22—21no—
276C22—21no—
277C22—1222no—
278C22—4881no—
279C22—4881no—
280C22—2442no—
281C22—2442no—
282C22—2441no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22—2441no—
287C22#1684073611yescharacteristic
288C22C2×#1451983511yescharacteristic
289C22D61⋊#10011yescharacteristic
290C4—21no—
291C4—22no—
292C4—41no—
293C4—82no—
294C4—4882no—
295C4—2441no—
296C4—2441no—
297C4#1684066812yes—
298C2—21no—
299C2—21no—
300C2—4881no—
301C2—2442no—
302C2#2146109411yescharacteristic
303C2C2×#1684066811yescharacteristic
304C2#2146212111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11564
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21460749C2semidirect
172. C61#11564semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214610562
#214607492
#214508152
#1156461