Finite Group Databasebeta

← #30604326

Subgroups — #30604326

Order 15616.

394 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461082C211yesmaximal, characteristic
2#21461062C211yesmaximal, characteristic
3#21460750C212yesmaximal
4#21460749C212yesmaximal
5#21450805C211yesmaximal, characteristic
6#16840782—21no—
7#16840778—21no—
8#16840607—21no—
9#16840607—21no—
10#16840607C2212yes—
11#16840607C2212yes—
12C2×#14519775C411yescharacteristic
13C2×#14519775C411yescharacteristic
14C2×Q8×Dic61C2211yescharacteristic
15#16839695—21no—
16#16839695—21no—
17#16839669C2211yescharacteristic
18#16839668C2211yescharacteristic
19#16839657—21no—
20#16839657—21no—
21C4×#11758196C411yescharacteristic
22C2×C4⋊Q8×C61C411yescharacteristic
23#14519844—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C22×Dic122C2×C411yescharacteristic
30#14519775—41no—
31#14519775—41no—
32#14519775—42no—
33Q8×Dic61—41no—
34Q8×Dic61—41no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61C2311yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61C2×C411yescharacteristic
53C22×Q8×C61C2×C411yescharacteristic
54C4⋊Q8×C61—42no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58C2×Q8×C61—22no—
59C2×Q8×C61—22no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×#92420—42no—
79C2×#92420—42no—
80C4⋊C4×C61—42no—
81C4⋊C4×C61—42no—
82C42×C61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86#11758196—24no—
87#11758196—42no—
88#11758196—42no—
89#11758196—42no—
90#11758196—41no—
91#11758196—41no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C23×C61C2×C22⋊C411yescharacteristic
100Q8×C61—44no—
101Q8×C61—82no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#10012yes—
116C2×C4×C61#13112yes—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#9911yescharacteristic
131C2×Dic61#9911yescharacteristic
132Dic122—82no—
133#92420—82no—
134#92420—82no—
135#11568—611nomaximal, Sylow
136C22×C61—21no—
137C22×C61—21no—
138C22×C61#40811yescharacteristic
139C22×C61C2×#9911yescharacteristic
140C22×C61C2×#10011yescharacteristic
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—42no—
144C4×C61—41no—
145C4×C61—81no—
146Dic61—21no—
147Dic61—42no—
148Dic61—41no—
149Dic61—41no—
150Dic61—41no—
151Dic61—81no—
152Dic61#35612yes—
153#2546—611no—
154#1467—611no—
155#1461—611no—
156#1319—612no—
157#1319—612no—
158C2×C61—21no—
159C2×C61—21no—
160C2×C61#147111yescharacteristic
161C2×C61#212911yescharacteristic
162C2×C61C2×#35611yescharacteristic
163C2×C4⋊Q8—611no—
164C2×C4⋊Q8—611no—
165C2×C4⋊Q8#692311yescharacteristic
166C2×C4×Q8—611no—
167#432—1221no—
168#431—1221no—
169#398—1221no—
170#398—1221no—
171#391—611no—
172#391—611no—
173#389—1221no—
174#389—1221no—
175C4×C4⋊C4—611no—
176#324—612no—
177#324—612no—
178#324—1221no—
179#324—1221no—
180C61#1156811yescharacteristic, complemented, Sylow
181C22×Q8—611no—
182C22×Q8C2×#692311yescharacteristic
183C22×Q8C2×#692311yescharacteristic
184C4⋊Q8—42no—
185C4⋊Q8—2441no—
186C4⋊Q8—2441no—
187C4⋊Q8—2442no—
188C4×Q8—2441no—
189C4×Q8—2441no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42C2×#692311yescharacteristic
205C4⋊C8—2441no—
206C4⋊C8—2441no—
207C22⋊C8—1222no—
208C22⋊C8—1222no—
209#97—2441no—
210C4×C8—2441no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—1222no—
223C2×Q8—2441no—
224C2×Q8—2441no—
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×C4C22⋊#692311yescharacteristic
234C22×C4C22⋊#692311yescharacteristic
235C22×C4C22×#692311yescharacteristic
236C2×C8—2442no—
237C2×C8—2442no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—1224no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2442no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C4⋊C4—2442no—
248C4⋊C4—2442no—
249C42—41no—
250C42—1221no—
251C42—1221no—
252C42—1221no—
253C42—1221no—
254C42—1221no—
255C42—1221no—
256C42—2441no—
257C23C2×C22⋊#692311yescharacteristic
258Q8—44no—
259Q8—82no—
260Q8—4882no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—1222no—
277C2×C4—1222no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4#1451983712yes—
290C2×C4#1451986412yes—
291C8—4882no—
292C8—4882no—
293C22—21no—
294C22—21no—
295C22#1684073511yescharacteristic
296C22D61⋊#9911yescharacteristic
297C22C2×#1451983711yescharacteristic
298C4—22no—
299C4—22no—
300C4—42no—
301C4—41no—
302C4—81no—
303C4—612no—
304C4—1221no—
305C4—4881no—
306C4—2442no—
307C4—2441no—
308C4—2441no—
309C4—2441no—
310C2—21no—
311C2—21no—
312C2#2146109511yescharacteristic
313C2#2146210211yescharacteristic
314C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11568
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
180. C61#11568semidirect

Maximal subgroups

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

subgroupindex
#214610822
#214610622
#214607502
#214607492
#214508052
#1156861