Finite Group Databasebeta

← #30605499

Subgroups — #30605499

Order 15616.

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

normal subgroups only

This group has 388 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#21461686C211yesmaximal, characteristic
2#21461063C211yesmaximal, characteristic
3#21460820C212yesmaximal
4#21460819C212yesmaximal
5#21451023C211yesmaximal, characteristic
6#16840778—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519775C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14#16839683C2211yescharacteristic
15#16839682C411yescharacteristic
16#16839681C2211yescharacteristic
17#16839666—21no—
18#16839659—21no—
19#16839657—21no—
20#16839631—21no—
21#16839613C411yescharacteristic
22C61×#395C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29C4×#92420—41no—
30C22×Dic122C2×C411yescharacteristic
31C22×Dic122D411yescharacteristic
32#14519775—41no—
33#14519775—41no—
34#14519742—41no—
35#14519742—41no—
36C2×C4⋊Dic61—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C22×Q8×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C2×Q8×C61—41no—
58C2×Q8×C61—81no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×Dic122—41no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—81no—
74C2×Dic122SD1612yes—
75C2×Dic122Q1612yes—
76#11758217—42no—
77#11758217—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—81no—
82C4⋊Dic61—81no—
83#11758196—24no—
84#11758196—41no—
85#11758196—41no—
86#11758196—42no—
87#11758196—41no—
88#11758196—41no—
89#11758196—81no—
90#11758196—81no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—42no—
98C23×C61C2×C22⋊C411yescharacteristic
99Q8×C61—82no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
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#10312yes—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—21no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61#9911yescharacteristic
127C2×Dic61#9911yescharacteristic
128C2×Dic61#10312yes—
129C2×Dic61C2×SD1611yescharacteristic
130C2×Dic61C2×Q1611yescharacteristic
131Dic122—42no—
132Dic122—42no—
133Dic122—82no—
134#92420—82no—
135#92420—82no—
136#11908—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61C2×#9911yescharacteristic
140C22×C61C2×#10311yescharacteristic
141C22×C61#42111yescharacteristic
142C4×C61—22no—
143C4×C61—42no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—81no—
147Dic61—21no—
148Dic61—21no—
149Dic61—22no—
150Dic61—21no—
151Dic61—42no—
152Dic61—41no—
153Dic61—81no—
154Dic61#35612yes—
155#2567—611no—
156#1801—611no—
157#1461—611no—
158#1354—612no—
159#1354—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61#152011yescharacteristic
163C2×C61#212211yescharacteristic
164C2×C61C2×#35611yescharacteristic
165C2×C4⋊Q8—611no—
166C2×C4×Q8—611no—
167#431—1221no—
168#423—1221no—
169C2×#101—1221no—
170#395—611no—
171#395—611no—
172#395—611no—
173#395#692311yescharacteristic
174#391—1221no—
175#389—1221no—
176#389—1221no—
177#384—1221no—
178C4×C4⋊C4—611no—
179#343—612no—
180#324—612no—
181#324—1221no—
182C61#1190811yescharacteristic, complemented, Sylow
183C22×Q8—611no—
184C22×Q8—611no—
185C22×Q8C2×#692311yescharacteristic
186C2×M16—1222no—
187C4⋊Q8—2441no—
188C4⋊Q8—2441no—
189C4×Q8—2441no—
190C4×Q8—2441no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4C2×#692311yescharacteristic
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—1221no—
205C4⋊C8—2441no—
206C4⋊C8—2441no—
207C4⋊C8—2441no—
208#101—2442no—
209C22⋊C8—1222no—
210C4×C8—2441no—
211#95—21no—
212#95—611no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95C2×#692311yescharacteristic
217C2×Q8—41no—
218C2×Q8—81no—
219C2×Q8—612no—
220C2×Q8—612no—
221C2×Q8—4881no—
222C2×Q8—2441no—
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
236M16—2442no—
237M16—2442no—
238C2×C8—2442no—
239C2×C8—2442no—
240C4⋊C4—41no—
241C4⋊C4—81no—
242C4⋊C4—1224no—
243C4⋊C4—4881no—
244C4⋊C4—4881no—
245C4⋊C4—4881no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C4⋊C4—2441no—
250C4⋊C4—2442no—
251C42—1221no—
252C42—1221no—
253C42—1221no—
254C42—1221no—
255C42—1221no—
256C42—1221no—
257C42—2442no—
258C23C2×C22⋊#692311yescharacteristic
259Q8—82no—
260Q8—4882no—
261Q8—2442no—
262Q8—2442no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
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—611no—
276C2×C4—611no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1222no—
286C2×C4—1221no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4#1451984012yes—
294C8—4882no—
295C8—4882no—
296C22—21no—
297C22—21no—
298C22D61⋊#9911yescharacteristic
299C22C2×#1451984011yescharacteristic
300C22#1684075911yescharacteristic
301C4—22no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—81no—
306C4—612no—
307C4—1221no—
308C4—1222no—
309C4—1221no—
310C4—1221no—
311C4—4881no—
312C4—2442no—
313C4—2441no—
314C2—21no—
315C2—21no—
316C2#2146125711yescharacteristic
317C2#2146207911yescharacteristic
318C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenter#395#6923
hypocenterC61#11908
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
182. C61#11908semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610632
#214608202
#214608192
#214510232
#1190861