Finite Group Databasebeta

← #30595835

Subgroups — #30595835

Order 15616.

410 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461746C211yesmaximal, characteristic
2#21461536C211yesmaximal, characteristic
3#21460640C212yesmaximal
4#21460639C212yesmaximal
5#21454194C211yesmaximal, characteristic
6C2×#14519832—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519775C411yescharacteristic
14#16839669C2211yescharacteristic
15#16839668C411yescharacteristic
16#16839667C2211yescharacteristic
17#16839666—21no—
18#16839666—21no—
19#16839626—21no—
20#16839626—21no—
21C42×Dic61C2211yescharacteristic
22C61×#391C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519832—24no—
26C22×Dic122—21no—
27C22×Dic122C2×C411yescharacteristic
28#14519776—42no—
29#14519775—42no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×Q8×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C42×C61C2×C411yescharacteristic
49#95×C61—21no—
50#95×C61—21no—
51C2×Q8×C61—22no—
52C2×Q8×C61—41no—
53C2×Q8×C61—41no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×Dic122—22no—
66C2×Dic122—42no—
67C2×Dic122—42no—
68C2×Dic122—42no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—41no—
78C42×C61—22no—
79C4⋊Dic61—41no—
80#11758196—42no—
81#11758196—42no—
82#11758196—42no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C23×C61C2×C22⋊C411yescharacteristic
90Q8×C61—82no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#13112yes—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61#10012yes—
121C2×Dic61#10412yes—
122C2×Dic61#13712yes—
123C2×Dic61#13712yes—
124Dic122—84no—
125Dic122—82no—
126#92420—44no—
127#92420—82no—
128#7702—611nomaximal, Sylow
129C22×C61#40811yescharacteristic
130C22×C61#41011yescharacteristic
131C22×C61C2×#10011yescharacteristic
132C22×C61#41911yescharacteristic
133C22×C61#41911yescharacteristic
134C22×C61C2×#10411yescharacteristic
135C22×C61#42111yescharacteristic
136C4×C61—22no—
137C4×C61—41no—
138C4×C61—41no—
139C4×C61—81no—
140C4×C61—81no—
141Dic61—22no—
142Dic61—22no—
143Dic61—22no—
144Dic61—22no—
145Dic61—81no—
146Dic61—81no—
147#2862—611no—
148#1839—611no—
149#1745—611no—
150#1272—612no—
151#1272—612no—
152C2×C61#146911yescharacteristic
153C2×C61#148511yescharacteristic
154C2×C61#149711yescharacteristic
155C2×C61#150611yescharacteristic
156C2×C61#151511yescharacteristic
157C2×C61#152711yescharacteristic
158C2×C61#155811yescharacteristic
159C2×C4⋊Q8—611no—
160C2×C4⋊Q8—611no—
161C2×#97—1221no—
162#391—611no—
163#391—611no—
164#391—611no—
165#391—1221no—
166#391—1221no—
167#391#692311yescharacteristic
168#382—1221no—
169#382—1221no—
170C43—611no—
171#336—612no—
172#336—612no—
173#336—1221no—
174#336—1221no—
175#336—1221no—
176C61#770211yescharacteristic, complemented, Sylow
177C22×Q8—611no—
178C22×Q8—1221no—
179C22×Q8C2×#692311yescharacteristic
180C22×C8—1222no—
181C22×C8—1222no—
182C4⋊Q8—2442no—
183C4⋊Q8—2442no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4C2×#692311yescharacteristic
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42C2×#692311yescharacteristic
196#97—1224no—
197#95—21no—
198#95—21no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—1222no—
209C2×Q8—2441no—
210C2×Q8—2441no—
211C2×Q8—2442no—
212C2×Q8—2442no—
213C2×Q8—2442no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4C22⋊#692311yescharacteristic
223C22×C4C22⋊#692311yescharacteristic
224C22×C4C22×#692311yescharacteristic
225C2×C8—1224no—
226C2×C8—2442no—
227C2×C8—2442no—
228C2×C8—2442no—
229C2×C8—2442no—
230C2×C8—2442no—
231C4⋊C4—41no—
232C4⋊C4—2441no—
233C4⋊C4—2442no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C42—22no—
237C42—1222no—
238C42—1222no—
239C42—1222no—
240C42—1222no—
241C42—2441no—
242C42—2441no—
243C23C2×C22⋊#692311yescharacteristic
244Q8—82no—
245Q8—4882no—
246Q8—4884no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—612no—
262C2×C4—612no—
263C2×C4—612no—
264C2×C4—612no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4#1451986412yes—
280C8—4882no—
281C8—2444no—
282C22#1684073511yescharacteristic
283C22#1684074111yescharacteristic
284C22D61⋊#10011yescharacteristic
285C22#1684075511yescharacteristic
286C22#1684075511yescharacteristic
287C22D61⋊#10411yescharacteristic
288C22#1684075911yescharacteristic
289C4—22no—
290C4—41no—
291C4—41no—
292C4—81no—
293C4—81no—
294C4—1222no—
295C4—1222no—
296C4—1222no—
297C4—1222no—
298C4—4881no—
299C4—4881no—
300C2#2146108811yescharacteristic
301C2#2146114111yescharacteristic
302C2#2146118111yescharacteristic
303C2#2146121211yescharacteristic
304C2#2146124111yescharacteristic
305C2#2146127911yescharacteristic
306C2#2146135311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#7702
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
176. C61#7702semidirect

Maximal subgroups

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

subgroupindex
#214617462
#214615362
#214606402
#214606392
#214541942
#770261