Finite Group Databasebeta

← #29596022

Subgroups — #29596022

Order 15616.

432 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 101 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#21448539C211yesmaximal, characteristic
2C2×#16839561C211yesmaximal, characteristic
3#21445813C212yesmaximal
4#21443945C212yesmaximal
5C2×C61×#356C211yesmaximal, characteristic
6C2×Q8×Dic61C411yescharacteristic
7C2×Q8×Dic61C2211yescharacteristic
8#16839785—22no—
9C2×#14519696C2212yes—
10#16839669C411yescharacteristic
11#16839669C2211yescharacteristic
12#16839648—22no—
13#16839648—22no—
14#16839628C411yescharacteristic
15#16839608C411yescharacteristic
16#16839561—22no—
17#16839530—22no—
18C2×C4⋊Q8×C61C2211yescharacteristic
19C2×#101×C61C2212yes—
20C61×#356—22no—
21C2×#11758194—22no—
22Q8×Dic61—42no—
23Q8×Dic61—42no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61D412yes—
28C2×C4×Dic61—21no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D412yes—
32#14519706—44no—
33#14519696—22no—
34#14519696—22no—
35#14519684—22no—
36#14519684—21no—
37#14519684—21no—
38#14519684—22no—
39#14519684—22no—
40C22×Q8×C61C2×C411yescharacteristic
41C22×Q8×C61C2311yescharacteristic
42C2×M16×C61—22no—
43C4⋊Q8×C61—22no—
44C4⋊Q8×C61D412yes—
45C4⋊Q8×C61Q812yes—
46C2×C4⋊C4×C61—22no—
47C2×C42×C61C2×C411yescharacteristic
48#101×C61—22no—
49#101×C61—22no—
50C2×Q8×C61—21no—
51C2×Q8×C61—41no—
52C2×Q8×C61—41no—
53C2×Q8×C61—41no—
54C2×Q8×C61—41no—
55C2×Q8×C61C4⋊C412yes—
56C2×Q8×C61C2×D411yescharacteristic
57C2×Q8×C61C2×Q811yescharacteristic
58C2×Q8×C61#4112yes—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D412yes—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C412yes—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68M16×C61—42no—
69M16×C61—42no—
70C2×C8×C61—42no—
71C4⋊C4×C61—24no—
72C4⋊C4×C61—24no—
73C42×C61—21no—
74C42×C61C4⋊C412yes—
75C4⋊Dic61—41no—
76C4⋊Dic61—42no—
77C4⋊Dic61—42no—
78C4⋊Dic61—41no—
79C4×Dic61—24no—
80C4×Dic61—22no—
81C4×Dic61—42no—
82C4×Dic61—41no—
83#11758194—42no—
84#11758194—42no—
85C2×#92418—42no—
86C23×C61C2×C22⋊C411yescharacteristic
87Q8×C61—41no—
88Q8×C61—41no—
89Q8×C61—42no—
90Q8×C61—42no—
91Q8×C61—42no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61C2×C4⋊C411yescharacteristic
103C2×C4×C61#11711yescharacteristic
104C2×C4×C61#12112yes—
105C2×C4×C61C22⋊Q812yes—
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—41no—
109C2×Dic61—42no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61#9912yes—
117C8×C61—82no—
118#92418—82no—
119#12804—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61#38011yescharacteristic
123C22×C61C2×#9911yescharacteristic
124C22×C61#41011yescharacteristic
125C4×C61—22no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—22no—
129C4×C61—42no—
130C4×C61—42no—
131Dic61—22no—
132Dic61—41no—
133Dic61—42no—
134Dic61—81no—
135Dic61—81no—
136#2327—611no—
137C2×#356—611no—
138C2×#356D6111yescharacteristic
139#1801—612no—
140#1394—612no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61#179911yescharacteristic
144C2×C61#213311yescharacteristic
145C2×C61#213511yescharacteristic
146C2×C4⋊Q8C2×D6111yescharacteristic
147C2×C4×Q8—611no—
148C2×C4×Q8—611no—
149#423—1222no—
150C2×#101—612no—
151C2×#101C2×D6112yes—
152#391—611no—
153#391—611no—
154#387—1222no—
155#387—1222no—
156#382—611no—
157#376—611no—
158#356—22no—
159#356—1222no—
160#343—1222no—
161C61#1280411yescharacteristic, complemented, Sylow
162C22×Q8C4×D6111yescharacteristic
163C22×Q8C22×D6111yescharacteristic
164C2×M16—22no—
165C2×M16—1222no—
166C4⋊Q8—22no—
167C4⋊Q8Dic12212yes—
168C4⋊Q8C22⋊D6112yes—
169C4×Q8—2442no—
170C4×Q8—2442no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—1221no—
176C2×C42—611no—
177C2×C42—612no—
178C2×C42—611no—
179C2×C42—1221no—
180C2×C42C4×D6111yescharacteristic
181C4⋊C8—2444no—
182#101—22no—
183#101—22no—
184#101—1222no—
185#101—1222no—
186#95—1221no—
187#95—1221no—
188#95—1222no—
189#95—1222no—
190#95—1222no—
191C2×Q8—21no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8#1175819612yes—
197C2×Q8C2×Dic12211yescharacteristic
198C2×Q8#1175822412yes—
199C2×Q8C2×C22⋊D6111yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—611no—
203C22×C4—612no—
204C22×C4—611no—
205C22×C4—1221no—
206C22×C4—1221no—
207C22×C4C2×C4×D6111yescharacteristic
208C22×C4D4×D6112yes—
209M16—42no—
210M16—42no—
211M16—2442no—
212M16—2442no—
213C2×C8—42no—
214C2×C8—2442no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—2441no—
218C4⋊C4—2442no—
219C4⋊C4—2441no—
220C4⋊C4—2442no—
221C42—21no—
222C42—1224no—
223C42—1222no—
224C42—2441no—
225C42—2442no—
226C42#1175819612yes—
227C23C22⋊C4×D6111yescharacteristic
228Q8—41no—
229Q8—42no—
230Q8—41no—
231Q8—42no—
232Q8—42no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—612no—
244C2×C4—1221no—
245C2×C4—1222no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2442no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2442no—
253C2×C4—2441no—
254C2×C4C2×#1175819611yescharacteristic
255C2×C4#1451973311yescharacteristic
256C2×C4#1451974912yes—
257C2×C4#1451975412yes—
258C8—82no—
259C8—4882no—
260C22—21no—
261C22—21no—
262C22#1683962011yescharacteristic
263C22#99×D6111yescharacteristic
264C22#1683973411yescharacteristic
265C4—22no—
266C4—21no—
267C4—21no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—1222no—
272C4—4881no—
273C4—4881no—
274C4—2441no—
275C4—2442no—
276C2—21no—
277C2—21no—
278C2#2144580511yescharacteristic
279C2#2144750711yescharacteristic
280C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC2×C61×#356C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenterC2×#356D61
hypocenterC61#12804
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
161. C61#12804semidirect

Maximal subgroups

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

subgroupindex
#214485392
C2×#168395612
#214458132
#214439452
C2×C61×#3562
#1280461