Finite Group Databasebeta

← #29576998

Subgroups — #29576998

Order 15616.

360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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#21457027C211yesmaximal, characteristic
2#21454924C211yesmaximal, characteristic
3#21444530C211yesmaximal, characteristic
4#21444445C211yesmaximal, characteristic
5#21444176C211yesmaximal, characteristic
6#21443682C211yesmaximal, characteristic
7C61×#1308C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519769C2211yescharacteristic
10#16840171—21no—
11#16840131—21no—
12#16840098C412yes—
13#16840093C412yes—
14#16840070—22no—
15#16839891—22no—
16#16839890—22no—
17#16839820—22no—
18#16839819C2211yescharacteristic
19#16839815C2211yescharacteristic
20#16839510—21no—
21#16839509—21no—
22#16839503—22no—
23#16839487—22no—
24C61×#432C2211yescharacteristic
25C61×#432C2211yescharacteristic
26C61×#432C2211yescharacteristic
27#14519777D411yescharacteristic
28#14519777D411yescharacteristic
29#14519769—21no—
30#14519769—21no—
31#14519769—21no—
32#14519769—21no—
33#14519769—21no—
34#14519756—21no—
35#14519756C2×C412yes—
36C4×Dic122—21no—
37C4×Dic122D412yes—
38#14519736—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43#14519711—22no—
44#14519709—22no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519706—24no—
48#14519702—22no—
49#14519702—22no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519688D412yes—
53#14519687—22no—
54C4×#92418—21no—
55C8×Dic61—22no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22⋊C8×C61—21no—
61C22⋊C8×C61C2×C412yes—
62C22⋊C8×C61D412yes—
63#97×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C2×Dic122—21no—
72C2×Dic122C22⋊C412yes—
73C2×C8×C61—22no—
74C2×C8×C61—22no—
75C2×C8×C61—41no—
76C42×C61C2×D411yescharacteristic
77C42×C61C2×D411yescharacteristic
78C42×C61C2×D411yescharacteristic
79C42×C61#4111yescharacteristic
80C22⋊Dic61—22no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61C22⋊C412yes—
89#11758196—22no—
90#11758196—22no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95C4×Dic61—22no—
96C2×#92418—22no—
97C2×#92418—41no—
98C23×C61C4×D411yescharacteristic
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61C4×D411yescharacteristic
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61#12111yescharacteristic
106C2×C4×C61#12111yescharacteristic
107C2×C4×C61#12311yescharacteristic
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—42no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—81no—
114Dic122—42no—
115Dic122—81no—
116C8×C61—42no—
117C8×C61—42no—
118C8×C61—81no—
119#92418—42no—
120#92418—81no—
121#9336—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#38611yescharacteristic
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—21no—
132Dic61—42no—
133Dic61—42no—
134Dic61—81no—
135Dic61—81no—
136#3236—611no—
137#2987—611no—
138#1554—611no—
139#1534—611no—
140#1470—611no—
141#1308D6111yescharacteristic
142#1287—611no—
143C2×C61—41no—
144C2×C61#188111yescharacteristic
145C2×C61#190511yescharacteristic
146C2×C61#191511yescharacteristic
147#533—611no—
148C2×#125—611no—
149#501—1221no—
150#491—1221no—
151#484—612no—
152#483—612no—
153#479—1222no—
154#446—1222no—
155#446—1222no—
156#433—1222no—
157#432—611no—
158#432C2×D6111yescharacteristic
159#432C2×D6111yescharacteristic
160#432C2×D6111yescharacteristic
161#431—611no—
162#333—1221no—
163#332—1221no—
164#330—1222no—
165#324—1222no—
166C61#933611yescharacteristic, complemented, Sylow
167C4⋊Q8—611no—
168C4⋊Q8—611no—
169#125—1221no—
170#125—1221no—
171#125—1221no—
172#125—1221no—
173#125—1221no—
174C22⋊Q8—612no—
175C22⋊Q8—1221no—
176C4×Q8—612no—
177C4×Q8—1221no—
178#117—1221no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4—1221no—
183C2×C42C22×D6111yescharacteristic
184#107—1222no—
185#106—1222no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—1224no—
190C4⋊C8—1221no—
191C4⋊C8—1221no—
192#103—1222no—
193#103—1222no—
194C22⋊C8—21no—
195C22⋊C8—1221no—
196C22⋊C8—1221no—
197C22⋊C8C4×D6112yes—
198C22⋊C8D24412yes—
199#97—21no—
200#97—21no—
201#97—21no—
202#97—612no—
203#97—1222no—
204C4×C8—1222no—
205C4×C8—1221no—
206C2×Q8—612no—
207C2×Q8—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4C2×C4×D6111yescharacteristic
211C22×C4C2×D24411yescharacteristic
212C22×C4#1175822211yescharacteristic
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—1222no—
217C2×C8—2441no—
218C4⋊C4—612no—
219C4⋊C4—1222no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—1222no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C22⋊C4—1222no—
233C42—1222no—
234C42D4×D6111yescharacteristic
235C42D4×D6111yescharacteristic
236C42D4×D6111yescharacteristic
237C42#1175822611yescharacteristic
238C23C4×D24411yescharacteristic
239Q8—4881no—
240Q8—2442no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—4881no—
247C2×C4—2442no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4C22⋊C4×D6111yescharacteristic
251C2×C4#1451973911yescharacteristic
252C2×C4#1451974711yescharacteristic
253C2×C4#1451975011yescharacteristic
254C2×C4#1451975211yescharacteristic
255C2×C4#1451976211yescharacteristic
256C8—42no—
257C8—42no—
258C8—81no—
259C8—4881no—
260C8—2442no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#1683964011yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—4881no—
272C4—4881no—
273C4—2442no—
274C4—2442no—
275C2—41no—
276C2#2144618011yescharacteristic
277C2#2144631211yescharacteristic
278C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1308C2
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1308D61
hypocenterC61#9336
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1308

Complements

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

NH ≅ G/Ntype
166. C61#9336semidirect

Maximal subgroups

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

subgroupindex
#214570272
#214549242
#214445302
#214444452
#214441762
#214436822
C61×#13082
#933661