Finite Group Databasebeta

← #29591192

Subgroups — #29591192

Order 15616.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#21456446C211yesmaximal, characteristic
2#21447633C211yesmaximal, characteristic, complemented
3#21447422C211yesmaximal, characteristic, complemented
4#21443853C211yesmaximal, characteristic, complemented
5#21443853C211yesmaximal, characteristic, complemented
6#21443852C211yesmaximal, characteristic, complemented
7C61×#1355C211yesmaximal, characteristic, complemented
8#16840375C411yescharacteristic
9#16840366C411yescharacteristic
10M32×D61—21no—
11#16840161C411yescharacteristic
12#16840134C411yescharacteristic
13#16840131C2211yescharacteristic
14#16840007—21no—
15#16839990—21no—
16#16839859—21no—
17#16839853—21no—
18#16839719C2211yescharacteristic
19#16839582—21no—
20#16839543—21no—
21#16839540C2211yescharacteristic
22#16839540C2211yescharacteristic
23#16839539—21no—
24C61×#490C2211yescharacteristic
25C61×#347C2211yescharacteristic
26C61×#347C2211yescharacteristic
27C2×#11758200—21no—
28C2×#11758200—21no—
29C2×#11758189D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519772—41no—
33#14519769C2×C411yescharacteristic
34#14519768—41no—
35#14519758—41no—
36#14519757—21no—
37#14519749—41no—
38#14519748—21no—
39#14519742—21no—
40D4×Dic61—21no—
41#14519734C2×C411yescharacteristic
42#14519717—21no—
43#14519717—21no—
44#14519716—22no—
45C16×D61—22no—
46#14519710—21no—
47#14519708—21no—
48#14519702—21no—
49#14519702—21no—
50#14519687D411yescharacteristic
51C4×#92418C2×C411yescharacteristic
52C8×Dic61D411yescharacteristic
53#127×C61C2×C411yescharacteristic
54#125×C61C2×C411yescharacteristic
55M32×C61—21no—
56M32×C61—21no—
57#102×C61—21no—
58#102×C61—21no—
59#97×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×C22⋊D61—41no—
63C22×Dic61—41no—
64C2×C4×D61C22⋊C411yescharacteristic
65C2×Dic122—21no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C42×C61C22×C411yescharacteristic
71C22⋊Dic61—41no—
72C22⋊Dic61—41no—
73#11758200—42no—
74#11758200—41no—
75#11758200—41no—
76#11758198—21no—
77#11758198—41no—
78C4⋊Dic61—21no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81#11758196—21no—
82#11758196—41no—
83#11758196—41no—
84C4×Dic61—41no—
85C4×Dic61C22⋊C411yescharacteristic
86C2×#92418C22⋊C411yescharacteristic
87C2×#92418C22⋊C411yescharacteristic
88#11758189—41no—
89C8×D61—21no—
90C8×D61—21no—
91C16×C61—22no—
92C16×C61—41no—
93#11758185—22no—
94#11758185—41no—
95C23×C61—41no—
96C22×D61#10011yescharacteristic
97D4×C61—41no—
98D4×C61—41no—
99D4×C61—161no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C22⋊D61—161no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—161no—
108C2×Dic61#10011yescharacteristic
109C4×D61—21no—
110C4×D61—21no—
111Dic122—41no—
112Dic122—41no—
113C8×C61—21no—
114C8×C61—21no—
115#92418—21no—
116#92418#10411yescharacteristic
117#92418#10411yescharacteristic
118#11912—611nomaximal, Sylow
119C22×C61—81no—
120C22×C61—81no—
121C22×C61—81no—
122C22×C61C2×#10011yescharacteristic
123C2×D61—21no—
124C2×D61—41no—
125C4×C61—41no—
126C4×C61—81no—
127C4×C61C2×#10411yescharacteristic
128C4×C61#42111yescharacteristic
129Dic61—21no—
130Dic61—41no—
131Dic61—81no—
132Dic61—81no—
133#3174—611no—
134#2166—611no—
135#2110—611no—
136#1356—611no—
137#1356—611no—
138#1355—611no—
139#1355D6111yescharacteristic, complemented
140C2×C61—21no—
141C2×C61—161no—
142C2×C61#153011yescharacteristic
143D61—41no—
144#541—611no—
145#540—611no—
146C2×M32—1221no—
147#499—611no—
148#492—611no—
149#491—611no—
150#490C2×D6111yescharacteristic
151#468—1221no—
152#465—1221no—
153#440—1221no—
154C4×SD16—1221no—
155#405—611no—
156#364—1221no—
157#349—1221no—
158#347—611no—
159#347—611no—
160#347—1221no—
161#347C2×D6111yescharacteristic
162#347C2×D6111yescharacteristic
163C61#1191211yescharacteristic, complemented, Sylow
164C2×SD16—1221no—
165C2×SD16—1221no—
166C2×M16—611no—
167C22×C8—611no—
168C4⋊Q8—611no—
169#127C4×D6111yescharacteristic
170#126—2441no—
171#125—611no—
172#125—2441no—
173#125C4×D6111yescharacteristic
174#123—2441no—
175C22⋊Q8—1221no—
176#121—1221no—
177#121—2441no—
178C4×Q8—1221no—
179C4×D4—1221no—
180#117—611no—
181M32—21no—
182M32—21no—
183M32—1222no—
184M32—1221no—
185M32—1221no—
186C2×C16—1222no—
187#107—1221no—
188#106—1221no—
189#103—1221no—
190#103—1221no—
191#102—21no—
192#102—21no—
193#97—611no—
194#97C22×D6111yescharacteristic
195C4×C8—611no—
196C4×C8—611no—
197C2×Q8—1221no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—2441no—
201C22×C4—611no—
202C22×C4—2441no—
203SD16—2441no—
204SD16—2441no—
205SD16—2442no—
206M16—2441no—
207C2×C8—611no—
208C2×C8—611no—
209C2×C8—1221no—
210C2×C8—1221no—
211C2×C8D4×D6111yescharacteristic
212C2×C8D4×D6111yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—1221no—
216C4⋊C4—1221no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—1221no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C42—611no—
226C42—2441no—
227C42C2×C4×D6111yescharacteristic
228C16—22no—
229C16—41no—
230C16—1222no—
231C16—2441no—
232C23—41no—
233C23—611no—
234Q8—2441no—
235Q8—2441no—
236D4—41no—
237D4—41no—
238D4—161no—
239D4—9761no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—611no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—9761no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4C22⋊C4×D6111yescharacteristic
250C8—21no—
251C8—21no—
252C8—611no—
253C8—611no—
254C8—1221no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22—1221no—
259C22—2441no—
260C22#100×D6111yescharacteristic
261C4—41no—
262C4—81no—
263C4—1221no—
264C4—4881no—
265C4—4881no—
266C4—2441no—
267C4#104×D6111yescharacteristic
268C4#1683977711yescharacteristic
269C2—21no—
270C2—161no—
271C2—2441no—
272C2#2144442811yescharacteristic
subgroupG/H
centerC2#21444428
commutatorC42×C61C22×C4
Frattini#97C22×D61
FittingC61×#1355C2
socleC2×C61#1530
prime radical#16840366C4
cosocle#97×C61C23
hypercenter#1355D61
hypocenterC61#11912
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #21447633C2semidirect
3. #21447422C2semidirect
4. #21443853C2semidirect
5. #21443853C2semidirect
6. #21443852C2semidirect
7. C61×#1355C2semidirect
139. #1355D61semidirect
163. C61#11912semidirect

Maximal subgroups

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

subgroupindex
#214564462
#214476332
#214474222
#214438532
#214438522
C61×#13552
#1191261