Finite Group Databasebeta

← #29591201

Subgroups — #29591201

Order 15616.

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

normal subgroups only

This group has 272 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#21456477C211yesmaximal, characteristic
2#21447633C211yesmaximal, characteristic
3#21447422C211yesmaximal, characteristic
4#21443854C211yesmaximal, characteristic, complemented
5#21443853C211yesmaximal, characteristic, complemented
6#21443853C211yesmaximal, characteristic, complemented
7C61×#1356C211yesmaximal, characteristic, complemented
8#16840375C411yescharacteristic
9#16840373C411yescharacteristic
10M32×D61—21no—
11#16840161C411yescharacteristic
12#16840141C411yescharacteristic
13#16840131C2211yescharacteristic
14#16840019—21no—
15#16840002—21no—
16#16839866—21no—
17#16839854—21no—
18#16839719C2211yescharacteristic
19#16839582—21no—
20#16839543—21no—
21#16839540C2211yescharacteristic
22#16839540C2211yescharacteristic
23#16839539—21no—
24C61×#491C2211yescharacteristic
25C61×#347C2211yescharacteristic
26C61×#347C2211yescharacteristic
27C2×#11758202—21no—
28C2×#11758202—21no—
29C2×#11758189D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519772—41no—
33#14519772—41no—
34#14519769C2×C411yescharacteristic
35#14519768—41no—
36#14519767—41no—
37#14519757—21no—
38#14519753—21no—
39Q8×Dic61—21no—
40#14519742—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
53C4⋊Q8×C61C2×C411yescharacteristic
54#125×C61C2×C411yescharacteristic
55M32×C61—21no—
56M32×C61—21no—
57#103×C61—21no—
58#103×C61—21no—
59#97×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×Dic122—21no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C42×C61C22×C411yescharacteristic
69#11758202—42no—
70#11758202—41no—
71#11758202—41no—
72#11758198—21no—
73#11758198—41no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—21no—
80#11758196—41no—
81#11758196—41no—
82#11758196—41no—
83C4×Dic61—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—
95C22×D61#10011yescharacteristic
96Q8×C61—41no—
97Q8×C61—41no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61#10011yescharacteristic
106C4×D61—21no—
107C4×D61—21no—
108Dic122—41no—
109Dic122—41no—
110C8×C61—21no—
111C8×C61—21no—
112#92418—21no—
113#92418#10411yescharacteristic
114#92418#10411yescharacteristic
115#11914—611nomaximal, Sylow
116C22×C61C2×#10011yescharacteristic
117C2×D61—21no—
118C2×D61—41no—
119C4×C61—41no—
120C4×C61—81no—
121C4×C61—81no—
122C4×C61C2×#10411yescharacteristic
123C4×C61#42111yescharacteristic
124Dic61—21no—
125Dic61—41no—
126Dic61—81no—
127Dic61—81no—
128#3177—611no—
129#2166—611no—
130#2110—611no—
131#1356—611no—
132#1356—611no—
133#1356—611no—
134#1356D6111yescharacteristic, complemented
135C2×C61—21no—
136C2×C61#153011yescharacteristic
137D61—41no—
138#541—611no—
139#541—611no—
140C2×M32—1221no—
141#499—611no—
142#494—611no—
143#491—611no—
144#491C2×D6111yescharacteristic
145#470—1221no—
146#467—1221no—
147#441—1221no—
148C4×Q16—1221no—
149#405—611no—
150#364—1221no—
151#349—1221no—
152#347—611no—
153#347—611no—
154#347—1221no—
155#347C2×D6111yescharacteristic
156#347C2×D6111yescharacteristic
157C61#1191411yescharacteristic, complemented, Sylow
158C2×Q16—1221no—
159C2×Q16—1221no—
160C2×M16—611no—
161C22×C8—611no—
162C4⋊Q8—611no—
163C4⋊Q8C4×D6111yescharacteristic
164#126—2441no—
165#126—2441no—
166#125—611no—
167#125—2441no—
168#125—2441no—
169#125C4×D6111yescharacteristic
170C22⋊Q8—1221no—
171C22⋊Q8—1221no—
172C4×Q8—1221no—
173C4×Q8—1221no—
174#117—611no—
175M32—21no—
176M32—21no—
177M32—1222no—
178M32—1221no—
179M32—1221no—
180C2×C16—1222no—
181#107—1221no—
182#106—1221no—
183#103—21no—
184#103—21no—
185#103—1221no—
186#103—1221no—
187#97—611no—
188#97C22×D6111yescharacteristic
189C4×C8—611no—
190C4×C8—611no—
191C2×Q8—21no—
192C2×Q8—1221no—
193C22×C4—611no—
194Q16—2441no—
195Q16—2441no—
196Q16—2442no—
197M16—2441no—
198C2×C8—611no—
199C2×C8—611no—
200C2×C8—1221no—
201C2×C8—1221no—
202C2×C8D4×D6111yescharacteristic
203C2×C8D4×D6111yescharacteristic
204C4⋊C4—21no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C22⋊C4—1221no—
216C22⋊C4—2441no—
217C22⋊C4—2441no—
218C42—611no—
219C42—2441no—
220C42—2441no—
221C42C2×C4×D6111yescharacteristic
222C16—22no—
223C16—41no—
224C16—1222no—
225C16—2441no—
226C23—611no—
227Q8—41no—
228Q8—41no—
229Q8—2441no—
230Q8—2441no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—611no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4C22⋊C4×D6111yescharacteristic
241C8—21no—
242C8—21no—
243C8—611no—
244C8—611no—
245C8—1221no—
246C22—1221no—
247C22—2441no—
248C22#100×D6111yescharacteristic
249C4—41no—
250C4—81no—
251C4—81no—
252C4—1221no—
253C4—4881no—
254C4—4881no—
255C4—2441no—
256C4#104×D6111yescharacteristic
257C4#1683977711yescharacteristic
258C2—21no—
259C2—2441no—
260C2#2144442811yescharacteristic
subgroupG/H
centerC2#21444428
commutatorC42×C61C22×C4
Frattini#97C22×D61
FittingC61×#1356C2
socleC2×C61#1530
prime radicalC22×D61#100
cosocle#97×C61C23
hypercenter#1356D61
hypocenterC61#11914
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
4. #21443854C2semidirect
5. #21443853C2semidirect
6. #21443853C2semidirect
7. C61×#1356C2semidirect
134. #1356D61semidirect
157. C61#11914semidirect

Maximal subgroups

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

subgroupindex
#214564772
#214476332
#214474222
#214438542
#214438532
C61×#13562
#1191461