Finite Group Databasebeta

← #29589341

Subgroups — #29589341

Order 15616.

356 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 87 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#21454527C211yesmaximal, characteristic
2#21447619C212yesmaximal, complemented
3#21443745C211yesmaximal, characteristic, complemented
4#21443744C212yesmaximal, complemented
5C61×#1315C211yesmaximal, characteristic, complemented
6C2×#14519785C411yescharacteristic
7C2×#14519784C411yescharacteristic
8#16840308C411yescharacteristic
9#16839837—22no—
10#16839825—22no—
11#16839785C411yescharacteristic
12#16839728C2211yescharacteristic
13C2×C8×Dic61C2211yescharacteristic
14#16839580—22no—
15C22⋊#11758185C2212yes—
16#16839537—22no—
17C61×#408C2211yescharacteristic
18C61×C22⋊C16C2212yes—
19C2×#11758222C2×C411yescharacteristic
20#14519785—42no—
21#14519784—42no—
22C2×#11758194—21no—
23C2×#11758194C2×C411yescharacteristic
24C2×#11758189—21no—
25C22×#92418—21no—
26C22×#92418C2×C411yescharacteristic
27C2×C8×D61—21no—
28#14519775C811yescharacteristic
29#14519773C811yescharacteristic
30#14519766C811yescharacteristic
31#14519764C811yescharacteristic
32#14519749—22no—
33C4×C22⋊D61—22no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×#11758185—22no—
36#14519706—22no—
37#14519689—22no—
38C8×Dic61D412yes—
39C8×Dic61D412yes—
40C2×#41×C61C2×C411yescharacteristic
41C2×M16×C61C2×C411yescharacteristic
42C22×C8×C61C2311yescharacteristic
43C2×C16×C61—22no—
44C22⋊C8×C61—22no—
45#41×C61—41no—
46#41×C61—41no—
47C2×Q8×C61C2×C811yescharacteristic
48C2×D4×C61—21no—
49C2×D4×C61C2×C811yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61C22×C411yescharacteristic
52C2×C22⋊D61—21no—
53C2×C22⋊D61—22no—
54C22×Dic61M1612yes—
55#11758222—41no—
56#11758222—41no—
57C2×D244C2×C811yescharacteristic
58C2×C4×D61—21no—
59C2×Dic122C2×C811yescharacteristic
60M16×C61—41no—
61C2×C8×C61—21no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D412yes—
64C22⋊Dic61—22no—
65#11758198—22no—
66#11758196—22no—
67C4×Dic61C22⋊C412yes—
68C4×Dic61C2×C811yescharacteristic
69C4×Dic61C2×C811yescharacteristic
70#11758194—42no—
71#11758194—41no—
72C2×#92418—22no—
73C2×#92418—21no—
74C2×#92418—42no—
75C2×#92418C22⋊C411yescharacteristic
76C2×#92418C22⋊C411yescharacteristic
77#11758189—42no—
78C8×D61—42no—
79C16×C61—42no—
80#11758185—42no—
81C23×C61—21no—
82C23×C61C2×M1611yescharacteristic
83C22×D61—21no—
84Q8×C61—41no—
85D4×C61—41no—
86D4×C61—42no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61C2×C22⋊C411yescharacteristic
93C2×C4×C61C22×C811yescharacteristic
94C22⋊D61—44no—
95C22⋊D61—42no—
96C2×Dic61—21no—
97C2×Dic61—42no—
98C2×Dic61C22⋊C812yes—
99C2×Dic61C22⋊C812yes—
100D244—41no—
101C4×D61—41no—
102C4×D61—41no—
103Dic122—41no—
104C8×C61—22no—
105C8×C61—41no—
106#92418—21no—
107#92418—41no—
108#92418#10012yes—
109#11491—611nomaximal, Sylow
110C22×C61—22no—
111C22×C61—21no—
112C22×C61—42no—
113C22×C61—41no—
114C22×C61C2×C22⋊C811yescharacteristic
115C2×D61—42no—
116C2×D61—41no—
117C4×C61—21no—
118C4×C61—41no—
119C4×C61#41011yescharacteristic
120C4×C61C2×#10011yescharacteristic
121Dic61—22no—
122Dic61—22no—
123Dic61—41no—
124#2931—611no—
125#2163—612no—
126#1315—611no—
127#1315—612no—
128#1315D6111yescharacteristic, complemented
129C2×C61—41no—
130C2×C61—81no—
131C2×C61#146011yescharacteristic
132C2×C61#211712yes—
133D61—81no—
134C2×#131—611no—
135C2×#131—611no—
136#532—611no—
137#436—1222no—
138C8×D4—1222no—
139#423—611no—
140#408—611no—
141#408C2×D6111yescharacteristic
142C2×C4×C8—611no—
143C4⋊C16—1222no—
144C22⋊C16—612no—
145C22⋊C16C2×D6112yes—
146#346—1222no—
147C61#1149111yescharacteristic, complemented, Sylow
148C2×#41—611no—
149C2×#41C4×D6111yescharacteristic
150#131—2442no—
151#131—2442no—
152C2×M16—611no—
153C2×M16—1221no—
154C2×M16—1221no—
155C2×M16C4×D6111yescharacteristic
156C22×C8—611no—
157C22×C8—1221no—
158C22×C8—1221no—
159C22×C8C22×D6111yescharacteristic
160C4⋊Q8—611no—
161#127—611no—
162#124—611no—
163#124—611no—
164#121—1222no—
165C4×D4—1222no—
166C2×C42—611no—
167C2×C16—22no—
168C2×C16—1222no—
169C4⋊C8—1222no—
170C22⋊C8—22no—
171C22⋊C8—1222no—
172C4×C8—612no—
173C4×C8—612no—
174#41—41no—
175#41—41no—
176#41—2441no—
177#41—2441no—
178C2×Q8—611no—
179C2×Q8C8×D6111yescharacteristic
180C2×D4—21no—
181C2×D4—611no—
182C2×D4—1222no—
183C2×D4—1221no—
184C2×D4C8×D6111yescharacteristic
185C22×C4—21no—
186C22×C4—612no—
187C22×C4—1221no—
188C22×C4C2×C4×D6111yescharacteristic
189M16—41no—
190M16—2442no—
191M16—2442no—
192M16—2441no—
193C2×C8—21no—
194C2×C8—41no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—1222no—
198C2×C8—1221no—
199C2×C8—2442no—
200C2×C8—2442no—
201C2×C8D4×D6112yes—
202C4⋊C4—1222no—
203C22⋊C4—1222no—
204C22⋊C4—1222no—
205C42—612no—
206C42—611no—
207C42—611no—
208C16—42no—
209C16—2442no—
210C23—21no—
211C23—1221no—
212C23M16×D6111yescharacteristic
213Q8—41no—
214Q8—2441no—
215D4—41no—
216D4—42no—
217D4—2441no—
218D4—2444no—
219D4—2442no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—612no—
226C2×C4—612no—
227C2×C4—1221no—
228C2×C4—2442no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4C22⋊C4×D6111yescharacteristic
232C2×C4C2×C8×D6111yescharacteristic
233C8—22no—
234C8—41no—
235C8—612no—
236C8—1221no—
237C8—2441no—
238C22—22no—
239C22—21no—
240C22—42no—
241C22—41no—
242C22—2442no—
243C22—2441no—
244C22C22⋊C8×D6111yescharacteristic
245C4—21no—
246C4—41no—
247C4—1222no—
248C4—1222no—
249C4—2441no—
250C4#1683973411yescharacteristic
251C4#100×D6111yescharacteristic
252C2—41no—
253C2—81no—
254C2—4881no—
255C2#2144413811yescharacteristic
256C2#2144744512yes—
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1315C2
socleC22×C61C2×C22⋊C8
prime radical#16840308C4
cosocleC22×C8×C61C23
hypercenter#1315D61
hypocenterC61#11491
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #21447619C2semidirect
3. #21443745C2semidirect
4. #21443744C2semidirect
5. C61×#1315C2semidirect
128. #1315D61semidirect
147. C61#11491semidirect

Maximal subgroups

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

subgroupindex
#214545272
#214476192
#214437452
#214437442
C61×#13152
#1149161