Finite Group Databasebeta

← #30604030

Subgroups — #30604030

Order 15616.

372 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462056C212yesmaximal, complemented
2#21460765C212yesmaximal, complemented
3#21460754C212yesmaximal, complemented
4#21454532C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C2×#14519783C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10#16840312C411yescharacteristic
11#16839841—22no—
12C8×D244—22no—
13#16839786C2211yescharacteristic
14#16839728C411yescharacteristic
15#16839728C2211yescharacteristic
16C2×C4×C8×C61C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×#11758222C2×C411yescharacteristic
21C2×#11758222C2×C411yescharacteristic
22#14519783—41no—
23#14519783—41no—
24#14519783—41no—
25#14519783—41no—
26C2×#11758194C2×C411yescharacteristic
27C2×#11758194C2311yescharacteristic
28C2×#11758189—21no—
29C2×#11758189D412yes—
30C2×C8×D61—21no—
31C2×C8×D61D412yes—
32#14519777C811yescharacteristic
33#14519774C811yescharacteristic
34#14519765C811yescharacteristic
35#14519765C811yescharacteristic
36#14519751—22no—
37C4×D244—22no—
38C4⋊#92418—22no—
39#14519689—22no—
40#14519689—22no—
41C22×C8×C61C2×C411yescharacteristic
42C22×C8×C61C2×C411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C4×C8×C61—21no—
45C4×C8×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C22×C411yescharacteristic
48C2×C22⋊D61—21no—
49C2×C22⋊D61M1612yes—
50#11758222—41no—
51#11758222—41no—
52#11758222—41no—
53#11758222—41no—
54C2×D244—22no—
55C2×D244C2×C811yescharacteristic
56C2×D244C2×C811yescharacteristic
57C2×C4×D61—21no—
58C2×C4×D61C22⋊C412yes—
59C2×Dic122C2×C811yescharacteristic
60C2×Dic122C2×C811yescharacteristic
61C2×C8×C61—21no—
62C2×C8×C61—21no—
63C2×C8×C61—21no—
64C2×C8×C61—41no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22⋊C411yescharacteristic
67C42×C61—21no—
68C42×C61C2×C811yescharacteristic
69C42×C61C2×C811yescharacteristic
70#11758198—22no—
71#11758198—22no—
72C4⋊Dic61—22no—
73#11758194—41no—
74#11758194—41no—
75C2×#92418—21no—
76C2×#92418C2×D412yes—
77#11758189—42no—
78#11758189—42no—
79C8×D61—22no—
80C8×D61—22no—
81C8×D61—41no—
82C8×D61—41no—
83#11758187—44no—
84C23×C61C2×M1611yescharacteristic
85C22×D61—21no—
86C22×D61C22⋊C812yes—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—42no—
92C2×C4×C61C2×C22⋊C411yescharacteristic
93C2×C4×C61C22×C811yescharacteristic
94C22⋊D61—42no—
95C22⋊D61—42no—
96C2×Dic61—21no—
97C2×Dic61C22⋊C812yes—
98D244—41no—
99D244—41no—
100D244—44no—
101C4×D61—22no—
102C4×D61—22no—
103C4×D61—41no—
104C4×D61—41no—
105Dic122—41no—
106Dic122—41no—
107C8×C61—21no—
108C8×C61—41no—
109C8×C61#9911yescharacteristic
110C8×C61#9911yescharacteristic
111#92418—22no—
112#92418—41no—
113#11485—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—41no—
116C22×C61C2×C22⋊C811yescharacteristic
117C2×D61—22no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—41no—
121C4×C61—22no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61C2×#9911yescharacteristic
125C4×C61#41311yescharacteristic
126Dic61—22no—
127Dic61—41no—
128#2931—611no—
129#2115—612no—
130#1327—612no—
131#1321—612no—
132C2×C61—21no—
133C2×C61—41no—
134C2×C61#145911yescharacteristic
135D61—42no—
136D61—81no—
137C2×#131—611no—
138C2×#131—611no—
139#532—611no—
140C2×M32—1222no—
141#436—1222no—
142C8×D4—1222no—
143#423—611no—
144#408—611no—
145#408—611no—
146C2×C4×C8#692311yescharacteristic
147#349—614no—
148#349—1222no—
149C61#1148511yescharacteristic, complemented, Sylow
150C2×#41—611no—
151C2×#41—611no—
152#131—2441no—
153#131—2441no—
154#131—2441no—
155#131—2441no—
156C2×M16—611no—
157C2×M16—612no—
158C2×M16—611no—
159C2×M16—1221no—
160C22×C8—612no—
161C22×C8—1221no—
162C22×C8C2×#692311yescharacteristic
163C22×C8C2×#692311yescharacteristic
164C4⋊Q8—611no—
165#127—611no—
166#124—611no—
167#124—611no—
168#121—1222no—
169C4×D4—1222no—
170C2×C42C2×#692311yescharacteristic
171M32—1224no—
172M32—2442no—
173C2×C16—2442no—
174C4⋊C8—1222no—
175C22⋊C8—1222no—
176C22⋊C8—1222no—
177C4×C8—21no—
178C4×C8—21no—
179#41—2441no—
180#41—2441no—
181#41—2441no—
182#41—2441no—
183C2×Q8—611no—
184C2×Q8—611no—
185C2×D4—612no—
186C2×D4—611no—
187C2×D4—611no—
188C2×D4—1222no—
189C2×D4—1221no—
190C22×C4—21no—
191C22×C4—612no—
192C22×C4—1221no—
193C22×C4C22×#692311yescharacteristic
194M16—2442no—
195M16—2442no—
196M16—2441no—
197M16—2441no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—41no—
202C2×C8—612no—
203C2×C8—1222no—
204C2×C8—1222no—
205C2×C8—1221no—
206C2×C8—2441no—
207C2×C8—2441no—
208C2×C8C22⋊#692311yescharacteristic
209C2×C8C22⋊#692311yescharacteristic
210C4⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—1222no—
213C42—21no—
214C42D61⋊C811yescharacteristic
215C42D61⋊C811yescharacteristic
216C16—2444no—
217C23—612no—
218C23—1221no—
219C23D61⋊M1611yescharacteristic
220Q8—2441no—
221Q8—2441no—
222D4—2441no—
223D4—2441no—
224D4—2444no—
225D4—2442no—
226D4—2442no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—612no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4C2×C22⋊#692311yescharacteristic
239C2×C4C2×D61⋊C811yescharacteristic
240C8—21no—
241C8—41no—
242C8—1222no—
243C8—2441no—
244C8#1451983611yescharacteristic
245C8#1451983611yescharacteristic
246C22—21no—
247C22—41no—
248C22—1222no—
249C22—2442no—
250C22—2442no—
251C22—2441no—
252C22D61⋊(C22⋊C8)11yescharacteristic
253C4—22no—
254C4—21no—
255C4—41no—
256C4—1222no—
257C4—2441no—
258C4C2×#1451983611yescharacteristic
259C4#1684074811yescharacteristic
260C2—21no—
261C2—41no—
262C2—4881no—
263C2—2442no—
264C2#2146105611yescharacteristic
subgroupG/H
centerC8#14519836
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×C8×C61C4
socleC2×C61#1459
prime radical#16840312C4
cosocleC2×#11758194C23
hypercenterC2×C4×C8#6923
hypocenterC61#11485
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
1. #21462056C2semidirect
2. #21460765C2semidirect
3. #21460754C2semidirect
149. C61#11485semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214607652
#214607542
#214545322
#1148561