Finite Group Databasebeta

← #30604031

Subgroups — #30604031

Order 15616.

372 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462055C212yesmaximal, complemented
2#21460766C212yesmaximal, complemented
3#21460754C212yesmaximal, complemented
4#21454527C211yesmaximal, characteristic
5C2×#14519851—22no—
6#16840658—22no—
7#16840658C2214yes—
8C2×#14519785C411yescharacteristic
9C2×#14519784C2211yescharacteristic
10#16840308C411yescharacteristic
11#16839837—22no—
12#16839825—22no—
13#16839785C2211yescharacteristic
14#16839728C2211yescharacteristic
15C2×C8×Dic61C411yescharacteristic
16C61×#408C411yescharacteristic
17#14519851—24no—
18#14519851—42no—
19C2×#11758187—42no—
20C2×#11758222C2×C411yescharacteristic
21#14519785—41no—
22#14519785—41no—
23#14519784—41no—
24#14519784—41no—
25C2×#11758194D412yes—
26C2×#11758194C2311yescharacteristic
27C2×#11758189—21no—
28C22×#92418C2×C411yescharacteristic
29C22×#92418D412yes—
30C2×C8×D61—21no—
31#14519775C811yescharacteristic
32#14519773C811yescharacteristic
33#14519766C811yescharacteristic
34#14519764C811yescharacteristic
35#14519749—22no—
36C4×C22⋊D61—22no—
37C2×C4×Dic61C2×C411yescharacteristic
38#14519706—22no—
39#14519689—22no—
40C8×Dic61—21no—
41C8×Dic61—21no—
42C2×#41×C61C2×C411yescharacteristic
43C2×M16×C61C2×C411yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45C22⋊C8×C61—22no—
46#41×C61—41no—
47#41×C61—41no—
48C2×Q8×C61C2×C811yescharacteristic
49C2×D4×C61C2×C811yescharacteristic
50C2×D4×C61M1612yes—
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61C22×C411yescharacteristic
53C2×C22⋊D61—22no—
54C2×C22⋊D61—21no—
55C22×Dic61—21no—
56#11758222—41no—
57#11758222—41no—
58C2×D244C2×C811yescharacteristic
59C2×C4×D61—21no—
60C2×Dic122C2×C811yescharacteristic
61M16×C61—41no—
62C2×C8×C61—21no—
63C2×C8×C61—21no—
64C2×C8×C61—41no—
65C22⋊Dic61—22no—
66#11758198—22no—
67#11758196—22no—
68C4×Dic61—21no—
69C4×Dic61C2×C811yescharacteristic
70C4×Dic61C2×C811yescharacteristic
71#11758194—42no—
72#11758194—41no—
73C2×#92418—22no—
74C2×#92418—22no—
75C2×#92418—21no—
76C2×#92418—21no—
77C2×#92418C22⋊C411yescharacteristic
78C2×#92418C22⋊C411yescharacteristic
79C2×#92418C2×D412yes—
80#11758189—42no—
81C8×D61—41no—
82C8×D61—41no—
83#11758187—44no—
84C23×C61C22⋊C812yes—
85C23×C61C2×M1611yescharacteristic
86C22×D61—21no—
87Q8×C61—41no—
88D4×C61—41no—
89D4×C61—42no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61C22⋊C812yes—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C22×C811yescharacteristic
97C22⋊D61—44no—
98C22⋊D61—42no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103D244—41no—
104C4×D61—41no—
105C4×D61—41no—
106Dic122—41no—
107C8×C61—41no—
108C8×C61—41no—
109#92418—22no—
110#92418—21no—
111#92418#9911yescharacteristic
112#92418#9911yescharacteristic
113#11485—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—22no—
116C22×C61—41no—
117C22×C61—42no—
118C22×C61C2×C22⋊C811yescharacteristic
119C2×D61—42no—
120C2×D61—41no—
121C4×C61—21no—
122C4×C61—22no—
123C4×C61C2×#9911yescharacteristic
124C4×C61#41311yescharacteristic
125Dic61—22no—
126Dic61—41no—
127Dic61—41no—
128#2931—611no—
129#2115—612no—
130#1327—612no—
131#1321—612no—
132C2×C61—21no—
133C2×C61—41no—
134C2×C61—42no—
135C2×C61#145911yescharacteristic
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#692311yescharacteristic
146C2×C4×C8—611no—
147#349—614no—
148#349—1222no—
149C61#1148511yescharacteristic, complemented, Sylow
150C2×#41—611no—
151C2×#41C2×#692311yescharacteristic
152#131—2441no—
153#131—2441no—
154#131—2441no—
155#131—2441no—
156C2×M16—612no—
157C2×M16—611no—
158C2×M16—1221no—
159C2×M16C2×#692311yescharacteristic
160C22×C8—612no—
161C22×C8—611no—
162C22×C8—1221no—
163C22×C8C2×#692311yescharacteristic
164C4⋊Q8—611no—
165#127—611no—
166#124—611no—
167#124—611no—
168#121—1222no—
169C4×D4—1222no—
170C2×C42—611no—
171M32—1224no—
172M32—2442no—
173C2×C16—2442no—
174C4⋊C8—1222no—
175C22⋊C8—22no—
176C22⋊C8—1222no—
177C4×C8—1221no—
178C4×C8—1221no—
179#41—41no—
180#41—41no—
181#41—2441no—
182#41—2441no—
183C2×Q8—611no—
184C2×Q8D61⋊C811yescharacteristic
185C2×D4—611no—
186C2×D4—1222no—
187C2×D4—1221no—
188C2×D4D61⋊C811yescharacteristic
189C2×D4#1175821312yes—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4C22⋊#692312yes—
193C22×C4C22×#692311yescharacteristic
194M16—41no—
195M16—2442no—
196M16—2441no—
197M16—2442no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—41no—
201C2×C8—611no—
202C2×C8—611no—
203C2×C8—612no—
204C2×C8—1222no—
205C2×C8—1222no—
206C2×C8—1221no—
207C2×C8—1221no—
208C2×C8—2441no—
209C2×C8—2441no—
210C4⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—1222no—
213C42—611no—
214C42—611no—
215C42—1221no—
216C16—2444no—
217C23—1221no—
218C23#1451983412yes—
219C23C2×#1175821311yescharacteristic
220Q8—41no—
221Q8—2441no—
222D4—41no—
223D4—42no—
224D4—2441no—
225D4—2444no—
226D4—2442no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—2442no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4#1451983412yes—
238C2×C4C2×C22⋊#692311yescharacteristic
239C2×C4C2×D61⋊C811yescharacteristic
240C8—41no—
241C8—41no—
242C8—611no—
243C8—611no—
244C8—1222no—
245C8—1221no—
246C22—21no—
247C22—22no—
248C22—41no—
249C22—42no—
250C22—2442no—
251C22—2441no—
252C22C2×#1451983411yescharacteristic
253C4—22no—
254C4—21no—
255C4—1222no—
256C4—2441no—
257C4—2441no—
258C4D61⋊#9911yescharacteristic
259C4#1684074911yescharacteristic
260C2—21no—
261C2—41no—
262C2—42no—
263C2—4881no—
264C2#2146105711yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61#1459
prime radical#16840308C4
cosocleC2×#11758194C23
hypercenter#408#6923
hypocenterC61#11485
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #21462055C2semidirect
2. #21460766C2semidirect
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
#214620552
#214607662
#214607542
#214545272
#1148561