Finite Group Databasebeta

← #30605719

Subgroups — #30605719

Order 15616.

292 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462195C211yesmaximal, characteristic, complemented
2#21462161C211yesmaximal, characteristic, complemented
3#21460840C211yesmaximal, characteristic, complemented
4#21460839C211yesmaximal, characteristic, complemented
5#21460827C211yesmaximal, characteristic, complemented
6#21460827C211yesmaximal, characteristic, complemented
7#21456468C211yesmaximal, characteristic
8D61⋊M32—21no—
9#16840685C2211yescharacteristic
10#16840685C2211yescharacteristic
11#16840685C2211yescharacteristic
12#16840685C2211yescharacteristic
13#16840684—21no—
14#16840659—21no—
15#16840655—21no—
16#16840368C411yescharacteristic
17#16840366C411yescharacteristic
18#16840161C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840127C411yescharacteristic
21#16840014—21no—
22#16839997—21no—
23#16839871—21no—
24#16839842—21no—
25#16839719C2211yescharacteristic
26C61×#490C411yescharacteristic
27#14519852—41no—
28#14519851—21no—
29#14519851—21no—
30#14519851—21no—
31#14519851—21no—
32D61⋊C16—41no—
33C2×#11758199—21no—
34C2×#11758199—21no—
35C2×#11758189D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519774C2×C411yescharacteristic
38#14519769C2×C411yescharacteristic
39#14519762—41no—
40#14519758—41no—
41#14519752—21no—
42#14519752—41no—
43#14519749—41no—
44#14519748—21no—
45D4×Dic61—21no—
46#14519739—21no—
47#14519734C2×C411yescharacteristic
48#14519710—21no—
49#14519708—21no—
50#14519699—21no—
51#14519699—21no—
52#14519687D411yescharacteristic
53C4×#92418C2311yescharacteristic
54C8×Dic61D411yescharacteristic
55#127×C61C2×C411yescharacteristic
56#125×C61C2×C411yescharacteristic
57#102×C61—21no—
58#102×C61—21no—
59#97×C61C2×C411yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×C22⋊D61—41no—
63C22×Dic61—41no—
64C2×D244—21no—
65C2×D244—41no—
66C2×D244—41no—
67C2×C4×D61—41no—
68C2×C4×D61C22⋊C411yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70C2×C8×C61C22⋊C411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C42×C61C22×C411yescharacteristic
74C22⋊Dic61—41no—
75C22⋊Dic61—41no—
76#11758199—41no—
77#11758199—41no—
78#11758199—41no—
79#11758199—41no—
80#11758198—21no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84#11758196—21no—
85#11758196—41no—
86C4×Dic61C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89#11758189—21no—
90#11758189—21no—
91C8×D61—21no—
92C8×D61—21no—
93#11758187—41no—
94#11758187—41no—
95#11758187—41no—
96#11758187—41no—
97C23×C61—41no—
98C22×D61—41no—
99C22×D61#10011yescharacteristic
100D4×C61—41no—
101D4×C61—41no—
102D4×C61—161no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C22⋊D61—161no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—161no—
110C2×Dic61#10011yescharacteristic
111D244—41no—
112D244—41no—
113D244—161no—
114D244—161no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—161no—
118C8×C61—21no—
119C8×C61—21no—
120#92418#13511yescharacteristic
121#92418#13511yescharacteristic
122#92418AGL(1,ℤ/8)11yescharacteristic
123#92418#13711yescharacteristic
124#11989—611nomaximal, Sylow
125C22×C61—81no—
126C22×C61—81no—
127C22×C61—81no—
128C22×C61C2×#10011yescharacteristic
129C2×D61—21no—
130C2×D61—41no—
131C2×D61—81no—
132C2×D61—81no—
133C2×D61—81no—
134C4×C61—41no—
135C4×C61—81no—
136C4×C61#41611yescharacteristic
137C4×C61#41711yescharacteristic
138Dic61—21no—
139Dic61—41no—
140Dic61—81no—
141#3176—611no—
142#2166—611no—
143#2153—611no—
144#1366—611no—
145#1366—611no—
146#1357—611no—
147#1357—611no—
148C2×C61—21no—
149C2×C61—161no—
150C2×C61#155111yescharacteristic
151D61—41no—
152D61—161no—
153#540—611no—
154#540—611no—
155C2×M32—1221no—
156#499—611no—
157#493—611no—
158#490—611no—
159#490#692311yescharacteristic
160#469—1221no—
161#466—1221no—
162#442—1221no—
163C4×D8—1221no—
164#405—611no—
165#364—611no—
166#364—611no—
167#364—611no—
168#364—611no—
169#364—1221no—
170#349—1221no—
171#347—1221no—
172C61#1198911yescharacteristic, complemented, Sylow
173C2×D8—1221no—
174C2×D8—1221no—
175C2×M16—611no—
176C22×C8—611no—
177#127—611no—
178#127C2×#692311yescharacteristic
179#125—611no—
180#125C2×#692311yescharacteristic
181#123—2441no—
182#123—2441no—
183#121—1221no—
184#121—1221no—
185#121—2441no—
186#121—2441no—
187C4×D4—1221no—
188C4×D4—1221no—
189#117—611no—
190M32—1221no—
191M32—1221no—
192M32—1221no—
193M32—1221no—
194M32—2441no—
195C2×C16—2441no—
196#107—1221no—
197#106—1221no—
198#102—21no—
199#102—21no—
200#102—1221no—
201#102—1221no—
202#97—611no—
203#97C2×#692311yescharacteristic
204C4×C8—611no—
205C4×C8—611no—
206C2×D4—21no—
207C2×D4—41no—
208C2×D4—1221no—
209C2×D4—2441no—
210C2×D4—2441no—
211C2×D4—2441no—
212C22×C4—611no—
213C22×C4—2441no—
214C22×C4—2441no—
215D8—2441no—
216D8—2441no—
217D8—2441no—
218D8—2441no—
219M16—1221no—
220M16—1221no—
221C2×C8—611no—
222C2×C8—611no—
223C2×C8—1221no—
224C2×C8—1221no—
225C2×C8C22⋊#692311yescharacteristic
226C2×C8C22⋊#692311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—41no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4—2441no—
232C22⋊C4—1221no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C22⋊C4—2441no—
237C42—611no—
238C42C22×#692311yescharacteristic
239C16—2441no—
240C16—2441no—
241C16—2441no—
242C16—2441no—
243C23—41no—
244C23—611no—
245C23—2441no—
246D4—41no—
247D4—41no—
248D4—161no—
249D4—9761no—
250D4—9761no—
251D4—9761no—
252D4—2441no—
253D4—2441no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—611no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—9761no—
261C2×C4—9761no—
262C2×C4—2441no—
263C2×C4C2×C22⋊#692311yescharacteristic
264C8—21no—
265C8—21no—
266C8—611no—
267C8—611no—
268C8—611no—
269C8—611no—
270C22—81no—
271C22—81no—
272C22—81no—
273C22—1221no—
274C22—4881no—
275C22—4881no—
276C22—4881no—
277C22—2441no—
278C22D61⋊#10011yescharacteristic
279C4—41no—
280C4—81no—
281C4—1221no—
282C4—4881no—
283C4—2441no—
284C4#1684075211yescharacteristic
285C4#1684075311yescharacteristic
286C2—21no—
287C2—161no—
288C2—9761no—
289C2—2441no—
290C2#2146133911yescharacteristic
subgroupG/H
centerC2#21461339
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#490C4
socleC2×C61#1551
prime radical#21456468C2
cosocleC4×#92418C23
hypercenter#490#6923
hypocenterC61#11989
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #21462195C2semidirect
2. #21462161C2semidirect
3. #21460840C2semidirect
4. #21460839C2semidirect
5. #21460827C2semidirect
6. #21460827C2semidirect
172. C61#11989semidirect

Maximal subgroups

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

subgroupindex
#214621952
#214621612
#214608402
#214608392
#214608272
#214564682
#1198961