Finite Group Databasebeta

← #29593613

Subgroups — #29593613

Order 15616.

306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458249C211yesmaximal, characteristic, complemented
2#21448044C211yesmaximal, characteristic, complemented
3#21447860C211yesmaximal, characteristic, complemented
4#21445175C211yesmaximal, characteristic
5#21443782C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×#1364C211yesmaximal, characteristic, complemented
8#16840486—21no—
9C2×#14519722—21no—
10#16840139C2211yescharacteristic
11#16840105—22no—
12#16840044—21no—
13#16840004—21no—
14#16839958—21no—
15C4×Dic244C2211yescharacteristic
16C8×D244C2211yescharacteristic
17#16839799—21no—
18#16839564—21no—
19#16839562—22no—
20C4×#11758185C2211yescharacteristic
21#16839505—21no—
22C61×#500C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×D488—21no—
27C2×D488—21no—
28C2×D488—41no—
29C2×C8×D61—21no—
30#14519774—21no—
31#14519772—42no—
32#14519766—41no—
33#14519757—22no—
34Q8×Dic61—41no—
35C4×Dic122—21no—
36C4×D244D411yescharacteristic
37#14519735—22no—
38#14519722—42no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519708—22no—
42C4⋊#92418D411yescharacteristic
43#14519702—21no—
44#14519700—22no—
45#14519699—41no—
46#14519689—21no—
47C4⋊Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61—21no—
50#107×C61D412yes—
51C4⋊C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244—41no—
57C2×D244D811yescharacteristic
58C2×C4×D61—21no—
59C2×Dic122—21no—
60C2×C8×C61—41no—
61C2×C8×C61C2×D411yescharacteristic
62C2×C8×C61C2×D411yescharacteristic
63C4⋊C4×C61—22no—
64C4⋊C4×C61—41no—
65C42×C61C2×D411yescharacteristic
66#11758198—21no—
67#11758198—42no—
68#11758198—42no—
69C4⋊Dic61—21no—
70C4⋊Dic61—42no—
71C4⋊Dic61D811yescharacteristic
72#11758196—41no—
73C4×Dic61—42no—
74C4×Dic61—41no—
75C2×#92418—21no—
76Dic244—21no—
77Dic244—21no—
78D488—42no—
79D488—41no—
80D488—41no—
81D488—82no—
82C8×D61—41no—
83C8×D61—41no—
84C16×C61—41no—
85#11758185—41no—
86C22×D61—21no—
87C22×D61—81no—
88Q8×C61—81no—
89Q8×C61—81no—
90C2×C4×C61—42no—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61C2×D811yescharacteristic
93C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97D244—21no—
98D244—21no—
99D244—81no—
100D244—81no—
101D244—81no—
102D244—81no—
103D244—161no—
104C4×D61—41no—
105C4×D61—41no—
106Dic122—41no—
107Dic122—41no—
108C8×C61—21no—
109C8×C61—81no—
110C8×C61#13511yescharacteristic
111C8×C61AGL(1,ℤ/8)11yescharacteristic
112#92418—41no—
113#12341—611nomaximal, Sylow
114C22×C61#44711yescharacteristic
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—161no—
119C2×D61—161no—
120C2×D61—161no—
121C4×C61—21no—
122C4×C61—82no—
123C4×C61#44911yescharacteristic
124C4×C61#45411yescharacteristic
125C4×C61#50811yescharacteristic
126C4×C61#50911yescharacteristic
127Dic61—41no—
128Dic61—81no—
129Dic61—81no—
130#3342—611no—
131#2240—611no—
132#2207—611no—
133#1667—611no—
134#1364D6111yescharacteristic, complemented
135#1332—611no—
136D4⋊C16—611no—
137C2×C61#162511yescharacteristic
138C2×C61#218611yescharacteristic
139C2×C61#219311yescharacteristic
140D61—81no—
141D61—321no—
142#556—1221no—
143C2×SD32—1221no—
144#500C2×D6111yescharacteristic
145#493—611no—
146#485—1222no—
147#475—1221no—
148#467—1221no—
149#459—1221no—
150C4×Q16—611no—
151C8×D4—611no—
152#427—1221no—
153C4⋊C16C2×D6111yescharacteristic
154#357—1221no—
155#357—1222no—
156C4×C16—611no—
157#335C2×D6111yescharacteristic
158#331—1221no—
159C61#1234111yescharacteristic, complemented, Sylow
160C2×Q16—611no—
161C2×D8—1221no—
162C2×D8—1221no—
163C2×D8—2441no—
164C22×C8—1221no—
165C4⋊Q8—21no—
166#127—1221no—
167#126—2442no—
168#124—2441no—
169C22⋊Q8—1222no—
170C4×Q8—1221no—
171C4×Q8—2441no—
172C4×D4—611no—
173#117—1222no—
174SD32—2442no—
175C2×C16—21no—
176C2×C16—1221no—
177#107—21no—
178#107—611no—
179#107D24412yes—
180#106—1222no—
181C4⋊C8—21no—
182C4⋊C8—611no—
183#103—1222no—
184#103—1221no—
185#102—2441no—
186C22⋊C8—1221no—
187C4×C8C22×D6111yescharacteristic
188C2×Q8—41no—
189C2×Q8—1221no—
190C2×D4—611no—
191C2×D4—2441no—
192C2×D4—2441no—
193C2×D4—2441no—
194C22×C4—1221no—
195Q16—1221no—
196Q16—1221no—
197D8—4882no—
198D8—2442no—
199D8—2441no—
200D8—2441no—
201C2×C8—41no—
202C2×C8—1221no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8C2×D24411yescharacteristic
206C2×C8D4×D6111yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—2442no—
212C4⋊C4—2441no—
213C22⋊C4—1221no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C42—2442no—
217C42—2441no—
218C42D4×D6111yescharacteristic
219C16—41no—
220C16—2441no—
221C23—1221no—
222C23—4881no—
223Q8—81no—
224Q8—81no—
225Q8—2441no—
226Q8—2441no—
227D4—1221no—
228D4—1221no—
229D4—9761no—
230D4—4881no—
231D4—4881no—
232D4—4881no—
233D4—4881no—
234C2×C4—42no—
235C2×C4—1221no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4#1451974711yescharacteristic
241C2×C4D8×D6111yescharacteristic
242C2×C4#1451980411yescharacteristic
243C8—21no—
244C8—81no—
245C8—2441no—
246C8#1451980011yescharacteristic
247C8#1451980411yescharacteristic
248C22—9761no—
249C22—9761no—
250C22—9761no—
251C22—2441no—
252C22—2441no—
253C22—2441no—
254C22#1683989711yescharacteristic
255C4—21no—
256C4—82no—
257C4—4881no—
258C4—4881no—
259C4—2441no—
260C4#1683991011yescharacteristic
261C4#1683993711yescharacteristic
262C4#1684019311yescharacteristic
263C4#1684019611yescharacteristic
264C2—19521no—
265C2—4881no—
266C2#2144490911yescharacteristic
267C2#2144774311yescharacteristic
268C2#2144778611yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socleC22×C61#447
prime radical#21445175C2
hypercenter#1364D61
hypocenterC61#12341
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #21458249C2semidirect
2. #21448044C2semidirect
3. #21447860C2semidirect
5. #21443782C2semidirect
6. #21443773C2semidirect
7. C61×#1364C2semidirect
134. #1364D61semidirect
159. C61#12341semidirect

Maximal subgroups

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

subgroupindex
#214582492
#214480442
#214478602
#214451752
#214437822
#214437732
C61×#13642
#1234161