Finite Group Databasebeta

← #29593748

Subgroups — #29593748

Order 15616.

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

normal subgroups only

This group has 308 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#21458775C211yesmaximal, characteristic, complemented
2#21448061C211yesmaximal, characteristic, complemented
3#21447854C211yesmaximal, characteristic
4#21445304C211yesmaximal, characteristic, complemented
5#21443872C211yesmaximal, characteristic, complemented
6#21443802C211yesmaximal, characteristic, complemented
7C61×#1333C211yesmaximal, characteristic, complemented
8#16840471—21no—
9C2×#14519718—21no—
10#16840170—21no—
11#16840164C2211yescharacteristic
12#16840139C2211yescharacteristic
13#16840062—21no—
14#16840060—21no—
15#16840040—21no—
16#16839963—21no—
17#16839892C2211yescharacteristic
18#16839874—21no—
19C4⋊#11758185C2211yescharacteristic
20#16839564—21no—
21#16839564—21no—
22#16839562—21no—
23#16839505—21no—
24C4×D8×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×#11758190—41no—
28C2×D488—21no—
29C2×D488—21no—
30#14519776—21no—
31#14519774—21no—
32#14519769—21no—
33#14519768—21no—
34#14519756—41no—
35#14519754—41no—
36#14519754—41no—
37C4×Dic122D411yescharacteristic
38D4×Dic61—21no—
39D4×Dic61—21no—
40C2×#11758196—41no—
41#14519718—42no—
42C2×#11758185—21no—
43#14519711D411yescharacteristic
44#14519711D411yescharacteristic
45#14519710—21no—
46#14519709—21no—
47#14519708—21no—
48C4⋊#92418D411yescharacteristic
49#14519706—21no—
50#14519699—41no—
51#14519698—21no—
52#14519698—21no—
53#14519687—21no—
54C2×D8×C61D411yescharacteristic
55C4×D4×C61—21no—
56C2×C16×C61—21no—
57#107×C61D411yescharacteristic
58C4⋊C8×C61—21no—
59#102×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D4×C61—21no—
62C22×C4×C61—41no—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C2×D244—41no—
66C2×D244—41no—
67C2×D244—41no—
68C2×Dic122—41no—
69C2×Dic122D811yescharacteristic
70D8×C61—21no—
71D8×C61SD1612yescomplemented
72C2×C8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—21no—
76C22⋊C4×C61—41no—
77C42×C61C2×D411yescharacteristic
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61—41no—
83C4⋊Dic61D811yescharacteristic
84#11758196—21no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C2×#92418—21no—
91D488—42no—
92D488—41no—
93D488—41no—
94#11758190—82no—
95C16×C61—41no—
96#11758185—41no—
97C23×C61—41no—
98C22×D61—81no—
99D4×C61—22no—
100D4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—161no—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61C2×D811yescharacteristic
105C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—82no—
111C2×Dic61—161no—
112D244—81no—
113D244—81no—
114D244—81no—
115D244—81no—
116D244—161no—
117Dic122—41no—
118Dic122—161no—
119C8×C61—21no—
120C8×C61—81no—
121C8×C61C2×SD1611yescharacteristic
122C8×C61#13711yescharacteristic
123#92418—41no—
124#12360—611nomaximal, Sylow
125C22×C61—42no—
126C22×C61—81no—
127C22×C61—81no—
128C22×C61#44711yescharacteristic
129C2×D61—161no—
130C2×D61—161no—
131C2×D61—161no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—81no—
135C4×C61#44811yescharacteristic
136C4×C61#45411yescharacteristic
137Dic61—41no—
138Dic61—41no—
139Dic61—81no—
140Dic61—81no—
141#3389—611no—
142#2244—611no—
143#2206—611no—
144#1688—611no—
145#1363—611no—
146#1338—611no—
147#1333D6111yescharacteristic, complemented
148C2×C61—82no—
149C2×C61#162711yescharacteristic
150C2×C61#219011yescharacteristic
151C2×C61#219211yescharacteristic
152D61—321no—
153#554—1221no—
154C2×D16—1221no—
155#501—1221no—
156#499—611no—
157#493—611no—
158#478—1221no—
159#478—1221no—
160#474—1221no—
161#460—1221no—
162#446—611no—
163#442—1221no—
164C4×D8C2×D6111yescharacteristic
165C4⋊C16—611no—
166#357—1221no—
167#357—1221no—
168#357—1221no—
169#346C2×D6111yescharacteristic
170#334C2×D6111yescharacteristic
171#331—1221no—
172C61#1236011yescharacteristic, complemented, Sylow
173C2×SD16—2441no—
174C2×D8—1221no—
175C2×D8—1221no—
176C2×D8D24411yescharacteristic
177C4⋊Q8—1221no—
178#127—1221no—
179#125—1221no—
180#125—1221no—
181C22⋊Q8—2441no—
182C22⋊Q8—2441no—
183C22⋊Q8—2441no—
184C4×Q8—611no—
185C4×D4—21no—
186C4×D4—1221no—
187C4×D4—1221no—
188C2×C4⋊C4—2441no—
189D16—2442no—
190C2×C16—21no—
191C2×C16—1221no—
192#107—611no—
193#107—611no—
194#107—1221no—
195#107D24411yescharacteristic
196#106—1221no—
197#106—1221no—
198C4⋊C8—21no—
199C4⋊C8—611no—
200C4⋊C8—1221no—
201#102—21no—
202#102—1221no—
203#102—1221no—
204#102—2441no—
205#97—1221no—
206C4×C8C22×D6111yescharacteristic
207C2×Q8—611no—
208C2×Q8—2441no—
209C2×D4—21no—
210C2×D4—2441no—
211C2×D4—2441no—
212C2×D4—2441no—
213C22×C4—41no—
214C22×C4—2441no—
215C22×C4—2441no—
216SD16—4882no—
217D8—21no—
218D8—2442no—
219D8—2441no—
220D8—2441no—
221D8#1175819012yescomplemented
222C2×C8—41no—
223C2×C8—1221no—
224C2×C8C2×D24411yescharacteristic
225C2×C8D4×D6111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—611no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4—2441no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C22⋊C4—41no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C42—1221no—
240C42D4×D6111yescharacteristic
241C16—41no—
242C16—2441no—
243C23—41no—
244C23—4881no—
245Q8—9761no—
246Q8—2441no—
247D4—22no—
248D4—41no—
249D4—9761no—
250D4—4881no—
251D4—4881no—
252D4—4881no—
253D4—4881no—
254C2×C4—41no—
255C2×C4—161no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—9761no—
259C2×C4—4882no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4#1451974711yescharacteristic
263C2×C4D8×D6111yescharacteristic
264C2×C4#1451980411yescharacteristic
265C8—21no—
266C8—81no—
267C8—2441no—
268C8C2×#1175819011yescharacteristic
269C8#1451981011yescharacteristic
270C22—42no—
271C22—81no—
272C22—81no—
273C22—9761no—
274C22—9761no—
275C22—9761no—
276C22#1683989711yescharacteristic
277C4—21no—
278C4—21no—
279C4—81no—
280C4—4881no—
281C4—4881no—
282C4—2441no—
283C4—2441no—
284C4#1683990311yescharacteristic
285C4#1683993611yescharacteristic
286C2—82no—
287C2—19521no—
288C2#2144492511yescharacteristic
289C2#2144776611yescharacteristic
290C2#2144777911yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1333C2
socleC22×C61#447
prime radical#21447854C2
hypercenter#1333D61
hypocenterC61#12360
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

Complements

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

NH ≅ G/Ntype
1. #21458775C2semidirect
2. #21448061C2semidirect
4. #21445304C2semidirect
5. #21443872C2semidirect
6. #21443802C2semidirect
7. C61×#1333C2semidirect
71. D8×C61SD16semidirect
147. #1333D61semidirect
172. C61#12360semidirect
221. D8#11758190semidirect

Maximal subgroups

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

subgroupindex
#214587752
#214480612
#214478542
#214453042
#214438722
#214438022
C61×#13332
#1236061