Finite Group Databasebeta

← #29593762

Subgroups — #29593762

Order 15616.

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

normal subgroups only

This group has 292 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
2#21448065C211yesmaximal, characteristic, complemented
3#21447864C211yesmaximal, characteristic
4#21445314C211yesmaximal, characteristic, complemented
5#21443872C211yesmaximal, characteristic, complemented
6#21443802C211yesmaximal, characteristic, complemented
7C61×#1333C211yesmaximal, characteristic
8#16840471—21no—
9C2×#14519721—21no—
10#16840170—21no—
11#16840164C2211yescharacteristic
12#16840142C2211yescharacteristic
13#16840062—21no—
14#16840060—21no—
15#16840048—21no—
16#16840040—21no—
17#16839892C2211yescharacteristic
18#16839874—21no—
19C4⋊#11758185C2211yescharacteristic
20#16839567—21no—
21#16839567—21no—
22#16839565—21no—
23#16839507—21no—
24C4×D8×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×Dic244—21no—
28C2×Dic244—21no—
29#14519777—21no—
30#14519776—21no—
31#14519769—21no—
32#14519768—21no—
33#14519756—41no—
34#14519754—41no—
35#14519754—41no—
36C4×Dic122D411yescharacteristic
37D4×Dic61—21no—
38D4×Dic61—21no—
39C2×#11758196—41no—
40#14519721—42no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519709—21no—
46#14519709—41no—
47#14519708—21no—
48C4⋊#92418D411yescharacteristic
49#14519706—21no—
50#14519702—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×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122D811yescharacteristic
68D8×C61—21no—
69D8×C61SD1612yes—
70C2×C8×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C22⋊C4×C61—41no—
75C42×C61C2×D411yescharacteristic
76C22⋊Dic61—41no—
77C22⋊Dic61—41no—
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
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—
91Dic244—42no—
92Dic244—41no—
93Dic244—41no—
94C16×C61—41no—
95#11758185—41no—
96C23×C61—41no—
97D4×C61—22no—
98D4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—161no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—82no—
109C2×Dic61—81no—
110C2×Dic61—161no—
111Dic122—41no—
112Dic122—81no—
113Dic122—81no—
114Dic122—161no—
115C8×C61—21no—
116C8×C61—81no—
117C8×C61C2×SD1611yescharacteristic
118C8×C61#13711yescharacteristic
119#92418—41no—
120#12362—611nomaximal, Sylow
121C22×C61—42no—
122C22×C61—81no—
123C22×C61—81no—
124C22×C61#44711yescharacteristic
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61#44811yescharacteristic
129C4×C61#45411yescharacteristic
130Dic61—41no—
131Dic61—41no—
132Dic61—81no—
133Dic61—81no—
134Dic61—161no—
135#3389—611no—
136#2245—611no—
137#2208—611no—
138#1690—611no—
139#1363—611no—
140#1338—611no—
141#1333D6111yescharacteristic
142C2×C61—82no—
143C2×C61#162711yescharacteristic
144C2×C61#219111yescharacteristic
145C2×C61#219411yescharacteristic
146#554—1221no—
147C2×SD32—1221no—
148#501—1221no—
149#499—611no—
150#494—611no—
151#478—1221no—
152#478—1221no—
153#475—1221no—
154#474—1221no—
155#446—611no—
156#442—1221no—
157C4×D8C2×D6111yescharacteristic
158C4⋊C16—611no—
159#358—1221no—
160#358—1221no—
161#358—1221no—
162#346C2×D6111yescharacteristic
163#334C2×D6111yescharacteristic
164#332—1221no—
165C61#1236211yescharacteristic, complemented, Sylow
166C2×Q16—1221no—
167C2×Q16—1221no—
168C2×D8D24411yescharacteristic
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171#125—1221no—
172#125—1221no—
173C22⋊Q8—2441no—
174C22⋊Q8—2441no—
175C22⋊Q8—2441no—
176C4×Q8—611no—
177C4×D4—21no—
178C4×D4—1221no—
179C4×D4—1221no—
180C2×C4⋊C4—2441no—
181SD32—2442no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—611no—
185#107—611no—
186#107—1221no—
187#107D24411yescharacteristic
188#106—1221no—
189#106—1221no—
190#106—2441no—
191C4⋊C8—21no—
192C4⋊C8—611no—
193C4⋊C8—1221no—
194#103—2441no—
195#102—21no—
196#102—1221no—
197#102—1221no—
198#97—1221no—
199C4×C8C22×D6111yescharacteristic
200C2×Q8—611no—
201C2×Q8—2441no—
202C2×Q8—2441no—
203C2×D4—21no—
204C22×C4—41no—
205C22×C4—2441no—
206C22×C4—2441no—
207Q16—2442no—
208Q16—2441no—
209Q16—2441no—
210D8—21no—
211D8#1175819012yes—
212C2×C8—41no—
213C2×C8—1221no—
214C2×C8C2×D24411yescharacteristic
215C2×C8D4×D6111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—611no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C22⋊C4—41no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—1221no—
232C42D4×D6111yescharacteristic
233C16—41no—
234C16—2441no—
235C23—41no—
236Q8—9761no—
237Q8—4881no—
238Q8—4881no—
239Q8—2441no—
240D4—22no—
241D4—41no—
242C2×C4—41no—
243C2×C4—161no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—9761no—
247C2×C4—4881no—
248C2×C4—4882no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4#1451974711yescharacteristic
252C2×C4D8×D6111yescharacteristic
253C2×C4#1451980411yescharacteristic
254C8—21no—
255C8—81no—
256C8—2441no—
257C8C2×#1175819011yescharacteristic
258C8#1451981011yescharacteristic
259C22—42no—
260C22—81no—
261C22—81no—
262C22#1683989711yescharacteristic
263C4—21no—
264C4—21no—
265C4—81no—
266C4—9761no—
267C4—4881no—
268C4—4881no—
269C4—2441no—
270C4—2441no—
271C4#1683990311yescharacteristic
272C4#1683993611yescharacteristic
273C2—82no—
274C2#2144492511yescharacteristic
275C2#2144777111yescharacteristic
276C2#2144779311yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1333C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#1333D61
hypocenterC61#12362
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
2. #21448065C2semidirect
4. #21445314C2semidirect
5. #21443872C2semidirect
6. #21443802C2semidirect
165. C61#12362semidirect

Maximal subgroups

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

subgroupindex
#214587752
#214480652
#214478642
#214453142
#214438722
#214438022
C61×#13332
#1236261