Finite Group Databasebeta

← #29593718

Subgroups — #29593718

Order 15616.

322 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 69 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#21458671C211yesmaximal, characteristic
2#21448048C211yesmaximal, characteristic, complemented
3#21447865C211yesmaximal, characteristic
4#21445190C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic
7C61×#1364C211yesmaximal, characteristic, complemented
8#16840427—21no—
9C2×#14519722—21no—
10#16840166—21no—
11#16840142C2211yescharacteristic
12#16840048—21no—
13#16840041—22no—
14#16840039—21no—
15C8×Dic122C2211yescharacteristic
16C4×D488C2211yescharacteristic
17#16839844—21no—
18#16839567—21no—
19#16839565—22no—
20C4×#11758185C2211yescharacteristic
21#16839507—21no—
22C61×#500C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Q8×D61—41no—
26C2×Dic244—21no—
27C2×Dic244—21no—
28C2×D488D411yescharacteristic
29#14519777—21no—
30#14519776—22no—
31#14519755—42no—
32#14519753—41no—
33C4×Dic122D411yescharacteristic
34C4×D244—21no—
35#14519739—22no—
36#14519722—42no—
37C2×#11758185—21no—
38#14519711D411yescharacteristic
39#14519710—22no—
40#14519709—41no—
41C4⋊#92418D411yescharacteristic
42#14519706—21no—
43#14519702—41no—
44#14519699—21no—
45#14519697—22no—
46C8×Dic61—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—
54Q8×D61—82no—
55Q8×D61—82no—
56C2×D244—21no—
57C2×C4×D61—42no—
58C2×C4×D61—41no—
59C2×Dic122—42no—
60C2×Dic122—41no—
61C2×Dic122D811yescharacteristic
62C2×C8×C61—41no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C4⋊C4×C61—22no—
66C4⋊C4×C61—41no—
67C42×C61C2×D411yescharacteristic
68#11758198—42no—
69#11758198—41no—
70C4⋊Dic61—21no—
71C4⋊Dic61—41no—
72C4⋊Dic61—41no—
73C4⋊Dic61D811yescharacteristic
74#11758196—21no—
75#11758196—42no—
76C4×Dic61—21no—
77C2×#92418—21no—
78Dic244—42no—
79Dic244—41no—
80Dic244—41no—
81D488—21no—
82D488SD1612yes—
83C16×C61—41no—
84#11758185—41no—
85C22×D61—41no—
86Q8×C61—81no—
87Q8×C61—81no—
88C2×C4×C61—42no—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—41no—
95C2×Dic61—81no—
96D244—22no—
97D244—41no—
98C4×D61—84no—
99C4×D61—81no—
100C4×D61—81no—
101Dic122—21no—
102Dic122—84no—
103Dic122—81no—
104Dic122—81no—
105Dic122SD3212yescomplemented
106C8×C61—21no—
107C8×C61—81no—
108C8×C61C2×SD1611yescharacteristic
109C8×C61#13711yescharacteristic
110#92418—41no—
111#12356—611nomaximal, Sylow
112C22×C61#44711yescharacteristic
113C2×D61—42no—
114C2×D61—81no—
115C2×D61—81no—
116C4×C61—21no—
117C4×C61—82no—
118C4×C61#44811yescharacteristic
119C4×C61#45411yescharacteristic
120C4×C61C2×SD3211yescharacteristic
121C4×C61#50911yescharacteristic
122Dic61—22no—
123Dic61—41no—
124Dic61—81no—
125Dic61—161no—
126Q8×D8—611no—
127#2241—611no—
128#2208—611no—
129#1670—611no—
130#1364D6111yescharacteristic, complemented
131Q8⋊C16—611no—
132#1331—611no—
133C2×C61#162711yescharacteristic
134C2×C61#218711yescharacteristic
135C2×C61#219511yescharacteristic
136D61—82no—
137D4×Q8—1221no—
138C2×SD32—1221no—
139#500—1221no—
140#500C2×D6111yescharacteristic
141#494—611no—
142#475—1221no—
143#474—1221no—
144#474—1222no—
145C8×Q8—611no—
146C4×D8—611no—
147C4×D8—1221no—
148C4⋊C16C2×D6111yescharacteristic
149#358—1221no—
150#358—1222no—
151C4×C16—611no—
152#335C2×D6111yescharacteristic
153#332—1221no—
154C61#1235611yescharacteristic, complemented, Sylow
155C22×Q8—2441no—
156C2×Q16—1221no—
157C2×Q16—1221no—
158C2×D8—611no—
159C4⋊Q8—21no—
160C4⋊Q8—1222no—
161C4⋊Q8—1221no—
162C22⋊Q8—2442no—
163C22⋊Q8—2441no—
164C4×Q8—611no—
165C4×D4—1222no—
166C4×D4—1221no—
167SD32—2442no—
168C2×C16—21no—
169C2×C16—1221no—
170#107—21no—
171#107—611no—
172#107—1222no—
173#107D24412yes—
174#106—2441no—
175C4⋊C8—21no—
176C4⋊C8—611no—
177C4⋊C8—1221no—
178#103—2441no—
179#102—1222no—
180#102—1221no—
181C4×C8—1221no—
182C4×C8C22×D6111yescharacteristic
183C2×Q8—41no—
184C2×Q8—611no—
185C2×Q8—4882no—
186C2×Q8—4882no—
187C2×Q8—2442no—
188C2×Q8—2441no—
189C2×D4—1221no—
190C22×C4—2442no—
191C22×C4—2441no—
192Q16—2442no—
193Q16—2441no—
194Q16—2441no—
195D8—612no—
196D8—1221no—
197C2×C8—41no—
198C2×C8—1221no—
199C2×C8C2×D24411yescharacteristic
200C2×C8D4×D6111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—611no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—2442no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C22⋊C4—2442no—
210C22⋊C4—2441no—
211C42—1221no—
212C42D4×D6111yescharacteristic
213C16—41no—
214C16—2441no—
215C23—2441no—
216Q8—81no—
217Q8—81no—
218Q8—612no—
219Q8—1221no—
220Q8—4884no—
221Q8—4881no—
222Q8—4881no—
223D4—1222no—
224D4—2441no—
225C2×C4—42no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—4884no—
229C2×C4—4881no—
230C2×C4—4881no—
231C2×C4—4881no—
232C2×C4—2441no—
233C2×C4#1451974711yescharacteristic
234C2×C4D8×D6111yescharacteristic
235C2×C4#1451980411yescharacteristic
236C8—21no—
237C8—81no—
238C8—2441no—
239C8SD16×D6111yescharacteristic
240C8#1451980911yescharacteristic
241C22—4881no—
242C22—4881no—
243C22—2442no—
244C22#1683989711yescharacteristic
245C4—21no—
246C4—82no—
247C4—1222no—
248C4—9761no—
249C4—4881no—
250C4—2441no—
251C4#1683990211yescharacteristic
252C4#1683993711yescharacteristic
253C4SD32×D6111yescharacteristic
254C4#1684019611yescharacteristic
255C2—4882no—
256C2#2144492311yescharacteristic
257C2#2144774911yescharacteristic
258C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#1364D61
hypocenterC61#12356
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
2. #21448048C2semidirect
4. #21445190C2semidirect
5. #21443797C2semidirect
7. C61×#1364C2semidirect
105. Dic122SD32semidirect
130. #1364D61semidirect
154. C61#12356semidirect

Maximal subgroups

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

subgroupindex
#214586712
#214480482
#214478652
#214451902
#214437972
#214437792
C61×#13642
#1235661