Finite Group Databasebeta

← #29593741

Subgroups — #29593741

Order 15616.

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

normal subgroups only

This group has 296 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#21458684C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic, complemented
3#21447864C211yesmaximal, characteristic
4#21445190C211yesmaximal, characteristic, complemented
5#21443878C211yesmaximal, characteristic, complemented
6#21443799C211yesmaximal, characteristic, complemented
7C61×#1331C211yesmaximal, characteristic
8#16840469—21no—
9C2×#14519721—21no—
10#16840167C2211yescharacteristic
11#16840163—21no—
12#16840142C2211yescharacteristic
13#16840060—22no—
14#16840052—21no—
15#16840048—21no—
16C8×Dic122C2211yescharacteristic
17D8×Dic61—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839567—22no—
20#16839565—21no—
21#16839507—21no—
22C4×D8×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27#14519777—21no—
28#14519777—21no—
29#14519768—22no—
30#14519756—41no—
31#14519754—42no—
32C4×Dic122D411yescharacteristic
33D4×Dic61—22no—
34C2×C4⋊Dic61—41no—
35#14519721—42no—
36C2×#11758185—21no—
37#14519711—21no—
38#14519711D412yes—
39#14519709—41no—
40#14519708—22no—
41C4⋊#92418D411yescharacteristic
42#14519706—21no—
43#14519702—41no—
44#14519698—22no—
45C8×Dic61—21no—
46C2×D8×C61D411yescharacteristic
47C4×D4×C61—21no—
48C2×C16×C61—21no—
49#107×C61D411yescharacteristic
50C4⋊C8×C61—21no—
51#102×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×D4×C61—21no—
54C22×C4×C61—41no—
55C22×Dic61—42no—
56C2×Dic122—41no—
57C2×Dic122—41no—
58C2×Dic122D811yescharacteristic
59D8×C61—21no—
60D8×C61SD1612yes—
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—21no—
65C22⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67C22⋊Dic61—42no—
68C4⋊Dic61—22no—
69C4⋊Dic61—42no—
70C4⋊Dic61—41no—
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—
81C16×C61—41no—
82#11758185—41no—
83C23×C61—41no—
84D4×C61—22no—
85D4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—81no—
88C2×C4×C61—81no—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—42no—
95C2×Dic61—81no—
96C2×Dic61—162no—
97Dic122—21no—
98Dic122—21no—
99Dic122—81no—
100Dic122—81no—
101Dic122—161no—
102C8×C61—21no—
103C8×C61—81no—
104C8×C61C2×SD1611yescharacteristic
105C8×C61#13711yescharacteristic
106#92418—41no—
107#12359—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—81no—
110C22×C61—81no—
111C22×C61#44711yescharacteristic
112C4×C61—21no—
113C4×C61—81no—
114C4×C61#44811yescharacteristic
115C4×C61#45411yescharacteristic
116C4×C61#50811yescharacteristic
117C4×C61#51011yescharacteristic
118Dic61—41no—
119Dic61—41no—
120Dic61—82no—
121Dic61—161no—
122#3380—611no—
123#2241—611no—
124#2208—611no—
125#1670—611no—
126#1365—611no—
127Q8⋊C16—611no—
128#1331D6111yescharacteristic
129C2×C61—82no—
130C2×C61#162711yescharacteristic
131C2×C61#218911yescharacteristic
132C2×C61#219411yescharacteristic
133#554—1221no—
134C2×SD32—1221no—
135#500—611no—
136#499—1221no—
137#494—611no—
138#478—1222no—
139#476—1221no—
140#475—1221no—
141C8×Q8—611no—
142C4×D8—1221no—
143C4×D8C2×D6111yescharacteristic
144C4⋊C16—611no—
145#358—1222no—
146#358—1221no—
147C4×C16C2×D6111yescharacteristic
148#335C2×D6111yescharacteristic
149#332—1221no—
150C61#1235911yescharacteristic, complemented, Sylow
151C2×Q16—1221no—
152C2×Q16—1221no—
153C2×D8D24411yescharacteristic
154C4⋊Q8—1221no—
155C4⋊Q8—1221no—
156#125—1222no—
157C22⋊Q8—2442no—
158C22⋊Q8—2441no—
159C4×Q8—611no—
160C4×D4—21no—
161C4×D4—1222no—
162C2×C4⋊C4—2441no—
163SD32—2442no—
164C2×C16—21no—
165C2×C16—1221no—
166#107—612no—
167#107—1221no—
168#107D24411yescharacteristic
169#106—1222no—
170#106—2441no—
171C4⋊C8—21no—
172C4⋊C8—611no—
173C4⋊C8—1221no—
174#103—2441no—
175#102—21no—
176#102—1222no—
177C4×C8—1221no—
178C4×C8C22×D6111yescharacteristic
179C2×Q8—611no—
180C2×Q8—2441no—
181C2×Q8—2441no—
182C2×D4—21no—
183C22×C4—41no—
184C22×C4—2442no—
185Q16—2442no—
186Q16—2441no—
187Q16—2441no—
188D8—21no—
189D8#1175819012yes—
190C2×C8—41no—
191C2×C8—1221no—
192C2×C8C2×D24411yescharacteristic
193C2×C8D4×D6111yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—611no—
196C4⋊C4—1221no—
197C4⋊C4—1222no—
198C4⋊C4—2442no—
199C4⋊C4—2442no—
200C4⋊C4—2441no—
201C4⋊C4—2441no—
202C4⋊C4—2441no—
203C22⋊C4—41no—
204C22⋊C4—2442no—
205C42—1221no—
206C42D4×D6111yescharacteristic
207C16—41no—
208C16—2441no—
209C23—41no—
210Q8—1221no—
211Q8—1221no—
212Q8—9761no—
213Q8—4881no—
214Q8—4881no—
215D4—22no—
216D4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—9762no—
223C2×C4—4881no—
224C2×C4—2442no—
225C2×C4#1451974711yescharacteristic
226C2×C4D8×D6111yescharacteristic
227C2×C4#1451980411yescharacteristic
228C8—21no—
229C8—81no—
230C8—2441no—
231C8C2×#1175819011yescharacteristic
232C8#1451981011yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1683989711yescharacteristic
237C4—21no—
238C4—81no—
239C4—9761no—
240C4—4882no—
241C4—2441no—
242C4—2441no—
243C4#1683990311yescharacteristic
244C4#1683993611yescharacteristic
245C4#1684019111yescharacteristic
246C4#1684020111yescharacteristic
247C2—82no—
248C2#2144492511yescharacteristic
249C2#2144776011yescharacteristic
250C2#2144779111yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1331C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#1331D61
hypocenterC61#12359
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #21448047C2semidirect
4. #21445190C2semidirect
5. #21443878C2semidirect
6. #21443799C2semidirect
150. C61#12359semidirect

Maximal subgroups

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

subgroupindex
#214586842
#214480472
#214478642
#214451902
#214438782
#214437992
C61×#13312
#1235961