Finite Group Databasebeta

← #29593894

Subgroups — #29593894

Order 15616.

288 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 67 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#21458824C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic
3#21447961C211yesmaximal, characteristic
4#21445214C211yesmaximal, characteristic
5#21443867C211yesmaximal, characteristic
6#21443799C211yesmaximal, characteristic
7C61×#1332C211yesmaximal, characteristic
8#16840490—21no—
9#16840167C2211yescharacteristic
10#16840142C2211yescharacteristic
11#16840140—21no—
12#16839973—21no—
13#16839972—21no—
14#16839971—22no—
15C8×Dic122C2211yescharacteristic
16#16839856—21no—
17#16839589—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839567—22no—
20#16839566—21no—
21#16839509—21no—
22C4×Q16×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—41no—
27C2×Dic244D412yes—
28C2×#11758202—22no—
29#14519777—21no—
30#14519777—21no—
31#14519775—22no—
32#14519769—41no—
33#14519767—42no—
34C4×Dic122—41no—
35C4×Dic122D411yescharacteristic
36#14519742—22no—
37C2×#11758185—21no—
38#14519711—21no—
39#14519711—21no—
40C4⋊#92418D411yescharacteristic
41#14519706—21no—
42#14519702—41no—
43#14519700—22no—
44C8×Dic61—21no—
45C2×Q16×C61D411yescharacteristic
46C4×Q8×C61—21no—
47C2×C16×C61—21no—
48#107×C61D411yescharacteristic
49C4⋊C8×C61—21no—
50#103×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—21no—
53C2×Dic122—22no—
54C2×Dic122—41no—
55C2×Dic122D811yescharacteristic
56Q16×C61—21no—
57Q16×C61—21no—
58C2×C8×C61—41no—
59C2×C8×C61C2×D411yescharacteristic
60C2×C8×C61C2×D411yescharacteristic
61C4⋊C4×C61—21no—
62C4⋊C4×C61—41no—
63C42×C61—41no—
64C42×C61C2×D411yescharacteristic
65#11758202—82no—
66C4⋊Dic61—41no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61D811yescharacteristic
71#11758196—21no—
72#11758196—42no—
73#11758196—42no—
74#11758196—42no—
75C4×Dic61—21no—
76C4×Dic61—42no—
77C2×#92418—21no—
78Dic244—42no—
79Dic244—41no—
80Dic244—41no—
81Dic244—82no—
82C16×C61—41no—
83#11758185—41no—
84Q8×C61—41no—
85Q8×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61#12011yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—42no—
94C2×Dic61—81no—
95Dic122—21no—
96Dic122—42no—
97Dic122—42no—
98Dic122—81no—
99Dic122—81no—
100Dic122SD3212yes—
101C8×C61—21no—
102C8×C61—81no—
103C8×C61#13511yescharacteristic
104C8×C61#13711yescharacteristic
105#92418—41no—
106#12382—611nomaximal, Sylow
107C22×C61#44711yescharacteristic
108C4×C61—21no—
109C4×C61—81no—
110C4×C61—81no—
111C4×C61#45211yescharacteristic
112C4×C61#45511yescharacteristic
113C4×C61C2×SD3211yescharacteristic
114C4×C61#51011yescharacteristic
115Dic61—22no—
116Dic61—41no—
117Dic61—82no—
118Dic61—161no—
119#3395—611no—
120#2241—611no—
121#2225—611no—
122#1674—611no—
123#1362—611no—
124Q8⋊C16—611no—
125#1332D6111yescharacteristic
126C2×C61#164111yescharacteristic
127C2×C61#218511yescharacteristic
128C2×C61#219511yescharacteristic
129#557—1221no—
130#500—611no—
131#494—611no—
132#494—1221no—
133#462—1222no—
134#462—1221no—
135#462—1221no—
136C8×Q8—611no—
137C4×Q16—1221no—
138C4×Q16C2×D6111yescharacteristic
139#367—1221no—
140C4⋊C16—611no—
141#358—1222no—
142#358—1221no—
143C4×C16C2×D6111yescharacteristic
144#335C2×D6111yescharacteristic
145#332—1221no—
146C61#1238211yescharacteristic, complemented, Sylow
147C2×Q16—612no—
148C2×Q16—1222no—
149C2×Q16—1221no—
150C2×Q16—2441no—
151C2×Q16D24411yescharacteristic
152C4⋊Q8—1222no—
153C4⋊Q8—1221no—
154C4⋊Q8—1221no—
155#125—2441no—
156#125—2442no—
157C4×Q8—21no—
158C4×Q8—611no—
159C4×Q8—1222no—
160C4×Q8—2441no—
161C2×C16—21no—
162C2×C16—1221no—
163#107—1221no—
164#107—1221no—
165#107D24411yescharacteristic
166C4⋊C8—21no—
167C4⋊C8—611no—
168C4⋊C8—1221no—
169#103—21no—
170#103—1222no—
171#103—2441no—
172C4×C8—1221no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—21no—
175C2×Q8—611no—
176C2×Q8—1222no—
177C2×Q8—2441no—
178Q16—21no—
179Q16—21no—
180Q16—4882no—
181Q16—4882no—
182Q16—2442no—
183Q16—2441no—
184Q16—2441no—
185C2×C8—41no—
186C2×C8—1221no—
187C2×C8C2×D24411yescharacteristic
188C2×C8D4×D6111yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—611no—
192C4⋊C4—1221no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C4⋊C4—2441no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C4⋊C4—2441no—
200C42—41no—
201C42—1221no—
202C42—2442no—
203C42D4×D6111yescharacteristic
204C16—41no—
205C16—2441no—
206Q8—41no—
207Q8—41no—
208Q8—612no—
209Q8—1221no—
210Q8—4881no—
211Q8—4881no—
212Q8—2442no—
213Q8—2442no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—4881no—
219C2×C4—2442no—
220C2×C4#1451974711yescharacteristic
221C2×C4D8×D6111yescharacteristic
222C2×C4#1451980411yescharacteristic
223C8—21no—
224C8—81no—
225C8—2441no—
226C8#1451979911yescharacteristic
227C8#1451981011yescharacteristic
228C22#1683989711yescharacteristic
229C4—21no—
230C4—81no—
231C4—81no—
232C4—1222no—
233C4—9761no—
234C4—4882no—
235C4—2441no—
236C4#1683992611yescharacteristic
237C4#1683994111yescharacteristic
238C4SD32×D6111yescharacteristic
239C4#1684020411yescharacteristic
240C2#2144501511yescharacteristic
241C2#2144773711yescharacteristic
242C2#2144779811yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1332C2
socle, prime radicalC22×C61#447
hypercenter#1332D61
hypocenterC61#12382
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
146. C61#12382semidirect

Maximal subgroups

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

subgroupindex
#214588242
#214480472
#214479612
#214452142
#214438672
#214437992
C61×#13322
#1238261