Finite Group Databasebeta

← #28308648

Subgroups — #28308648

Order 13568.

292 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 86 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#20291078C211yesmaximal, characteristic
2#20291075C211yesmaximal, characteristic
3#20289684C212yesmaximal, complemented
4#20289683C212yesmaximal, complemented
5#20283644C211yesmaximal, characteristic
6#16811544—21no—
7C4⋊#11719910C2212yes—
8#16811518—21no—
9#16811518—21no—
10#16811511C2212yes—
11#16811509—21no—
12#16811177C411yescharacteristic
13#16810754C2211yescharacteristic
14#16810752—21no—
15#16810750C2211yescharacteristic
16C8×Dic106—21no—
17C8×Dic106C411yescharacteristic
18#16810648—21no—
19#16810645C411yescharacteristic
20#16810577—21no—
21C4×C8×D53C2211yescharacteristic
22C8×Q8×C53C411yescharacteristic
23C2×#11719910—22no—
24C2×#11719910—22no—
25C2×#11719912—21no—
26C2×C8×D53D411yescharacteristic
27C2×C8×D53D411yescharacteristic
28#13133216C811yescharacteristic
29#13133215C811yescharacteristic
30#13133207—21no—
31#13133197C811yescharacteristic
32#13133195—21no—
33#13133193C811yescharacteristic
34C4×Dic106—21no—
35C4×Dic106C2×C411yescharacteristic
36#13133174—21no—
37C42×D53C2×C411yescharacteristic
38C4⋊#88322—21no—
39C4⋊#88322C2×C411yescharacteristic
40#13133146—21no—
41#13133146—21no—
42#13133146—21no—
43#13133128—21no—
44#13133127—21no—
45C4×#88322C2311yescharacteristic
46C8×Dic53—21no—
47C8×Dic53D411yescharacteristic
48C8×Dic53D411yescharacteristic
49C4×Q8×C53C2×C411yescharacteristic
50C4⋊C8×C53—21no—
51C4⋊C8×C53C2×C411yescharacteristic
52C4×C8×C53—21no—
53C4×C8×C53C2×C411yescharacteristic
54C2×Q8×C53C2×C811yescharacteristic
55C2×C4×D53C22⋊C411yescharacteristic
56C2×C4×D53C2×C811yescharacteristic
57C2×C4×D53M1611yescharacteristic
58C2×Dic106—21no—
59C2×Dic106C2×C811yescharacteristic
60C2×C8×C53—21no—
61C2×C8×C53C22⋊C411yescharacteristic
62C2×C8×C53C22⋊C411yescharacteristic
63C4⋊C4×C53—21no—
64C4⋊C4×C53C2×C811yescharacteristic
65C42×C53—21no—
66C42×C53C22×C411yescharacteristic
67#11719921—21no—
68#11719921—21no—
69C4⋊Dic53—21no—
70C4⋊Dic53C2×C811yescharacteristic
71#11719919—21no—
72#11719919—21no—
73#11719919—21no—
74#11719919—21no—
75#11719919—21no—
76C4×Dic53—21no—
77C4×Dic53C22⋊C411yescharacteristic
78C4×Dic53C2×C811yescharacteristic
79C4×Dic53M1611yescharacteristic
80C2×#88322—21no—
81C2×#88322C2×D411yescharacteristic
82C2×#88322C2×D411yescharacteristic
83#11719912—42no—
84C8×D53—22no—
85C8×D53—41no—
86#11719910—42no—
87#11719910—42no—
88C22×D53C22⋊C811yescharacteristic
89Q8×C53—41no—
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53C2×C22⋊C411yescharacteristic
93C2×C4×C53C22×C811yescharacteristic
94C2×C4×C53C2×M1611yescharacteristic
95C2×Dic53—21no—
96C2×Dic53—21no—
97C2×Dic53C22⋊C811yescharacteristic
98C2×Dic53C22⋊C811yescharacteristic
99C2×Dic53C22⋊C811yescharacteristic
100C4×D53—21no—
101C4×D53—21no—
102C4×D53—22no—
103C4×D53—41no—
104Dic106—42no—
105Dic106—41no—
106C8×C53—21no—
107C8×C53—21no—
108C8×C53—41no—
109#88322—21no—
110#88322—41no—
111#88322#13712yes—
112#11641—531nomaximal, Sylow
113C22×C53C2×C22⋊C811yescharacteristic
114C2×D53—21no—
115C2×D53—21no—
116C2×D53—21no—
117C4×C53—21no—
118C4×C53—21no—
119C4×C53—41no—
120C4×C53—41no—
121C4×C53#41911yescharacteristic
122C4×C53#42111yescharacteristic
123Dic53—21no—
124Dic53—21no—
125Dic53—41no—
126Dic53—41no—
127Dic53#35012yes—
128#2960—531no—
129#2163—531no—
130#2162—531no—
131#1338—532no—
132#1338—532no—
133C2×C53#147911yescharacteristic
134C2×C53#211511yescharacteristic
135C2×C53C2×#35011yescharacteristic
136D53—41no—
137#533—531no—
138#446—531no—
139#446—531no—
140#446—1061no—
141C8×Q8—531no—
142C8×Q8—1061no—
143C8×Q8#615711yescharacteristic
144#424—1061no—
145#423—531no—
146#405—1061no—
147C2×C4×C8—531no—
148C4⋊C16—532no—
149C4⋊C16—1061no—
150C22⋊C16—1061no—
151C22⋊C16—1061no—
152#346—532no—
153C4×C16—1061no—
154C53#1164111yescharacteristic, complemented, Sylow
155C2×M16—1061no—
156C22×C8—531no—
157C22×C8—531no—
158C4⋊Q8—531no—
159C4⋊Q8—531no—
160#125—1061no—
161C22⋊Q8—531no—
162C22⋊Q8—531no—
163C22⋊Q8—1061no—
164C4×Q8—531no—
165C4×Q8—1061no—
166C4×Q8C2×#615711yescharacteristic
167#117—1061no—
168C2×C42—531no—
169C2×C16—1062no—
170C2×C16—1062no—
171C4⋊C8—21no—
172C4⋊C8—531no—
173C4⋊C8—1061no—
174C4⋊C8—1061no—
175C4⋊C8—1061no—
176C4⋊C8—1061no—
177C4⋊C8C2×#615711yescharacteristic
178#97—1061no—
179#97—1061no—
180C4×C8—21no—
181C4×C8—531no—
182C4×C8—531no—
183C4×C8—531no—
184C4×C8—1061no—
185C4×C8C2×#615711yescharacteristic
186C2×Q8—531no—
187C2×Q8—1061no—
188C2×Q8D53⋊C811yescharacteristic
189C22×C4—531no—
190C22×C4—531no—
191C22×C4—531no—
192M16—2122no—
193C2×C8—21no—
194C2×C8—531no—
195C2×C8—531no—
196C2×C8—1062no—
197C2×C8—1061no—
198C2×C8—2121no—
199C2×C8C22⋊#615711yescharacteristic
200C2×C8C22⋊#615711yescharacteristic
201C4⋊C4—21no—
202C4⋊C4—531no—
203C4⋊C4—1061no—
204C4⋊C4—1061no—
205C4⋊C4—1061no—
206C4⋊C4—1061no—
207C4⋊C4—1061no—
208C4⋊C4—1061no—
209C4⋊C4D53⋊C811yescharacteristic
210C22⋊C4—1061no—
211C22⋊C4—1061no—
212C42—21no—
213C42—531no—
214C42—531no—
215C42—531no—
216C42—1061no—
217C42C22×#615711yescharacteristic
218C16—2122no—
219C16—2122no—
220C23—531no—
221Q8—41no—
222Q8—2121no—
223Q8—2122no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—531no—
227C2×C4—531no—
228C2×C4—531no—
229C2×C4—1062no—
230C2×C4—1061no—
231C2×C4—1061no—
232C2×C4—1061no—
233C2×C4—1061no—
234C2×C4—2121no—
235C2×C4C2×C22⋊#615711yescharacteristic
236C2×C4C2×D53⋊C811yescharacteristic
237C2×C4D53⋊M1611yescharacteristic
238C8—21no—
239C8—21no—
240C8—41no—
241C8—532no—
242C8—1061no—
243C8—2121no—
244C22—1061no—
245C22—1061no—
246C22—1061no—
247C22D53⋊(C22⋊C8)11yescharacteristic
248C4—21no—
249C4—21no—
250C4—41no—
251C4—41no—
252C4—532no—
253C4—1061no—
254C4—1061no—
255C4—2121no—
256C4—2121no—
257C4#1681161611yescharacteristic
258C4#1681162011yescharacteristic
259C2—2121no—
260C2#2029001811yescharacteristic
261C2#2029095211yescharacteristic
262C2D53⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6157
commutatorC2×C4×C53C22×C8
FrattiniC42C22×#6157
FittingC8×Q8×C53C4
socleC22×C53C2×C22⋊C8
prime radicalC22×D53C22⋊C8
cosocleC4×#88322C23
hypercenterC8×Q8#6157
hypocenterC53#11641
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
3. #20289684C2semidirect
4. #20289683C2semidirect
154. C53#11641semidirect

Maximal subgroups

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

subgroupindex
#202910782
#202910752
#202896842
#202896832
#202836442
#1164153