Finite Group Databasebeta

← #28308148

Subgroups — #28308148

Order 13568.

292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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#20291077C211yesmaximal, characteristic
2#20291073C211yesmaximal, characteristic
3#20289654C212yesmaximal
4#20289653C212yesmaximal
5#20283647C211yesmaximal, characteristic
6#16811544—21no—
7#16811544—21no—
8C22⋊#11719910C2212yes—
9C22⋊#11719910C2212yes—
10#16811512—21no—
11#16811509—21no—
12#16811176C411yescharacteristic
13#16810751—21no—
14#16810751—21no—
15C8×Dic106—21no—
16C8×Dic106—21no—
17#16810651C2211yescharacteristic
18#16810650C2211yescharacteristic
19#16810646C411yescharacteristic
20#16810578C411yescharacteristic
21C2×C8×Dic53C2211yescharacteristic
22C53×#405C411yescharacteristic
23C2×#11719910—22no—
24C2×#11719910—22no—
25C2×#11719917C2×C411yescharacteristic
26C22×#88322C2311yescharacteristic
27#13133216C811yescharacteristic
28#13133216C811yescharacteristic
29#13133208C811yescharacteristic
30#13133208C811yescharacteristic
31#13133194—21no—
32#13133194—21no—
33C4×Dic106—21no—
34C4×Dic106—21no—
35#13133176C2×C411yescharacteristic
36C2×C4×Dic53C2×C411yescharacteristic
37C4⋊#88322—21no—
38C4⋊#88322—21no—
39#13133146—21no—
40#13133146—21no—
41#13133146—21no—
42#13133146—21no—
43#13133127—21no—
44C8×Dic53—21no—
45C8×Dic53D411yescharacteristic
46C8×Dic53D411yescharacteristic
47C8×Dic53D411yescharacteristic
48C8×Dic53D411yescharacteristic
49C2×M16×C53C2×C411yescharacteristic
50C22×C8×C53C2×C411yescharacteristic
51#117×C53C2×C411yescharacteristic
52#97×C53—21no—
53C4×C8×C53—21no—
54C22×C4×C53C22×C411yescharacteristic
55C22×Dic53M1611yescharacteristic
56C22×Dic53M1611yescharacteristic
57C2×Dic106—21no—
58C2×Dic106—21no—
59M16×C53—41no—
60C2×C8×C53—22no—
61C2×C8×C53—21no—
62C2×C8×C53C22⋊C411yescharacteristic
63C2×C8×C53C22⋊C411yescharacteristic
64C4⋊C4×C53C2×C811yescharacteristic
65C4⋊C4×C53C2×C811yescharacteristic
66C22⋊C4×C53—21no—
67C42×C53—21no—
68C22⋊Dic53—21no—
69C4⋊Dic53—21no—
70C4⋊Dic53—21no—
71C4⋊Dic53C2×C811yescharacteristic
72C4⋊Dic53C2×C811yescharacteristic
73#11719919—21no—
74#11719919—21no—
75#11719919—21no—
76#11719919—21no—
77C4×Dic53—21no—
78C4×Dic53C22⋊C411yescharacteristic
79C4×Dic53C22⋊C411yescharacteristic
80C4×Dic53C2×C811yescharacteristic
81C4×Dic53C2×C811yescharacteristic
82#11719917—41no—
83C2×#88322—21no—
84C2×#88322—41no—
85C2×#88322C2×D411yescharacteristic
86C2×#88322C2×D411yescharacteristic
87#11719910—42no—
88#11719910—42no—
89C23×C53C2×M1611yescharacteristic
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53—21no—
93C2×C4×C53—21no—
94C2×C4×C53C2×C22⋊C411yescharacteristic
95C2×C4×C53C22×C811yescharacteristic
96C2×Dic53—22no—
97C2×Dic53—21no—
98C2×Dic53—21no—
99C2×Dic53—41no—
100C2×Dic53C22⋊C811yescharacteristic
101C2×Dic53C22⋊C811yescharacteristic
102C2×Dic53C22⋊C811yescharacteristic
103C2×Dic53C22⋊C811yescharacteristic
104Dic106—42no—
105Dic106—42no—
106C8×C53—21no—
107C8×C53—41no—
108C8×C53#10112yes—
109#88322—21no—
110#88322—21no—
111#88322—41no—
112#11498—531nomaximal, Sylow
113C22×C53—21no—
114C22×C53—21no—
115C22×C53—21no—
116C22×C53C2×C22⋊C811yescharacteristic
117C4×C53—21no—
118C4×C53—41no—
119C4×C53—41no—
120C4×C53#41011yescharacteristic
121C4×C53C2×#10111yescharacteristic
122Dic53—21no—
123Dic53—21no—
124Dic53—21no—
125Dic53—41no—
126Dic53—41no—
127Dic53#35012yes—
128#2960—531no—
129#2163—531no—
130#2162—531no—
131#1323—532no—
132#1323—532no—
133C2×C53—41no—
134C2×C53#146111yescharacteristic
135C2×C53C2×#35011yescharacteristic
136C2×C53#211711yescharacteristic
137#533—531no—
138#446—1061no—
139#446—1061no—
140C8×Q8—1061no—
141C8×Q8—1061no—
142#424—531no—
143#424—531no—
144#423—531no—
145#405—531no—
146#405#615711yescharacteristic
147C2×C4×C8—531no—
148C4⋊C16—1061no—
149C4⋊C16—1061no—
150C22⋊C16—532no—
151C22⋊C16—532no—
152#346—1061no—
153C4×C16—1061no—
154C53#1149811yescharacteristic, complemented, Sylow
155C2×M16—531no—
156C2×M16C2×#615711yescharacteristic
157C22×C8—531no—
158C22×C8C2×#615711yescharacteristic
159C4⋊Q8—531no—
160C4⋊Q8—531no—
161#125—531no—
162#125—531no—
163C22⋊Q8—1061no—
164C22⋊Q8—1061no—
165C4×Q8—1061no—
166C4×Q8—1061no—
167#117—531no—
168#117C2×#615711yescharacteristic
169C2×C42—531no—
170C2×C16—1062no—
171C2×C16—1062no—
172C4⋊C8—1061no—
173C4⋊C8—1061no—
174C4⋊C8—1061no—
175C4⋊C8—1061no—
176C4⋊C8—1061no—
177C4⋊C8—1061no—
178#97—21no—
179#97—1061no—
180C4×C8—21no—
181C4×C8—531no—
182C4×C8—531no—
183C4×C8—531no—
184C4×C8—531no—
185C4×C8—1061no—
186C2×Q8—1061no—
187C2×Q8—1061no—
188C22×C4—531no—
189C22×C4—531no—
190C22×C4C22×#615711yescharacteristic
191M16—41no—
192M16—2121no—
193C2×C8—22no—
194C2×C8—21no—
195C2×C8—531no—
196C2×C8—531no—
197C2×C8—1061no—
198C2×C8—2121no—
199C2×C8C22⋊#615711yescharacteristic
200C2×C8C22⋊#615711yescharacteristic
201C4⋊C4—531no—
202C4⋊C4—531no—
203C4⋊C4—1061no—
204C4⋊C4—1061no—
205C4⋊C4—1061no—
206C4⋊C4—1061no—
207C4⋊C4—1061no—
208C4⋊C4—1061no—
209C4⋊C4D53⋊C811yescharacteristic
210C4⋊C4D53⋊C811yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—1061no—
213C42—21no—
214C42—531no—
215C42—531no—
216C42—531no—
217C42—531no—
218C42—1061no—
219C16—2122no—
220C16—2122no—
221C23D53⋊M1611yescharacteristic
222Q8—2122no—
223Q8—2122no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—531no—
229C2×C4—531no—
230C2×C4—531no—
231C2×C4—531no—
232C2×C4—1062no—
233C2×C4—1061no—
234C2×C4—1061no—
235C2×C4—2121no—
236C2×C4C2×C22⋊#615711yescharacteristic
237C2×C4C2×D53⋊C811yescharacteristic
238C8—21no—
239C8—41no—
240C8—1061no—
241C8—1061no—
242C8—2121no—
243C8#1313327812yes—
244C22—21no—
245C22—21no—
246C22—21no—
247C22D53⋊(C22⋊C8)11yescharacteristic
248C4—21no—
249C4—41no—
250C4—41no—
251C4—532no—
252C4—1061no—
253C4—1061no—
254C4—1061no—
255C4—2121no—
256C4—2121no—
257C4#1681160211yescharacteristic
258C4C2×#1313327811yescharacteristic
259C2—41no—
260C2#2028995711yescharacteristic
261C2D53⋊#35011yescharacteristic
262C2#2029095811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6157
commutatorC2×C4×C53C22×C8
FrattiniC22×C4C22×#6157
FittingC53×#405C4
socleC22×C53C2×C22⋊C8
prime radicalC23×C53C2×M16
cosocleC22×#88322C23
hypercenter#405#6157
hypocenterC53#11498
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
154. C53#11498semidirect

Maximal subgroups

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

subgroupindex
#202910772
#202910732
#202896542
#202896532
#202836472
#1149853