Finite Group Databasebeta

← #28309569

Subgroups — #28309569

Order 13568.

372 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 74 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#20290582C211yesmaximal, characteristic
2#20289959C211yesmaximal, characteristic
3#20289715C212yesmaximal
4#20289714C212yesmaximal
5#20280078C211yesmaximal, characteristic
6#16811639—21no—
7#16811626—21no—
8C2×#13133278—21no—
9#16811503C2212yes—
10#16811469—21no—
11#16811469C2212yes—
12C2×#13133182C411yescharacteristic
13C2×#13133182C2211yescharacteristic
14#16810561C2211yescharacteristic
15#16810544C2211yescharacteristic
16#16810543C411yescharacteristic
17#16810527—21no—
18#16810520—21no—
19#16810506—21no—
20#16810505—21no—
21#16810487C411yescharacteristic
22C53×#400C411yescharacteristic
23C2×#11719940—22no—
24#13133284—41no—
25C4⋊#88324—41no—
26C4⋊#88324—41no—
27#13133278—42no—
28C22⋊#88324—22no—
29C4×#88324—41no—
30C22×Dic106C2×C411yescharacteristic
31C22×Dic106D411yescharacteristic
32#13133182—41no—
33#13133182—41no—
34#13133182—41no—
35#13133182—41no—
36C2×C4⋊Dic53—21no—
37C2×#11719919—21no—
38C2×#11719919—21no—
39C2×#11719919—21no—
40C2×#11719919D411yescharacteristic
41C2×#11719919C2311yescharacteristic
42C2×C4×Dic53—21no—
43C2×C4×Dic53C2×C411yescharacteristic
44C2×C4×Dic53D411yescharacteristic
45C2×C4×Dic53D411yescharacteristic
46#13133124—21no—
47#13133124—21no—
48#13133124—21no—
49#13133124—21no—
50#13133124—21no—
51#13133124C2×C411yescharacteristic
52C2×C4⋊C4×C53C2×C411yescharacteristic
53C2×C4⋊C4×C53C2×C411yescharacteristic
54#95×C53—21no—
55#95×C53—21no—
56#95×C53C2×C411yescharacteristic
57C22×C4×C53—21no—
58C22×C4×C53—21no—
59C22×C4×C53C22⋊C411yescharacteristic
60C22×C4×C53C22⋊C411yescharacteristic
61C22×C4×C53C22×C411yescharacteristic
62C22×Dic53—21no—
63C22×Dic53—21no—
64C22×Dic53C22⋊C411yescharacteristic
65C22×Dic53C22⋊C411yescharacteristic
66C22×Dic53C2×D411yescharacteristic
67C22×Dic53C2×D411yescharacteristic
68C2×Dic106—41no—
69C2×Dic106—41no—
70C2×Dic106—41no—
71C2×Dic106—42no—
72C2×Dic106SD1612yes—
73C2×Dic106Q1612yes—
74#11719940—42no—
75#11719940—42no—
76C2×#88324—42no—
77C2×#88324—42no—
78C4⋊C4×C53—41no—
79C4⋊C4×C53—41no—
80C4⋊Dic53—42no—
81#11719919—41no—
82#11719919—41no—
83#11719919—42no—
84#11719919—42no—
85#11719919—41no—
86#11719919—41no—
87C4×Dic53—21no—
88C4×Dic53—21no—
89C4×Dic53—21no—
90C4×Dic53—21no—
91C4×Dic53—21no—
92C4×Dic53—21no—
93C4×Dic53—42no—
94C23×C53C2×C22⋊C411yescharacteristic
95C2×C4×C53—21no—
96C2×C4×C53—21no—
97C2×C4×C53—21no—
98C2×C4×C53—21no—
99C2×C4×C53—41no—
100C2×C4×C53—41no—
101C2×C4×C53—41no—
102C2×C4×C53—42no—
103C2×C4×C53—41no—
104C2×C4×C53—41no—
105C2×C4×C53—41no—
106C2×C4×C53#10312yes—
107C2×Dic53—21no—
108C2×Dic53—21no—
109C2×Dic53—21no—
110C2×Dic53—21no—
111C2×Dic53—22no—
112C2×Dic53—21no—
113C2×Dic53—41no—
114C2×Dic53—41no—
115C2×Dic53—41no—
116C2×Dic53—41no—
117C2×Dic53—41no—
118C2×Dic53—41no—
119C2×Dic53—41no—
120C2×Dic53#9911yescharacteristic
121C2×Dic53#9911yescharacteristic
122C2×Dic53#10312yes—
123C2×Dic53C2×SD1611yescharacteristic
124C2×Dic53C2×Q1611yescharacteristic
125Dic106—42no—
126Dic106—42no—
127Dic106—42no—
128Dic106—42no—
129#88324—82no—
130#88324—82no—
131#11905—531nomaximal, Sylow
132C22×C53—21no—
133C22×C53—21no—
134C22×C53C2×#9911yescharacteristic
135C22×C53C2×#10311yescharacteristic
136C22×C53#42111yescharacteristic
137C4×C53—22no—
138C4×C53—41no—
139C4×C53—41no—
140C4×C53—81no—
141C4×C53—81no—
142Dic53—21no—
143Dic53—21no—
144Dic53—21no—
145Dic53—22no—
146Dic53—21no—
147Dic53—41no—
148Dic53—42no—
149Dic53—81no—
150#2581—531no—
151#1801—531no—
152#1461—531no—
153#1354—532no—
154#1353—532no—
155C2×C53—21no—
156C2×C53—21no—
157C2×C53#152011yescharacteristic
158C2×C53#212011yescharacteristic
159C2×C53#213311yescharacteristic
160C2×C4×Q8—531no—
161C2×C4×Q8—531no—
162#431—1061no—
163#423—1061no—
164C2×#101—1061no—
165#400—531no—
166#400#615711yescharacteristic
167#395—531no—
168#395—531no—
169#391—1061no—
170#389—1061no—
171#387—1061no—
172#387—1061no—
173#382—531no—
174#343—532no—
175#324—532no—
176#324—1061no—
177C53#1190511yescharacteristic, complemented, Sylow
178C22×Q8—531no—
179C22×Q8—531no—
180C2×M16—1062no—
181C4×Q8—2121no—
182C4×Q8—2121no—
183C4×Q8—2121no—
184C4×Q8—2121no—
185C2×C4⋊C4—531no—
186C2×C4⋊C4—531no—
187C2×C4⋊C4—1061no—
188C2×C4⋊C4—1061no—
189C2×C4⋊C4—1061no—
190C2×C4⋊C4—1061no—
191C2×C4⋊C4C2×#615711yescharacteristic
192C2×C4⋊C4C2×#615711yescharacteristic
193C2×C42—531no—
194C2×C42—531no—
195C2×C42—531no—
196C2×C42—1061no—
197C4⋊C8—2121no—
198C4⋊C8—2121no—
199C4⋊C8—2121no—
200#101—2122no—
201C22⋊C8—1062no—
202C4×C8—2121no—
203#95—21no—
204#95—21no—
205#95—531no—
206#95—1061no—
207#95—1061no—
208#95—1061no—
209#95—1061no—
210#95—1061no—
211#95C2×#615711yescharacteristic
212C2×Q8—532no—
213C2×Q8—532no—
214C2×Q8—2121no—
215C2×Q8—2121no—
216C2×Q8—2121no—
217C2×Q8—2122no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—531no—
221C22×C4—531no—
222C22×C4—531no—
223C22×C4—531no—
224C22×C4—1061no—
225C22×C4—1061no—
226C22×C4C22⋊#615711yescharacteristic
227C22×C4C22⋊#615711yescharacteristic
228C22×C4C22×#615711yescharacteristic
229M16—2122no—
230M16—2122no—
231C2×C8—2122no—
232C2×C8—2122no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—2121no—
236C4⋊C4—2121no—
237C4⋊C4—2121no—
238C4⋊C4—2121no—
239C4⋊C4—2122no—
240C4⋊C4—2122no—
241C4⋊C4—2122no—
242C42—1061no—
243C42—1061no—
244C42—1061no—
245C42—1061no—
246C42—1061no—
247C42—1061no—
248C42—2122no—
249C23C2×C22⋊#615711yescharacteristic
250Q8—2122no—
251Q8—2122no—
252Q8—2122no—
253Q8—2122no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—531no—
266C2×C4—531no—
267C2×C4—532no—
268C2×C4—531no—
269C2×C4—531no—
270C2×C4—1061no—
271C2×C4—1061no—
272C2×C4—1061no—
273C2×C4—1061no—
274C2×C4—1062no—
275C2×C4—1061no—
276C2×C4—2121no—
277C2×C4—2121no—
278C2×C4—2121no—
279C2×C4—2121no—
280C2×C4—2121no—
281C2×C4—2121no—
282C2×C4—2121no—
283C2×C4#1313328012yes—
284C8—4242no—
285C8—4242no—
286C22—21no—
287C22—21no—
288C22D53⋊#9911yescharacteristic
289C22C2×#1313328011yescharacteristic
290C22#1681162011yescharacteristic
291C4—22no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—1061no—
297C4—1062no—
298C4—1061no—
299C4—1061no—
300C4—1061no—
301C4—4241no—
302C4—2121no—
303C4—2122no—
304C2—21no—
305C2—21no—
306C2#2029015311yescharacteristic
307C2#2029096911yescharacteristic
308C2#2029101111yescharacteristic
subgroupG/H
centerC22D53⋊#99
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC53×#400C4
socleC22×C53C2×#99
prime radicalC23×C53C2×C22⋊C4
cosocleC2×#11719919C23
hypercenter#400#6157
hypocenterC53#11905
LCSG ▷ C22×C4×C53 ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
177. C53#11905semidirect

Maximal subgroups

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

subgroupindex
#202905822
#202899592
#202897152
#202897142
#202800782
#1190553