Finite Group Databasebeta

← #16794780

Subgroups — #16794780

Order 3328.

1178 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 240 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#13131515C212yesmaximal
2#13130369C214yesmaximal, complemented
3#13130350C218yesmaximal, complemented
4C2×D13×C4⋊Q8C211yesmaximal, characteristic
5C22×Q8×D13C412yes—
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×#88198C2212yes—
8D13×C4⋊Q8—22no—
9D13×C4⋊Q8—22no—
10D13×C4⋊Q8C414yes—
11D13×C4⋊Q8C2214yes—
12C2×C4⋊C4×D13—22no—
13C2×#88142—22no—
14C2×C42×D13C2211yescharacteristic
15C2×#88123C411yescharacteristic
16#11719128C2214yes—
17#11719127—22no—
18#11719125—22no—
19#11719055—22no—
20#11719053C2214yes—
21#11719049C2214yes—
22C4×#6118—22no—
23#11718303C22116yescomplemented
24C22×Q8×C13C2×C412yes—
25C2×Q8×D13—24no—
26C2×Q8×D13—48no—
27C2×Q8×D13C2×C418yes—
28C22×C4×D13—22no—
29C22×C4×D13C2×C411yescharacteristic
30C22×C4×D13D412yes—
31C22×Dic26—22no—
32C22×Dic26C2×C412yes—
33C2×#6118—24no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8C2×C414yes—
37C2×C13×C4⋊C4—22no—
38C2×C42×C13C2×C411yescharacteristic
39#88198—24no—
40#88198C2×C414yes—
41#88198C2314yes—
42C2×C4⋊Dic13—22no—
43C2×#6101—24no—
44C2×C4×Dic13D412yes—
45C2×C4×Dic13C2311yescharacteristic
46C4⋊C4×D13—24no—
47C4⋊C4×D13—24no—
48C4⋊C4×D13—24no—
49C4⋊C4×D13—24no—
50#88142—24no—
51#88142—24no—
52#88142—24no—
53#88142—24no—
54C42×D13C2×C412yes—
55C42×D13D412yes—
56C42×D13D412yes—
57C42×D13C2312yes—
58#88123—21no—
59#88123—21no—
60#88123C2×C414yes—
61C22⋊#1057—24no—
62#88112—24no—
63#88112C2318yes—
64#88111—24no—
65#88110—24no—
66C4×#1057—24no—
67#17746—131nomaximal, Sylow
68C23×D13C22⋊C411yescharacteristic
69C2×Q8×C13—22no—
70C2×Q8×C13—44no—
71C2×Q8×C13C22×C414yes—
72C22×C4×C13—22no—
73C22×C4×C13C22⋊C412yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×Dic13—22no—
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C2×D412yes—
78Q8×D13—416no—
79Q8×D13—416no—
80C2×C4×D13—24no—
81C2×C4×D13—28no—
82C2×C4×D13—28no—
83C2×C4×D13—48no—
84C2×C4×D13C22⋊C412yes—
85C2×C4×D13C22⋊C412yes—
86C2×C4×D13C22⋊C412yes—
87C2×C4×D13C22×C412yes—
88C2×C4×D13C2×D412yes—
89C2×C4×D13C2×D412yes—
90C2×Dic26—22no—
91C2×Dic26—28no—
92C2×Dic26—48no—
93C2×Dic26—44no—
94C2×Dic26C22×C414yes—
95C2×#1057—28no—
96#6118—48no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—24no—
99C42×C13C22⋊C411yescharacteristic
100C42×C13C22⋊C411yescharacteristic
101C42×C13C22×C412yes—
102C4⋊Dic13—24no—
103C4⋊Dic13—24no—
104#6101—28no—
105#6101—28no—
106C4×Dic13C22⋊C412yes—
107C4×Dic13C22⋊C412yes—
108C4×Dic13C22×C411yescharacteristic
109C4×Dic13C2×D412yes—
110C4×Dic13C2×D412yes—
111C4×Dic13C2×D412yes—
112C4×Dic13C2411yescharacteristic
113C22×C4⋊Q8—131no—
114#2920—132no—
115#1558—134no—
116#1548—138no—
117C23×C13C2×C22⋊C411yescharacteristic
118C22×D13—22no—
119C22×D13—24no—
120C22×D13C2×C22⋊C412yes—
121Q8×C13—44no—
122Q8×C13—44no—
123C2×C4×C13—22no—
124C2×C4×C13—24no—
125C2×C4×C13—24no—
126C2×C4×C13—44no—
127C2×C4×C13C2×C22⋊C412yes—
128C2×C4×C13C2×C22⋊C411yescharacteristic
129C2×C4×C13C2×C22⋊C412yes—
130C2×C4×C13C23×C411yescharacteristic
131C2×Dic13—24no—
132C2×Dic13—24no—
133C2×Dic13—44no—
134C2×Dic13#10014yes—
135C2×Dic13C2×C22⋊C412yes—
136C2×Dic13C2×C22⋊C412yes—
137C2×Dic13C22×D412yes—
138C4×D13—24no—
139C4×D13—24no—
140C4×D13—24no—
141C4×D13—24no—
142C4×D13—24no—
143C4×D13—416no—
144C4×D13#13718yes—
145Dic26—44no—
146Dic26—416no—
147Dic26—44no—
148#1057—48no—
149C23×Q8—132no—
150C2×C4⋊Q8—132no—
151C2×C4⋊Q8—134no—
152C2×C4⋊Q8—134no—
153C2×C4⋊Q8—131no—
154C2×C4⋊Q8—262no—
155C2×C4⋊Q8—262no—
156C2×C4⋊Q8—262no—
157C2×C4⋊Q8#26111yescharacteristic
158C22×C4⋊C4—262no—
159C22×C42—131no—
160#432—134no—
161#432—262no—
162#431—134no—
163#431—262no—
164#423—134no—
165#407—262no—
166C4×M16—262no—
167#333—1316no—
168C22×C13—22no—
169C22×C13C2×#10012yes—
170C22×C13C22×C22⋊C411yescharacteristic
171C2×D13—28no—
172C2×D13—22no—
173C2×D13—22no—
174C2×D13#41914yes—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—22no—
178C4×C13—44no—
179C4×C13#41914yes—
180Dic13—22no—
181Dic13—44no—
182Dic13C2×#10014yes—
183Dic13C2×#13714yes—
184C22×Q8—138no—
185C22×Q8—132no—
186C22×Q8—262no—
187C22×Q8—264no—
188C22×Q8—528no—
189C22×Q8C2×#26112yes—
190C23×C4—132no—
191C23×C4—131no—
192C23×C4—262no—
193C2×M16—264no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—134no—
197C4⋊Q8—134no—
198C4⋊Q8—134no—
199C4⋊Q8—264no—
200C4⋊Q8—264no—
201C4⋊Q8—264no—
202C4⋊Q8—264no—
203C4⋊Q8—264no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8C2×#26114yes—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—264no—
209C2×C4⋊C4—264no—
210C2×C4⋊C4—264no—
211C2×C4⋊C4—264no—
212C2×C4⋊C4—264no—
213C2×C4⋊C4—262no—
214C2×C42—132no—
215C2×C42—131no—
216C2×C42—132no—
217C2×C42—132no—
218C2×C42—132no—
219C2×C42—132no—
220C2×C42C2×#26111yescharacteristic
221C4⋊C8—138no—
222C4⋊C8—264no—
223C22⋊C8—264no—
224C22⋊C8—264no—
225#97—264no—
226C4×C8—264no—
227C2×C13—22no—
228C2×C13C22×#10011yescharacteristic
229C2×C13C2×#41912yes—
230D13—24no—
231C24—131no—
232C2×Q8—22no—
233C2×Q8—44no—
234C2×Q8—134no—
235C2×Q8—268no—
236C2×Q8—262no—
237C2×Q8—524no—
238C2×Q8—528no—
239C2×Q8—5216no—
240C2×Q8—5216no—
241C2×Q8C22×#26114yes—
242C22×C4—22no—
243C22×C4—131no—
244C22×C4—132no—
245C22×C4—132no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—132no—
249C22×C4—132no—
250C22×C4—132no—
251C22×C4—264no—
252C22×C4—268no—
253C22×C4—268no—
254C22×C4—262no—
255C22×C4—528no—
256C22×C4C22⋊#26112yes—
257C22×C4C22×#26111yescharacteristic
258M16—528no—
259C2×C8—268no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—268no—
263C4⋊C4—268no—
264C4⋊C4—264no—
265C4⋊C4—264no—
266C42—132no—
267C42—132no—
268C42—132no—
269C42—132no—
270C42—132no—
271C42—131no—
272C42—131no—
273C42C22⋊#26111yescharacteristic
274C42C22⋊#26111yescharacteristic
275C42C22×#26112yes—
276C13#1774611yescharacteristic, complemented, Sylow
277C23—132no—
278C23—264no—
279C23—262no—
280C23C2×C22⋊#26111yescharacteristic
281Q8—44no—
282Q8—44no—
283Q8—524no—
284Q8—524no—
285Q8—5216no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—44no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—134no—
293C2×C4—138no—
294C2×C4—132no—
295C2×C4—264no—
296C2×C4—264no—
297C2×C4—264no—
298C2×C4—264no—
299C2×C4—264no—
300C2×C4—264no—
301C2×C4—264no—
302C2×C4—5216no—
303C2×C4—524no—
304C2×C4C2×C22⋊#26111yescharacteristic
305C2×C4C2×C22⋊#26112yes—
306C2×C4C2×C22⋊#26112yes—
307C2×C4C23×#26111yescharacteristic
308C8—528no—
309C22—22no—
310C22—134no—
311C22—268no—
312C22—262no—
313C22—262no—
314C22D13⋊#10012yes—
315C22C22×C22⋊#26111yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—44no—
320C4—134no—
321C4—134no—
322C4—262no—
323C4—524no—
324C4#1171915314yes—
325C2—22no—
326C2—264no—
327C2C2×D13⋊#10011yescharacteristic
328C2C2×#1171915312yes—
subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C4⋊Q8#261
hypocenterC13#17746
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13130369C2semidirect
3. #13130350C2semidirect
23. #11718303C22semidirect
276. C13#17746semidirect

Maximal subgroups

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

subgroupindex
#131315152
#131303692
#131303502
C2×D13×C4⋊Q82
#1774613