Finite Group Databasebeta

← #16786555

Subgroups — #16786555

Order 3328.

926 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 172 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
1C2×#11718291C212yesmaximal
2C2×#11718291C212yesmaximal
3#13130499C212yesmaximal
4C22×#88143C211yesmaximal, characteristic
5C22×#6122C2214yes—
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C22×#6101C411yescharacteristic
9C22×#6101C411yescharacteristic
10C22×#6101C2211yescharacteristic
11C22×#6101C2211yescharacteristic
12C22×C4×Dic13C2211yescharacteristic
13C2×#88143—24no—
14C2×#88143—24no—
15C2×#88143—24no—
16#11718291—24no—
17#11718291—24no—
18#11718290—24no—
19C23×C4×C13C2×C411yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2311yescharacteristic
26C2×#6122—24no—
27C2×#6122—24no—
28C2×#6122—24no—
29C2×#6122—24no—
30C2×#6122—24no—
31C2×#6122Q818yes—
32C22×#1057—24no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C4⋊Dic13—22no—
37C2×C4⋊Dic13—22no—
38C2×C4⋊Dic13—22no—
39C2×#6101—22no—
40C2×#6101—22no—
41C2×#6101—22no—
42C2×#6101—22no—
43C2×#6101—22no—
44C2×#6101—22no—
45C2×#6101—22no—
46C2×#6101—22no—
47C2×#6101—22no—
48C2×#6101—22no—
49C2×#6101D414yes—
50C2×#6101D414yes—
51C2×C4×Dic13—22no—
52C2×C4×Dic13—22no—
53C2×C4×Dic13D414yes—
54#88143—232no—
55#11383—131nomaximal, Sylow
56C24×C13C22×C411yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22⋊C412yes—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C22×Dic13C22⋊C412yes—
79C22×Dic13C22⋊C412yes—
80C22×Dic13C22⋊C412yes—
81C22×Dic13C2×D412yes—
82C22×Dic13C2×D412yes—
83C22×Dic13C2×D412yes—
84C22×Dic13C2×Q814yes—
85C22×Dic13#4114yes—
86#6122—28no—
87#6122—28no—
88#6122—44no—
89#6122—44no—
90C2×#1057—28no—
91C2×#1057—44no—
92C2×#1057—44no—
93C13×C4⋊C4—28no—
94C4⋊Dic13—28no—
95#6101—28no—
96#6101—28no—
97#6101—28no—
98#6101—28no—
99C4×Dic13—28no—
100C22×#125—131no—
101C2×#343—132no—
102C2×#343—132no—
103#1728—132no—
104C23×C13—22no—
105C23×C13—22no—
106C23×C13C2×C22⋊C411yescharacteristic
107C23×C13C2×C22⋊C411yescharacteristic
108C23×C13C2×C22⋊C411yescharacteristic
109C23×C13C4×Q814yes—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—24no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×Dic13—22no—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—24no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13#12014yes—
135C2×Dic13C22⋊Q814yes—
136C2×Dic13C22⋊Q814yes—
137C2×Dic13C22⋊Q814yes—
138C2×Dic13#12412yes—
139C2×Dic13#12412yes—
140C2×Dic13#12412yes—
141C2×Dic13C4⋊Q812yes—
142C2×Dic13C4⋊Q812yes—
143C2×Dic13C4⋊Q812yes—
144#1057—48no—
145C22×M16—134no—
146C2×#125—264no—
147C2×#125—264no—
148C2×#125—264no—
149C22×C4⋊C4—131no—
150C22×C4⋊C4—131no—
151C22×C4⋊C4—131no—
152C22×C4⋊C4—131no—
153C22×C4⋊C4—131no—
154C22×C4⋊C4#26111yescharacteristic
155C22×C42—131no—
156#343—264no—
157#343—264no—
158#336—264no—
159C22×C13—28no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#37911yescharacteristic
165C22×C13#39112yes—
166C22×C13#39112yes—
167C22×C13#39112yes—
168C22×C13#41312yes—
169C22×C13#41312yes—
170C4×C13—42no—
171C4×C13—42no—
172C4×C13—42no—
173Dic13—42no—
174Dic13—42no—
175Dic13—42no—
176Dic13#39314yes—
177Dic13#39514yes—
178C23×C4—131no—
179C23×C4—131no—
180C23×C4—131no—
181C23×C4—131no—
182C23×C4C2×#26111yescharacteristic
183C23×C4C2×#26111yescharacteristic
184C23×C4C2×#26111yescharacteristic
185C2×M16—138no—
186C2×M16—264no—
187C2×M16—264no—
188C2×M16—264no—
189C2×M16—264no—
190C2×M16—264no—
191C22×C8—264no—
192#125—2632no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—134no—
197C2×C4⋊C4—134no—
198C2×C4⋊C4—262no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—262no—
203C2×C4⋊C4—262no—
204C2×C4⋊C4—262no—
205C2×C4⋊C4—262no—
206C2×C4⋊C4—262no—
207C2×C4⋊C4—262no—
208C2×C4⋊C4—262no—
209C2×C4⋊C4—262no—
210C2×C4⋊C4—262no—
211C2×C42—134no—
212C2×C42—262no—
213C2×C42—262no—
214C2×C13—22no—
215C2×C13—22no—
216C2×C13#144611yescharacteristic
217C2×C13#178511yescharacteristic
218C2×C13#178511yescharacteristic
219C2×C13#199814yes—
220C24C22×#26111yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—134no—
231C22×C4—134no—
232C22×C4—132no—
233C22×C4—132no—
234C22×C4—132no—
235C22×C4—132no—
236C22×C4—132no—
237C22×C4—132no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—522no—
245C22×C4—522no—
246C22×C4—522no—
247C22×C4C22⋊#26112yes—
248C22×C4C22⋊#26112yes—
249C22×C4C22⋊#26112yes—
250M16—268no—
251M16—268no—
252M16—524no—
253M16—524no—
254C2×C8—268no—
255C2×C8—524no—
256C2×C8—524no—
257C4⋊C4—28no—
258C4⋊C4—268no—
259C4⋊C4—268no—
260C4⋊C4—268no—
261C4⋊C4—268no—
262C4⋊C4—268no—
263C42—268no—
264C13#1138311yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23Q8×#26114yes—
268C23C2×C22⋊#26111yescharacteristic
269C23C2×C22⋊#26111yescharacteristic
270C23C2×C22⋊#26111yescharacteristic
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—134no—
284C2×C4—134no—
285C2×C4—132no—
286C2×C4—134no—
287C2×C4—134no—
288C2×C4—132no—
289C2×C4—132no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—132no—
293C2×C4—262no—
294C2×C4—262no—
295C2×C4—262no—
296C2×C4—264no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4—522no—
304C2×C4—522no—
305C8—528no—
306C22—28no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#1171913212yes—
312C22#1171914812yes—
313C22(C2×#261)⋊Q812yes—
314C22(C2×#261)⋊Q812yes—
315C22(C2×#261)⋊Q812yes—
316C22#1171917111yescharacteristic
317C4—42no—
318C4—42no—
319C4—42no—
320C4—134no—
321C4—134no—
322C4—522no—
323C4—522no—
324C4—522no—
325C2—22no—
326C2—22no—
327C2#1313002611yescharacteristic
328C2#1313067211yescharacteristic
329C2#1313067311yescharacteristic
330C2#1313103014yes—
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11383
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
264. C13#11383semidirect

Maximal subgroups

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

subgroupindex
C2×#117182912
#131304992
C22×#881432
#1138313