Finite Group Databasebeta

← #16785088

Subgroups — #16785088

Order 3328.

600 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 122 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#13130692C211yesmaximal, characteristic
2#13130562C211yesmaximal, characteristic
3#13129674C214yesmaximal
4C2×#11718634C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×#6101C412yes—
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057C2212yes—
10C2×C22⋊#1057C2212yes—
11C2×#88112—21no—
12C2×#88110—21no—
13C2×#88071C2212yes—
14#11718634—21no—
15#11718634—21no—
16#11718634—21no—
17#11718634—21no—
18#11718290—21no—
19#11718290—21no—
20C23×C4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C412yes—
24C23×Dic13C2311yescharacteristic
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—42no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—24no—
33C2×#6101—22no—
34C2×#6101—22no—
35C2×#6101—44no—
36C2×C4×Dic13—42no—
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C22⋊#1057—22no—
42C22⋊#1057—24no—
43C22⋊#1057Q814yes—
44#88112—42no—
45#88110—42no—
46#88071—22no—
47#88071—22no—
48#9883—131nomaximal, Sylow
49C24×C13C22×C411yescharacteristic
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—24no—
55C22×C4×C13—42no—
56C22×C4×C13—42no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—41no—
64C22×Dic13—41no—
65C22×Dic13—41no—
66C22×Dic13—42no—
67C22×Dic13—42no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13M1614yes—
71C22×Dic13C2×D411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×Q812yes—
74C22×Dic13#4112yes—
75C2×#1057—24no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C4⋊Dic13—24no—
84C4⋊Dic13—24no—
85#6101—44no—
86#6101—44no—
87C4×Dic13—22no—
88C4×Dic13—22no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C2×#389—131no—
92#1797—131no—
93#1749—131no—
94#1280—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13C4×Q812yes—
101C23×C13C2×M1612yes—
102C23×C13#13112yes—
103C2×C4×C13—28no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—84no—
112C2×C4×C13#9912yes—
113C2×C4×C13#10112yes—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—24no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—44no—
127C2×Dic13—44no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—44no—
131C2×Dic13#10012yes—
132C2×Dic13C22⋊Q812yes—
133C2×Dic13#12411yescharacteristic
134C2×Dic13C4⋊Q811yescharacteristic
135#1057—44no—
136#1057—82no—
137C22×C4⋊C4—131no—
138C22×C4⋊C4—132no—
139C22×C4⋊C4#26111yescharacteristic
140C22×C42—131no—
141C2×C4⋊C8—261no—
142C2×C22⋊C8—132no—
143C2×C22⋊C8—132no—
144C2×#97—261no—
145#389—261no—
146#389—261no—
147#389—261no—
148#389—261no—
149C2×#95—132no—
150#336—261no—
151#336—261no—
152C22×C13—22no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13#39111yescharacteristic
159C22×C13#40711yescharacteristic
160C22×C13#40811yescharacteristic
161C22×C13C2×#9911yescharacteristic
162C22×C13#41011yescharacteristic
163C22×C13C2×#10011yescharacteristic
164C22×C13C2×#10111yescharacteristic
165C22×C13#44614yes—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—82no—
169Dic13—22no—
170Dic13—22no—
171Dic13—21no—
172Dic13—21no—
173Dic13—44no—
174Dic13—41no—
175C23×C4—131no—
176C23×C4—131no—
177C23×C4—132no—
178C23×C4C2×#26112yes—
179C23×C4C2×#26111yescharacteristic
180C22×C8—262no—
181C22×C8—262no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—264no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—524no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—522no—
196C4⋊C8—522no—
197C22⋊C8—134no—
198C22⋊C8—262no—
199C22⋊C8—264no—
200#97—522no—
201#95—262no—
202#95—262no—
203C2×C13—24no—
204C2×C13#146311yescharacteristic
205C2×C13#146611yescharacteristic
206C2×C13#147011yescharacteristic
207C2×C13#147111yescharacteristic
208C2×C13#198511yescharacteristic
209C2×C13#199611yescharacteristic
210C2×C13#199711yescharacteristic
211C24C22×#26111yescharacteristic
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—132no—
223C22×C4—132no—
224C22×C4—131no—
225C22×C4—134no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4—521no—
231C22×C4—521no—
232C22×C4—521no—
233C22×C4—522no—
234C22×C4—522no—
235C22×C4C22⋊#26111yescharacteristic
236C22×C4C22⋊#26111yescharacteristic
237C2×C8—264no—
238C2×C8—522no—
239C2×C8—522no—
240C2×C8—522no—
241C2×C8—522no—
242C2×C8—522no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—264no—
246C4⋊C4—264no—
247C4⋊C4—524no—
248C4⋊C4—524no—
249C42—262no—
250C42—262no—
251C42—521no—
252C42—521no—
253C13#988311yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23D13⋊M1612yes—
259C23#8823812yes—
260C23Q8×#26112yes—
261C23C2×C22⋊#26111yescharacteristic
262C2×C4—28no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—84no—
271C2×C4—132no—
272C2×C4—132no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—264no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—524no—
288C2×C4—524no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4—524no—
292C2×C4#8811312yes—
293C2×C4#8811912yes—
294C8—524no—
295C8—1042no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22#1171907814yes—
303C22#1171912611yescharacteristic
304C22C2×#8811311yescharacteristic
305C22#1171914711yescharacteristic
306C22D13⋊#10011yescharacteristic
307C22#1171915611yescharacteristic
308C22(C2×#261)⋊Q811yescharacteristic
309C22C2×#8811911yescharacteristic
310C4—22no—
311C4—22no—
312C4—82no—
313C4—262no—
314C4—261no—
315C4—261no—
316C4—262no—
317C4—524no—
318C4—521no—
319C2—24no—
320C2#1313008611yescharacteristic
321C2#1313009711yescharacteristic
322C2#1313010911yescharacteristic
323C2#1313011111yescharacteristic
324C2#1313100811yescharacteristic
325C2#1313102511yescharacteristic
326C2#1313102911yescharacteristic
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#9883
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
253. C13#9883semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131305622
#131296742
C2×#117186342
#988313