Finite Group Databasebeta

← #16787796

Subgroups — #16787796

Order 3328.

402 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#88113C211yesmaximal, characteristic
2#13130078C211yesmaximal, characteristic
3#13129837C212yesmaximal
4#13129820C212yesmaximal
5#13118127C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113—21no—
9#11719125—21no—
10C4×#6122—21no—
11#11718890C411yescharacteristic
12#11718890C2211yescharacteristic
13#11718644—21no—
14#11718641C411yescharacteristic
15#11718641C2211yescharacteristic
16#11718640—21no—
17#11718593C411yescharacteristic
18C4×#6101—21no—
19C4×#6101—21no—
20#11718291C2212yes—
21#11718286C2212yes—
22#11718285—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Dic26D411yescharacteristic
25C2×#6122—22no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C4⋊Dic13D411yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101C2×C411yescharacteristic
38C2×#6101C2311yescharacteristic
39C2×C4×Dic13—21no—
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C4×Dic26—41no—
43C4×Dic26—41no—
44C22⋊#1057—22no—
45#88113—24no—
46#88112—41no—
47#88110—41no—
48C4×#1057—41no—
49C4×#1057—41no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071C2×C411yescharacteristic
56#88071C2×C411yescharacteristic
57#11736—131nomaximal, Sylow
58C2×Q8×C13—42no—
59C2×Q8×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C2×D411yescharacteristic
70C22×Dic13C2×D411yescharacteristic
71C2×Dic26—22no—
72C2×Dic26—22no—
73C2×Dic26—41no—
74#6122—24no—
75#6122—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—41no—
83C42×C13—41no—
84C4⋊Dic13—41no—
85#6101—41no—
86#6101—41no—
87#6101—42no—
88#6101—42no—
89#6101—42no—
90#6101—42no—
91C4×Dic13—24no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96#2399—131no—
97C4×#101—131no—
98#1461—131no—
99#1354—132no—
100#1346—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—42no—
103Q8×C13—42no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13#9911yescharacteristic
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13—22no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13#10412yes—
133C2×Dic13#13512yes—
134Dic26—44no—
135#1057—44no—
136#1057—82no—
137C2×C4×Q8—131no—
138C2×C4×Q8#26111yescharacteristic
139#431—261no—
140C2×#101—261no—
141C4×M16—261no—
142#398—131no—
143#398—131no—
144#398—261no—
145#395—131no—
146#395—131no—
147#395—261no—
148C4×C4⋊C4—261no—
149C4×C4⋊C4—261no—
150#376—131no—
151#343—132no—
152#324—132no—
153#324—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13C2×#9911yescharacteristic
157C22×C13#41611yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C4×C13—21no—
160C4×C13—42no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—81no—
164C4×C13#35612yes—
165Dic13—22no—
166Dic13—22no—
167Dic13—42no—
168Dic13—42no—
169Dic13—41no—
170Dic13—41no—
171C22×Q8—131no—
172C22×Q8C2×#26111yescharacteristic
173C2×M16—262no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×Q8—521no—
177C4×Q8—521no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4C2×#26111yescharacteristic
187C2×C42—21no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—261no—
191C2×C42C2×#26111yescharacteristic
192C4⋊C8—521no—
193#101—264no—
194C22⋊C8—262no—
195#97—521no—
196C4×C8—521no—
197C4×C8—521no—
198#95—131no—
199#95—131no—
200#95—261no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13#150111yescharacteristic
208C2×C13#212011yescharacteristic
209C2×C13C2×#35611yescharacteristic
210C2×Q8—42no—
211C2×Q8—41no—
212C2×Q8—262no—
213C2×Q8—262no—
214C2×Q8—521no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—261no—
222C22×C4—261no—
223C22×C4C22⋊#26111yescharacteristic
224C22×C4C22⋊#26111yescharacteristic
225C22×C4C22×#26111yescharacteristic
226M16—264no—
227M16—522no—
228C2×C8—522no—
229C2×C8—522no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—521no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—522no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C42—21no—
240C42—21no—
241C42—41no—
242C42—41no—
243C42—264no—
244C42—261no—
245C42—261no—
246C42—261no—
247C42—261no—
248C13#1173611yescharacteristic, complemented, Sylow
249C23C2×C22⋊#26111yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—524no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—132no—
266C2×C4—132no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4#8811911yescharacteristic
282C2×C4#8811911yescharacteristic
283C8—524no—
284C8—1042no—
285C22—21no—
286C22—21no—
287C22D13⋊#10411yescharacteristic
288C22#1171916511yescharacteristic
289C22C2×#8811911yescharacteristic
290C4—21no—
291C4—42no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—262no—
296C4—262no—
297C4—522no—
298C4—522no—
299C4—521no—
300C4—521no—
301C4#1171830112yes—
302C2—21no—
303C2—21no—
304C2#1313021111yescharacteristic
305C2#1313108711yescharacteristic
306C2C2×#1171830111yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×#6101C23
hypercenterC2×C4×Q8#261
hypocenterC13#11736
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
248. C13#11736semidirect

Maximal subgroups

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

subgroupindex
C4×#881132
#131300782
#131298372
#131298202
#131181272
#1173613