Finite Group Databasebeta

← #15773298

Subgroups — #15773298

Order 3328.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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×#88076C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112866C212yesmaximal
4#13112842C212yesmaximal
5C13×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398—21no—
9C13×#398C411yescharacteristic
10C13×#398C2211yescharacteristic
11C13×#395—21no—
12C13×#395C411yescharacteristic
13C13×#395C2211yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4—21no—
16C13×#376C411yescharacteristic
17C2×#88076—21no—
18#11718586—21no—
19C4×#6099—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×C42×C13—21no—
39C2×C42×C13—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×#6099—22no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88076—24no—
52C22⋊#1055—22no—
53C4⋊#1055—41no—
54#88043—41no—
55C4×#1055—41no—
56C4×#1055—41no—
57#11736—131nomaximal, Sylow
58C2×Q8×C13—22no—
59C2×Q8×C13—22no—
60C2×Q8×C13—41no—
61C2×Q8×C13—42no—
62C2×Q8×C13—41no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C42×C13—24no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—41no—
91C42×C13—41no—
92#6099—24no—
93#6099—42no—
94C2×#1055—42no—
95C2×#1055—42no—
96#2399D1311yescharacteristic
97C4×#101—131no—
98#1461—131no—
99#1354—132no—
100#1346—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—44no—
103Q8×C13—42no—
104Q8×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#10412yes—
134C2×C4×C13#13512yes—
135#1055—44no—
136#1055—82no—
137C2×C4×Q8Dic1311yescharacteristic
138C2×C4×Q8C2×D1311yescharacteristic
139#431—261no—
140C2×#101—261no—
141C4×M16—261no—
142#398—21no—
143#398Dic1311yescharacteristic
144#398C2×D1311yescharacteristic
145#395—21no—
146#395Dic1311yescharacteristic
147#395C2×D1311yescharacteristic
148C4×C4⋊C4—21no—
149C4×C4⋊C4—21no—
150#376Dic1311yescharacteristic
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—22no—
161C4×C13—22no—
162C4×C13—42no—
163C4×C13—42no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—42no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—81no—
170C4×C13#35612yes—
171C22×Q8C2×Dic1311yescharacteristic
172C22×Q8C22⋊D1311yescharacteristic
173C2×M16—262no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C2×Dic1311yescharacteristic
190C2×C42C22⋊D1311yescharacteristic
191C2×C42C22⋊D1311yescharacteristic
192C4⋊C8—521no—
193#101—264no—
194C22⋊C8—262no—
195#97—521no—
196C4×C8—521no—
197C4×C8—521no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95C2×Dic1311yescharacteristic
204#95C2×Dic1311yescharacteristic
205C2×C13—21no—
206C2×C13—21no—
207C2×C13#150111yescharacteristic
208C2×C13#212011yescharacteristic
209C2×C13C2×#35611yescharacteristic
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—42no—
214C2×Q8—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22⋊Dic1311yescharacteristic
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22⋊Dic1311yescharacteristic
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22×Dic1311yescharacteristic
224C22×C4C2×C22⋊D1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—264no—
227M16—522no—
228C2×C8—522no—
229C2×C8—522no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C42—24no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C13#1173611yescharacteristic, complemented, Sylow
249C23C2×C22⋊Dic1311yescharacteristic
250Q8—44no—
251Q8—42no—
252Q8—42no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4#8807411yescharacteristic
280C2×C4#8807411yescharacteristic
281C2×C4#8807712yes—
282C2×C4#8820412yes—
283C8—524no—
284C8—1042no—
285C22—21no—
286C22—21no—
287C22C2×#8807411yescharacteristic
288C22#1171889411yescharacteristic
289C22C2×#8807711yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—42no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4#1171814012yes—
302C2—21no—
303C2—21no—
304C2#1311332711yescharacteristic
305C2#1311647711yescharacteristic
306C2C2×#1171814011yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2399C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2399D13
hypocenterC13#11736
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2399

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×#880762
#131131602
#131128662
#131128422
C13×#23992
#1173613