Finite Group Databasebeta

← #15773299

Subgroups — #15773299

Order 3328.

402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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#13118127C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13112867C212yesmaximal
4#13112843C212yesmaximal
5C13×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8C13×#431—21no—
9#11718890—21no—
10C2×#88076—21no—
11#11718644C411yescharacteristic
12#11718644C2211yescharacteristic
13#11718641—21no—
14#11718640C411yescharacteristic
15#11718640C2211yescharacteristic
16#11718593C411yescharacteristic
17C4×#6101—21no—
18C4×#6101—21no—
19C4×#6099—21no—
20C13×#324—21no—
21C13×#324C2212yes—
22#11718122C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×#6099—22no—
42C4×Dic26—41no—
43C4×Dic26—41no—
44C13×C4⋊C8—41no—
45C13×C22⋊C8—22no—
46C4×C8×C13—41no—
47#88076—24no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55#88043—41no—
56C4×#1055—41no—
57#11736—131nomaximal, Sylow
58C2×Q8×C13—22no—
59C2×Q8×C13—22no—
60C2×Q8×C13—41no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C2×Dic26—41no—
73C2×Dic26—42no—
74C2×C8×C13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C4⋊Dic13—41no—
85#6101—42no—
86#6101—42no—
87#6101—42no—
88#6101—42no—
89#6101—42no—
90C4×Dic13—24no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93#6099—24no—
94#6099—42no—
95C2×#1055—42no—
96#2399—131no—
97C4×#101—131no—
98#1461D1311yescharacteristic
99#1354—132no—
100#1346—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—44no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#9911yescharacteristic
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#10412yes—
120C2×C4×C13#13512yes—
121C2×Dic13—22no—
122C2×Dic13—22no—
123C2×Dic13—22no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133Dic26—42no—
134Dic26—42no—
135C8×C13—82no—
136#1055—44no—
137C2×C4×Q8—131no—
138C2×C4×Q8C2×D1311yescharacteristic
139#431—21no—
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—21no—
153#324C2×D1312yes—
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—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13#35612yes—
167Dic13—42no—
168Dic13—42no—
169Dic13—42no—
170Dic13—81no—
171C22×Q8—131no—
172C22×Q8D5211yescharacteristic
173C2×M16—262no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×Q8—521no—
177C4×Q8—521no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C4×D1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C42—261no—
188C2×C42—261no—
189C2×C42C4×D1311yescharacteristic
190C2×C42D5211yescharacteristic
191C2×C42C22⋊D1311yescharacteristic
192C4⋊C8—41no—
193#101—264no—
194C22⋊C8—22no—
195#97—521no—
196C4×C8—41no—
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—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—521no—
214C2×Q8—522no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4—261no—
219C22×C4#610311yescharacteristic
220C22×C4#610311yescharacteristic
221C22×C4#610311yescharacteristic
222C22×C4#610311yescharacteristic
223C22×C4C2×C4×D1311yescharacteristic
224C22×C4C2×D5211yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—264no—
227M16—522no—
228C2×C8—42no—
229C2×C8—522no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—521no—
234C4⋊C4—522no—
235C4⋊C4—522no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—264no—
246C42—521no—
247C42—521no—
248C13#1173611yescharacteristic, complemented, Sylow
249C23C2×#610311yescharacteristic
250Q8—44no—
251Q8—522no—
252Q8—522no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4#8804611yescharacteristic
280C2×C4#8804611yescharacteristic
281C2×C4#8806512yes—
282C2×C4#8815812yes—
283C8—82no—
284C8—524no—
285C22—21no—
286C22—21no—
287C22C2×#8804611yescharacteristic
288C22#1171877411yescharacteristic
289C22C2×#8806511yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—522no—
298C4—522no—
299C4—522no—
300C4—1041no—
301C4#1171807012yes—
302C2—21no—
303C2—21no—
304C2#1311332811yescharacteristic
305C2#1311647511yescharacteristic
306C2C2×#1171807011yescharacteristic
subgroupG/H
centerC2×C4#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1461C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1461D13
hypocenterC13#11736
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

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
#131181272
C4×#880762
#131128672
#131128432
C13×#14612
#1173613