Finite Group Databasebeta

← #16782209

Subgroups — #16782209

Order 3328.

404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130067C211yesmaximal, characteristic
2#13130067C211yesmaximal, characteristic
3#13129664C212yesmaximal, complemented
4#13129660C212yesmaximal, complemented
5#13117332C211yesmaximal, characteristic
6C2×#88180C2211yescharacteristic
7#11719119C2212yes—
8#11719119C2212yes—
9C4×C13×C22⋊C4C411yescharacteristic
10C4×C22⋊Dic13C411yescharacteristic
11#11718606—21no—
12#11718605—21no—
13#11718593C2211yescharacteristic
14C4×#6101C411yescharacteristic
15C4×#6101C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718315—21no—
18#11718314—21no—
19#11718305—21no—
20#11718305—21no—
21#11718285—21no—
22#11718285—21no—
23C23×C4×C13C2×C411yescharacteristic
24C2×C13×C22⋊C4—21no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—21no—
28C2×C22⋊Dic13D411yescharacteristic
29C2×C22⋊Dic13D411yescharacteristic
30#88180—22no—
31#88180—22no—
32C2×C4⋊Dic13D411yescharacteristic
33C2×C4⋊Dic13D411yescharacteristic
34C2×#6101—21no—
35C2×#6101—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42C22⋊#1057—22no—
43C22⋊#1057—22no—
44C4⋊#1057—22no—
45C4⋊#1057—22no—
46C4×#1057—22no—
47C4×#1057—22no—
48C13×#95—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#8732—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C22×Dic13C2×D411yescharacteristic
70C2×#1057—42no—
71C2×#1057—42no—
72C13×C22⋊C4—42no—
73C42×C13—22no—
74C42×C13—22no—
75C22⋊Dic13—22no—
76C22⋊Dic13—22no—
77C22⋊Dic13—42no—
78C4⋊Dic13—22no—
79C4⋊Dic13—22no—
80#6101—42no—
81#6101—42no—
82C4×Dic13—21no—
83C4×Dic13—21no—
84C4×Dic13—22no—
85C4×Dic13—22no—
86C4×Dic13—42no—
87C4×Dic13—42no—
88C4×Dic13#4112yes—
89C4×Dic13#4112yes—
90#2298—131no—
91#1458—131no—
92#1458—131no—
93#1276—132no—
94#1274—132no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13#11711yescharacteristic
113C2×C4×C13#11711yescharacteristic
114C2×C4×C13#13112yes—
115C2×C4×C13#13112yes—
116C2×Dic13—22no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13#12312yes—
129C2×Dic13#12312yes—
130#1057—82no—
131#1057—82no—
132C2×#117—131no—
133#431—132no—
134#431—132no—
135#388—261no—
136#388—261no—
137#387—261no—
138#387—261no—
139C4×C4⋊C4—131no—
140C4×C4⋊C4—131no—
141C4×C22⋊C4—131no—
142C4×C22⋊C4#26111yescharacteristic
143#376—131no—
144C43—131no—
145#324—261no—
146#324—261no—
147#323—261no—
148#323—261no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—81no—
155C22×C13—81no—
156C22×C13#38111yescharacteristic
157C22×C13#40811yescharacteristic
158C22×C13#40811yescharacteristic
159C4×C13—42no—
160C4×C13—41no—
161C4×C13—81no—
162C4×C13#43312yes—
163C4×C13#43312yes—
164Dic13—22no—
165Dic13—22no—
166Dic13—42no—
167Dic13—41no—
168Dic13—41no—
169Dic13—81no—
170C23×C4C2×#26111yescharacteristic
171#117—262no—
172#117—262no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—261no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—131no—
179C2×C22⋊C4—131no—
180C2×C22⋊C4—261no—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—131no—
185C2×C42—261no—
186C2×C42—261no—
187C2×C42C2×#26111yescharacteristic
188C2×C42C2×#26111yescharacteristic
189C4⋊C8—262no—
190C4⋊C8—262no—
191C22⋊C8—262no—
192C22⋊C8—262no—
193C4×C8—262no—
194C4×C8—262no—
195#95—21no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—81no—
204C2×C13#181811yescharacteristic
205C2×C13#182711yescharacteristic
206C2×C13#182711yescharacteristic
207C24C22⋊#26111yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—131no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4C22⋊#26111yescharacteristic
221C22×C4C22×#26111yescharacteristic
222C2×C8—522no—
223C2×C8—522no—
224C4⋊C4—262no—
225C4⋊C4—262no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C22⋊C4—42no—
229C22⋊C4—262no—
230C22⋊C4—262no—
231C22⋊C4—522no—
232C42—22no—
233C42—22no—
234C42—132no—
235C42—132no—
236C42—261no—
237C42—261no—
238C42—262no—
239C42—262no—
240C42—522no—
241C42—522no—
242C13#873211yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×C22⋊#26111yescharacteristic
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—132no—
261C2×C4—132no—
262C2×C4—262no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4#8823711yescharacteristic
275C2×C4#8823711yescharacteristic
276C2×C4#8823812yes—
277C2×C4#8823812yes—
278C8—1042no—
279C8—1042no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1171913511yescharacteristic
288C22#1171914611yescharacteristic
289C22#1171914611yescharacteristic
290C4—42no—
291C4—41no—
292C4—81no—
293C4—262no—
294C4—262no—
295C4—522no—
296C4—521no—
297C4—521no—
298C4—1041no—
299C4#1171906812yes—
300C4#1171906812yes—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#1313072911yescharacteristic
305C2#1313074511yescharacteristic
306C2#1313074611yescharacteristic
subgroupG/H
centerC2×C4#88237
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C22⋊C4C4
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C22⋊C4#261
hypocenterC13#8732
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129664C2semidirect
4. #13129660C2semidirect
242. C13#8732semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131296642
#131296602
#131173322
#873213