Finite Group Databasebeta

← #15772397

Subgroups — #15772397

Order 3328.

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

normal subgroups only

This group has 412 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
1C4×#88198C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112781C212yesmaximal
4#13112769C212yesmaximal
5C13×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88198C411yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C13×#432—21no—
10#11718891C411yescharacteristic
11#11718637C2211yescharacteristic
12#11718635C2211yescharacteristic
13#11718633—21no—
14#11718633—21no—
15C4×#6101—21no—
16C4×#6101—21no—
17C42×Dic13C411yescharacteristic
18#11718587—21no—
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33#88198—22no—
34#88198—22no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C4×Dic26—41no—
47C4×Dic26—41no—
48C13×C4⋊C8—41no—
49C13×C22⋊C8—22no—
50C13×#97—41no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57#88043—41no—
58#11532—131nomaximal, Sylow
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C2×Dic26—21no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26M1612yes—
78C2×C8×C13—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C4⋊Dic13—41no—
89#6101—24no—
90#6101—24no—
91#6101—42no—
92#6101—42no—
93#6101—42no—
94C4×Dic13—24no—
95C4×Dic13—21no—
96C4×Dic13—42no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100C4×Dic13M1612yes—
101C2×#1055—42no—
102C4×C4⋊Q8—131no—
103#1467—131no—
104#1467D1311yescharacteristic
105#1325—132no—
106#1319—132no—
107C23×C13C2×C22⋊C411yescharacteristic
108Q8×C13—42no—
109Q8×C13—42no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
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—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13C2×M1611yescharacteristic
128C2×C4×C13C2×M1611yescharacteristic
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—22no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141Dic26—42no—
142Dic26—42no—
143C8×C13—82no—
144#1055—82no—
145C2×C4⋊Q8—131no—
146C2×C4×Q8—131no—
147C2×C4×Q8C2×D1311yescharacteristic
148#432—21no—
149#432—261no—
150#391—131no—
151#391—131no—
152#389—261no—
153#389—261no—
154#384—131no—
155C4×C4⋊C4—261no—
156C4×C4⋊C4—261no—
157C43—131no—
158#324—21no—
159#324—132no—
160#324—261no—
161#324C2×D1312yes—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#40711yescharacteristic
165C22×C13C2×#9911yescharacteristic
166C22×C13#41311yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13#35612yes—
176Dic13—24no—
177Dic13—42no—
178Dic13—42no—
179Dic13—81no—
180C22×Q8—131no—
181C22×Q8C4×D1311yescharacteristic
182C4⋊Q8—262no—
183C4⋊Q8—262no—
184C4×Q8—41no—
185C4×Q8—41no—
186C4×Q8—521no—
187C4×Q8—521no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4D5211yescharacteristic
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C4⋊C4C22×D1311yescharacteristic
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—261no—
200C2×C42—261no—
201C2×C42—261no—
202C2×C42C4×D1311yescharacteristic
203C2×C42D5211yescharacteristic
204C2×C42C22⋊D1311yescharacteristic
205C4⋊C8—41no—
206C4⋊C8—521no—
207C22⋊C8—22no—
208C22⋊C8—262no—
209#97—41no—
210#97—521no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13#146511yescharacteristic
218C2×C13#212611yescharacteristic
219C2×C13C2×#35611yescharacteristic
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—132no—
225C2×Q8—261no—
226C2×Q8—521no—
227C2×Q8—521no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4#610311yescharacteristic
233C22×C4#610311yescharacteristic
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4C2×C4×D1311yescharacteristic
237C22×C4C2×D5211yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239C2×C8—42no—
240C2×C8—522no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—264no—
245C4⋊C4—264no—
246C4⋊C4—521no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C4⋊C4—522no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—132no—
257C42—264no—
258C42—261no—
259C42—521no—
260C42—522no—
261C42—521no—
262C42—521no—
263C13#1153211yescharacteristic, complemented, Sylow
264C23C2×#610311yescharacteristic
265Q8—42no—
266Q8—42no—
267Q8—522no—
268Q8—522no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—262no—
285C2×C4—262no—
286C2×C4—262no—
287C2×C4—262no—
288C2×C4—262no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4#8804611yescharacteristic
297C2×C4#8804611yescharacteristic
298C2×C4M16×D1311yescharacteristic
299C2×C4M16×D1311yescharacteristic
300C8—82no—
301C8—1042no—
302C22—21no—
303C22—21no—
304C22C2×#8804611yescharacteristic
305C22#1171878711yescharacteristic
306C22#1171879311yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—264no—
316C4—522no—
317C4—522no—
318C4—1041no—
319C4#1171807012yes—
320C2—21no—
321C2—21no—
322C2#1311317211yescharacteristic
323C2#1311649911yescharacteristic
324C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11532
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
263. C13#11532semidirect

Maximal subgroups

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

subgroupindex
C4×#881982
#131131802
#131127812
#131127692
C13×#14672
#1153213