Finite Group Databasebeta

← #15773286

Subgroups — #15773286

Order 3328.

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

normal subgroups only

This group has 434 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#13118119C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic, complemented
3#13112862C212yesmaximal, complemented
4#13112838C212yesmaximal
5C4×C13×#101C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D52C411yescharacteristic
8C2×C13×#101—21no—
9C4×C13×M16—21no—
10#11718892—21no—
11#11718654—21no—
12#11718652C411yescharacteristic
13#11718652C2211yescharacteristic
14#11718647C411yescharacteristic
15#11718647C2211yescharacteristic
16C4×#6103—21no—
17C4×#6103—21no—
18#11718593C411yescharacteristic
19#11718586—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C2×C13×M16—22no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4×Dic13—21no—
42C4×D52—41no—
43C4×D52—41no—
44C13×#101—24no—
45C13×#97—41no—
46C4×C8×C13—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56C4×#1055—41no—
57#11734—131nomaximal, Sylow
58C23×D13—21no—
59C2×Q8×C13—22no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C2×D52—41no—
73C2×D52—42no—
74C2×C4×D13—42no—
75C2×C4×D13—42no—
76C2×C4×D13—41no—
77C2×C4×D13—41no—
78C13×M16—24no—
79C13×M16—42no—
80C2×C8×C13—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90#6103—42no—
91#6103—42no—
92#6103—42no—
93#6103—42no—
94#6103—42no—
95C4⋊Dic13—41no—
96C4×Dic13—42no—
97C2×#1055—42no—
98#2398—131no—
99C4×#101D1311yescharacteristic, complemented
100#1461—131no—
101#1353—132no—
102#1345—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104C22×D13—22no—
105C22×D13—41no—
106C22×D13—41no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111Q8×C13—44no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13#10412yes—
129C2×C4×C13#13512yes—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139D52—42no—
140D52—42no—
141C4×D13—82no—
142C4×D13—82no—
143C8×C13—44no—
144#1055—82no—
145C2×C4×Q8C2×D1311yescharacteristic
146C2×C4×D4—131no—
147#431—261no—
148C2×#101—21no—
149C4×M16—21no—
150#400—131no—
151#400—131no—
152#397—261no—
153#394—131no—
154#394—131no—
155#393—261no—
156C4×C22⋊C4—261no—
157C4×C22⋊C4—261no—
158#376—131no—
159#343C2×D1312yes—
160#324—132no—
161#324—261no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13C2×#9911yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13C2×#10411yescharacteristic
167C2×D13—42no—
168C2×D13—42no—
169C2×D13—42no—
170C2×D13—81no—
171C2×D13—81no—
172C2×D13—81no—
173C2×D13—81no—
174C4×C13—21no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13#35512yes—
182Dic13—81no—
183Dic13—81no—
184Dic13—81no—
185C22×Q8C22⋊D1311yescharacteristic
186C22×D4—131no—
187C23×C4—261no—
188C2×M16—22no—
189C4×Q8—41no—
190C4×Q8—41no—
191C4×D4—521no—
192C4×D4—521no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4C4×D1311yescharacteristic
195C2×C4⋊C4D5211yescharacteristic
196C2×C4⋊C4C22×D1311yescharacteristic
197C2×C22⋊C4—261no—
198C2×C22⋊C4—261no—
199C2×C22⋊C4—261no—
200C2×C22⋊C4—261no—
201C2×C22⋊C4—261no—
202C2×C42—261no—
203C2×C42C4×D1311yescharacteristic
204C2×C42D5211yescharacteristic
205C2×C42C22⋊D1311yescharacteristic
206C4⋊C8—521no—
207#101—24no—
208C22⋊C8—262no—
209#97—41no—
210C4×C8—41no—
211C4×C8—521no—
212#95—131no—
213#95—131no—
214#95—261no—
215#95—261no—
216#95—261no—
217#95—261no—
218#95—261no—
219C2×C13—21no—
220C2×C13—21no—
221C2×C13#150111yescharacteristic
222C2×C13#212011yescharacteristic
223C2×C13C2×#35511yescharacteristic
224D13—82no—
225C24—261no—
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—41no—
229C2×D4—521no—
230C2×D4—522no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—522no—
235C22×C4—522no—
236C22×C4—521no—
237C22×C4—521no—
238C22×C4#610311yescharacteristic
239C22×C4#610311yescharacteristic
240C22×C4#610311yescharacteristic
241C22×C4#610311yescharacteristic
242C22×C4C2×C4×D1311yescharacteristic
243C22×C4C2×D5211yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245M16—24no—
246M16—42no—
247C2×C8—42no—
248C2×C8—522no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—521no—
253C22⋊C4—522no—
254C22⋊C4—522no—
255C22⋊C4—522no—
256C22⋊C4—522no—
257C22⋊C4—522no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—522no—
265C13#1173411yescharacteristic, complemented, Sylow
266C23—262no—
267C23—521no—
268C23—521no—
269C23—521no—
270C23—521no—
271C23—521no—
272C23—521no—
273C23C2×#610311yescharacteristic
274Q8—44no—
275D4—522no—
276D4—522no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—1042no—
301C2×C4—1042no—
302C2×C4#8804512yes—
303C2×C4#8804611yescharacteristic
304C2×C4#8804611yescharacteristic
305C2×C4#8820412yes—
306C8—44no—
307C8—1042no—
308C22—21no—
309C22—21no—
310C22—522no—
311C22—522no—
312C22—522no—
313C22—1041no—
314C22—1041no—
315C22—1041no—
316C22—1041no—
317C22C2×#8804511yescharacteristic
318C22C2×#8804611yescharacteristic
319C22#1171866311yescharacteristic
320C4—21no—
321C4—22no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—1041no—
328C4—1041no—
329C4—1041no—
330C4#1171806912yes—
331C2—21no—
332C2—21no—
333C2—1042no—
334C2#1311332511yescharacteristic
335C2#1311647811yescharacteristic
336C2C2×#1171806911yescharacteristic
subgroupG/H
centerC2×C4#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC4×C13×#101C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenterC4×#101D13
hypocenterC13#11734
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #13113160C2semidirect
3. #13112862C2semidirect
5. C4×C13×#101C2semidirect
99. C4×#101D13semidirect
265. C13#11734semidirect

Maximal subgroups

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

subgroupindex
#131181192
#131131602
#131128622
#131128382
C4×C13×#1012
#1173413