Finite Group Databasebeta

← #15773552

Subgroups — #15773552

Order 3328.

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

normal subgroups only

This group has 572 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#13118201C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112865C214yesmaximal, complemented
4C4×C13×#100C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178—21no—
8C2×C13×#100—21no—
9C4×C13×M16—21no—
10#11718881—21no—
11#11718873C411yescharacteristic
12#11718868—21no—
13#11718640C2212yes—
14#11718608C412yes—
15#11718607—21no—
16#11718590—21no—
17C13×#343C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C22×Dic26—21no—
25C22×Dic26—44no—
26C22×Dic26—41no—
27C22×Dic26—41no—
28C22×Dic26C2×C412yes—
29C2×C13×M16—22no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39#88178—44no—
40C2×#6101—22no—
41C2×#6099—41no—
42C13×#100—24no—
43C13×#97—41no—
44C4×C8×C13—41no—
45#88071—22no—
46#88071—22no—
47#88071C2×C412yes—
48C22⋊#1055—22no—
49C22⋊#1055—41no—
50#11791—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C22⋊C411yescharacteristic
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—41no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—44no—
70C22×Dic13—42no—
71C2×Dic26—24no—
72C2×Dic26—42no—
73C2×Dic26—48no—
74C2×Dic26—44no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26—42no—
78C2×Dic26—44no—
79C2×Dic26—44no—
80C13×M16—24no—
81C13×M16—42no—
82C2×C8×C13—42no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C22⋊Dic13—44no—
89C22⋊Dic13—42no—
90C4⋊Dic13—42no—
91#6101—44no—
92#6099—82no—
93C2×#1055—42no—
94#2409—131no—
95C4×#100D1311yescharacteristic
96#1465—131no—
97#1354—134no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13#10412yes—
108C23×C13C2×C22⋊C411yescharacteristic
109D4×C13—44no—
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—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—81no—
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#13712yes—
126C2×Dic13—24no—
127C2×Dic13—42no—
128C2×Dic13—48no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133Dic26—44no—
134Dic26—44no—
135Dic26—44no—
136Dic26—44no—
137C8×C13—44no—
138#1055—82no—
139C23×Q8—131no—
140C2×C22⋊Q8—261no—
141C2×C4×D4C2×D1311yescharacteristic
142C2×#100—21no—
143#407—261no—
144C4×M16—21no—
145#395—132no—
146#393—132no—
147#391—261no—
148#386—261no—
149#385—261no—
150#380—131no—
151#343C2×D1312yes—
152#324—132no—
153#323—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—22no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—81no—
166C22×C13C2×#9911yescharacteristic
167C22×C13#41911yescharacteristic
168C22×C13C2×#10411yescharacteristic
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13AΣL(1,𝔽16)12yes—
175Dic13—44no—
176Dic13—82no—
177C22×Q8—132no—
178C22×Q8—261no—
179C22×Q8—521no—
180C22×Q8—521no—
181C22×Q8—524no—
182C22×D4C22⋊D1311yescharacteristic
183C23×C4—261no—
184C23×C4C4×D1311yescharacteristic
185C23×C4D5211yescharacteristic
186C2×M16—22no—
187C2×M16—521no—
188C22⋊Q8—524no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—262no—
193C2×C4⋊C4C22×D1311yescharacteristic
194C2×C22⋊C4—262no—
195C2×C22⋊C4—261no—
196C2×C22⋊C4C4×D1311yescharacteristic
197C2×C22⋊C4D5211yescharacteristic
198C2×C42C22⋊D1311yescharacteristic
199#100—24no—
200C22⋊C8—262no—
201C22⋊C8—521no—
202#97—41no—
203C4×C8—41no—
204#95—132no—
205#95—262no—
206#95—262no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—42no—
210C2×C13—81no—
211C2×C13#150811yescharacteristic
212C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
213C2×C13#213511yescharacteristic
214C24#610311yescharacteristic
215C24#610311yescharacteristic
216C2×Q8—264no—
217C2×Q8—522no—
218C2×Q8—522no—
219C2×Q8—524no—
220C2×Q8—524no—
221C2×Q8—528no—
222C2×Q8—524no—
223C2×Q8—521no—
224C2×Q8—521no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—262no—
235C22×C4—262no—
236C22×C4—524no—
237C22×C4—522no—
238C22×C4#610311yescharacteristic
239C22×C4#610311yescharacteristic
240C22×C4C2×C4×D1311yescharacteristic
241C22×C4C2×D5211yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243M16—24no—
244M16—42no—
245M16—1042no—
246C2×C8—42no—
247C2×C8—522no—
248C4⋊C4—41no—
249C4⋊C4—522no—
250C4⋊C4—524no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—524no—
254C22⋊C4—522no—
255C42—21no—
256C42—21no—
257C13#1179111yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23#8804512yes—
268C23C2×#610311yescharacteristic
269Q8—524no—
270Q8—524no—
271Q8—524no—
272Q8—524no—
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—264no—
288C2×C4—522no—
289C2×C4—528no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4—522no—
294C2×C4#8804611yescharacteristic
295C2×C4#8804611yescharacteristic
296C2×C4#8820512yes—
297C8—44no—
298C8—1042no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×#8804511yescharacteristic
312C22C2×#8804611yescharacteristic
313C22#1171866511yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—524no—
320C4—1042no—
321C4#1171806712yes—
322C2—21no—
323C2—21no—
324C2—42no—
325C2—81no—
326C2#1311335511yescharacteristic
327C2C2×#1171806711yescharacteristic
328C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC4×C13×#100C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenterC4×#100D13
hypocenterC13#11791
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. #13112865C2semidirect
257. C13#11791semidirect

Maximal subgroups

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

subgroupindex
#131182012
#131131742
#131128652
C4×C13×#1002
#1179113