Finite Group Databasebeta

← #16778463

Subgroups — #16778463

Order 3328.

506 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 96 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#13130728C211yesmaximal, characteristic
2#13130563C211yesmaximal, characteristic
3#13129657C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5C4×#88151C211yesmaximal, characteristic
6C2×#88151C411yescharacteristic
7C2×C42×D13C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×#88111—21no—
10C2×#88111—21no—
11C2×#88110—21no—
12C4×C13×C4⋊C4C411yescharacteristic
13#11718648C411yescharacteristic
14#11718646C2211yescharacteristic
15#11718635C2211yescharacteristic
16C4×#6103—21no—
17C4×C4⋊Dic13—21no—
18#11718329—21no—
19#11718314—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×C4×D13C2×C411yescharacteristic
24C22×C4×D13D411yescharacteristic
25C22×C4×D13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×#1057—22no—
28C22×#1057—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13—21no—
32C2×C42×C13C2×C411yescharacteristic
33C2×#6103—21no—
34C2×#6103—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43#88151—22no—
44#88151—22no—
45C42×D13—42no—
46C4×Dic26—42no—
47#88111—24no—
48#88111—42no—
49#88110—42no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#7623—131nomaximal, Sylow
56C23×D13C22⋊C411yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×C4×D13—22no—
68C2×C4×D13—22no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—22no—
72C2×C4×D13—22no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×Dic26—21no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×Dic26M1612yes—
81C2×#1057—24no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4M1612yes—
90C42×C13—22no—
91C42×C13—42no—
92#6103—24no—
93#6103—42no—
94C4⋊Dic13—24no—
95C4⋊Dic13—42no—
96C4⋊Dic13—41no—
97#6101—42no—
98C4×Dic13—22no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101C4×Dic13—42no—
102C4×C22⋊Q8—131no—
103#1817—131no—
104#1749—131no—
105#1272—132no—
106#1271—132no—
107C23×C13C2×C22⋊C411yescharacteristic
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13—21no—
113C22×D13—21no—
114C22×D13#10412yes—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—22no—
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—41no—
127C2×C4×C13—41no—
128C2×C4×C13#9912yes—
129C2×C4×C13C2×M1611yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—22no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13#13512yes—
145C2×Dic13#13712yes—
146C4×D13—44no—
147C4×D13—44no—
148C4×D13—42no—
149C4×D13—42no—
150Dic26—42no—
151Dic26—42no—
152#1057—44no—
153#1057—82no—
154C2×C22⋊Q8—131no—
155C2×C4×Q8—131no—
156C22×C42—131no—
157C2×C22⋊C8—261no—
158C2×C22⋊C8—261no—
159C2×#97—261no—
160#391—131no—
161#389—131no—
162#387—261no—
163#385—261no—
164#380—131no—
165C4×C4⋊C4—261no—
166C4×C4⋊C4#26111yescharacteristic
167C4×C22⋊C4—261no—
168#336—132no—
169#336—132no—
170#336—261no—
171C22×C13#40711yescharacteristic
172C22×C13C2×#9911yescharacteristic
173C22×C13#41311yescharacteristic
174C22×C13#41611yescharacteristic
175C22×C13#41911yescharacteristic
176C22×C13C2×#10411yescharacteristic
177C22×C13#42111yescharacteristic
178C2×D13—22no—
179C2×D13—22no—
180C2×D13—22no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—22no—
188C4×C13—42no—
189C4×C13—41no—
190C4×C13—81no—
191Dic13—22no—
192Dic13—22no—
193Dic13—42no—
194Dic13—41no—
195Dic13—81no—
196C22×Q8—131no—
197C23×C4—131no—
198C23×C4—131no—
199C23×C4—131no—
200C22×C8—262no—
201C22×C8—262no—
202C22⋊Q8—262no—
203C22⋊Q8—262no—
204C4×Q8—522no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4C2×#26111yescharacteristic
210C2×C4⋊C4C2×#26111yescharacteristic
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C42—21no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—261no—
218C2×C42—522no—
219C2×C42C2×#26111yescharacteristic
220C22⋊C8—264no—
221C22⋊C8—522no—
222#97—522no—
223#95—21no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13#146511yescharacteristic
229C2×C13#148811yescharacteristic
230C2×C13#149111yescharacteristic
231C2×C13#150111yescharacteristic
232C2×C13#151111yescharacteristic
233C2×C13#153211yescharacteristic
234C2×C13#155411yescharacteristic
235D13—42no—
236C24—131no—
237C2×Q8—132no—
238C2×Q8—261no—
239C2×Q8—521no—
240C2×Q8—521no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4—262no—
249C22×C4—261no—
250C22×C4—262no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4—521no—
257C22×C4—521no—
258C22×C4C22⋊#26111yescharacteristic
259C22×C4C22⋊#26111yescharacteristic
260C22×C4C22×#26111yescharacteristic
261C2×C8—264no—
262C2×C8—522no—
263C2×C8—522no—
264C2×C8—522no—
265C2×C8—522no—
266C2×C8—522no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—264no—
270C4⋊C4—521no—
271C4⋊C4—522no—
272C4⋊C4—522no—
273C4⋊C4#611812yes—
274C22⋊C4—264no—
275C22⋊C4—522no—
276C42—22no—
277C42—42no—
278C42—262no—
279C42—521no—
280C42—521no—
281C42—522no—
282C13#762311yescharacteristic, complemented, Sylow
283C23—132no—
284C23—261no—
285C23—261no—
286C23—261no—
287C23—261no—
288C23—261no—
289C23—261no—
290C23C2×C22⋊#26111yescharacteristic
291Q8—522no—
292Q8—522no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—132no—
307C2×C4—132no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—262no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—524no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—524no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4#8810712yes—
326C2×C4C2×#611811yescharacteristic
327C2×C4D13⋊M1611yescharacteristic
328C8—524no—
329C8—1042no—
330C22—262no—
331C22—262no—
332C22—262no—
333C22—521no—
334C22—521no—
335C22—521no—
336C22—521no—
337C22C2×#8810711yescharacteristic
338C22#1171912711yescharacteristic
339C22#1171913211yescharacteristic
340C22#1171914011yescharacteristic
341C22#1171915311yescharacteristic
342C22D13⋊#10411yescharacteristic
343C22#1171916511yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—41no—
349C4—81no—
350C4—262no—
351C4—262no—
352C4—521no—
353C4—522no—
354C4—1041no—
355C2—522no—
356C2#1313009311yescharacteristic
357C2#1313016811yescharacteristic
358C2#1313017911yescharacteristic
359C2#1313021311yescharacteristic
360C2#1313024411yescharacteristic
361C2#1313031111yescharacteristic
362C2#1313036111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#7623
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129657C2semidirect
4. #13129654C2semidirect
282. C13#7623semidirect

Maximal subgroups

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

subgroupindex
#131307282
#131305632
#131296572
#131296542
C4×#881512
#762313