Finite Group Databasebeta

← #15773937

Subgroups — #15773937

Order 3328.

472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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#13119144C211yesmaximal, characteristic
2#13113157C211yesmaximal, characteristic
3#13112835C214yesmaximal, complemented
4C13×#1799C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88189—21no—
7C22×C4⋊Dic13C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C13×#380—21no—
10#11718873—21no—
11#11718873C411yescharacteristic, complemented
12#11718644C412yescomplemented
13#11718614C2212yes—
14#11718604—21no—
15#11718589—21no—
16#11718586—21no—
17C13×#342C2212yes—
18#11718117—21no—
19#11718117C2212yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2311yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—22no—
34#88189—42no—
35#88189—42no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—41no—
39C2×C4⋊Dic13—41no—
40C2×C4⋊Dic13C2×C412yes—
41C2×#6101—22no—
42C13×#99—42no—
43C13×#95—41no—
44#88071—22no—
45#88071—22no—
46#88071C2×C412yes—
47C22⋊#1055—22no—
48C4⋊#1055—41no—
49C4×#1055—41no—
50#11874—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13D812yes—
56C2×D4×C13SD1612yes—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—42no—
72C22×Dic13—42no—
73C22×Dic13—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—82no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C42×C13—21no—
81C42×C13—21no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C4⋊Dic13—42no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—42no—
89#6101—44no—
90C2×#1055—42no—
91#2486—131no—
92#1799D1311yescharacteristic
93#1460—131no—
94#1344—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13#10212yes—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13C2×D811yescharacteristic
106C23×C13C2×SD1611yescharacteristic
107D4×C13—42no—
108D4×C13—42no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—81no—
122C2×C4×C13—82no—
123C2×C4×C13—82no—
124C2×C4×C13—82no—
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#10212yes—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—84no—
135#1055—82no—
136C2×#123—261no—
137C2×C4×D4C2×D1311yescharacteristic
138C22×C4⋊C4—131no—
139#431—261no—
140C2×#99—21no—
141#398—132no—
142#397—132no—
143#389—261no—
144#381—261no—
145#380—21no—
146#380—131no—
147#380—261no—
148#342C2×D1312yes—
149#323—132no—
150#323—261no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—42no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13C2×#9911yescharacteristic
166C22×C13C2×#10211yescharacteristic
167C22×C13#42111yescharacteristic
168C4×C13—21no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—162no—
174C4×C13#35212yes—
175Dic13—82no—
176Dic13—82no—
177C22×D4C22⋊D1311yescharacteristic
178C23×C4—261no—
179C23×C4C4×D1311yescharacteristic
180C23×C4C22⋊D1311yescharacteristic
181#123—522no—
182#123—522no—
183C4×D4—41no—
184C4×D4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—132no—
187C2×C4⋊C4—262no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—521no—
191C2×C4⋊C4—521no—
192C2×C4⋊C4C4×D1311yescharacteristic
193C2×C22⋊C4—22no—
194C2×C22⋊C4—261no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4D5211yescharacteristic
197C2×C22⋊C4C22×D1311yescharacteristic
198C2×C42D5211yescharacteristic
199C4⋊C8—521no—
200#99—42no—
201C22⋊C8—262no—
202C4×C8—521no—
203#95—41no—
204#95—132no—
205#95—262no—
206#95—262no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—41no—
210C2×C13—42no—
211C2×C13—41no—
212C2×C13#151911yescharacteristic
213C2×C13C2×#35211yescharacteristic
214C2×C13#212911yescharacteristic
215C24#610311yescharacteristic
216C24C2×C22⋊D1311yescharacteristic
217C2×D4—41no—
218C2×D4—41no—
219C2×D4#610412yes—
220C2×D4#610612yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4—522no—
231C22×C4—522no—
232C22×C4—522no—
233C22×C4#610311yescharacteristic
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4C2×C4×D1311yescharacteristic
237C22×C4C2×D5211yescharacteristic
238C2×C8—522no—
239C4⋊C4—41no—
240C4⋊C4—82no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C4⋊C4—521no—
244C4⋊C4—521no—
245C4⋊C4—524no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—522no—
251C22⋊C4—522no—
252C22⋊C4—522no—
253C42—21no—
254C42—21no—
255C13#1187411yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23#8804912yes—
265C23C2×#610311yescharacteristic
266C23C2×#610411yescharacteristic
267C23C2×#610611yescharacteristic
268D4—42no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—1044no—
293C2×C4#8804611yescharacteristic
294C2×C4#8804611yescharacteristic
295C2×C4#8804912yes—
296C8—1042no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×#8804611yescharacteristic
312C22C2×#8804911yescharacteristic
313C22#1171866611yescharacteristic
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—162no—
320C4—1042no—
321C4—1042no—
322C4#1171806412yes—
323C2—21no—
324C2—21no—
325C2—41no—
326C2—42no—
327C2—41no—
328C2#1311340311yescharacteristic
329C2C2×#1171806411yescharacteristic
330C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1799C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1799D13
hypocenterC13#11874
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13112835C2semidirect
7. C22×C4⋊Dic13C4semidirect
11. #11718873C4semidirect
12. #11718644C4semidirect
255. C13#11874semidirect

Maximal subgroups

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

subgroupindex
#131191442
#131131572
#131128352
C13×#17992
#1187413