Finite Group Databasebeta

← #15774074

Subgroups — #15774074

Order 3328.

372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 95 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#13120198C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13112867C212yesmaximal
4#13112864C212yesmaximal
5C13×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8C13×#431—21no—
9#11718891—21no—
10C2×#88076—21no—
11#11718647C411yescharacteristic
12#11718647C2211yescharacteristic
13#11718640C411yescharacteristic
14#11718640C2211yescharacteristic
15#11718634—21no—
16#11718597C411yescharacteristic
17#11718594—21no—
18#11718594—21no—
19#11718585—21no—
20C13×#324—21no—
21C13×#324C2212yes—
22#11718122C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—21no—
39C2×#6099—22no—
40C4×Dic26—41no—
41C4×Dic26—41no—
42C13×C4⋊C8—41no—
43C13×C22⋊C8—22no—
44C4×C8×C13—41no—
45#88076—42no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C4⋊#1055—41no—
56C4⋊#1055—41no—
57#11905—131nomaximal, Sylow
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13SD1612yes—
61C2×Q8×C13Q1612yes—
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—
72C22×Dic13—21no—
73C2×Dic26—41no—
74C2×Dic26—42no—
75C2×C8×C13—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C4⋊Dic13—42no—
86C4⋊Dic13—41no—
87#6101—42no—
88#6101—42no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—42no—
92#6099—42no—
93#6099—42no—
94C2×#1055—42no—
95#2581—131no—
96#1801—131no—
97#1461D1311yescharacteristic
98#1354—132no—
99#1353—132no—
100C23×C13C2×C22⋊C411yescharacteristic
101Q8×C13—42no—
102Q8×C13—42no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13#9911yescharacteristic
118C2×C4×C13#10312yes—
119C2×C4×C13#10312yes—
120C2×C4×C13C2×SD1611yescharacteristic
121C2×C4×C13C2×Q1611yescharacteristic
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—42no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133Dic26—42no—
134Dic26—42no—
135C8×C13—82no—
136#1055—82no—
137C2×C4×Q8—131no—
138C2×C4×Q8C2×D1311yescharacteristic
139#431—21no—
140#423—261no—
141C2×#101—261no—
142#400—131no—
143#400—131no—
144#395—131no—
145#395—131no—
146#391—261no—
147#389—261no—
148#387—261no—
149#387—261no—
150#382—131no—
151#343—132no—
152#324—21no—
153#324C2×D1312yes—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10311yescharacteristic
158C22×C13#42111yescharacteristic
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—22no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168Dic13—42no—
169Dic13—81no—
170Dic13—81no—
171Dic13—81no—
172C22×Q8—131no—
173C22×Q8D5211yescharacteristic
174C2×M16—262no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—521no—
178C4×Q8—521no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C4×D1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C42—261no—
188C2×C42C4×D1311yescharacteristic
189C2×C42D5211yescharacteristic
190C2×C42C22⋊D1311yescharacteristic
191C4⋊C8—41no—
192C4⋊C8—521no—
193C4⋊C8—521no—
194#101—522no—
195C22⋊C8—22no—
196C4×C8—41no—
197#95—131no—
198#95—131no—
199#95—261no—
200#95—261no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206C2×C13—21no—
207C2×C13—21no—
208C2×C13#152011yescharacteristic
209C2×C13#212011yescharacteristic
210C2×C13#213311yescharacteristic
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—521no—
214C2×Q8—522no—
215C2×Q8#609512yes—
216C2×Q8Dic5212yes—
217C22×C4—261no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4#610311yescharacteristic
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4#610311yescharacteristic
225C22×C4C2×C4×D1311yescharacteristic
226C22×C4C2×D5211yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228M16—522no—
229M16—522no—
230C2×C8—42no—
231C2×C8—522no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—521no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—522no—
248C13#1190511yescharacteristic, complemented, Sylow
249C23C2×#610311yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—522no—
253Q8—522no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—262no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—522no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4#8804611yescharacteristic
279C2×C4#8804611yescharacteristic
280C2×C4#8805612yes—
281C2×C4#8805612yes—
282C2×C4C2×#609511yescharacteristic
283C2×C4C2×Dic5211yescharacteristic
284C8—82no—
285C8—1042no—
286C22—21no—
287C22—21no—
288C22C2×#8804611yescharacteristic
289C22C2×#8805611yescharacteristic
290C22#1171880011yescharacteristic
291C4—21no—
292C4—21no—
293C4—22no—
294C4—22no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—522no—
301C4—1041no—
302C4—1041no—
303C4—1041no—
304C2—21no—
305C2—21no—
306C2#1311340911yescharacteristic
307C2#1311647511yescharacteristic
308C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1461C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1461D13
hypocenterC13#11905
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
248. C13#11905semidirect

Maximal subgroups

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

subgroupindex
#131201982
#131148322
#131128672
#131128642
C13×#14612
#1190513