Finite Group Databasebeta

← #16788397

Subgroups — #16788397

Order 3328.

372 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 76 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#13130702C211yesmaximal, characteristic
2#13130078C211yesmaximal, characteristic
3#13129837C212yesmaximal
4#13129835C212yesmaximal
5#13120202C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113—21no—
9#11719129—21no—
10#11719125—21no—
11#11718890C411yescharacteristic
12#11718890C2211yescharacteristic
13#11718643C411yescharacteristic
14#11718643C2211yescharacteristic
15#11718639—21no—
16#11718639—21no—
17#11718597C411yescharacteristic
18#11718590—21no—
19#11718589—21no—
20#11718291C2212yes—
21#11718286C2212yes—
22#11718285—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Dic26D411yescharacteristic
25C2×#6122—22no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13D411yescharacteristic
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101C2×C411yescharacteristic
37C2×#6101C2311yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C4×Dic26—41no—
41C4×Dic26—41no—
42C22⋊#1057—22no—
43#88113—42no—
44#88112—41no—
45#88112—41no—
46C4⋊#1057—41no—
47C4×#1057—41no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071C2×C411yescharacteristic
56#88071C2×C411yescharacteristic
57#11905—131nomaximal, Sylow
58C2×Q8×C13—42no—
59C2×Q8×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C2×D411yescharacteristic
70C22×Dic13C2×D411yescharacteristic
71C2×Dic26—41no—
72C2×Dic26—41no—
73C2×Dic26SD1612yes—
74C2×Dic26Q1612yes—
75#6122—42no—
76#6122—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—42no—
85C4⋊Dic13—41no—
86C4⋊Dic13—42no—
87#6101—41no—
88#6101—41no—
89#6101—42no—
90#6101—42no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95#2581—131no—
96#1801—131no—
97#1461—131no—
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—22no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13#10312yes—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13#10312yes—
131C2×Dic13C2×SD1611yescharacteristic
132C2×Dic13C2×Q1611yescharacteristic
133Dic26—42no—
134Dic26—42no—
135#1057—82no—
136#1057—82no—
137C2×C4×Q8—131no—
138C2×C4×Q8#26111yescharacteristic
139#431—261no—
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—132no—
153#324—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10311yescharacteristic
158C22×C13#42111yescharacteristic
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—22no—
162C4×C13—42no—
163C4×C13—41no—
164C4×C13—81no—
165Dic13—21no—
166Dic13—22no—
167Dic13—21no—
168Dic13—41no—
169Dic13—41no—
170Dic13—81no—
171Dic13—81no—
172C22×Q8—131no—
173C22×Q8C2×#26111yescharacteristic
174C2×M16—262no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—521no—
178C4×Q8—521no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4C2×#26111yescharacteristic
187C2×C42—21no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42C2×#26111yescharacteristic
191C4⋊C8—521no—
192C4⋊C8—521no—
193C4⋊C8—521no—
194#101—522no—
195C22⋊C8—262no—
196C4×C8—521no—
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—42no—
212C2×Q8—41no—
213C2×Q8—132no—
214C2×Q8—132no—
215C2×Q8—521no—
216C2×Q8—521no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4C22⋊#26111yescharacteristic
226C22×C4C22⋊#26111yescharacteristic
227C22×C4C22×#26111yescharacteristic
228M16—522no—
229M16—522no—
230C2×C8—522no—
231C2×C8—522no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C4⋊C4—521no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C4⋊C4—522no—
241C42—21no—
242C42—21no—
243C42—42no—
244C42—261no—
245C42—261no—
246C42—261no—
247C42—261no—
248C13#1190511yescharacteristic, complemented, Sylow
249C23C2×C22⋊#26111yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—522no—
253Q8—522no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—131no—
265C2×C4—132no—
266C2×C4—131no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4#8811712yes—
282C2×C4#8811911yescharacteristic
283C2×C4#8811911yescharacteristic
284C8—1042no—
285C8—1042no—
286C22—21no—
287C22—21no—
288C22C2×#8811711yescharacteristic
289C22#1171915511yescharacteristic
290C22C2×#8811911yescharacteristic
291C4—22no—
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—81no—
297C4—261no—
298C4—262no—
299C4—261no—
300C4—521no—
301C4—521no—
302C4—1041no—
303C4—1041no—
304C2—21no—
305C2—21no—
306C2#1313027611yescharacteristic
307C2#1313108711yescharacteristic
308C2#1313113111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×#6101C23
hypercenterC2×C4×Q8#261
hypocenterC13#11905
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

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
#131307022
#131300782
#131298372
#131298352
#131202022
#1190513