Finite Group Databasebeta

← #16788209

Subgroups — #16788209

Order 3328.

396 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 70 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#13130735C211yesmaximal, characteristic
2C2×#11718286C211yesmaximal, characteristic
3#13129835C212yesmaximal, complemented
4#13129820C212yesmaximal, complemented
5#13119119C211yesmaximal, characteristic
6C2×C13×#117C411yescharacteristic
7C22×#6101C2211yescharacteristic
8#11719169—21no—
9C2×C22⋊#1057—21no—
10#11718872C411yescharacteristic
11#11718643C411yescharacteristic
12#11718643C2211yescharacteristic
13#11718641C411yescharacteristic
14#11718641C2211yescharacteristic
15#11718607—21no—
16#11718604—21no—
17#11718594—21no—
18#11718594—21no—
19#11718291—21no—
20#11718291C2212yes—
21#11718286—21no—
22#11718286C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C2×#6122—22no—
27C22×#1057—41no—
28C13×#117—41no—
29C13×#117—41no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C42×C13—21no—
34C2×C22⋊Dic13—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—41no—
38C2×#6101—41no—
39C2×#6101C2×C411yescharacteristic
40C2×#6101D411yescharacteristic
41C2×#6101D411yescharacteristic
42C2×#6101C2311yescharacteristic
43C22⋊#1057—22no—
44C22⋊#1057—41no—
45C22⋊#1057—41no—
46C22⋊#1057—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56#11850—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—22no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—41no—
73C22×Dic13—42no—
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C2×D411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78#6122—42no—
79#6122—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—82no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C42×C13—42no—
88C22⋊Dic13—42no—
89#6101—41no—
90#6101—41no—
91#6101—41no—
92#6101—41no—
93#6101—42no—
94#6101—42no—
95#2484—131no—
96#1821—131no—
97C2×#324—131no—
98#1353—132no—
99#1346—132no—
100C23×C13—22no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13#9911yescharacteristic
105C23×C13#9911yescharacteristic
106C23×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—81no—
137C2×Dic13#13512yes—
138#1057—82no—
139#1057—82no—
140C2×#117#26111yescharacteristic
141C22×C4⋊C4—131no—
142#407—261no—
143C2×C22⋊C8—261no—
144#400—131no—
145#400—131no—
146#398—131no—
147#398—131no—
148#387—261no—
149#387—261no—
150#385—261no—
151#381—131no—
152#381—261no—
153#343—132no—
154#343—261no—
155#324—132no—
156#324—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—42no—
165C22×C13—42no—
166C22×C13#35212yes—
167C22×C13C2×#9911yescharacteristic
168C22×C13#41611yescharacteristic
169C22×C13#42111yescharacteristic
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—81no—
173C4×C13—81no—
174Dic13—22no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—81no—
179Dic13—81no—
180C23×C4—131no—
181C23×C4—131no—
182C23×C4C2×#26111yescharacteristic
183C2×M16—262no—
184C22×C8—521no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—521no—
194C2×C4⋊C4—521no—
195C2×C4⋊C4C2×#26111yescharacteristic
196C2×C4⋊C4C2×#26111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—261no—
199C2×C42—21no—
200C22⋊C8—262no—
201C22⋊C8—521no—
202C22⋊C8—521no—
203C22⋊C8—521no—
204#95—131no—
205#95—131no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210#95—261no—
211#95—261no—
212#95—261no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—22no—
216C2×C13—41no—
217C2×C13#151611yescharacteristic
218C2×C13C2×#35211yescharacteristic
219C2×C13#213311yescharacteristic
220C24C22⋊#26111yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—262no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—521no—
238C22×C4—522no—
239C22×C4C22⋊#26111yescharacteristic
240C22×C4C22×#26111yescharacteristic
241M16—522no—
242M16—522no—
243C2×C8—522no—
244C2×C8—522no—
245C2×C8—1042no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—521no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—522no—
253C4⋊C4—522no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—522no—
257C42—42no—
258C13#1185011yescharacteristic, complemented, Sylow
259C23—22no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23#8811911yescharacteristic
264C23#8811911yescharacteristic
265C23C2×C22⋊#26111yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—132no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—1041no—
297C8—1042no—
298C8—1042no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22#1171828812yes—
309C22#1171916511yescharacteristic
310C22#1171916611yescharacteristic
311C22C2×#8811911yescharacteristic
312C4—41no—
313C4—41no—
314C4—81no—
315C4—81no—
316C4—262no—
317C4—521no—
318C4—521no—
319C4—521no—
320C4—1041no—
321C4—1041no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2#1313026211yescharacteristic
327C2C2×#1171828811yescharacteristic
328C2#1313113111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×#6101C23
hypercenterC2×#117#261
hypocenterC13#11850
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #13129835C2semidirect
4. #13129820C2semidirect
258. C13#11850semidirect

Maximal subgroups

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

subgroupindex
#131307352
C2×#117182862
#131298352
#131298202
#131191192
#1185013