Finite Group Databasebeta

← #15773663

Subgroups — #15773663

Order 3328.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#13118104C211yesmaximal, characteristic
2#13114919C211yesmaximal, characteristic
3#13112867C212yesmaximal, complemented
4#13112864C212yesmaximal, complemented
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8C13×#432—21no—
9C4×C22⋊Dic13—21no—
10#11718868—21no—
11#11718647C2211yescharacteristic
12#11718645—21no—
13#11718640C2211yescharacteristic
14#11718610C411yescharacteristic
15#11718609—21no—
16#11718608C411yescharacteristic
17C4×C4⋊Dic13C411yescharacteristic
18C4×#6101—21no—
19C13×#324C2212yes—
20C13×#323—21no—
21#11718122—21no—
22#11718122C2212yes—
23C23×C4×C13D411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C13×#117—41no—
26C13×#117—41no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C13×C22⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—21no—
42C2×#6099—22no—
43C4×Dic26—41no—
44C4×Dic26—41no—
45C13×C4⋊C8—41no—
46C13×C22⋊C8—22no—
47C13×#97—41no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—41no—
55C22⋊#1055—41no—
56#11816—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C2×Dic26—41no—
73C2×Dic26—42no—
74C2×C8×C13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C4⋊Dic13—42no—
86C4⋊Dic13—41no—
87#6101—42no—
88#6101—42no—
89#6101—42no—
90C4×Dic13—42no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93#6099—42no—
94#6099—42no—
95C2×#1055—42no—
96#2396—131no—
97#1822—131no—
98#1464D1311yescharacteristic
99#1354—132no—
100#1353—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#13712yes—
124C2×Dic13—22no—
125C2×Dic13—22no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136Dic26—42no—
137Dic26—42no—
138C8×C13—82no—
139#1055—82no—
140C2×C4×Q8—131no—
141C2×#117C2×D1311yescharacteristic
142#432—21no—
143#407—261no—
144#400—131no—
145#399—131no—
146#398—261no—
147#396—261no—
148#395—131no—
149#393—131no—
150C4×C4⋊C4—131no—
151C4×C4⋊C4—261no—
152C4×C22⋊C4—261no—
153#343—132no—
154#343—261no—
155#324C2×D1312yes—
156#323—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—81no—
164C22×C13C2×#9911yescharacteristic
165C22×C13#41911yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—22no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174Dic13—42no—
175Dic13—42no—
176Dic13—81no—
177Dic13—81no—
178C22×Q8—131no—
179C23×C4D5211yescharacteristic
180C2×M16—262no—
181C4×Q8—521no—
182C4×Q8—521no—
183#117—41no—
184#117—41no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4D5211yescharacteristic
191C2×C4⋊C4C22×D1311yescharacteristic
192C2×C22⋊C4—261no—
193C2×C22⋊C4—261no—
194C2×C22⋊C4C4×D1311yescharacteristic
195C2×C22⋊C4C22⋊D1311yescharacteristic
196C2×C42—261no—
197C2×C42—261no—
198C2×C42C4×D1311yescharacteristic
199C2×C42C22⋊D1311yescharacteristic
200C4⋊C8—41no—
201C22⋊C8—22no—
202C22⋊C8—521no—
203C22⋊C8—521no—
204#97—41no—
205#95—131no—
206#95—131no—
207#95—261no—
208#95—261no—
209#95—261no—
210#95—261no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—81no—
214C2×C13#151111yescharacteristic
215C2×C13#212011yescharacteristic
216C2×C13#213211yescharacteristic
217C24#610311yescharacteristic
218C2×Q8—521no—
219C2×Q8—522no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4#610311yescharacteristic
229C22×C4#610311yescharacteristic
230C22×C4#610311yescharacteristic
231C22×C4C2×C4×D1311yescharacteristic
232C22×C4C2×D5211yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234M16—522no—
235M16—522no—
236C2×C8—42no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—521no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—522no—
248C22⋊C4—522no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—522no—
254C42—521no—
255C42—521no—
256C13#1181611yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23C2×#610311yescharacteristic
263Q8—522no—
264Q8—522no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—262no—
280C2×C4—262no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4#8804611yescharacteristic
292C2×C4#8804611yescharacteristic
293C2×C4#8816312yes—
294C8—82no—
295C8—1042no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#8804611yescharacteristic
304C22#1171878111yescharacteristic
305C22#1171880011yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—522no—
314C4—522no—
315C4—1041no—
316C4—1041no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1311337011yescharacteristic
321C2#1311647511yescharacteristic
322C2#1311651911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1464C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1464D13
hypocenterC13#11816
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
4. #13112864C2semidirect
256. C13#11816semidirect

Maximal subgroups

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

subgroupindex
#131181042
#131149192
#131128672
#131128642
C13×#14642
#1181613