Finite Group Databasebeta

← #15756525

Subgroups — #15756525

Order 3328.

446 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C4×#88073C211yesmaximal, characteristic
2#13113177C211yesmaximal, characteristic
3#13112729C212yesmaximal, complemented
4#13112700C212yesmaximal, complemented
5C13×#2353C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#388—21no—
8C13×#387—21no—
9C13×#386—21no—
10C13×#383C2211yescharacteristic
11C13×#381C411yescharacteristic
12C13×#380C411yescharacteristic
13C4×C13×C22⋊C4—21no—
14C4×C13×C22⋊C4C411yescharacteristic
15C13×#376C2211yescharacteristic
16C2×C13×#95C411yescharacteristic
17C2×#88073—21no—
18#11718587C2212yes—
19C4×#6099C2212yes—
20#11718122—21no—
21#11718117—21no—
22#11718117—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6099—22no—
40C13×#95—21no—
41C13×#95—21no—
42C13×#95—21no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95C2×C411yescharacteristic
46C13×#95C2×C411yescharacteristic
47C13×#95C2×C411yescharacteristic
48C13×#95C2×C411yescharacteristic
49#88073—24no—
50C22⋊#1055—22no—
51C4⋊#1055—22no—
52#88043—22no—
53#88043—22no—
54C4×#1055—22no—
55#8772—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C22⋊C411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—81no—
72C22×C4×C13—81no—
73C22×C4×C13—81no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×C4⋊C4—22no—
80C13×C4⋊C4—81no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—81no—
86C42×C13—42no—
87C42×C13—81no—
88C42×C13#4112yes—
89C42×C13#4112yes—
90#6099—24no—
91#6099—42no—
92C2×#1055—42no—
93C2×#1055—42no—
94#2353D1311yescharacteristic
95C4×#100—131no—
96#1466—131no—
97#1300—132no—
98#1288—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13#10412yes—
109C23×C13C2×C22⋊C411yescharacteristic
110D4×C13—44no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—84no—
136C2×C4×C13#11711yescharacteristic
137C2×C4×C13#11711yescharacteristic
138C2×C4×C13#12312yes—
139C2×C4×C13#12312yes—
140#1055—44no—
141#1055—82no—
142C2×C4×D4C2×D1311yescharacteristic
143#432—132no—
144C2×#100—261no—
145C4×M16—132no—
146#388—21no—
147#387—21no—
148#386—21no—
149#383C2×D1311yescharacteristic
150#381Dic1311yescharacteristic
151#380Dic1311yescharacteristic
152C4×C22⋊C4—21no—
153C4×C22⋊C4Dic1311yescharacteristic
154#376C2×D1311yescharacteristic
155C2×#95Dic1311yescharacteristic
156#343—261no—
157#323—261no—
158#323—261no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—22no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13#38111yescharacteristic
172C22×C13C2×#10411yescharacteristic
173C22×C13#42111yescharacteristic
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—42no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13—81no—
184C22×D4C22⋊D1311yescharacteristic
185C23×C4—21no—
186C23×C4C2×Dic1311yescharacteristic
187C23×C4C2×Dic1311yescharacteristic
188C2×M16—262no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C22⋊D1311yescharacteristic
193C2×C22⋊C4—21no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4C22⋊D1311yescharacteristic
197C2×C22⋊C4C22⋊D1311yescharacteristic
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C22×D1311yescharacteristic
201C4⋊C8—262no—
202#100—264no—
203C22⋊C8—262no—
204#97—262no—
205#97—262no—
206C4×C8—262no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95C2×Dic1311yescharacteristic
213#95C2×Dic1311yescharacteristic
214#95C2×Dic1311yescharacteristic
215#95C2×Dic1311yescharacteristic
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—42no—
219C2×C13—81no—
220C2×C13#182611yescharacteristic
221C2×C13#182711yescharacteristic
222C2×C13#182911yescharacteristic
223C24C22⋊Dic1311yescharacteristic
224C24C22⋊Dic1311yescharacteristic
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22×Dic1311yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246M16—264no—
247M16—522no—
248C2×C8—522no—
249C2×C8—522no—
250C4⋊C4—22no—
251C4⋊C4—81no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—81no—
257C42—42no—
258C42—81no—
259C42#612712yes—
260C42#612712yes—
261C13#877211yescharacteristic, complemented, Sylow
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#8807712yes—
272C23C2×C22⋊Dic1311yescharacteristic
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—84no—
299C2×C4#8818011yescharacteristic
300C2×C4#8818011yescharacteristic
301C2×C4#8818312yes—
302C2×C4#8818312yes—
303C8—524no—
304C8—1042no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—42no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22#1171887211yescharacteristic
318C22C2×#8807711yescharacteristic
319C22#1171889711yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—81no—
334C2#1311493511yescharacteristic
335C2#1311494011yescharacteristic
336C2#1311494711yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2353C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2353D13
hypocenterC13#8772
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2353

Complements

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

NH ≅ G/Ntype
3. #13112729C2semidirect
4. #13112700C2semidirect
261. C13#8772semidirect

Maximal subgroups

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

subgroupindex
C4×#880732
#131131772
#131127292
#131127002
C13×#23532
#877213