Finite Group Databasebeta

← #15773308

Subgroups — #15773308

Order 3328.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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×#88076C211yesmaximal, characteristic, complemented
2#13113160C211yesmaximal, characteristic, complemented
3#13112866C212yesmaximal, complemented
4#13112839C212yesmaximal
5C13×#2632C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#399—21no—
9C13×#395C411yescharacteristic
10C13×#395C2211yescharacteristic
11C13×#394C411yescharacteristic
12C13×#394C2211yescharacteristic
13C13×#393—21no—
14C13×#388—21no—
15C13×#388—21no—
16C13×#383C411yescharacteristic
17C2×#88076—21no—
18#11718586—21no—
19C4×#6099—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C22×D4×C13C2×C411yescharacteristic
26C13×#124—41no—
27C13×#124—41no—
28C4×Q8×C13—41no—
29C4×Q8×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×#6099—22no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88076—24no—
52C22⋊#1055—22no—
53C4⋊#1055—41no—
54#88043—41no—
55C4×#1055—41no—
56C4×#1055—41no—
57#11738—131nomaximal, Sylow
58C24×C13—21no—
59C2×Q8×C13—22no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13—81no—
64C2×D4×C13—41no—
65C2×D4×C13—81no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—81no—
80C13×C4⋊C4—81no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—81no—
87C13×C22⋊C4—81no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—21no—
94#6099—24no—
95#6099—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98#2632D1311yescharacteristic
99C4×#101—131no—
100#1461—131no—
101#1354—132no—
102#1345—132no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13C2×C22⋊C411yescharacteristic
111Q8×C13—44no—
112Q8×C13—82no—
113D4×C13—82no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
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—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13#9911yescharacteristic
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13#10412yes—
140C2×C4×C13#13512yes—
141#1055—44no—
142#1055—82no—
143C2×#124Dic1311yescharacteristic
144C2×C4×Q8C2×D1311yescharacteristic
145#431—261no—
146C2×#101—261no—
147C4×M16—261no—
148#399—21no—
149#395Dic1311yescharacteristic
150#395C2×D1311yescharacteristic
151#394Dic1311yescharacteristic
152#394C2×D1311yescharacteristic
153#393—21no—
154#388—21no—
155#388—21no—
156#383Dic1311yescharacteristic
157#343—132no—
158#324—132no—
159#324—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13—81no—
169C22×C13C2×#9911yescharacteristic
170C22×C13#41611yescharacteristic
171C22×C13C2×#10411yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183C22×Q8C2×Dic1311yescharacteristic
184C22×Q8C22⋊D1311yescharacteristic
185C22×D4C2×Dic1311yescharacteristic
186C2×M16—262no—
187#124—41no—
188#124—41no—
189C4×Q8—41no—
190C4×Q8—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×Dic1311yescharacteristic
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C4⋊C4C22×D1311yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C42C2×Dic1311yescharacteristic
203C2×C42C22⋊D1311yescharacteristic
204C2×C42C22⋊D1311yescharacteristic
205C4⋊C8—521no—
206#101—264no—
207C22⋊C8—262no—
208#97—521no—
209C4×C8—521no—
210C4×C8—521no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95C2×Dic1311yescharacteristic
216#95C2×Dic1311yescharacteristic
217C2×C13—21no—
218C2×C13—21no—
219C2×C13—161no—
220C2×C13#150111yescharacteristic
221C2×C13#212211yescharacteristic
222C2×C13#213311yescharacteristic
223C24—21no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—81no—
229C2×D4—41no—
230C2×D4—81no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4C22⋊Dic1311yescharacteristic
235C22×C4C22⋊Dic1311yescharacteristic
236C22×C4C22⋊Dic1311yescharacteristic
237C22×C4C22⋊Dic1311yescharacteristic
238C22×C4C22×Dic1311yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—264no—
242M16—522no—
243C2×C8—522no—
244C2×C8—522no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—81no—
249C4⋊C4—81no—
250C22⋊C4—42no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—81no—
256C22⋊C4—81no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C13#1173811yescharacteristic, complemented, Sylow
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C2×C22⋊Dic1311yescharacteristic
272Q8—44no—
273Q8—82no—
274D4—82no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
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—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4#8807411yescharacteristic
299C2×C4#8807411yescharacteristic
300C2×C4#8807712yes—
301C2×C4#8820412yes—
302C8—524no—
303C8—1042no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C2×#8807411yescharacteristic
314C22#1171889411yescharacteristic
315C22C2×#8807711yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C2—21no—
328C2—21no—
329C2—161no—
330C2#1311332711yescharacteristic
331C2#1311648611yescharacteristic
332C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2632C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2632D13
hypocenterC13#11738
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2632

Complements

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

NH ≅ G/Ntype
1. C4×#88076C2semidirect
2. #13113160C2semidirect
3. #13112866C2semidirect
263. C13#11738semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131131602
#131128662
#131128392
C13×#26322
#1173813