Finite Group Databasebeta

← #15773288

Subgroups — #15773288

Order 3328.

434 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 95 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#13112863C212yesmaximal, complemented
4#13112839C212yesmaximal
5C13×#2398C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C411yescharacteristic
8C13×#400C411yescharacteristic
9C13×#400C2211yescharacteristic
10C13×#397—21no—
11C13×#394C411yescharacteristic
12C13×#394C2211yescharacteristic
13C13×#393—21no—
14C4×C13×C22⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C13×#376C411yescharacteristic
17C2×#88076—21no—
18#11718586—21no—
19C4×#6099—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13—21no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C42×C13—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×#6099—22no—
44C13×#95—21no—
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#11734—131nomaximal, Sylow
58C24×C13—21no—
59C2×Q8×C13—22no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13—42no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—42no—
94#6099—24no—
95#6099—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98#2398D1311yescharacteristic
99C4×#101—131no—
100#1461—131no—
101#1353—132no—
102#1345—132no—
103C23×C13—22no—
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—
112D4×C13—42no—
113D4×C13—42no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
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—82no—
138C2×C4×C13—82no—
139C2×C4×C13#9911yescharacteristic
140C2×C4×C13#9911yescharacteristic
141C2×C4×C13#10412yes—
142C2×C4×C13#13512yes—
143#1055—44no—
144#1055—82no—
145C2×C4×Q8C2×D1311yescharacteristic
146C2×C4×D4Dic1311yescharacteristic
147#431—261no—
148C2×#101—261no—
149C4×M16—261no—
150#400Dic1311yescharacteristic
151#400C2×D1311yescharacteristic
152#397—21no—
153#394Dic1311yescharacteristic
154#394C2×D1311yescharacteristic
155#393—21no—
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158#376Dic1311yescharacteristic
159#343—132no—
160#324—132no—
161#324—261no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—42no—
165C22×C13—42no—
166C22×C13—42no—
167C22×C13—81no—
168C22×C13—81no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13C2×#9911yescharacteristic
172C22×C13#41611yescharacteristic
173C22×C13C2×#10411yescharacteristic
174C4×C13—21no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13—81no—
184C4×C13#35512yes—
185C22×Q8C22⋊D1311yescharacteristic
186C22×D4C2×Dic1311yescharacteristic
187C23×C4—21no—
188C2×M16—262no—
189C4×Q8—41no—
190C4×Q8—41no—
191C4×D4—41no—
192C4×D4—41no—
193C2×C4⋊C4C2×Dic1311yescharacteristic
194C2×C4⋊C4C2×Dic1311yescharacteristic
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C4⋊C4C22×D1311yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C42—21no—
203C2×C42C2×Dic1311yescharacteristic
204C2×C42C22⋊D1311yescharacteristic
205C2×C42C22⋊D1311yescharacteristic
206C4⋊C8—521no—
207#101—264no—
208C22⋊C8—262no—
209#97—521no—
210C4×C8—521no—
211C4×C8—521no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95C2×Dic1311yescharacteristic
218#95C2×Dic1311yescharacteristic
219C2×C13—21no—
220C2×C13—21no—
221C2×C13—82no—
222C2×C13#150111yescharacteristic
223C2×C13#212011yescharacteristic
224C2×C13C2×#35511yescharacteristic
225C24—21no—
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—41no—
229C2×D4—41no—
230C2×D4—42no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4C22⋊Dic1311yescharacteristic
239C22×C4C22⋊Dic1311yescharacteristic
240C22×C4C22⋊Dic1311yescharacteristic
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22×Dic1311yescharacteristic
243C22×C4C2×C22⋊D1311yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245M16—264no—
246M16—522no—
247C2×C8—522no—
248C2×C8—522no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—42no—
265C13#1173411yescharacteristic, complemented, Sylow
266C23—22no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23C2×C22⋊Dic1311yescharacteristic
274Q8—44no—
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
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—41no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4#8807411yescharacteristic
303C2×C4#8807411yescharacteristic
304C2×C4#8807712yes—
305C2×C4#8820412yes—
306C8—524no—
307C8—1042no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22C2×#8807411yescharacteristic
318C22#1171889411yescharacteristic
319C22C2×#8807711yescharacteristic
320C4—21no—
321C4—22no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4#1171813412yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#1311332711yescharacteristic
335C2#1311647711yescharacteristic
336C2C2×#1171813411yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2398C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2398D13
hypocenterC13#11734
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. C4×#88076C2semidirect
2. #13113160C2semidirect
3. #13112863C2semidirect
265. C13#11734semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131131602
#131128632
#131128392
C13×#23982
#1173413