Finite Group Databasebeta

← #16787442

Subgroups — #16787442

Order 3328.

368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 90 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#13131196C211yesmaximal, characteristic, complemented
2#13131195C211yesmaximal, characteristic, complemented
3#13129787C212yesmaximal, complemented
4D4⋊#6092C212yesmaximal, complemented
5#13123545C211yesmaximal, characteristic
6C2×#88161—21no—
7#11719253C411yescharacteristic
8C13×#436C411yescharacteristic
9#11718789—21no—
10D4×#1055C2211yescharacteristic
11#11718498C411yescharacteristic
12#11718495C2211yescharacteristic
13#11718388—21no—
14#11718386—21no—
15#11718349C411yescharacteristic
16C4×C8×D13C2211yescharacteristic
17#11718260—21no—
18#11718259—21no—
19#11718259—21no—
20#11718257—21no—
21C4⋊#6092C2212yes—
22C4×#6092C2212yes—
23C2×#6127—21no—
24C2×C13×M16—21no—
25C4×D4×C13C2×C411yescharacteristic
26#88194C811yescharacteristic
27#88192C811yescharacteristic
28C4×C22⋊D13—21no—
29C22×#1055—21no—
30#88161—44no—
31C2×#6094—21no—
32C2×#6094—21no—
33C2×C8×D13—21no—
34C2×C8×D13D411yescharacteristic
35C2×C8×D13D411yescharacteristic
36#88149C811yescharacteristic
37#88142C811yescharacteristic
38#88139—21no—
39#88138—21no—
40C4×D52C2×C411yescharacteristic
41C42×D13C2×C411yescharacteristic
42C2×#6092—22no—
43C2×#6092—22no—
44C13×C4⋊C8C2×C411yescharacteristic
45C13×C22⋊C8—21no—
46C4×C8×C13C2×C411yescharacteristic
47C22⋊#1055—21no—
48#88060—21no—
49#88060—21no—
50#88054—21no—
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C4⋊#1055C2×C411yescharacteristic
54C4×#1055C2311yescharacteristic
55#11630—131nomaximal, Sylow
56C2×D4×C13C2×C811yescharacteristic
57C22×C4×C13—21no—
58C2×C22⋊D13—21no—
59C2×C22⋊D13—21no—
60C2×C22⋊D13—21no—
61#6127—42no—
62#6127—42no—
63C2×D52—21no—
64C2×D52C2×C811yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13C22⋊C411yescharacteristic
67C2×C4×D13C2×C811yescharacteristic
68C2×C4×D13M1611yescharacteristic
69C2×Dic26—21no—
70C13×M16—42no—
71C2×C8×C13—21no—
72C2×C8×C13C22⋊C411yescharacteristic
73C2×C8×C13C22⋊C411yescharacteristic
74C13×C4⋊C4C2×C811yescharacteristic
75C13×C22⋊C4—21no—
76C42×C13C22×C411yescharacteristic
77C22⋊Dic13—21no—
78#6103—21no—
79#6103—21no—
80C4⋊Dic13C2×C811yescharacteristic
81#6101—21no—
82C4×Dic13C22⋊C411yescharacteristic
83C4×Dic13C2×C811yescharacteristic
84C4×Dic13M1611yescharacteristic
85C2×#1055—21no—
86C2×#1055—42no—
87C2×#1055C2×D411yescharacteristic
88C2×#1055C2×D411yescharacteristic
89#6094—42no—
90#6094—42no—
91C8×D13—22no—
92C8×D13—41no—
93C8×D13—42no—
94#6092—42no—
95#6092—42no—
96#2931—131no—
97#2162—131no—
98#2162—131no—
99D4⋊C16—132no—
100D4⋊C16—132no—
101C23×C13—21no—
102C22×D13—21no—
103C22×D13C22⋊C811yescharacteristic
104D4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13C22×C811yescharacteristic
110C2×C4×C13C2×M1611yescharacteristic
111C22⋊D13—42no—
112C22⋊D13—42no—
113C22⋊D13—42no—
114C2×Dic13—21no—
115C2×Dic13C22⋊C811yescharacteristic
116C2×Dic13C22⋊C811yescharacteristic
117C2×Dic13C22⋊C811yescharacteristic
118D52—22no—
119D52—42no—
120C4×D13—21no—
121C4×D13—21no—
122C4×D13—22no—
123C4×D13—22no—
124C4×D13—41no—
125C4×D13—41no—
126Dic26—42no—
127C8×C13—21no—
128C8×C13—21no—
129C8×C13—41no—
130#1055—21no—
131#1055—41no—
132#1055AGL(1,ℤ/8)12yes—
133C2×#131—261no—
134#532—131no—
135#436—131no—
136#436—261no—
137#436#26111yescharacteristic
138C8×D4—131no—
139C8×D4—131no—
140C8×D4—261no—
141#423—131no—
142#408—261no—
143C2×C4×C8—131no—
144C4⋊C16—132no—
145C4⋊C16—261no—
146C22⋊C16—261no—
147C22⋊C16—261no—
148C4×C16—132no—
149C4×C16—261no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13C2×C22⋊C811yescharacteristic
154C2×D13—21no—
155C2×D13—21no—
156C2×D13—21no—
157C2×D13—41no—
158C2×D13—41no—
159C2×D13—41no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13#41811yescharacteristic
163C4×C13#42111yescharacteristic
164C4×C13#50412yes—
165Dic13—21no—
166Dic13—21no—
167Dic13—41no—
168Dic13#35012yes—
169C2×#41—261no—
170#131—524no—
171C2×M16—21no—
172C2×M16—261no—
173C2×M16—261no—
174C22×C8—131no—
175C22×C8—131no—
176C22×C8—261no—
177C22×C8—261no—
178C4⋊Q8—131no—
179#127—131no—
180#124—261no—
181#121—131no—
182#121—131no—
183#121—261no—
184C4×D4—131no—
185C4×D4—261no—
186C4×D4C2×#26111yescharacteristic
187C2×C42—131no—
188C2×C16—262no—
189C2×C16—262no—
190C4⋊C8—131no—
191C4⋊C8—261no—
192C4⋊C8C2×#26111yescharacteristic
193C22⋊C8—21no—
194C22⋊C8—261no—
195C22⋊C8—261no—
196C22⋊C8—261no—
197C4×C8—131no—
198C4×C8—131no—
199C4×C8—131no—
200C4×C8C2×#26111yescharacteristic
201C2×C13—81no—
202C2×C13#147811yescharacteristic
203C2×C13#211311yescharacteristic
204C2×C13C2×#35011yescharacteristic
205D13—41no—
206D13—81no—
207#41—522no—
208#41—522no—
209C2×Q8—261no—
210C2×D4—131no—
211C2×D4—261no—
212C2×D4—261no—
213C2×D4—261no—
214C2×D4—261no—
215C2×D4D13⋊C811yescharacteristic
216C22×C4—21no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—261no—
221M16—42no—
222M16—522no—
223M16—522no—
224C2×C8—21no—
225C2×C8—131no—
226C2×C8—131no—
227C2×C8—262no—
228C2×C8—261no—
229C2×C8—521no—
230C2×C8—522no—
231C2×C8—522no—
232C2×C8C22⋊#26111yescharacteristic
233C2×C8C22⋊#26111yescharacteristic
234C4⋊C4—131no—
235C4⋊C4—261no—
236C4⋊C4D13⋊C811yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—261no—
239C22⋊C4—261no—
240C22⋊C4—261no—
241C42—131no—
242C42—131no—
243C42—131no—
244C42C22×#26111yescharacteristic
245C16—522no—
246C16—522no—
247C13#1163011yescharacteristic, complemented, Sylow
248C23—21no—
249C23—131no—
250C23—261no—
251Q8—522no—
252D4—22no—
253D4—262no—
254D4—522no—
255D4—522no—
256D4—522no—
257D4—522no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—131no—
262C2×C4—131no—
263C2×C4—131no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4C2×D13⋊C811yescharacteristic
272C2×C4D13⋊M1611yescharacteristic
273C2×C4C2×C22⋊#26111yescharacteristic
274C8—21no—
275C8—21no—
276C8—41no—
277C8—132no—
278C8—261no—
279C8—521no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—261no—
284C22—261no—
285C22—261no—
286C22—521no—
287C22—521no—
288C22—521no—
289C22D13⋊(C22⋊C8)11yescharacteristic
290C4—21no—
291C4—41no—
292C4—132no—
293C4—261no—
294C4—261no—
295C4—521no—
296C4#1171909612yes—
297C4#1171913811yescharacteristic
298C4#1171916611yescharacteristic
299C2—81no—
300C2—521no—
301C2—1041no—
302C2#1313013611yescharacteristic
303C2#1313106711yescharacteristic
304C2D13⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC13×#436C4
socleC22×C13C2×C22⋊C8
prime radical#11719253C4
cosocleC4×#1055C23
hypercenter#436#261
hypocenterC13#11630
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #13131196C2semidirect
2. #13131195C2semidirect
3. #13129787C2semidirect
4. D4⋊#6092C2semidirect
247. C13#11630semidirect

Maximal subgroups

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

subgroupindex
#131311962
#131311952
#131297872
D4⋊#60922
#131235452
#1163013