Finite Group Databasebeta

← #16791125

Subgroups — #16791125

Order 3328.

420 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 84 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#13130702C211yesmaximal, characteristic
2C4×#88113C211yesmaximal, characteristic
3#13129934C214yesmaximal
4#13120045C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Dic26C2211yescharacteristic
7C2×#88113C2212yes—
8C2×#88113C2212yes—
9#11719129—21no—
10C4×#6122—21no—
11#11718890—21no—
12#11718890—21no—
13#11718637C412yes—
14#11718635C2212yes—
15#11718634—21no—
16#11718634—21no—
17C4×C4⋊Dic13C411yescharacteristic
18#11718291—21no—
19#11718291—21no—
20C22×Q8×C13—21no—
21C22×Dic26C2311yescharacteristic
22C2×#6122—22no—
23C2×#6122—22no—
24C13×C4⋊Q8—41no—
25C13×C4⋊Q8—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×#6101—22no—
32C2×#6101—22no—
33C2×#6101D411yescharacteristic
34C2×#6101D411yescharacteristic
35C2×C4×Dic13C2×C412yes—
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C4×Dic26—41no—
39C4×Dic26—41no—
40#88113—22no—
41#88113—24no—
42#88113Q814yescomplemented
43#88112—41no—
44#88110—41no—
45C4⋊#1057—41no—
46C4×#1057—41no—
47#88071—21no—
48#88071—22no—
49#88071—22no—
50#13302—131nomaximal, Sylow
51C2×Q8×C13—42no—
52C2×Q8×C13—82no—
53C22×C4×C13—22no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—22no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C2×Dic26—41no—
63C2×Dic26—41no—
64C2×Dic26C2×Q812yes—
65C2×Dic26#4112yes—
66#6122—24no—
67#6122—42no—
68#6122—42no—
69#6122—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C42×C13—21no—
76C42×C13—21no—
77C4⋊Dic13—24no—
78C4⋊Dic13—41no—
79#6101—41no—
80#6101—41no—
81#6101—82no—
82#6101—82no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13—42no—
88#2567—131no—
89#1801—131no—
90C4×#101—131no—
91#1394—134no—
92C23×C13C2×C22⋊C411yescharacteristic
93Q8×C13—84no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13#9911yescharacteristic
103C2×C4×C13#9911yescharacteristic
104C2×C4×C13C4×Q812yes—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—24no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13C22⋊Q812yes—
117C2×Dic13#12411yescharacteristic
118C2×Dic13C4⋊Q811yescharacteristic
119Dic26—42no—
120Dic26—42no—
121#1057—44no—
122#1057—82no—
123C2×C4⋊Q8#26111yescharacteristic
124C2×C4×Q8—131no—
125#423—261no—
126C2×#101—132no—
127C2×#101—132no—
128C4×M16—261no—
129#395—261no—
130#395—261no—
131#391—132no—
132#389—261no—
133#389—261no—
134#384—132no—
135C4×C4⋊C4—131no—
136#343—261no—
137#343—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#39111yescharacteristic
141C22×C13C2×#9911yescharacteristic
142C22×C13#41011yescharacteristic
143C4×C13—21no—
144C4×C13—22no—
145C4×C13—41no—
146C4×C13—82no—
147C4×C13#35612yes—
148Dic13—22no—
149Dic13—21no—
150Dic13—21no—
151Dic13—44no—
152Dic13—41no—
153Dic13—41no—
154C22×Q8—21no—
155C22×Q8—131no—
156C2×M16—262no—
157C2×M16—262no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4×Q8—521no—
161C4×Q8—521no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—261no—
167C2×C4⋊C4—262no—
168C2×C4⋊C4—262no—
169C2×C4⋊C4C2×#26112yes—
170C2×C42—131no—
171C2×C42—131no—
172C2×C42—132no—
173C2×C42C2×#26111yescharacteristic
174C4⋊C8—521no—
175C4⋊C8—521no—
176#101—134no—
177#101—262no—
178#101—264no—
179#97—521no—
180C4×C8—521no—
181#95—262no—
182#95—262no—
183#95—261no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#199611yescharacteristic
187C2×C13C2×#35611yescharacteristic
188C2×C13#213411yescharacteristic
189C2×Q8—42no—
190C2×Q8—82no—
191C2×Q8—132no—
192C2×Q8—132no—
193C2×Q8—521no—
194C2×Q8—521no—
195C22×C4—22no—
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—262no—
201C22×C4C22⋊#26111yescharacteristic
202C22×C4C22⋊#26111yescharacteristic
203C22×C4C22×#26111yescharacteristic
204M16—264no—
205M16—522no—
206M16—522no—
207M16—522no—
208C2×C8—522no—
209C2×C8—522no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—264no—
214C4⋊C4—521no—
215C4⋊C4—521no—
216C4⋊C4—521no—
217C4⋊C4—1042no—
218C4⋊C4—1042no—
219C42—21no—
220C42—21no—
221C42—261no—
222C42—261no—
223C42—261no—
224C42—261no—
225C42—522no—
226C13#1330211yescharacteristic, complemented, Sylow
227C23C2×C22⋊#26111yescharacteristic
228Q8—84no—
229Q8—522no—
230Q8—522no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—132no—
240C2×C4—131no—
241C2×C4—131no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—264no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4#8811911yescharacteristic
254C2×C4#8811911yescharacteristic
255C2×C4Q8×#26112yes—
256C8—524no—
257C8—1042no—
258C22—21no—
259C22—21no—
260C22#1171915611yescharacteristic
261C22(C2×#261)⋊Q811yescharacteristic
262C22C2×#8811911yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—82no—
267C4—262no—
268C4—261no—
269C4—261no—
270C4—524no—
271C4—521no—
272C4—521no—
273C4#1171830112yes—
274C2—21no—
275C2—21no—
276C2#1313102511yescharacteristic
277C2C2×#1171830111yescharacteristic
278C2#1313113511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Dic26C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#13302
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
42. #88113Q8semidirect
226. C13#13302semidirect

Maximal subgroups

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

subgroupindex
#131307022
C4×#881132
#131299342
#131200452
#1330213