Finite Group Databasebeta

← #16788407

Subgroups — #16788407

Order 3328.

388 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 80 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
2#13130078C211yesmaximal, characteristic
3#13129837C214yesmaximal
4#13120045C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Dic26C2211yescharacteristic
7C2×#88113—21no—
8#11719129—21no—
9#11719125—21no—
10#11718890C412yes—
11#11718890C2212yes—
12#11718637—21no—
13#11718635—21no—
14#11718634—21no—
15#11718634—21no—
16C4×C4⋊Dic13C411yescharacteristic
17#11718291C2212yes—
18#11718286C2212yes—
19#11718285—21no—
20C22×Q8×C13C2×C412yes—
21C22×Dic26D411yescharacteristic
22C2×#6122—22no—
23C13×C4⋊Q8—41no—
24C13×C4⋊Q8—41no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13D411yescharacteristic
30C2×#6101—22no—
31C2×#6101—22no—
32C2×#6101C2×C411yescharacteristic
33C2×#6101C2311yescharacteristic
34C2×C4×Dic13—21no—
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C4×Dic26—41no—
38C4×Dic26—41no—
39C22⋊#1057—22no—
40#88113—42no—
41#88112—41no—
42#88112—41no—
43C4⋊#1057—41no—
44C4×#1057—41no—
45#88071—22no—
46#88071—22no—
47#88071C2×C412yes—
48#11908—131nomaximal, Sylow
49C2×Q8×C13—42no—
50C2×Q8×C13—82no—
51C22×C4×C13—22no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—22no—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C2×D411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26SD1612yes—
63C2×Dic26Q1612yes—
64#6122—42no—
65#6122—42no—
66C2×#1057—42no—
67C2×#1057—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C42×C13—21no—
72C42×C13—21no—
73C4⋊Dic13—24no—
74C4⋊Dic13—41no—
75#6101—41no—
76#6101—41no—
77#6101—82no—
78#6101—82no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13—21no—
83C4×Dic13—42no—
84#2567—131no—
85#1801—131no—
86#1461—131no—
87#1354—134no—
88C23×C13C2×C22⋊C411yescharacteristic
89Q8×C13—84no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13#9911yescharacteristic
99C2×C4×C13#9911yescharacteristic
100C2×C4×C13#10312yes—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—24no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13#10312yes—
113C2×Dic13C2×SD1611yescharacteristic
114C2×Dic13C2×Q1611yescharacteristic
115Dic26—42no—
116Dic26—42no—
117#1057—82no—
118#1057—82no—
119C2×C4⋊Q8#26111yescharacteristic
120C2×C4×Q8—131no—
121#431—261no—
122#423—261no—
123C2×#101—261no—
124#395—132no—
125#395—132no—
126#391—261no—
127#389—261no—
128#389—261no—
129#384—261no—
130C4×C4⋊C4—131no—
131#343—132no—
132#324—132no—
133#324—261no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13C2×#9911yescharacteristic
137C22×C13C2×#10311yescharacteristic
138C22×C13#42111yescharacteristic
139C4×C13—21no—
140C4×C13—22no—
141C4×C13—41no—
142C4×C13—82no—
143C4×C13#35612yes—
144Dic13—21no—
145Dic13—22no—
146Dic13—21no—
147Dic13—44no—
148Dic13—41no—
149Dic13—41no—
150C22×Q8—131no—
151C22×Q8C2×#26112yes—
152C2×M16—262no—
153C4⋊Q8—41no—
154C4⋊Q8—41no—
155C4×Q8—521no—
156C4×Q8—521no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—131no—
160C2×C4⋊C4—131no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—261no—
163C2×C4⋊C4—262no—
164C2×C4⋊C4—262no—
165C2×C42—131no—
166C2×C42—131no—
167C2×C42—261no—
168C2×C42C2×#26111yescharacteristic
169C4⋊C8—521no—
170C4⋊C8—521no—
171C4⋊C8—521no—
172#101—522no—
173C22⋊C8—262no—
174C4×C8—521no—
175#95—132no—
176#95—262no—
177#95—262no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13#152011yescharacteristic
181C2×C13#212211yescharacteristic
182C2×C13C2×#35611yescharacteristic
183C2×Q8—42no—
184C2×Q8—82no—
185C2×Q8—132no—
186C2×Q8—132no—
187C2×Q8—521no—
188C2×Q8—521no—
189C22×C4—22no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—262no—
195C22×C4C22⋊#26111yescharacteristic
196C22×C4C22⋊#26111yescharacteristic
197C22×C4C22×#26111yescharacteristic
198M16—522no—
199M16—522no—
200C2×C8—522no—
201C2×C8—522no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—264no—
206C4⋊C4—521no—
207C4⋊C4—521no—
208C4⋊C4—521no—
209C4⋊C4—1042no—
210C4⋊C4—1042no—
211C42—21no—
212C42—21no—
213C42—261no—
214C42—261no—
215C42—261no—
216C42—261no—
217C42—522no—
218C13#1190811yescharacteristic, complemented, Sylow
219C23C2×C22⋊#26111yescharacteristic
220Q8—84no—
221Q8—522no—
222Q8—522no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—131no—
232C2×C4—132no—
233C2×C4—131no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—264no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—522no—
242C2×C4—522no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4#8811712yes—
246C2×C4#8811911yescharacteristic
247C2×C4#8811911yescharacteristic
248C8—1042no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22C2×#8811711yescharacteristic
253C22#1171915511yescharacteristic
254C22C2×#8811911yescharacteristic
255C4—22no—
256C4—21no—
257C4—41no—
258C4—82no—
259C4—261no—
260C4—262no—
261C4—261no—
262C4—524no—
263C4—521no—
264C4—521no—
265C4#1171830112yes—
266C2—21no—
267C2—21no—
268C2#1313027611yescharacteristic
269C2#1313109511yescharacteristic
270C2C2×#1171830111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×#6101C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11908
LCSG ▷ C22×C4×C13 ▷ C23×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
218. C13#11908semidirect

Maximal subgroups

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

subgroupindex
#131307022
#131300782
#131298372
#131200452
#1190813