Finite Group Databasebeta

← #16782795

Subgroups — #16782795

Order 3328.

534 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 126 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#13131729C211yesmaximal, characteristic
2#13130138C212yesmaximal
3#13130079C211yesmaximal, characteristic
4#13129664C212yesmaximal
5C4⋊Q8×Dic13C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C2×Q8×Dic13C2211yescharacteristic
9Q8×#1057—24no—
10#11719119—22no—
11#11719119C2212yes—
12#11719119C2212yes—
13#11718891C411yescharacteristic
14#11718891C411yescharacteristic
15#11718646—22no—
16C4⋊C4×Dic13—22no—
17#11718596C411yescharacteristic
18C42×Dic13C2211yescharacteristic
19Q8⋊#1057—24no—
20#11718285—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×Q8×C13C2×C411yescharacteristic
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8C814yescomplemented
25C2×C13×C4⋊C4—22no—
26C2×C42×C13C2×C411yescharacteristic
27Q8×Dic13—22no—
28Q8×Dic13—22no—
29Q8×Dic13—22no—
30Q8×Dic13—22no—
31C2×C4⋊Dic13—22no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13D412yes—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D412yes—
41C2×C4×Dic13C2311yescharacteristic
42C22⋊#1057—22no—
43C22⋊#1057—22no—
44C4⋊#1057—24no—
45C4⋊#1057—22no—
46C4⋊#1057D414yes—
47C4×#1057—24no—
48C4×#1057—22no—
49C4×#1057—22no—
50#88071—22no—
51#88071—22no—
52#8958—131nomaximal, Sylow
53C2×Q8×C13—22no—
54C2×Q8×C13—21no—
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13C2×C812yes—
59C2×Q8×C13C2×C812yes—
60C2×Q8×C13M1612yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C412yes—
68C22×Dic13C2×D411yescharacteristic
69C22×Dic13C2×D411yescharacteristic
70C2×#1057—24no—
71C2×#1057—42no—
72C13×C4⋊C4—28no—
73C42×C13—21no—
74C42×C13C2×C812yes—
75C4⋊Dic13—22no—
76C4⋊Dic13—24no—
77C4⋊Dic13—22no—
78C4⋊Dic13—44no—
79C4⋊Dic13—42no—
80C4×Dic13—24no—
81C4×Dic13—22no—
82C4×Dic13—22no—
83C4×Dic13—22no—
84C4×Dic13—42no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87C4×Dic13C2×D412yes—
88C4×Dic13#4112yes—
89#2982—131no—
90C4×C4⋊Q8—131no—
91#1479—132no—
92#1461—131no—
93#1276—132no—
94C23×C13C2×C22⋊C411yescharacteristic
95Q8×C13—24no—
96Q8×C13—24no—
97Q8×C13—24no—
98Q8×C13—42no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13C22⋊C814yes—
108C2×C4×C13C4×D412yes—
109C2×C4×C13C22×C811yescharacteristic
110C2×C4×C13C2×M1611yescharacteristic
111C2×C4×C13#13112yes—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—41no—
121C2×Dic13#12011yescharacteristic
122C2×Dic13#12112yes—
123C2×Dic13#12311yescharacteristic
124#1057—44no—
125#1057—82no—
126C2×C4⋊Q8#26111yescharacteristic
127C2×C4×Q8—131no—
128C2×C4×Q8—131no—
129C8×Q8—264no—
130#431—132no—
131#431—132no—
132#431—262no—
133#391—131no—
134#391—131no—
135#389—262no—
136#384—131no—
137C4×C4⋊C4—262no—
138C43—131no—
139Q8⋊C8—264no—
140#324—262no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13#38611yescharacteristic
144C22×C13C2×C22⋊C811yescharacteristic
145C22×C13#40811yescharacteristic
146C4×C13—24no—
147C4×C13—24no—
148C4×C13—42no—
149C4×C13C8×D412yes—
150C4×C13#43512yes—
151Dic13—22no—
152Dic13—21no—
153Dic13—42no—
154Dic13—42no—
155Dic13—81no—
156Dic13#45612yes—
157C22×Q8C2×#26111yescharacteristic
158C22×Q8C2×#26111yescharacteristic
159C4⋊Q8—22no—
160C4⋊Q8#105714yescomplemented
161C4×Q8—262no—
162C4×Q8—262no—
163C4×Q8—262no—
164C4×Q8—262no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—262no—
171C2×C42—131no—
172C2×C42—132no—
173C2×C42—131no—
174C2×C42—261no—
175C2×C42—261no—
176C2×C42—261no—
177C2×C42C2×#26111yescharacteristic
178C4⋊C8—134no—
179C4⋊C8—262no—
180C4⋊C8—264no—
181C22⋊C8—262no—
182C22⋊C8—262no—
183C4×C8—262no—
184C4×C8—262no—
185C4×C8—264no—
186#95—262no—
187#95—262no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13#186911yescharacteristic
191C2×C13#188411yescharacteristic
192C2×C13#188611yescharacteristic
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—21no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8C2×#105712yes—
199C2×Q8C2×#105712yes—
200C2×Q8#612212yes—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—132no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4C22⋊#26112yes—
209C22×C4C22×#26111yescharacteristic
210C2×C8—264no—
211C2×C8—522no—
212C4⋊C4—28no—
213C4⋊C4—264no—
214C4⋊C4—262no—
215C4⋊C4—262no—
216C4⋊C4—524no—
217C4⋊C4—522no—
218C42—21no—
219C42—132no—
220C42—132no—
221C42—262no—
222C42—262no—
223C42—264no—
224C42—262no—
225C42—522no—
226C42—521no—
227C42—521no—
228C42C2×#105712yes—
229C13#895811yescharacteristic, complemented, Sylow
230C23C2×C22⋊#26111yescharacteristic
231Q8—24no—
232Q8—24no—
233Q8—24no—
234Q8—42no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—131no—
244C2×C4—131no—
245C2×C4—132no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4—521no—
255C2×C4C22⋊#105714yes—
256C2×C4#8823812yes—
257C2×C4D4×#26112yes—
258C2×C4C22×#105711yescharacteristic
259C2×C4C2×#612211yescharacteristic
260C8—524no—
261C8—1042no—
262C22—21no—
263C22—21no—
264C22#1171914611yescharacteristic
265C22#1171915011yescharacteristic
266C22C2×C22⋊#105711yescharacteristic
267C4—24no—
268C4—24no—
269C4—42no—
270C4—132no—
271C4—262no—
272C4—261no—
273C4—522no—
274C4—522no—
275C4—1041no—
276C4D4×#105712yes—
277C4#1171914412yes—
278C2—21no—
279C2—21no—
280C2#1313080911yescharacteristic
281C2#1313083811yescharacteristic
282C2#1313084211yescharacteristic
subgroupG/H
centerC22#11719150
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#8958
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
24. C13×C4⋊Q8C8semidirect
160. C4⋊Q8#1057semidirect
229. C13#8958semidirect

Maximal subgroups

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

subgroupindex
#131317292
#131301382
#131300792
#131296642
C4⋊Q8×Dic132
#895813