Finite Group Databasebeta

← #16788322

Subgroups — #16788322

Order 3328.

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

normal subgroups only

This group has 408 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#13129820C214yesmaximal
4#13119825C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×#88198—21no—
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113—21no—
9#11719129—21no—
10#11719125—21no—
11#11718891—21no—
12#11718641C412yes—
13#11718641C2212yes—
14#11718634—21no—
15#11718634—21no—
16C4×C4⋊Dic13C411yescharacteristic
17#11718291C2212yes—
18#11718286C2212yes—
19#11718285—21no—
20C22×Q8×C13—21no—
21C22×Dic26D411yescharacteristic
22C2×#6122—22no—
23C13×C4⋊Q8—41no—
24C13×C4⋊Q8—41no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C412yes—
27C2×C42×C13C2×C411yescharacteristic
28#88198—42no—
29#88198—42no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13D411yescharacteristic
32C2×#6101—22no—
33C2×#6101—22no—
34C2×#6101C2×C411yescharacteristic
35C2×#6101C2311yescharacteristic
36C2×C4×Dic13—21no—
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C4×Dic26—41no—
40C4×Dic26—41no—
41C22⋊#1057—22no—
42#88113—42no—
43#88112—41no—
44#88112—41no—
45C4⋊#1057—41no—
46C4×#1057—41no—
47#88071—22no—
48#88071—22no—
49#88071C2×C412yes—
50#11883—131nomaximal, Sylow
51C2×Q8×C13—42no—
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C2×Dic26—41no—
64C2×Dic26—41no—
65C2×Dic26D812yes—
66C2×Dic26SD1612yes—
67#6122—42no—
68#6122—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C42×C13—21no—
75C42×C13—21no—
76C4⋊Dic13—24no—
77C4⋊Dic13—41no—
78#6101—41no—
79#6101—41no—
80#6101—44no—
81#6101—42no—
82#6101—42no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13—42no—
88#2546—131no—
89#1801—131no—
90#1461—131no—
91#1346—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×C13#10212yes—
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×Dic13#10212yes—
117C2×Dic13C2×D811yescharacteristic
118C2×Dic13C2×SD1611yescharacteristic
119Dic26—42no—
120Dic26—42no—
121#1057—82no—
122#1057—82no—
123C2×C4⋊Q8—261no—
124C2×C4⋊Q8#26111yescharacteristic
125C2×C4×Q8—131no—
126#431—261no—
127#423—261no—
128C2×#101—261no—
129#398—132no—
130#398—132no—
131#391—261no—
132#389—261no—
133#389—261no—
134C4×C4⋊C4—131no—
135#343—132no—
136#324—132no—
137#324—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13C2×#9911yescharacteristic
141C22×C13C2×#10211yescharacteristic
142C22×C13#42111yescharacteristic
143C4×C13—21no—
144C4×C13—22no—
145C4×C13—41no—
146C4×C13—82no—
147C4×C13#35612yes—
148Dic13—21no—
149Dic13—22no—
150Dic13—21no—
151Dic13—44no—
152Dic13—41no—
153Dic13—41no—
154C22×Q8—21no—
155C22×Q8—131no—
156C2×M16—262no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—522no—
160C4⋊Q8—522no—
161C4×Q8—521no—
162C4×Q8—521no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—262no—
169C2×C4⋊C4—262no—
170C2×C4⋊C4C2×#26112yes—
171C2×C42—131no—
172C2×C42—131no—
173C2×C42—261no—
174C2×C42C2×#26111yescharacteristic
175C4⋊C8—521no—
176C4⋊C8—521no—
177C4⋊C8—521no—
178#101—522no—
179C22⋊C8—262no—
180C4×C8—521no—
181#95—132no—
182#95—262no—
183#95—262no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#151911yescharacteristic
187C2×C13#212311yescharacteristic
188C2×C13C2×#35611yescharacteristic
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—132no—
193C2×Q8—132no—
194C2×Q8—521no—
195C2×Q8—521no—
196C22×C4—22no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—262no—
202C22×C4C22⋊#26111yescharacteristic
203C22×C4C22⋊#26111yescharacteristic
204C22×C4C22×#26111yescharacteristic
205M16—522no—
206M16—522no—
207C2×C8—522no—
208C2×C8—522no—
209C4⋊C4—42no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—264no—
213C4⋊C4—521no—
214C4⋊C4—521no—
215C4⋊C4—521no—
216C4⋊C4—522no—
217C4⋊C4—524no—
218C4⋊C4—522no—
219C42—21no—
220C42—21no—
221C42—261no—
222C42—261no—
223C42—261no—
224C42—261no—
225C42—522no—
226C13#1188311yescharacteristic, 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—131no—
240C2×C4—132no—
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#8811512yes—
254C2×C4#8811911yescharacteristic
255C2×C4#8811911yescharacteristic
256C8—1042no—
257C8—1042no—
258C22—21no—
259C22—21no—
260C22C2×#8811511yescharacteristic
261C22#1171914011yescharacteristic
262C22C2×#8811911yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—82no—
267C4—261no—
268C4—262no—
269C4—261no—
270C4—524no—
271C4—521no—
272C4—521no—
273C4#1171830112yes—
274C2—21no—
275C2—21no—
276C2#1313027211yescharacteristic
277C2#1313109811yescharacteristic
278C2C2×#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#11883
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
226. C13#11883semidirect

Maximal subgroups

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

subgroupindex
#131307022
#131300782
#131298202
#131198252
#1188313