Finite Group Databasebeta

← #16788404

Subgroups — #16788404

Order 3328.

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

normal subgroups only

This group has 372 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#13129835C214yesmaximal
4#13120052C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Dic26C2211yescharacteristic
7C2×#88113—21no—
8#11719129—21no—
9#11719125—21no—
10#11718891—21no—
11#11718891—21no—
12#11718643C412yes—
13#11718643C2212yes—
14#11718638—21no—
15#11718635—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
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13D411yescharacteristic
30C2×#6101C2×C411yescharacteristic
31C2×#6101C2311yescharacteristic
32C2×C4×Dic13—21no—
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C4×Dic26—41no—
36C4×Dic26—41no—
37C22⋊#1057—22no—
38#88113—42no—
39#88112—41no—
40#88112—41no—
41C4⋊#1057—41no—
42C4×#1057—41no—
43#88071—22no—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#88071C2×C412yes—
48#11907—131nomaximal, Sylow
49C2×Q8×C13—44no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C22×C4×C13—22no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C2×Dic26—41no—
62C2×Dic26—41no—
63C2×Dic26SD1612yes—
64C2×Dic26Q1612yes—
65#6122—42no—
66#6122—42no—
67C2×#1057—42no—
68C2×#1057—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C42×C13—21no—
72C42×C13—21no—
73C4⋊Dic13—41no—
74C4⋊Dic13—42no—
75#6101—41no—
76#6101—41no—
77C4×Dic13—21no—
78C4×Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—42no—
82#2568—131no—
83#1801—131no—
84#1461—131no—
85#1353—134no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—82no—
88Q8×C13—82no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—41no—
94C2×C4×C13—44no—
95C2×C4×C13—42no—
96C2×C4×C13#9911yescharacteristic
97C2×C4×C13#9911yescharacteristic
98C2×C4×C13#10312yes—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—41no—
106C2×Dic13—41no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13#10312yes—
111C2×Dic13C2×SD1611yescharacteristic
112C2×Dic13C2×Q1611yescharacteristic
113Dic26—42no—
114Dic26—42no—
115#1057—82no—
116#1057—82no—
117C2×C4⋊Q8#26111yescharacteristic
118C2×C4×Q8—131no—
119#431—261no—
120#423—261no—
121C2×#101—261no—
122#400—132no—
123#400—132no—
124#391—261no—
125#391—261no—
126#391—261no—
127#382—261no—
128C4×C4⋊C4—131no—
129#343—132no—
130#324—132no—
131#324—261no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13C2×#9911yescharacteristic
135C22×C13C2×#10311yescharacteristic
136C22×C13#42111yescharacteristic
137C4×C13—21no—
138C4×C13—22no—
139C4×C13—41no—
140C4×C13—82no—
141C4×C13#35512yes—
142Dic13—21no—
143Dic13—22no—
144Dic13—21no—
145Dic13—41no—
146Dic13—41no—
147Dic13—82no—
148C22×Q8—21no—
149C22×Q8—131no—
150C2×M16—262no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—521no—
154C4×Q8—521no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4C2×#26112yes—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—261no—
164C2×C42C2×#26111yescharacteristic
165C4⋊C8—521no—
166C4⋊C8—521no—
167C4⋊C8—521no—
168#101—522no—
169C22⋊C8—262no—
170C4×C8—521no—
171#95—132no—
172#95—262no—
173#95—262no—
174#95—262no—
175#95—262no—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13#152011yescharacteristic
179C2×C13#212311yescharacteristic
180C2×C13C2×#35511yescharacteristic
181C2×Q8—44no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—132no—
185C2×Q8—132no—
186C2×Q8—521no—
187C2×Q8—521no—
188C22×C4—22no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—131no—
193C22×C4—262no—
194C22×C4C22⋊#26111yescharacteristic
195C22×C4C22⋊#26111yescharacteristic
196C22×C4C22×#26111yescharacteristic
197M16—522no—
198M16—522no—
199C2×C8—522no—
200C2×C8—522no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—521no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C4⋊C4—522no—
207C42—21no—
208C42—21no—
209C42—261no—
210C42—261no—
211C42—261no—
212C42—261no—
213C42—522no—
214C13#1190711yescharacteristic, complemented, Sylow
215C23C2×C22⋊#26111yescharacteristic
216Q8—82no—
217Q8—82no—
218Q8—522no—
219Q8—522no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—131no—
228C2×C4—132no—
229C2×C4—131no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—521no—
237C2×C4—521no—
238C2×C4—522no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4#8811712yes—
242C2×C4#8811911yescharacteristic
243C2×C4#8811911yescharacteristic
244C8—1042no—
245C8—1042no—
246C22—21no—
247C22—21no—
248C22C2×#8811711yescharacteristic
249C22#1171915511yescharacteristic
250C22C2×#8811911yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—82no—
255C4—261no—
256C4—262no—
257C4—261no—
258C4—521no—
259C4—521no—
260C4—1042no—
261C4#1171829512yes—
262C2—21no—
263C2—21no—
264C2#1313027611yescharacteristic
265C2#1313109811yescharacteristic
266C2C2×#1171829511yescharacteristic
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#11907
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
214. C13#11907semidirect

Maximal subgroups

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

subgroupindex
#131307022
#131300782
#131298352
#131200522
#1190713