Finite Group Databasebeta

← #15754685

Subgroups — #15754685

Order 3328.

738 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×Q8×Dic26C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113520C212yesmaximal
4#13113266C212yesmaximal
5C13×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×Q8×Dic13—21no—
8Q8×Dic26—24no—
9Q8×Dic26—24no—
10C2×#88142—21no—
11C2×#88142—22no—
12C2×#88123C412yes—
13C2×#88123C2211yescharacteristic
14C2×C4×Dic26C412yes—
15C2×C4×Dic26C2211yescharacteristic
16C13×#431C2212yes—
17C2×#88076—21no—
18#11718585C2212yes—
19C13×#324—22no—
20#11718122—21no—
21#11718074—24no—
22#11718048—24no—
23C22×Q8×C13D411yescharacteristic
24C22×Dic26—22no—
25C22×Dic26—21no—
26C22×Dic26C2×C411yescharacteristic
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D412yes—
31C2×C42×C13C2×C412yes—
32C2×C42×C13C2311yescharacteristic
33Q8×Dic13—28no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13C2×C412yes—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—22no—
39C2×#6101—21no—
40C2×C4×Dic13—22no—
41C2×C4×Dic13—21no—
42C2×#6099—22no—
43#88142—216no—
44#88142—28no—
45#88123—22no—
46#88123—24no—
47#88123—24no—
48#88123D414yes—
49C4×Dic26—24no—
50C4×Dic26—22no—
51C4×Dic26—24no—
52C4×Dic26D414yes—
53C13×C4⋊C8—22no—
54C13×C22⋊C8—22no—
55C4×C8×C13—22no—
56#88076—42no—
57C4⋊#1055—22no—
58C4⋊#1055—22no—
59#8396—131nomaximal, Sylow
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13SD1612yes—
63C2×Q8×C13Q1612yes—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—22no—
71C22×Dic13—21no—
72C2×Dic26—21no—
73C2×Dic26—24no—
74C2×Dic26—28no—
75C2×Dic26—24no—
76C2×Dic26—82no—
77C2×Dic26—84no—
78C2×Dic26C22⋊C412yes—
79C2×C8×C13—42no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—24no—
82C42×C13—22no—
83C42×C13—22no—
84C42×C13C2×D412yes—
85C42×C13C2×D412yes—
86C4⋊Dic13—28no—
87C4⋊Dic13—21no—
88C4⋊Dic13—22no—
89C4⋊Dic13—24no—
90C4⋊Dic13C22⋊C414yes—
91C4⋊Dic13C22⋊C412yes—
92#6101—28no—
93#6101—24no—
94C4×Dic13—28no—
95C4×Dic13—24no—
96#6099—42no—
97#6099—42no—
98C2×#1055—42no—
99C2×Q82—131no—
100#1801—131no—
101#1549—132no—
102#1487—132no—
103#1461D1311yescharacteristic
104C23×C13C2×C22⋊C411yescharacteristic
105Q8×C13—24no—
106Q8×C13—24no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13#10314yes—
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13#12012yes—
117C2×C4×C13#12012yes—
118C2×C4×C13C2×SD1611yescharacteristic
119C2×C4×C13C2×Q1611yescharacteristic
120C2×C4×C13#13712yes—
121C2×Dic13—24no—
122C2×Dic13—22no—
123C2×Dic13—24no—
124C2×Dic13—22no—
125C2×Dic13—44no—
126C2×Dic13—42no—
127Dic26—24no—
128Dic26—22no—
129Dic26—84no—
130Dic26—88no—
131Dic26#10114yescomplemented
132C8×C13—82no—
133#1055—82no—
134Q82—264no—
135Q82—264no—
136C2×C4⋊Q8—132no—
137C2×C4⋊Q8—131no—
138C2×C4⋊Q8—261no—
139C2×C4⋊Q8—262no—
140C2×C4×Q8—132no—
141C2×C4×Q8—131no—
142C2×C4×Q8—261no—
143C2×C4×Q8C2×D1311yescharacteristic
144#431C2×D1312yes—
145#423—132no—
146C2×#101—261no—
147#343—261no—
148#332—264no—
149Q8⋊C8—264no—
150#324—22no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13#37911yescharacteristic
154C22×C13C2×#10311yescharacteristic
155C22×C13#41911yescharacteristic
156C4×C13—22no—
157C4×C13—21no—
158C4×C13—24no—
159C4×C13—42no—
160C4×C13C2×#10112yes—
161C4×C13#44812yes—
162C4×C13#45112yes—
163Dic13—24no—
164Dic13—44no—
165Dic13—42no—
166C22×Q8—131no—
167C22×Q8—262no—
168C22×Q8—261no—
169C22×Q8D5211yescharacteristic
170C2×M16—262no—
171C4⋊Q8—134no—
172C4⋊Q8—264no—
173C4⋊Q8—264no—
174C4⋊Q8—2616no—
175C4⋊Q8—268no—
176C4⋊Q8—262no—
177C4×Q8—22no—
178C4×Q8—22no—
179C4×Q8—134no—
180C4×Q8—264no—
181C4×Q8—264no—
182C4×Q8—268no—
183C4×Q8—262no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—132no—
186C2×C4⋊C4—262no—
187C2×C4⋊C4—262no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4D5211yescharacteristic
191C2×C4⋊C4C22⋊D1312yes—
192C2×C42—262no—
193C2×C42—261no—
194C2×C42C4×D1312yes—
195C2×C42C22×D1311yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—262no—
198C4⋊C8—262no—
199#101—522no—
200C22⋊C8—22no—
201C4×C8—22no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13#178411yescharacteristic
205C2×C13#178711yescharacteristic
206C2×C13#179511yescharacteristic
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—132no—
210C2×Q8—264no—
211C2×Q8—268no—
212C2×Q8—261no—
213C2×Q8—264no—
214C2×Q8—1042no—
215C2×Q8—1044no—
216C2×Q8#609512yes—
217C2×Q8Dic5212yes—
218C22×C4—261no—
219C22×C4—262no—
220C22×C4—261no—
221C22×C4#610312yes—
222C22×C4#610312yes—
223C22×C4C2×C4×D1311yescharacteristic
224C22×C4C2×D5211yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—522no—
227M16—522no—
228C2×C8—42no—
229C2×C8—522no—
230C4⋊C4—22no—
231C4⋊C4—24no—
232C4⋊C4—132no—
233C4⋊C4—134no—
234C4⋊C4—268no—
235C4⋊C4—268no—
236C4⋊C4—261no—
237C4⋊C4—262no—
238C4⋊C4—264no—
239C4⋊C4—264no—
240C42—22no—
241C42—22no—
242C42—268no—
243C42—264no—
244C42D4×D1312yes—
245C42D4×D1312yes—
246C13#839611yescharacteristic, complemented, Sylow
247C23C2×#610311yescharacteristic
248Q8—24no—
249Q8—24no—
250Q8—134no—
251Q8—264no—
252Q8—262no—
253Q8—1044no—
254Q8—1048no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—264no—
262C2×C4—262no—
263C2×C4—264no—
264C2×C4—262no—
265C2×C4—524no—
266C2×C4—522no—
267C2×C4#8805614yes—
268C2×C4C22⋊C4×D1311yescharacteristic
269C2×C4C22⋊C4×D1311yescharacteristic
270C2×C4#8813612yes—
271C2×C4C2×#609511yescharacteristic
272C2×C4C2×Dic5211yescharacteristic
273C2×C4#8816312yes—
274C2×C4#8819112yes—
275C8—82no—
276C8—1042no—
277C22—21no—
278C22—21no—
279C22#1171861611yescharacteristic
280C22C2×#8805611yescharacteristic
281C22#1171878111yescharacteristic
282C4—21no—
283C4—24no—
284C4—22no—
285C4—42no—
286C4—264no—
287C4—524no—
288C4—522no—
289C4#1171839912yes—
290C4#1171840012yes—
291C4D13×#10112yes—
292C2—21no—
293C2—21no—
294C2#1311475811yescharacteristic
295C2#1311477211yescharacteristic
296C2#1311480411yescharacteristic
subgroupG/H
centerC22#11718616
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1461C2
socleC22×C13#379
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1461D13
hypocenterC13#8396
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
131. Dic26#101semidirect
246. C13#8396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic262
#131148322
#131135202
#131132662
C13×#14612
#839613