Finite Group Databasebeta

← #15761726

Subgroups — #15761726

Order 3328.

558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C4×#88129C211yesmaximal, characteristic
2#13114953C211yesmaximal, characteristic, complemented
3C2×#11718048C212yesmaximal, complemented
4C2×#11718051C212yesmaximal
5C13×#1744C211yesmaximal, characteristic, complemented
6C2×#88129C411yescharacteristic
7C2×C4×D52C2211yescharacteristic
8C2×C4×Dic26C2211yescharacteristic
9C2×C4×C8×C13C2212yes—
10C43×C13C2211yescharacteristic
11#11718601—22no—
12#11718600C411yescharacteristic
13C4×#6103—22no—
14#11718597C411yescharacteristic
15#11718590C411yescharacteristic
16C2×C4⋊#1055C2212yes—
17C13×#336—22no—
18#11718116—22no—
19#11718051—24no—
20#11718048—24no—
21C22×D52C2×C411yescharacteristic
22C22×C4×D13—21no—
23C22×Dic26C2×C411yescharacteristic
24C22×C8×C13—22no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13D412yes—
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30C2×#6103—22no—
31C2×#6103—22no—
32C2×#6103—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×C4×Dic13—21no—
37C22×#1055—22no—
38#88129—22no—
39#88129—22no—
40C4×D52—22no—
41C4×D52—22no—
42C4×Dic26—22no—
43C4×Dic26—22no—
44C4×C8×C13—22no—
45C4×C8×C13D414yes—
46#88071—22no—
47#88071—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50#9645—131nomaximal, Sylow
51C23×D13—21no—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22×C411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13—21no—
60C2×D52—22no—
61C2×D52—22no—
62C2×D52—21no—
63C2×D52M1612yes—
64C2×C4×D13—41no—
65C2×C4×D13—41no—
66C2×C4×D13—44no—
67C2×Dic26—22no—
68C2×Dic26—22no—
69C2×Dic26—21no—
70C2×Dic26M1612yes—
71C2×C8×C13—24no—
72C2×C8×C13—44no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—22no—
76C42×C13—24no—
77C42×C13—42no—
78C42×C13C2×D412yes—
79C42×C13#4112yes—
80#6103—28no—
81#6103—44no—
82#6103—42no—
83C4⋊Dic13—22no—
84C4⋊Dic13—22no—
85#6101—42no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C2×#1055—42no—
89C2×#1055—44no—
90C4×#124—131no—
91#1831—131no—
92#1744D1311yescharacteristic, complemented
93C2×Q8⋊C8—132no—
94C2×D4⋊C8—132no—
95C23×C13C2×C22⋊C411yescharacteristic
96C22×D13—22no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—42no—
100C22×D13—42no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13C4×D412yes—
109C2×C4×C13#12112yes—
110C2×C4×C13#12411yescharacteristic
111C2×C4×C13#12711yescharacteristic
112C2×C4×C13C2×M1611yescharacteristic
113C2×C4×C13C2×M1611yescharacteristic
114C2×C4×C13#13112yes—
115C2×C4×C13#13514yes—
116C2×Dic13—22no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123D52—24no—
124D52—42no—
125C4×D13—82no—
126C4×D13—82no—
127Dic26—24no—
128Dic26—42no—
129C8×C13—44no—
130#1055—82no—
131C2×#124—131no—
132C2×C4×Q8—131no—
133C2×C4×D4—131no—
134C2×C4⋊C8—132no—
135C2×C4×C8C2×D1312yes—
136#391—131no—
137#390—131no—
138#388—262no—
139#382—131no—
140C4×C22⋊C4—262no—
141C43C2×D1311yescharacteristic
142#336—22no—
143#336—262no—
144Q8⋊C8—264no—
145D4⋊C8—264no—
146C22×C13#39011yescharacteristic
147C22×C13#40711yescharacteristic
148C22×C13#40811yescharacteristic
149C22×C13#41612yes—
150C22×C13#42112yes—
151C2×D13—42no—
152C2×D13—44no—
153C2×D13—81no—
154C2×D13—81no—
155C2×D13—82no—
156C4×C13—22no—
157C4×C13—42no—
158C4×C13—42no—
159C4×C13#43512yes—
160C4×C13#43512yes—
161C4×C13#48812yes—
162C4×C13#49512yes—
163Dic13—42no—
164Dic13—81no—
165Dic13—81no—
166C22×Q8—131no—
167C22×D4—131no—
168C23×C4—261no—
169C22×C8—22no—
170C22×C8—262no—
171#124—262no—
172#124—262no—
173C4×Q8—262no—
174C4×Q8—262no—
175C4×D4—262no—
176C4×D4—262no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—261no—
180C2×C22⋊C4—262no—
181C2×C22⋊C4—262no—
182C2×C22⋊C4—261no—
183C2×C42—261no—
184C2×C42C4×D1311yescharacteristic
185C2×C42C4×D1311yescharacteristic
186C2×C42D5212yes—
187C2×C42C22⋊D1312yes—
188C2×C42C22×D1311yescharacteristic
189C4⋊C8—262no—
190C4⋊C8—262no—
191C4×C8—22no—
192C4×C8D5214yes—
193#95—262no—
194#95—262no—
195C2×C13#148212yes—
196C2×C13#148812yes—
197C2×C13#195511yescharacteristic
198C2×C13#195811yescharacteristic
199C2×C13#196311yescharacteristic
200D13—82no—
201C24—261no—
202C2×Q8—132no—
203C2×Q8—261no—
204C2×Q8—262no—
205C2×Q8—262no—
206C2×D4—132no—
207C2×D4—262no—
208C2×D4—261no—
209C2×D4—262no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4—261no—
213C22×C4—521no—
214C22×C4—521no—
215C22×C4—524no—
216C22×C4#610312yes—
217C22×C4#610312yes—
218C22×C4C2×C4×D1311yescharacteristic
219C22×C4C2×D5211yescharacteristic
220C22×C4C2×C22⋊D1311yescharacteristic
221C2×C8—24no—
222C2×C8—44no—
223C2×C8—522no—
224C2×C8—524no—
225C4⋊C4—262no—
226C4⋊C4—262no—
227C4⋊C4—522no—
228C22⋊C4—268no—
229C22⋊C4—524no—
230C22⋊C4—522no—
231C42—24no—
232C42—21no—
233C42—21no—
234C42—22no—
235C42—42no—
236C42—521no—
237C42—521no—
238C42C2×D5212yes—
239C42#612712yes—
240C13#964511yescharacteristic, complemented, Sylow
241C23—262no—
242C23—522no—
243C23—522no—
244C23—521no—
245C23—521no—
246C23C2×#610311yescharacteristic
247Q8—264no—
248Q8—522no—
249D4—264no—
250D4—522no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—262no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—1042no—
266C2×C4—1042no—
267C2×C4C4×D5212yes—
268C2×C4#8812811yescharacteristic
269C2×C4#8812911yescharacteristic
270C2×C4#8815814yes—
271C2×C4M16×D1311yescharacteristic
272C2×C4M16×D1311yescharacteristic
273C2×C4#8816112yes—
274C2×C4#8818412yes—
275C8—44no—
276C8—1042no—
277C22—524no—
278C22—522no—
279C22—1041no—
280C22—1042no—
281C22—1041no—
282C22#1171860011yescharacteristic
283C22#1171866612yes—
284C22#1171877412yes—
285C22#1171878711yescharacteristic
286C22#1171879011yescharacteristic
287C4—22no—
288C4—42no—
289C4—42no—
290C4—522no—
291C4—1041no—
292C4—1041no—
293C4#1171835712yes—
294C4#1171835812yes—
295C4#1171836712yes—
296C4#1171836712yes—
297C2—1042no—
298C2#1311324512yes—
299C2#1311327112yes—
300C2#1311563411yescharacteristic
301C2#1311564711yescharacteristic
302C2#1311566811yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1744C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1744D13
hypocenterC13#9645
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1744

Complements

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

NH ≅ G/Ntype
2. #13114953C2semidirect
3. C2×#11718048C2semidirect
5. C13×#1744C2semidirect
92. #1744D13semidirect
240. C13#9645semidirect

Maximal subgroups

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

subgroupindex
C4×#881292
#131149532
C2×#117180482
C2×#117180512
C13×#17442
#964513