Finite Group Databasebeta

← #15750719

Subgroups — #15750719

Order 3328.

290 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 63 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×#11718134C211yesmaximal, characteristic
2C2×#11718133C211yesmaximal, characteristic
3C13×#1959C211yesmaximal, characteristic
4C2×C13×#124C2211yescharacteristic
5C2×C13×#103—21no—
6C2×C13×#102—21no—
7C2×C13×#97C411yescharacteristic, complemented
8C13×#384C411yescharacteristic, complemented
9C2×#88076—21no—
10C2×#88074—21no—
11#11718134—21no—
12#11718134C412yescomplemented
13#11718133—21no—
14#11718133C412yescomplemented
15C22×Q8×C13D411yescharacteristic
16C22×D4×C13D411yescharacteristic
17C22×C8×C13—21no—
18C13×#124—41no—
19C13×#124C2×C411yescharacteristic
20C13×#124C2×C411yescharacteristic
21C13×#124D411yescharacteristic
22C13×#124Q811yescharacteristic
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—41no—
25C2×C13×C22⋊C4—41no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—41no—
28C2×#6099—41no—
29C13×#103—42no—
30C13×#102—42no—
31C13×#97—41no—
32#88076—22no—
33#88076—41no—
34#88074—22no—
35#88074—41no—
36#7508—131nomaximal, Sylow
37C24×C13—21no—
38C2×Q8×C13—21no—
39C2×Q8×C13—41no—
40C2×Q8×C13—41no—
41C2×Q8×C13C22⋊C411yescharacteristic
42C2×Q8×C13C4⋊C411yescharacteristic
43C2×D4×C13—21no—
44C2×D4×C13—41no—
45C2×D4×C13—41no—
46C2×D4×C13C22⋊C411yescharacteristic
47C2×D4×C13C4⋊C411yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—41no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×Dic13—81no—
53C2×C8×C13—22no—
54C2×C8×C13—41no—
55C2×C8×C13—41no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—82no—
59C13×C22⋊C4—41no—
60C13×C22⋊C4—41no—
61C13×C22⋊C4—41no—
62C13×C22⋊C4—41no—
63C42×C13—21no—
64C42×C13C4211yescharacteristic
65C42×C13C4⋊C411yescharacteristic
66C22⋊Dic13—42no—
67C22⋊Dic13—81no—
68#6099—42no—
69#6099—81no—
70C2×#1055—81no—
71C2×#355—131no—
72C2×#354—131no—
73#1959D1311yescharacteristic
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—41no—
77C23×C13—41no—
78C23×C13—81no—
79C23×C13—81no—
80C23×C13#9911yescharacteristic
81Q8×C13—41no—
82Q8×C13—41no—
83Q8×C13—81no—
84D4×C13—41no—
85D4×C13—41no—
86D4×C13—81no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—82no—
98C2×C4×C13—81no—
99C2×C4×C13#9511yescharacteristic
100C2×C4×C13#9911yescharacteristic
101C2×Dic13—82no—
102C2×Dic13—161no—
103C2×Dic13—161no—
104C8×C13—42no—
105#1055—82no—
106C2×#124C2×D1311yescharacteristic
107C2×#103—21no—
108C2×#102—21no—
109C2×#101—261no—
110C2×#99—261no—
111C2×#97Dic1311yescharacteristic, complemented
112#384Dic1311yescharacteristic, complemented
113#355—132no—
114#355—261no—
115#354—132no—
116#354—261no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13—41no—
120C22×C13—41no—
121C22×C13—81no—
122C22×C13—81no—
123C22×C13—81no—
124C22×C13—81no—
125C22×C13—161no—
126C22×C13#34211yescharacteristic
127C22×C13#35311yescharacteristic
128C22×C13#35411yescharacteristic
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—41no—
132C4×C13—41no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13—161no—
136Dic13—162no—
137C22×Q8C22⋊D1311yescharacteristic
138C22×D4C22⋊D1311yescharacteristic
139C2×M16—521no—
140C22×C8—21no—
141#124—41no—
142#124Dic2611yescharacteristic
143#124C4×D1311yescharacteristic
144#124C4×D1311yescharacteristic
145#124D5211yescharacteristic
146C2×C4⋊C4—21no—
147C2×C4⋊C4—41no—
148C2×C22⋊C4—41no—
149C2×C22⋊C4—521no—
150C2×C42C2×Dic1311yescharacteristic
151#103—42no—
152#102—42no—
153#101—262no—
154#101—521no—
155#99—262no—
156#99—521no—
157#97—41no—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—81no—
161C2×C13—81no—
162C2×C13#139311yescharacteristic
163C2×C13#140611yescharacteristic
164C2×C13#140711yescharacteristic
165C24—21no—
166C2×Q8—21no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8#610111yescharacteristic
170C2×Q8#610311yescharacteristic
171C2×D4—21no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4#610111yescharacteristic
175C2×D4#610311yescharacteristic
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—41no—
179C22×C4—1041no—
180C22×C4C22⋊Dic1311yescharacteristic
181M16—522no—
182M16—1041no—
183C2×C8—22no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—1041no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—82no—
190C22⋊C4—41no—
191C22⋊C4—41no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—522no—
195C22⋊C4—1041no—
196C42—21no—
197C42C4×Dic1311yescharacteristic
198C42C4⋊Dic1311yescharacteristic
199C13#750811yescharacteristic, complemented, Sylow
200C23—21no—
201C23—21no—
202C23—41no—
203C23—41no—
204C23—81no—
205C23—81no—
206C23#8807411yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—81no—
210D4—41no—
211D4—41no—
212D4—81no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—82no—
224C2×C4—81no—
225C2×C4—1042no—
226C2×C4—2081no—
227C2×C4—2081no—
228C2×C4#8807111yescharacteristic
229C2×C4#8807411yescharacteristic
230C8—42no—
231C8—1042no—
232C22—21no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—81no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—161no—
241C22#1171811811yescharacteristic
242C22#1171813311yescharacteristic
243C22#1171813711yescharacteristic
244C4—21no—
245C4—21no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—161no—
251C4—2082no—
252C2—21no—
253C2—21no—
254C2—81no—
255C2—81no—
256C2#1311296111yescharacteristic
257C2#1311299311yescharacteristic
258C2#1311299611yescharacteristic
subgroupG/H
centerC22#11718137
commutatorC42×C13C42
FrattiniC2×#124C2×D13
FittingC13×#1959C2
socleC22×C13#353
prime radicalC22×D4×C13D4
cosocleC2×C13×#124C22
hypercenter#1959D13
hypocenterC13#7508
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ #1959

Complements

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

NH ≅ G/Ntype
7. C2×C13×#97C4semidirect
8. C13×#384C4semidirect
12. #11718134C4semidirect
14. #11718133C4semidirect
111. C2×#97Dic13semidirect
112. #384Dic13semidirect
199. C13#7508semidirect

Maximal subgroups

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

subgroupindex
C2×#117181342
C2×#117181332
C13×#19592
#750813