Finite Group Databasebeta

← #15776797

Subgroups — #15776797

Order 3328.

288 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 75 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#13117063C211yesmaximal, characteristic
2#13116978C211yesmaximal, characteristic
3#13114230C211yesmaximal, characteristic
4#13112885C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#3395C211yesmaximal, characteristic
8C13×#557—21no—
9C13×#494—21no—
10C13×#494C2211yescharacteristic
11C13×#462—22no—
12C13×#462—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×Q16—21no—
15C4×C13×Q16C2211yescharacteristic
16#11718692—21no—
17#11718343C2211yescharacteristic
18#11718156—21no—
19#11718156—22no—
20#11718082—21no—
21#11718078—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16—22no—
26C2×C13×Q16—21no—
27C2×C13×Q16D411yescharacteristic
28C2×C13×Q16D412yes—
29C13×C4⋊Q8—22no—
30C13×C4⋊Q8—21no—
31C13×#125—42no—
32C13×#125—41no—
33C4×Q8×C13—22no—
34C4×Q8×C13—21no—
35C4×Q8×C13—41no—
36C4×Q8×C13D411yescharacteristic
37C2×#6107—41no—
38#88123—21no—
39C13×#107D411yescharacteristic
40C13×C4⋊C8—21no—
41C13×C4⋊C8D411yescharacteristic
42C13×#103—22no—
43C13×#103—21no—
44C4×C8×C13—21no—
45C4×C8×C13C2311yescharacteristic
46#88058—21no—
47#88058—21no—
48C2×#6090—21no—
49C2×#6090—21no—
50#88050—41no—
51C4⋊#1055—21no—
52#12382—131nomaximal, Sylow
53C2×Q8×C13—21no—
54C2×Q8×C13—22no—
55C2×Q8×C13D811yescharacteristic
56C2×Dic26—41no—
57C13×Q16—21no—
58C13×Q16—21no—
59C13×Q16—42no—
60C13×Q16—41no—
61C13×Q16—41no—
62C13×Q16—82no—
63C2×C8×C13—21no—
64C2×C8×C13C2×D411yescharacteristic
65C2×C8×C13C2×D411yescharacteristic
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4D811yescharacteristic
75C42×C13—21no—
76C42×C13—42no—
77C42×C13—41no—
78C42×C13C2×D411yescharacteristic
79#6107—82no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82C2×#1055—41no—
83#6090—41no—
84#6090—41no—
85#3395D1311yescharacteristic
86#2241—131no—
87#2225—131no—
88#1674—131no—
89#1362—131no—
90Q8⋊C16—131no—
91#1332—131no—
92Q8×C13—21no—
93Q8×C13—41no—
94Q8×C13—42no—
95Q8×C13—42no—
96Q8×C13—41no—
97Q8×C13SD3212yes—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13#12011yescharacteristic
104C2×C4×C13C2×D811yescharacteristic
105C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
106C2×Dic13—81no—
107Dic26—81no—
108Dic26—81no—
109C8×C13—21no—
110C8×C13—41no—
111C8×C13#13511yescharacteristic
112C8×C13#13711yescharacteristic
113#1055—81no—
114#557—21no—
115#500—131no—
116#494—21no—
117#494C2×D1311yescharacteristic
118#462—22no—
119#462—21no—
120#462—261no—
121C8×Q8C2×D1311yescharacteristic
122C4×Q16—21no—
123C4×Q16C2×D1311yescharacteristic
124#367—261no—
125C4⋊C16—131no—
126#358—261no—
127#358—262no—
128C4×C16—131no—
129#335—131no—
130#332—261no—
131C22×C13#44711yescharacteristic
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—41no—
135C4×C13—81no—
136C4×C13—82no—
137C4×C13—81no—
138C4×C13#45211yescharacteristic
139C4×C13#45511yescharacteristic
140C4×C13C2×SD3211yescharacteristic
141C4×C13#51011yescharacteristic
142Dic13—161no—
143C2×Q16—22no—
144C2×Q16—21no—
145C2×Q16—521no—
146C2×Q16C22⋊D1311yescharacteristic
147C2×Q16C22⋊D1312yes—
148C4⋊Q8—22no—
149C4⋊Q8—21no—
150C4⋊Q8—261no—
151#125—42no—
152#125—41no—
153C4×Q8—22no—
154C4×Q8—21no—
155C4×Q8—41no—
156C4×Q8C22⋊D1311yescharacteristic
157C2×C16—261no—
158C2×C16—261no—
159#107—261no—
160#107—261no—
161#107C22⋊D1311yescharacteristic
162C4⋊C8—21no—
163C4⋊C8—261no—
164C4⋊C8C22⋊D1311yescharacteristic
165#103—22no—
166#103—21no—
167#103—521no—
168C4×C8—21no—
169C4×C8C22×D1311yescharacteristic
170C2×C13#164111yescharacteristic
171C2×C13#218511yescharacteristic
172C2×C13#219511yescharacteristic
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—521no—
176C2×Q8#610411yescharacteristic
177Q16—21no—
178Q16—21no—
179Q16—42no—
180Q16—41no—
181Q16—41no—
182Q16—82no—
183Q16—1042no—
184C2×C8—21no—
185C2×C8—521no—
186C2×C8C2×C22⋊D1311yescharacteristic
187C2×C8C2×C22⋊D1311yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—521no—
197C4⋊C4—521no—
198C4⋊C4#610411yescharacteristic
199C42—21no—
200C42—42no—
201C42—41no—
202C42C2×C22⋊D1311yescharacteristic
203C16—521no—
204C16—521no—
205C13#1238211yescharacteristic, complemented, Sylow
206Q8—21no—
207Q8—41no—
208Q8—42no—
209Q8—42no—
210Q8—41no—
211Q8—1041no—
212Q8—1041no—
213Q8#8806812yes—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—1041no—
220C2×C4C2×#610411yescharacteristic
221C2×C4#8818611yescharacteristic
222C2×C4#8820711yescharacteristic
223C8—21no—
224C8—41no—
225C8—1041no—
226C8#8820411yescharacteristic
227C8#8820511yescharacteristic
228C22#1171887811yescharacteristic
229C4—22no—
230C4—21no—
231C4—41no—
232C4—81no—
233C4—81no—
234C4—82no—
235C4—2081no—
236C4C2×#8806811yescharacteristic
237C4#1171884011yescharacteristic
238C4#1171890011yescharacteristic
239C4#1171890311yescharacteristic
240C2#1311402911yescharacteristic
241C2#1311675311yescharacteristic
242C2#1311681411yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3395C2
socle, prime radicalC22×C13#447
hypercenter#3395D13
hypocenterC13#12382
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3395

Complements

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

NH ≅ G/Ntype
205. C13#12382semidirect

Maximal subgroups

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

subgroupindex
#131170632
#131169782
#131142302
#131128852
Q8⋊#60902
#131128002
C13×#33952
#1238213