Finite Group Databasebeta

← #15776958

Subgroups — #15776958

Order 3328.

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

normal subgroups only

This group has 276 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#13117109C211yesmaximal, characteristic
2#13116978C211yesmaximal, characteristic
3#13114230C211yesmaximal, characteristic
4#13112891C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#3383C211yesmaximal, characteristic
8C13×#557—21no—
9C13×#500C2211yescharacteristic
10C13×#499—21no—
11C13×#479—22no—
12C13×#475—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×Q16—21no—
15C4×C13×Q16C2211yescharacteristic
16#11718692—21no—
17#11718343C2211yescharacteristic
18#11718156—21no—
19#11718082—21no—
20#11718081—22no—
21#11718078—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16D411yescharacteristic
26C13×C4⋊Q8—21no—
27C13×C4⋊Q8—41no—
28C13×#125—22no—
29C13×#125—42no—
30C4×Q8×C13—22no—
31C4×Q8×C13—21no—
32C4×Q8×C13—41no—
33C4×Q8×C13D411yescharacteristic
34C2×#6107—41no—
35#88123—21no—
36C13×#107—21no—
37C13×#107D411yescharacteristic
38C13×#107D412yes—
39C13×#106—22no—
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#12405—131nomaximal, Sylow
53C2×Q8×C13—21no—
54C2×Q8×C13—41no—
55C2×Q8×C13D811yescharacteristic
56C2×Dic26—41no—
57C13×Q16—21no—
58C13×Q16Q1612yescomplemented
59C2×C8×C13—21no—
60C2×C8×C13C2×D411yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C13×C4⋊C4—21no—
63C13×C4⋊C4—21no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4D811yescharacteristic
71C42×C13—21no—
72C42×C13—42no—
73C42×C13—41no—
74C42×C13C2×D411yescharacteristic
75#6107—82no—
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78C2×#1055—41no—
79#6090—22no—
80#6090—41no—
81#3383D1311yescharacteristic
82#2252—131no—
83#2225—131no—
84#1674—131no—
85#1364—131no—
86Q8⋊C16—131no—
87#1332—131no—
88Q8×C13—22no—
89Q8×C13—21no—
90Q8×C13—21no—
91Q8×C13—41no—
92Q8×C13—81no—
93Q8×C13—81no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13C2×D811yescharacteristic
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×Dic13—81no—
103Dic26—81no—
104Dic26—81no—
105C8×C13—21no—
106C8×C13—41no—
107C8×C13C2×Q1611yescharacteristic
108C8×C13#13711yescharacteristic
109#1055—81no—
110#557—21no—
111#500—131no—
112#500C2×D1311yescharacteristic
113#499—21no—
114#479—22no—
115#475—21no—
116#462—261no—
117C8×Q8C2×D1311yescharacteristic
118C4×Q16—21no—
119C4×Q16C2×D1311yescharacteristic
120#367—261no—
121#366—262no—
122C4⋊C16—131no—
123#358—261no—
124C4×C16—131no—
125#335—131no—
126#332—261no—
127C22×C13#44711yescharacteristic
128C4×C13—21no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13—41no—
132C4×C13—82no—
133C4×C13—81no—
134C4×C13#45111yescharacteristic
135C4×C13#45611yescharacteristic
136C4×C13#50811yescharacteristic
137C4×C13#50911yescharacteristic
138Dic13—161no—
139C2×Q16—521no—
140C2×Q16C22⋊D1311yescharacteristic
141C4⋊Q8—21no—
142C4⋊Q8—41no—
143C4⋊Q8—261no—
144#125—22no—
145#125—42no—
146C4×Q8—22no—
147C4×Q8—21no—
148C4×Q8—41no—
149C4×Q8C22⋊D1311yescharacteristic
150C2×C16—261no—
151C2×C16—261no—
152#107—21no—
153#107—261no—
154#107—261no—
155#107C22⋊D1312yes—
156#107C22⋊D1311yescharacteristic
157#106—22no—
158C4⋊C8—21no—
159C4⋊C8—261no—
160C4⋊C8C22⋊D1311yescharacteristic
161#103—22no—
162#103—21no—
163#103—521no—
164C4×C8—21no—
165C4×C8C22×D1311yescharacteristic
166C2×C13#164911yescharacteristic
167C2×C13#218611yescharacteristic
168C2×C13#219511yescharacteristic
169C2×Q8—21no—
170C2×Q8—41no—
171C2×Q8—521no—
172C2×Q8#610411yescharacteristic
173Q16—21no—
174Q16—1042no—
175Q16#610712yescomplemented
176C2×C8—21no—
177C2×C8—521no—
178C2×C8C2×C22⋊D1311yescharacteristic
179C2×C8C2×C22⋊D1311yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—521no—
189C4⋊C4—521no—
190C4⋊C4#610411yescharacteristic
191C42—21no—
192C42—42no—
193C42—41no—
194C42C2×C22⋊D1311yescharacteristic
195C16—262no—
196C16—521no—
197C13#1240511yescharacteristic, complemented, Sylow
198Q8—21no—
199Q8—21no—
200Q8—22no—
201Q8—41no—
202Q8—81no—
203Q8—81no—
204Q8—1041no—
205Q8—1041no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—1041no—
212C2×C4C2×#610411yescharacteristic
213C2×C4#8818611yescharacteristic
214C2×C4#8820711yescharacteristic
215C8—21no—
216C8—41no—
217C8—1041no—
218C8#8819611yescharacteristic
219C8C2×#610711yescharacteristic
220C22#1171887811yescharacteristic
221C4—21no—
222C4—41no—
223C4—41no—
224C4—42no—
225C4—82no—
226C4—81no—
227C4—2081no—
228C4#1171885411yescharacteristic
229C4#1171885511yescharacteristic
230C4#1171888911yescharacteristic
231C4#1171890711yescharacteristic
232C2#1311408511yescharacteristic
233C2#1311675911yescharacteristic
234C2#1311681411yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3383C2
socle, prime radicalC22×C13#447
hypercenter#3383D13
hypocenterC13#12405
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
58. C13×Q16Q16semidirect
175. Q16#6107semidirect
197. C13#12405semidirect

Maximal subgroups

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

subgroupindex
#131171092
#131169782
#131142302
#131128912
Q8⋊#60902
#131128002
C13×#33832
#1240513