Finite Group Databasebeta

← #16790689

Subgroups — #16790689

Order 3328.

246 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 82 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#13131179C211yesmaximal, characteristic
2#13131059C211yesmaximal, characteristic
3#13129887C211yesmaximal, characteristic
4#13129886C211yesmaximal, characteristic
5#13129883C211yesmaximal, characteristic
6#13129877C211yesmaximal, characteristic
7#13114719C211yesmaximal, characteristic
8C2×#88106C2211yescharacteristic
9C2×#88106C2211yescharacteristic
10C2×#88106C2211yescharacteristic
11C2×#88106C2211yescharacteristic
12C2×#88062C411yescharacteristic
13#11718783C2211yescharacteristic
14#11718659C411yescharacteristic
15#11718658C2211yescharacteristic
16C2×#88043C2211yescharacteristic
17#11718262—22no—
18#11718233—22no—
19C13×#339C411yescharacteristic
20#11718115C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C13×#117C2×C411yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24#88180C2×C411yescharacteristic
25C2×#6099C2×C411yescharacteristic
26C22×#1055C2×C411yescharacteristic
27C22×#1055C2311yescharacteristic
28#88106—21no—
29#88106—21no—
30#88106—21no—
31#88106—21no—
32#88106—21no—
33#88106—21no—
34#88106—21no—
35#88106D412yes—
36C2×#6092—21no—
37C2×#6092—21no—
38C2×#6092—21no—
39C2×#6092Q812yes—
40#88062—22no—
41#88055—21no—
42C8×Dic13—21no—
43#88048—21no—
44#88047—21no—
45#88043—21no—
46#88043—21no—
47#88043—21no—
48C4×#1055—21no—
49#13108—131nomaximal, Sylow
50C22×C4×C13—21no—
51C22×C4×C13C22×C411yescharacteristic
52C13×M16—21no—
53C13×M16—21no—
54C2×C8×C13—21no—
55C13×C4⋊C4—21no—
56C13×C22⋊C4—21no—
57C42×C13—21no—
58C42×C13—21no—
59C42×C13—21no—
60C22⋊Dic13—21no—
61C4⋊Dic13—21no—
62C4×Dic13—21no—
63#6099—21no—
64#6099M1612yes—
65C2×#1055—21no—
66C2×#1055—21no—
67C2×#1055—21no—
68C2×#1055M1611yescharacteristic
69C2×#1055M1611yescharacteristic
70C2×#1055C2×D411yescharacteristic
71C2×#1055C2×Q811yescharacteristic
72C2×#1055#4111yescharacteristic
73C2×#1055#4111yescharacteristic
74C2×#1055#4111yescharacteristic
75C2×#1055#4111yescharacteristic
76#6092—22no—
77#6092—22no—
78#6092—41no—
79#6092—41no—
80#2153—131no—
81#2110—131no—
82#1773—131no—
83#1378—131no—
84#1378—131no—
85#1377—131no—
86#1375—131no—
87C23×C13#13111yescharacteristic
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—81no—
91C2×C4×C13#11711yescharacteristic
92C2×C4×C13C4×D411yescharacteristic
93C2×C4×C13C4×Q811yescharacteristic
94C2×C4×C13C2×M1611yescharacteristic
95C2×C4×C13C2×M1611yescharacteristic
96C2×C4×C13#13111yescharacteristic
97C2×Dic13—41no—
98C8×C13—41no—
99#1055—21no—
100#1055—21no—
101#1055—22no—
102#1055C22⋊Q811yescharacteristic
103#1055#12311yescharacteristic
104#1055#12511yescharacteristic
105#1055#12611yescharacteristic
106C2×M32—131no—
107C2×M32—131no—
108C2×M32—131no—
109C2×M32—131no—
110C2×#108—131no—
111#427—131no—
112#405—131no—
113#405—131no—
114C2×#97—131no—
115#364—262no—
116#347—262no—
117#339—131no—
118#339#26111yescharacteristic
119C22×C13—41no—
120C22×C13#43311yescharacteristic
121C22×C13#43611yescharacteristic
122C22×C13#44611yescharacteristic
123C4×C13—81no—
124C4×C13—81no—
125C4×C13#38711yescharacteristic
126C4×C13#43211yescharacteristic
127C4×C13#43511yescharacteristic
128C4×C13#44611yescharacteristic
129Dic13—81no—
130C2×M16—131no—
131C2×M16C2×#26111yescharacteristic
132C22×C8—131no—
133C22×C8—131no—
134#117—131no—
135#117C2×#26111yescharacteristic
136C2×C42C2×#26111yescharacteristic
137M32—132no—
138M32—261no—
139M32—261no—
140M32—261no—
141M32—261no—
142M32—261no—
143M32—261no—
144M32—261no—
145C2×C16—132no—
146C2×C16—261no—
147C2×C16—261no—
148C2×C16—261no—
149#108—262no—
150#107—261no—
151#106—261no—
152#97—261no—
153#97—261no—
154#97—261no—
155#97—261no—
156C4×C8—261no—
157C4×C8—261no—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—21no—
161C2×C13#191711yescharacteristic
162C22×C4—21no—
163C22×C4C22×#26111yescharacteristic
164M16—21no—
165M16—21no—
166M16—132no—
167M16—261no—
168C2×C8—21no—
169C2×C8—131no—
170C2×C8—131no—
171C2×C8—131no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—131no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8—261no—
178C2×C8—261no—
179C2×C8—261no—
180C4⋊C4—21no—
181C4⋊C4—261no—
182C22⋊C4—21no—
183C22⋊C4—261no—
184C42—21no—
185C42—21no—
186C42—21no—
187C42—261no—
188C16—262no—
189C16—262no—
190C16—521no—
191C16—521no—
192C13#1310811yescharacteristic, complemented, Sylow
193C23#8823811yescharacteristic
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—521no—
198C2×C4D13⋊M1611yescharacteristic
199C2×C4D13⋊M1611yescharacteristic
200C2×C4#8823711yescharacteristic
201C2×C4#8823811yescharacteristic
202C2×C4D4×#26111yescharacteristic
203C2×C4Q8×#26111yescharacteristic
204C8—41no—
205C8—131no—
206C8—131no—
207C8—131no—
208C8—131no—
209C8—261no—
210C8—261no—
211C8—262no—
212C22—41no—
213C22#1171906611yescharacteristic
214C22#1171906811yescharacteristic
215C22#1171907811yescharacteristic
216C4—81no—
217C4—81no—
218C4—1041no—
219C4#1171905511yescharacteristic
220C4#1171906511yescharacteristic
221C4#1171907811yescharacteristic
222C4#1171908211yescharacteristic
223C2—21no—
224C2—21no—
225C2—21no—
226C2#1313089511yescharacteristic
subgroupG/H
centerC4#11719082
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#339C4
socleC2×C13#1917
prime radicalC23×C13#131
cosocleC22×#1055C23
hypercenter#339#261
hypocenterC13#13108
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
192. C13#13108semidirect

Maximal subgroups

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

subgroupindex
#131311792
#131310592
#131298872
#131298862
#131298832
#131298772
#131147192
#1310813