Finite Group Databasebeta

← #15783280

Subgroups — #15783280

Order 3328.

312 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 59 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#13125215C211yesmaximal, characteristic
2D13×#356C212yesmaximal
3#13113009C211yesmaximal, characteristic, complemented
4#13113008C212yesmaximal, complemented
5C13×#1413C211yesmaximal, characteristic, complemented
6D13×C4⋊Q8C2211yescharacteristic
7#11719393C411yescharacteristic
8C13×#491C2211yescharacteristic
9#11718743C2211yescharacteristic
10#11718730C411yescharacteristic
11#11718463—22no—
12#11718453—22no—
13D13×#101—22no—
14#11718368C411yescharacteristic
15#11718364C411yescharacteristic
16C13×#356C2212yes—
17#11718140C2212yes—
18#11718070—22no—
19C2×Q8×D13D412yes—
20C13×C4⋊Q8C2311yescharacteristic
21C13×#125C2×C411yescharacteristic
22#88198D412yes—
23M16×D13—42no—
24C2×#6094—21no—
25#88150—41no—
26#88146—21no—
27C4⋊C4×D13—41no—
28#88142—21no—
29#88142—41no—
30#88141—41no—
31C42×D13C2×C411yescharacteristic
32#88124C2×C411yescharacteristic
33#88123C2×C411yescharacteristic
34C13×#103—22no—
35C13×#101—22no—
36C13×#97C2×C411yescharacteristic
37#88076—22no—
38#88075—22no—
39#88064—42no—
40#88056—22no—
41C8×Dic13—21no—
42#88050—22no—
43#88043C2×C411yescharacteristic
44#13599—131nomaximal, Sylow
45C2×Q8×C13C2×D412yes—
46Q8×D13—42no—
47Q8×D13—42no—
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×C4×D13C22⋊C411yescharacteristic
51C2×Dic26—22no—
52C2×Dic26—41no—
53C2×Dic26C22⋊C412yes—
54C13×M16—42no—
55C2×C8×C13—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C42×C13C22×C411yescharacteristic
60#6103—41no—
61C4⋊Dic13—21no—
62C4⋊Dic13—41no—
63#6101—42no—
64#6101—41no—
65#6101—41no—
66C4×Dic13—21no—
67C4×Dic13—41no—
68C4×Dic13C22⋊C411yescharacteristic
69#6099—42no—
70C2×#1055—21no—
71#6094—42no—
72#6094—82no—
73C8×D13—82no—
74#3139—131no—
75C2×#356—132no—
76#1413—131no—
77#1413—132no—
78#1413D1311yescharacteristic, complemented
79C22×D13#9911yescharacteristic
80Q8×C13—42no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—41no—
84C2×C4×C13C2×C22⋊C411yescharacteristic
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13—41no—
88C2×Dic13#9911yescharacteristic
89C4×D13—22no—
90C4×D13—42no—
91C4×D13—42no—
92C4×D13—42no—
93Dic26—42no—
94Dic26—82no—
95Dic26—82no—
96C8×C13—41no—
97C8×C13—82no—
98#1055—41no—
99#1055—82no—
100#533—131no—
101C2×C4⋊Q8—131no—
102#491—131no—
103#491—131no—
104#491—131no—
105#491C2×D1311yescharacteristic
106#487—262no—
107#419—262no—
108C2×#101—262no—
109C4×M16—131no—
110#356—132no—
111#356—262no—
112#356C2×D1312yes—
113C22×C13C2×#9911yescharacteristic
114C2×D13—41no—
115C2×D13#35412yes—
116C4×C13—21no—
117C4×C13—41no—
118C4×C13—42no—
119C4×C13—81no—
120Dic13—22no—
121Dic13—21no—
122Dic13—42no—
123Dic13—81no—
124C22×Q8—132no—
125C2×M16—261no—
126C2×M16—522no—
127C4⋊Q8—132no—
128C4⋊Q8—131no—
129C4⋊Q8—261no—
130C4⋊Q8—521no—
131C4⋊Q8C22×D1311yescharacteristic
132#125—131no—
133#125C4×D1311yescharacteristic
134C22⋊Q8—521no—
135C4×Q8—521no—
136#117—261no—
137C2×C4⋊C4—521no—
138C2×C42—131no—
139#103—22no—
140#103—262no—
141#103—262no—
142#103—262no—
143#101—22no—
144#101—262no—
145#101—522no—
146#97—131no—
147#97C4×D1311yescharacteristic
148C4×C8—261no—
149C2×C13—21no—
150C2×C13C2×#35411yescharacteristic
151D13—22no—
152C2×Q8—132no—
153C2×Q8—262no—
154C2×Q8—521no—
155C2×Q8—522no—
156C2×Q8—522no—
157C2×Q8D4×D1312yes—
158C22×C4—131no—
159C22×C4—261no—
160C22×C4—262no—
161M16—42no—
162M16—522no—
163M16—522no—
164M16—1042no—
165C2×C8—21no—
166C2×C8—261no—
167C2×C8—1042no—
168C4⋊C4—21no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—261no—
172C4⋊C4—522no—
173C4⋊C4—521no—
174C4⋊C4—521no—
175C4⋊C4—521no—
176C22⋊C4—521no—
177C42—131no—
178C42—261no—
179C42—521no—
180C42C2×C4×D1311yescharacteristic
181C13#1359911yescharacteristic, complemented, Sylow
182C23—131no—
183Q8—42no—
184Q8—522no—
185Q8—1042no—
186Q8—1042no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—131no—
191C2×C4—262no—
192C2×C4—261no—
193C2×C4—262no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4—521no—
198C2×C4C22⋊C4×D1311yescharacteristic
199C8—41no—
200C8—82no—
201C8—521no—
202C8—1042no—
203C22—132no—
204C22—521no—
205C22D13×#9911yescharacteristic
206C4—21no—
207C4—41no—
208C4—42no—
209C4—81no—
210C4—262no—
211C4—261no—
212C4—522no—
213C4—1041no—
214C2—21no—
215C2—262no—
216C2D13×#35411yescharacteristic
subgroupG/H
centerC2D13×#354
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC13×#1413C2
socleC2×C13C2×#354
prime radicalC22×D13#99
cosocleC13×C4⋊Q8C23
hypercenter#1413D13
hypocenterC13#13599
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1413

Complements

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

NH ≅ G/Ntype
3. #13113009C2semidirect
4. #13113008C2semidirect
5. C13×#1413C2semidirect
78. #1413D13semidirect
181. C13#13599semidirect

Maximal subgroups

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

subgroupindex
#131252152
D13×#3562
#131130092
#131130082
C13×#14132
#1359913