Finite Group Databasebeta

← #15756075

Subgroups — #15756075

Order 3328.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11718340C211yesmaximal, characteristic
2#13113584C211yesmaximal, characteristic
3#13113264C212yesmaximal
4#13112731C212yesmaximal
5C13×#1837C211yesmaximal, characteristic
6C2×C4×Dic26C2211yescharacteristic
7C13×#423C2212yes—
8C2×C4×C8×C13C2211yescharacteristic
9C2×#88055—21no—
10C2×#88054—21no—
11#11718586C2212yes—
12C2×C4⋊#1055C2211yescharacteristic
13#11718340—21no—
14#11718340—21no—
15#11718340C412yes—
16#11718340C412yes—
17C13×#341—21no—
18C13×#341—21no—
19#11718076—24no—
20#11718050—21no—
21#11718049—21no—
22C22×Dic26Q811yescharacteristic
23C2×C13×M16—22no—
24C22×C8×C13D411yescharacteristic
25C22×C8×C13D411yescharacteristic
26C2×C42×C13C2311yescharacteristic
27C2×C4⋊Dic13Q811yescharacteristic
28C2×#6101—21no—
29C2×C4×Dic13—21no—
30C22×#1055—21no—
31C4×Dic26—21no—
32C4×Dic26—21no—
33C4×Dic26C2×C412yes—
34C4×Dic26D412yes—
35C13×C4⋊C8—22no—
36C13×C4⋊C8—22no—
37C4×C8×C13C2×C411yescharacteristic
38C4×C8×C13C2×C411yescharacteristic
39C4×C8×C13D411yescharacteristic
40C4×C8×C13D411yescharacteristic
41C22⋊#1055—22no—
42#88055—22no—
43#88055—22no—
44#88054—22no—
45#88054—22no—
46C4⋊#1055—21no—
47C4⋊#1055—22no—
48C4⋊#1055C2×C412yes—
49C4×#1055—22no—
50#8665—131nomaximal, Sylow
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×Q811yescharacteristic
53C22×C4×C13#4111yescharacteristic
54C22×Dic13—21no—
55C22×Dic13—21no—
56C2×Dic26—21no—
57C2×Dic26—42no—
58C2×Dic26C4⋊C412yes—
59C13×M16—42no—
60C13×M16—42no—
61C2×C8×C13—22no—
62C2×C8×C13—22no—
63C2×C8×C13—42no—
64C2×C8×C13C22⋊C411yescharacteristic
65C2×C8×C13C22⋊C411yescharacteristic
66C2×C8×C13C22⋊C411yescharacteristic
67C2×C8×C13C22⋊C411yescharacteristic
68C42×C13C22×C411yescharacteristic
69C42×C13C2×D411yescharacteristic
70C42×C13C2×D411yescharacteristic
71C42×C13#4111yescharacteristic
72C4⋊Dic13—21no—
73C4⋊Dic13C4⋊C412yes—
74#6101—22no—
75#6101—22no—
76C4×Dic13—22no—
77C4×Dic13—22no—
78C2×#1055—22no—
79C2×#1055—42no—
80C2×#1055—42no—
81C2×#446—131no—
82#1837D1311yescharacteristic
83#1564—131no—
84#1487—132no—
85#1301—132no—
86C23×C13C22⋊Q811yescharacteristic
87C2×C4×C13—22no—
88C2×C4×C13—41no—
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C2×C4×C13C2×C4⋊C411yescharacteristic
91C2×C4×C13#11711yescharacteristic
92C2×C4×C13#12111yescharacteristic
93C2×C4×C13#12111yescharacteristic
94C2×C4×C13C22⋊Q811yescharacteristic
95C2×C4×C13#13512yes—
96C2×C4×C13#13712yes—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101Dic26—24no—
102Dic26—42no—
103C8×C13—21no—
104C8×C13—21no—
105C8×C13—21no—
106C8×C13—21no—
107C8×C13—82no—
108#1055—42no—
109#1055—82no—
110C2×C4×Q8—131no—
111#446—132no—
112#446—132no—
113#446—261no—
114#446—261no—
115#431—132no—
116#423C2×D1312yes—
117C2×C4⋊C8—131no—
118C2×C4⋊C8—261no—
119C2×#97—261no—
120C2×C4×C8C2×D1311yescharacteristic
121#341—21no—
122#341—21no—
123#335—261no—
124#334—261no—
125Q8⋊C8—264no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13#38011yescharacteristic
129C22×C13#47912yes—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13#41611yescharacteristic
134C4×C13#41911yescharacteristic
135C4×C13#43012yes—
136C4×C13#46412yes—
137Dic13—42no—
138Dic13—42no—
139C22×Q8—131no—
140C2×M16—22no—
141C22×C8—261no—
142C22×C8C22⋊D1311yescharacteristic
143C22×C8C22⋊D1311yescharacteristic
144C4×Q8—132no—
145C4×Q8—132no—
146C4×Q8—261no—
147C4×Q8—261no—
148C2×C4⋊C4—131no—
149C2×C4⋊C4—261no—
150C2×C42—261no—
151C2×C42C22×D1311yescharacteristic
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8—132no—
155C4⋊C8—262no—
156C4⋊C8—262no—
157C4⋊C8—261no—
158C4⋊C8—262no—
159C22⋊C8—262no—
160#97—262no—
161#97—262no—
162C4×C8—262no—
163C4×C8C4×D1311yescharacteristic
164C4×C8C4×D1311yescharacteristic
165C4×C8D5211yescharacteristic
166C4×C8D5211yescharacteristic
167C2×C13—22no—
168C2×C13#180511yescharacteristic
169C2×C13#181111yescharacteristic
170C2×C13#181411yescharacteristic
171C2×Q8—132no—
172C2×Q8—261no—
173C2×Q8—522no—
174C22×C4—261no—
175C22×C4—261no—
176C22×C4Q8×D1311yescharacteristic
177C22×C4#613111yescharacteristic
178C22×C4C2×C22⋊D1311yescharacteristic
179M16—42no—
180M16—42no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—42no—
184C2×C8—262no—
185C2×C8—522no—
186C2×C8—522no—
187C2×C8#610311yescharacteristic
188C2×C8#610311yescharacteristic
189C2×C8#610311yescharacteristic
190C2×C8#610311yescharacteristic
191C4⋊C4—132no—
192C4⋊C4—262no—
193C4⋊C4—262no—
194C4⋊C4—261no—
195C42—262no—
196C42—262no—
197C42C2×C4×D1311yescharacteristic
198C42C2×D5211yescharacteristic
199C42D4×D1311yescharacteristic
200C42#612911yescharacteristic
201C13#866511yescharacteristic, complemented, Sylow
202C23#8820011yescharacteristic
203Q8—264no—
204Q8—522no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4C4⋊C4×D1311yescharacteristic
212C2×C4#8814611yescharacteristic
213C2×C4#8814911yescharacteristic
214C2×C4#8815111yescharacteristic
215C2×C4C2×#610311yescharacteristic
216C2×C4#8819211yescharacteristic
217C2×C4#8820412yes—
218C2×C4#8820512yes—
219C8—21no—
220C8—21no—
221C8—21no—
222C8—21no—
223C8—82no—
224C8—522no—
225C8—1042no—
226C22—21no—
227C22—21no—
228C22#1171864811yescharacteristic
229C22#1171872412yes—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—522no—
234C4—522no—
235C4#1171855412yes—
236C4#1171866311yescharacteristic
237C4#1171866511yescharacteristic
238C4#1171871512yes—
239C2—22no—
240C2#1311484811yescharacteristic
241C2#1311487511yescharacteristic
242C2#1311489111yescharacteristic
subgroupG/H
centerC2×C4#88192
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1837C2
socleC22×C13#380
prime radicalC23×C13C22⋊Q8
cosocleC2×C42×C13C23
hypercenter#1837D13
hypocenterC13#8665
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1837

Complements

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

NH ≅ G/Ntype
201. C13#8665semidirect

Maximal subgroups

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

subgroupindex
C2×#117183402
#131135842
#131132642
#131127312
C13×#18372
#866513