Finite Group Databasebeta

← #15782389

Subgroups — #15782389

Order 3328.

444 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 77 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×#11718140C212yesmaximal
2#13115230C212yesmaximal
3#13115050C211yesmaximal, characteristic
4#13112963C211yesmaximal, characteristic
5C13×#2734C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2212yes—
7#11719517C2211yescharacteristic
8C13×#398—21no—
9C13×#395—22no—
10C13×#391C2211yescharacteristic
11C13×#389—21no—
12C13×#387—22no—
13C2×#88076C2212yes—
14C2×#88076C2211yescharacteristic
15#11718886—22no—
16#11718625—21no—
17#11718140—24no—
18#11718115—22no—
19#11718115—21no—
20C22×Q8×C13D412yes—
21C22×Q8×C13C2311yescharacteristic
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13D412yes—
33C2×C42×C13D411yescharacteristic
34Q8×Dic13—41no—
35Q8×Dic13—41no—
36#88180—21no—
37#88180—22no—
38C2×#6099—21no—
39C2×#6099—22no—
40C13×#95—21no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95—22no—
44#88076—21no—
45#88076—22no—
46#88076—22no—
47#88076D412yes—
48#88075—42no—
49#88075—42no—
50#88048—41no—
51#88047—41no—
52#13428—131nomaximal, Sylow
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13—42no—
58C2×Q8×C13—42no—
59C2×Q8×C13C2×D411yescharacteristic
60C2×Q8×C13#4111yescharacteristic
61C2×Q8×C13#4112yes—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C13×C4⋊C4—24no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—81no—
75C13×C4⋊C4—81no—
76C42×C13—22no—
77C42×C13—22no—
78C42×C13—41no—
79C22⋊Dic13—41no—
80C4⋊Dic13—22no—
81C4⋊Dic13—22no—
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4×Dic13—41no—
85C4×Dic13—42no—
86#6099—22no—
87#6099—41no—
88#6099—42no—
89#6099—42no—
90C2×#1055—41no—
91C2×#1055—42no—
92#2734D1311yescharacteristic
93C2×#356—132no—
94#1886—132no—
95#1857—131no—
96#1394—131no—
97C23×C13#12011yescharacteristic
98Q8×C13—41no—
99Q8×C13—41no—
100Q8×C13—42no—
101Q8×C13—44no—
102Q8×C13—82no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—24no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12112yes—
120C2×C4×C13#12312yes—
121C2×C4×C13#12411yescharacteristic
122C2×Dic13—41no—
123C2×Dic13—41no—
124#1055—42no—
125#1055—82no—
126C2×C4⋊Q8C2×D1312yes—
127#519—131no—
128#428—261no—
129#419—262no—
130C2×#101—131no—
131C2×#101—132no—
132#398—21no—
133#395—22no—
134#391C2×D1311yescharacteristic
135#389—21no—
136#387—22no—
137#356—264no—
138#339—261no—
139#339—262no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#39411yescharacteristic
143C22×C13B(4,𝔽2)11yescharacteristic
144C22×C13#45811yescharacteristic
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—22no—
148C4×C13—21no—
149C4×C13—44no—
150C4×C13—42no—
151C4×C13—81no—
152C4×C13—82no—
153Dic13—81no—
154Dic13—81no—
155C22×Q8C22⋊D1312yes—
156C22×Q8C22×D1311yescharacteristic
157C2×M16—261no—
158C2×M16—262no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4×Q8—521no—
164C4×Q8—521no—
165#117—262no—
166#117—261no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C22⋊D1311yescharacteristic
173C2×C42C22⋊D1312yes—
174C2×C42C22⋊D1311yescharacteristic
175#107—521no—
176#106—521no—
177#103—522no—
178#103—522no—
179#101—132no—
180#101—261no—
181#101—262no—
182#101—262no—
183#95—21no—
184#95—22no—
185#95—22no—
186#95—22no—
187C2×C13—21no—
188C2×C13—21no—
189C2×C13#204411yescharacteristic
190C2×C13#220311yescharacteristic
191C2×C13#220511yescharacteristic
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8D4×D1311yescharacteristic
199C2×Q8#612911yescharacteristic
200C2×Q8#612912yes—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4C2×C22⋊D1312yes—
206C22×C4C2×C22⋊D1311yescharacteristic
207M16—262no—
208M16—521no—
209M16—522no—
210M16—522no—
211C2×C8—521no—
212C2×C8—522no—
213C4⋊C4—24no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—262no—
222C4⋊C4—262no—
223C4⋊C4—261no—
224C4⋊C4—261no—
225C22⋊C4—521no—
226C42—22no—
227C42—22no—
228C42—41no—
229C42—521no—
230C42—522no—
231C13#1342811yescharacteristic, complemented, Sylow
232C23#8820711yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—44no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4#8818912yes—
256C2×C4#8819011yescharacteristic
257C2×C4#8819211yescharacteristic
258C2×C4#8819312yes—
259C8—522no—
260C8—1042no—
261C22—21no—
262C22—21no—
263C22#1171888311yescharacteristic
264C22#1171890411yescharacteristic
265C22#1171890511yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—81no—
274C4—1041no—
275C4—1041no—
276C2—21no—
277C2—21no—
278C2#1311608411yescharacteristic
279C2#1311685711yescharacteristic
280C2#1311686611yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC22×Q8×C13C23
FrattiniC22×Q8C22×D13
FittingC13×#2734C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2734D13
hypocenterC13#13428
LCSG ▷ C22×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2734

Complements

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

NH ≅ G/Ntype
231. C13#13428semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131152302
#131150502
#131129632
C13×#27342
#1342813