Finite Group Databasebeta

← #15760778

Subgroups — #15760778

Order 3328.

518 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 115 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#13120190C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13113266C212yesmaximal, complemented
4#13112695C212yesmaximal, complemented
5C13×#2975C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C13×#436—24no—
9C13×#431C2212yes—
10C13×#407—22no—
11#11718882—21no—
12C2×#88073—21no—
13#11718871—22no—
14#11718634—21no—
15#11718610C412yes—
16#11718608C412yes—
17#11718597C2211yescharacteristic
18#11718585C2212yes—
19#11718122—21no—
20#11718048—24no—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D412yes—
23C22×Dic26C2×C411yescharacteristic
24C2×C13×M16—24no—
25C4×D4×C13—22no—
26C4×D4×C13—22no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C22⋊C4C2×C412yes—
29C2×C42×C13C2311yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—22no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×#6101—22no—
36C2×C4×Dic13—21no—
37C2×#6099—22no—
38C4×Dic26—22no—
39C4×Dic26—22no—
40C13×C4⋊C8—22no—
41C13×C22⋊C8—24no—
42C13×C22⋊C8—22no—
43C4×C8×C13D414yes—
44#88073—42no—
45#88071—22no—
46#88071—21no—
47#88071C2×C412yes—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50#9487—131nomaximal, Sylow
51C24×C13C22⋊C412yes—
52C2×D4×C13—22no—
53C2×D4×C13—21no—
54C2×D4×C13—22no—
55C2×D4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—82no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—22no—
65C22×Dic13—21no—
66C2×Dic26—22no—
67C2×Dic26—42no—
68C13×M16—84no—
69C2×C8×C13—24no—
70C13×C4⋊C4—22no—
71C13×C22⋊C4—24no—
72C42×C13C2×D412yes—
73C42×C13#4112yes—
74C22⋊Dic13—44no—
75C22⋊Dic13—82no—
76C4⋊Dic13—22no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79#6101—41no—
80#6101—41no—
81#6101—82no—
82C4×Dic13—42no—
83#6099—42no—
84#6099—42no—
85C2×#1055—42no—
86#2975D1311yescharacteristic
87#2580—131no—
88#1800—131no—
89#1487—132no—
90#1286—132no—
91C23×C13—22no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13C2×C22⋊C411yescharacteristic
97D4×C13—42no—
98D4×C13—42no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—44no—
103C2×C4×C13—42no—
104C2×C4×C13—82no—
105C2×C4×C13C4×D412yes—
106C2×C4×C13#12011yescharacteristic
107C2×C4×C13#12112yes—
108C2×C4×C13#12311yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C13#13712yes—
111C2×C4×C13#13711yescharacteristic
112C2×Dic13—22no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—42no—
121Dic26—24no—
122Dic26—42no—
123C8×C13—44no—
124#1055—82no—
125C2×C4×Q8—131no—
126C2×C4×D4C2×D1311yescharacteristic
127#436—24no—
128#431C2×D1312yes—
129#423—132no—
130C2×#100—261no—
131#407—22no—
132#399—132no—
133#393—132no—
134#390—261no—
135#389—261no—
136#385—262no—
137#382—131no—
138#343—261no—
139Q8⋊C8—264no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—44no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—82no—
147C22×C13#38611yescharacteristic
148C22×C13#41711yescharacteristic
149C22×C13#41911yescharacteristic
150C4×C13—22no—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—42no—
154C4×C13#46812yes—
155C4×C13#47012yes—
156Dic13—42no—
157Dic13—82no—
158Dic13—81no—
159C22×Q8—131no—
160C22×D4D5211yescharacteristic
161C23×C4C22⋊D1312yes—
162C2×M16—24no—
163C2×M16—262no—
164C4×Q8—262no—
165C4×Q8—262no—
166C4×D4—22no—
167C4×D4—22no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—262no—
172C2×C4⋊C4D5211yescharacteristic
173C2×C22⋊C4—262no—
174C2×C22⋊C4—262no—
175C2×C22⋊C4C4×D1312yes—
176C2×C42—261no—
177C2×C42C22×D1311yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—262no—
180C4⋊C8—262no—
181#100—522no—
182C22⋊C8—24no—
183C22⋊C8—22no—
184C4×C8C22⋊D1314yes—
185#95—132no—
186#95—262no—
187#95—261no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—82no—
191C2×C13#189111yescharacteristic
192C2×C13#189411yescharacteristic
193C2×C13#191111yescharacteristic
194C24#610312yes—
195C2×Q8—262no—
196C2×Q8—522no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—21no—
200C2×D4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—82no—
204C22×C4—261no—
205C22×C4—262no—
206C22×C4—261no—
207C22×C4#610312yes—
208C22×C4C2×C4×D1311yescharacteristic
209C22×C4C2×D5211yescharacteristic
210C22×C4C2×C22⋊D1311yescharacteristic
211M16—84no—
212M16—522no—
213M16—522no—
214C2×C8—24no—
215C2×C8—522no—
216C4⋊C4—22no—
217C4⋊C4—262no—
218C4⋊C4—521no—
219C4⋊C4—521no—
220C4⋊C4—521no—
221C4⋊C4—521no—
222C4⋊C4—1042no—
223C22⋊C4—24no—
224C22⋊C4—524no—
225C22⋊C4—1042no—
226C42—522no—
227C42#612712yes—
228C42C2×C22⋊D1312yes—
229C13#948711yescharacteristic, complemented, Sylow
230C23—22no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—42no—
235C23C2×#610311yescharacteristic
236Q8—264no—
237Q8—522no—
238D4—42no—
239D4—42no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—82no—
246C2×C4—262no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4—522no—
250C2×C4—521no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4—522no—
254C2×C4—521no—
255C2×C4#8816211yescharacteristic
256C2×C4#8816312yes—
257C2×C4#8816311yescharacteristic
258C2×C4C4×C22⋊D1312yes—
259C2×C4#8818311yescharacteristic
260C2×C4#8818412yes—
261C2×C4#8820711yescharacteristic
262C8—44no—
263C8—1042no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—82no—
271C22#1171878111yescharacteristic
272C22#1171879411yescharacteristic
273C22#1171887411yescharacteristic
274C4—22no—
275C4—21no—
276C4—21no—
277C4—42no—
278C4—522no—
279C4—1042no—
280C4—1041no—
281C4#1171879512yes—
282C4#1171879812yes—
283C2—21no—
284C2—21no—
285C2—82no—
286C2#1311525411yescharacteristic
287C2#1311526911yescharacteristic
288C2#1311536811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2975C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2975D13
hypocenterC13#9487
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
3. #13113266C2semidirect
4. #13112695C2semidirect
229. C13#9487semidirect

Maximal subgroups

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

subgroupindex
#131201902
#131148282
#131132662
#131126952
C13×#29752
#948713