Finite Group Databasebeta

← #15779845

Subgroups — #15779845

Order 3328.

470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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#13127939C211yesmaximal, characteristic, complemented
2#13123537C211yesmaximal, characteristic
3C2×#11718106C212yesmaximal, complemented
4#13112921C212yesmaximal, complemented
5C13×#2115C211yesmaximal, characteristic, complemented
6C2×C13×#131C2211yescharacteristic
7#11719533C411yescharacteristic
8C22×#6094C2211yescharacteristic
9C2×C13×M32C2212yes—
10#11718895C411yescharacteristic
11#11718801—24no—
12#11718789—22no—
13#11718787C411yescharacteristic
14#11718780C411yescharacteristic
15#11718772—22no—
16#11718762C2211yescharacteristic
17C2×#88052—22no—
18C2×#88052C2212yes—
19C13×#349—22no—
20#11718106—24no—
21C2×C13×#41C2×C411yescharacteristic
22C22×C4×D13C2×C411yescharacteristic
23C13×#131—22no—
24C13×#131—22no—
25C2×C13×M16C2×C411yescharacteristic
26C2×C13×M16D412yes—
27C22×C8×C13D412yes—
28C22×C8×C13C2311yescharacteristic
29#88200—21no—
30#88192—21no—
31#88191C812yes—
32#88189C812yes—
33C4×C22⋊D13—22no—
34#88180C2×C411yescharacteristic
35C2×#6099C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C2×#6094—21no—
38C2×#6094—21no—
39C2×#6094—22no—
40C2×#6094—22no—
41C13×M32—22no—
42C13×M32—22no—
43C2×C13×C16—22no—
44C22⋊#1055—22no—
45#88060—22no—
46#88055—21no—
47#88054—22no—
48C8×Dic13—21no—
49#88052—24no—
50#88052—22no—
51#88052D414yescomplemented
52C2×#6090—24no—
53C2×#6090—22no—
54#12989—131nomaximal, Sylow
55C23×D13C2×C811yescharacteristic
56C13×#41—22no—
57C13×#41—22no—
58C2×Q8×C13M1611yescharacteristic
59C2×D4×C13C2×C812yes—
60C2×D4×C13M1611yescharacteristic
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22×C411yescharacteristic
63C2×C22⋊D13—22no—
64C22×Dic13C2×C811yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—22no—
67C2×C4×D13—21no—
68C2×C4×D13—22no—
69C13×M16—22no—
70C13×M16—24no—
71C2×C8×C13—22no—
72C2×C8×C13—22no—
73C2×C8×C13C22⋊C412yes—
74C2×C8×C13C2×D412yes—
75C2×C8×C13C2×D411yescharacteristic
76C2×C8×C13C2×D411yescharacteristic
77C2×C8×C13#4112yes—
78C22⋊Dic13—22no—
79C22⋊Dic13C2×C812yes—
80#6103—22no—
81C4⋊Dic13—21no—
82#6101—22no—
83C4×Dic13—21no—
84#6099—22no—
85C2×#1055—21no—
86C2×#1055—21no—
87C2×#1055—22no—
88#6094—41no—
89#6094—42no—
90#6094—41no—
91C13×C16—42no—
92#6090—24no—
93#3407—131no—
94#2930—131no—
95#2115D1311yescharacteristic, complemented
96C2×#349—132no—
97#1378—132no—
98C23×C13C22⋊C812yes—
99C23×C13C22×C811yescharacteristic
100C22×D13—21no—
101C22×D13—22no—
102C22×D13—81no—
103Q8×C13—22no—
104D4×C13—24no—
105D4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13C22⋊C812yes—
109C2×C4×C13C2×C22⋊C411yescharacteristic
110C2×C4×C13C4×D412yes—
111C2×C4×C13C2×M1611yescharacteristic
112C2×C4×C13#13112yes—
113C22⋊D13—82no—
114C2×Dic13—22no—
115C2×Dic13—21no—
116C2×Dic13—22no—
117C4×D13—41no—
118C4×D13—41no—
119C4×D13—42no—
120C8×C13—22no—
121C8×C13#12011yescharacteristic
122C8×C13#12112yes—
123C8×C13#12311yescharacteristic
124#1055—41no—
125#1055—41no—
126C2×#131C2×D1311yescharacteristic
127C22×M16—131no—
128#525—131no—
129#504—264no—
130C2×M32—132no—
131C2×M32—262no—
132C2×M32C2×D1312yes—
133#436—262no—
134#435—262no—
135#424—131no—
136#408—131no—
137#407—131no—
138#405—131no—
139#349—22no—
140#349—264no—
141C22×C13—22no—
142C22×C13—41no—
143C22×C13—42no—
144C22×C13C2×C22⋊C811yescharacteristic
145C22×C13C8×D412yes—
146C2×D13—41no—
147C2×D13—41no—
148C2×D13—41no—
149C2×D13—82no—
150C4×C13—22no—
151C4×C13#38611yescharacteristic
152C4×C13#40811yescharacteristic
153C4×C13#43512yes—
154Dic13—42no—
155Dic13—41no—
156C2×#41C4×D1311yescharacteristic
157C23×C4—131no—
158#131—22no—
159#131—22no—
160C2×M16—131no—
161C2×M16—261no—
162C2×M16—262no—
163C2×M16—262no—
164C2×M16—261no—
165C2×M16C4×D1311yescharacteristic
166C2×M16C22⋊D1312yes—
167C22×C8—131no—
168C22×C8D5212yes—
169C22×C8C22×D1311yescharacteristic
170#123—132no—
171C22⋊Q8—261no—
172#121—261no—
173#120—132no—
174C4×D4—262no—
175#117—131no—
176M32—22no—
177M32—22no—
178M32—134no—
179M32—264no—
180M32—262no—
181C2×C16—22no—
182C2×C16—264no—
183C2×C16—262no—
184C4⋊C8—262no—
185C22⋊C8—262no—
186C22⋊C8—262no—
187#97—261no—
188C4×C8—261no—
189C2×C13—21no—
190C2×C13—22no—
191C2×C13—42no—
192C2×C13#186911yescharacteristic
193D13—81no—
194C24—131no—
195#41—22no—
196#41—22no—
197C2×Q8#609411yescharacteristic
198C2×D4—262no—
199C2×D4C8×D1312yes—
200C2×D4#609411yescharacteristic
201C22×C4—131no—
202C22×C4—262no—
203C22×C4—261no—
204C22×C4—262no—
205C22×C4—261no—
206C22×C4#610312yes—
207C22×C4C2×C4×D1311yescharacteristic
208M16—22no—
209M16—24no—
210M16—262no—
211M16—521no—
212M16—521no—
213M16—522no—
214C2×C8—22no—
215C2×C8—22no—
216C2×C8—262no—
217C2×C8—261no—
218C2×C8—261no—
219C2×C8#610312yes—
220C2×C8C2×D5211yescharacteristic
221C2×C8D4×D1312yes—
222C2×C8#612912yes—
223C2×C8C2×C22⋊D1311yescharacteristic
224C4⋊C4—261no—
225C4⋊C4—262no—
226C22⋊C4—132no—
227C22⋊C4—262no—
228C22⋊C4—262no—
229C42—261no—
230C16—42no—
231C16—264no—
232C13#1298911yescharacteristic, complemented, Sylow
233C23—261no—
234C23—262no—
235C23—1041no—
236C23#8806012yes—
237C23C2×C8×D1311yescharacteristic
238Q8—22no—
239D4—24no—
240D4—22no—
241D4—1042no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—262no—
245C2×C4—261no—
246C2×C4—262no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4—522no—
250C2×C4#8806012yes—
251C2×C4#8813512yes—
252C2×C4C2×#609411yescharacteristic
253C2×C4#8816112yes—
254C2×C4C2×#610311yescharacteristic
255C8—22no—
256C8—521no—
257C8—521no—
258C8#8813611yescharacteristic
259C8#8814011yescharacteristic
260C8#8819312yes—
261C22—22no—
262C22—41no—
263C22—42no—
264C22—521no—
265C22—521no—
266C22—521no—
267C22—1042no—
268C22#1171838612yes—
269C22C2×#8806011yescharacteristic
270C4—22no—
271C4—522no—
272C4—521no—
273C4#1171839112yes—
274C4#1171861911yescharacteristic
275C4#1171879011yescharacteristic
276C2—21no—
277C2—22no—
278C2—42no—
279C2—1041no—
280C2#1311512611yescharacteristic
subgroupG/H
centerC4#11718619
commutatorC23×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#2115C2
socleC2×C13#1869
prime radical#11719533C4
cosocleC22×C8×C13C23
hypercenter#2115D13
hypocenterC13#12989
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2115

Complements

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

NH ≅ G/Ntype
1. #13127939C2semidirect
3. C2×#11718106C2semidirect
4. #13112921C2semidirect
5. C13×#2115C2semidirect
51. #88052D4semidirect
95. #2115D13semidirect
232. C13#12989semidirect

Maximal subgroups

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

subgroupindex
#131279392
#131235372
C2×#117181062
#131129212
C13×#21152
#1298913