Finite Group Databasebeta

← #15782586

Subgroups — #15782586

Order 3328.

540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 81 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#13115116C212yesmaximal
2#13115045C211yesmaximal, characteristic
3#13112961C211yesmaximal, characteristic
4#13112954C212yesmaximal
5C13×#2683C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—22no—
7#11719503C2211yescharacteristic
8C13×#396—22no—
9C13×#395—21no—
10C13×#390C2211yescharacteristic
11C13×#389—21no—
12C13×#386C2212yes—
13C2×#88074C2212yes—
14C2×#88073C2211yescharacteristic
15#11718871—22no—
16#11718625—21no—
17#11718119—22no—
18#11718115—21no—
19C22×Q8×C13—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13D412yes—
22C13×C22⋊Q8—48no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4D412yes—
31C2×C42×C13D411yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—22no—
34D4×Dic13—41no—
35D4×Dic13—41no—
36#88180—21no—
37C2×#6101—42no—
38C2×#6099—21no—
39C13×#95—21no—
40C13×#95—22no—
41#88074—22no—
42#88074Q814yescomplemented
43#88073—21no—
44#88073Q812yescomplemented
45#88071—42no—
46#88048—41no—
47#88047—41no—
48#13461—131nomaximal, Sylow
49C24×C13C2×D412yes—
50C2×Q8×C13—44no—
51C2×Q8×C13—81no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13C2×Q811yescharacteristic
55C2×D4×C13C2×Q812yes—
56C2×D4×C13#4111yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—44no—
62C22×C4×C13—42no—
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—42no—
67C13×C4⋊C4—24no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—44no—
70C13×C4⋊C4—44no—
71C13×C4⋊C4—81no—
72C13×C22⋊C4—44no—
73C13×C22⋊C4—44no—
74C13×C22⋊C4—42no—
75C42×C13—41no—
76C22⋊Dic13—24no—
77C22⋊Dic13—42no—
78C22⋊Dic13—42no—
79C22⋊Dic13—41no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82#6101—84no—
83C4×Dic13—41no—
84#6099—22no—
85#6099—41no—
86C2×#1055—41no—
87#2683D1311yescharacteristic
88#1867—132no—
89#1856—131no—
90#1393—131no—
91#1390—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13#12011yescharacteristic
97C23×C13C22⋊Q812yes—
98C23×C13C4⋊Q812yes—
99Q8×C13—84no—
100D4×C13—41no—
101D4×C13—42no—
102D4×C13—41no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—24no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—44no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—82no—
118C2×C4×C13C22⋊Q811yescharacteristic
119C2×C4×C13C4⋊Q811yescharacteristic
120C2×Dic13—44no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—82no—
124C2×Dic13—82no—
125C2×Dic13—82no—
126C2×Dic13—82no—
127#1055—42no—
128C2×C22⋊Q8—22no—
129#518—131no—
130#428—261no—
131C2×#100—131no—
132C2×#99—132no—
133#396—22no—
134#395—21no—
135#390C2×D1311yescharacteristic
136#389—21no—
137#386C2×D1312yes—
138#385—262no—
139#342—262no—
140#339—261no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—82no—
150C22×C13#39511yescharacteristic
151C22×C13B(4,𝔽2)11yescharacteristic
152C22×C13#45811yescharacteristic
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—42no—
156C4×C13—44no—
157C4×C13—82no—
158C4×C13—81no—
159Dic13—84no—
160Dic13—81no—
161Dic13—81no—
162C22×Q8—21no—
163C22×D4C22×D1311yescharacteristic
164C23×C4C22⋊D1312yes—
165C2×M16—261no—
166C22⋊Q8—48no—
167C4×D4—521no—
168C4×D4—521no—
169#117—261no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—522no—
175C2×C4⋊C4C22⋊D1311yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—262no—
179C2×C22⋊C4—262no—
180C2×C22⋊C4C22⋊D1312yes—
181C2×C42C22⋊D1311yescharacteristic
182#107—521no—
183#106—521no—
184#100—132no—
185#100—261no—
186#99—134no—
187#99—262no—
188#95—21no—
189#95—22no—
190#95—522no—
191C2×C13—21no—
192C2×C13—21no—
193C2×C13—42no—
194C2×C13—42no—
195C2×C13#206211yescharacteristic
196C2×C13#219611yescharacteristic
197C2×C13#220111yescharacteristic
198C24C2×C22⋊D1312yes—
199C2×Q8—44no—
200C2×Q8—81no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4Q8×D1312yes—
204C2×D4Q8×D1311yescharacteristic
205C2×D4#613111yescharacteristic
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—262no—
213C22×C4—262no—
214C22×C4—522no—
215C22×C4C2×C22⋊D1311yescharacteristic
216M16—262no—
217M16—521no—
218C2×C8—521no—
219C4⋊C4—24no—
220C4⋊C4—41no—
221C4⋊C4—44no—
222C4⋊C4—44no—
223C4⋊C4—81no—
224C4⋊C4—261no—
225C4⋊C4—261no—
226C4⋊C4—1044no—
227C22⋊C4—44no—
228C22⋊C4—44no—
229C22⋊C4—42no—
230C22⋊C4—264no—
231C22⋊C4—522no—
232C22⋊C4—522no—
233C22⋊C4—521no—
234C42—41no—
235C42—521no—
236C13#1346111yescharacteristic, complemented, Sylow
237C23—22no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23#8819812yes—
242C23#8820012yes—
243C23#8820711yescharacteristic
244Q8—84no—
245D4—41no—
246D4—42no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—82no—
263C2×C4—524no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—1042no—
267C2×C4—1042no—
268C2×C4—1042no—
269C2×C4—1042no—
270C2×C4#8819811yescharacteristic
271C2×C4#8820011yescharacteristic
272C8—522no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—82no—
282C22#1171889011yescharacteristic
283C22#1171890411yescharacteristic
284C22#1171890511yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—44no—
289C4—82no—
290C4—81no—
291C4—1044no—
292C4—1041no—
293C4—1041no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2#1311618811yescharacteristic
299C2#1311682011yescharacteristic
300C2#1311684911yescharacteristic
subgroupG/H
centerC22#11718905
commutator, prime radical, cosocleC22×D4×C13C23
FrattiniC22×D4C22×D13
FittingC13×#2683C2
socleC22×C13B(4,𝔽2)
hypercenter#2683D13
hypocenterC13#13461
LCSG ▷ C22×D4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2683

Complements

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

NH ≅ G/Ntype
42. #88074Q8semidirect
44. #88073Q8semidirect
236. C13#13461semidirect

Maximal subgroups

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

subgroupindex
#131151162
#131150452
#131129612
#131129542
C13×#26832
#1346113