Finite Group Databasebeta

← #15782598

Subgroups — #15782598

Order 3328.

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

normal subgroups only

This group has 484 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×#2804C211yesmaximal, characteristic
6#11719503C2211yescharacteristic
7C13×#400—21no—
8C13×#393—22no—
9C13×#391—21no—
10C13×#390C2211yescharacteristic
11C13×#386C2212yes—
12C13×#385—22no—
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—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C22⋊C4—22no—
26C2×C13×C22⋊C4—22no—
27C2×C13×C22⋊C4D412yes—
28C2×C42×C13D411yescharacteristic
29C2×C22⋊Dic13—22no—
30C2×C22⋊Dic13—22no—
31D4×Dic13—41no—
32D4×Dic13—41no—
33#88180—21no—
34C2×#6101—42no—
35C2×#6099—21no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95—21no—
39C13×#95—22no—
40#88074—22no—
41#88074Q814yescomplemented
42#88073—21no—
43#88073Q812yescomplemented
44#88071—42no—
45#88048—41no—
46#88047—41no—
47#13463—131nomaximal, Sylow
48C24×C13C2×D412yes—
49C2×Q8×C13—42no—
50C2×Q8×C13—81no—
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—21no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—82no—
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—81no—
69C13×C4⋊C4—81no—
70C13×C22⋊C4—44no—
71C13×C22⋊C4—42no—
72C13×C22⋊C4—82no—
73C42×C13—41no—
74C22⋊Dic13—24no—
75C22⋊Dic13—42no—
76C22⋊Dic13—42no—
77C22⋊Dic13—41no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80#6101—84no—
81C4×Dic13—41no—
82#6099—22no—
83#6099—41no—
84C2×#1055—41no—
85#2804D1311yescharacteristic
86#1867—132no—
87#1856—131no—
88#1393—131no—
89#1390—132no—
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13#12011yescharacteristic
95C23×C13C22⋊Q812yes—
96C23×C13C4⋊Q812yes—
97Q8×C13—84no—
98D4×C13—41no—
99D4×C13—42no—
100D4×C13—41no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—44no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—82no—
116C2×C4×C13C22⋊Q811yescharacteristic
117C2×C4×C13C4⋊Q811yescharacteristic
118C2×Dic13—44no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—82no—
122C2×Dic13—82no—
123C2×Dic13—82no—
124C2×Dic13—82no—
125#1055—42no—
126#518—131no—
127#428—261no—
128C2×#100—131no—
129C2×#99—132no—
130#400—21no—
131#393—22no—
132#391—21no—
133#390C2×D1311yescharacteristic
134#386C2×D1312yes—
135#385—22no—
136#385—262no—
137#342—262no—
138#339—261no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—82no—
148C22×C13#39511yescharacteristic
149C22×C13B(4,𝔽2)11yescharacteristic
150C22×C13#45811yescharacteristic
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—42no—
154C4×C13—82no—
155C4×C13—81no—
156C4×C13—82no—
157Dic13—84no—
158Dic13—81no—
159Dic13—81no—
160C22×Q8—21no—
161C22×D4C22×D1311yescharacteristic
162C23×C4C22⋊D1312yes—
163C2×M16—261no—
164C4×D4—521no—
165C4×D4—521no—
166#117—261no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—522no—
170C2×C4⋊C4C22⋊D1311yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—262no—
174C2×C22⋊C4—262no—
175C2×C22⋊C4C22⋊D1312yes—
176C2×C42C22⋊D1311yescharacteristic
177#107—521no—
178#106—521no—
179#100—132no—
180#100—261no—
181#99—134no—
182#99—262no—
183#95—22no—
184#95—22no—
185#95—21no—
186#95—22no—
187#95—522no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13—42no—
192C2×C13#206211yescharacteristic
193C2×C13#219811yescharacteristic
194C2×C13#219911yescharacteristic
195C24C2×C22⋊D1312yes—
196C2×Q8—42no—
197C2×Q8—81no—
198C2×Q8—81no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4Q8×D1312yes—
202C2×D4Q8×D1311yescharacteristic
203C2×D4#613111yescharacteristic
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—82no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4—522no—
213C22×C4C2×C22⋊D1311yescharacteristic
214M16—262no—
215M16—521no—
216C2×C8—521no—
217C4⋊C4—41no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C4⋊C4—261no—
221C4⋊C4—261no—
222C4⋊C4—1044no—
223C22⋊C4—44no—
224C22⋊C4—42no—
225C22⋊C4—82no—
226C22⋊C4—264no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C22⋊C4—521no—
230C42—41no—
231C42—521no—
232C13#1346311yescharacteristic, complemented, Sylow
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23#8819812yes—
238C23#8820012yes—
239C23#8820711yescharacteristic
240Q8—84no—
241D4—41no—
242D4—42no—
243D4—41no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—82no—
259C2×C4—524no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—1042no—
263C2×C4—1042no—
264C2×C4—1042no—
265C2×C4—1042no—
266C2×C4#8819811yescharacteristic
267C2×C4#8820011yescharacteristic
268C8—522no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22#1171889011yescharacteristic
279C22#1171890411yescharacteristic
280C22#1171890511yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—82no—
285C4—81no—
286C4—82no—
287C4—1044no—
288C4—1041no—
289C4—1041no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2#1311618811yescharacteristic
295C2#1311683211yescharacteristic
296C2#1311683711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, prime radical, cosocleC22×D4×C13C23
FrattiniC22×D4C22×D13
FittingC13×#2804C2
socleC22×C13B(4,𝔽2)
hypercenter#2804D13
hypocenterC13#13463
LCSG ▷ C22×D4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2804

Complements

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

NH ≅ G/Ntype
41. #88074Q8semidirect
43. #88073Q8semidirect
232. C13#13463semidirect

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×#28042
#1346313