Finite Group Databasebeta

← #15782601

Subgroups — #15782601

Order 3328.

484 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 79 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#13122782C211yesmaximal, characteristic
2#13115117C212yesmaximal
3#13112961C211yesmaximal, characteristic
4#13112955C212yesmaximal
5C13×#1856C211yesmaximal, characteristic
6C13×#518C2211yescharacteristic
7C13×#428—21no—
8C2×C13×#100C2211yescharacteristic
9C13×#390C2211yescharacteristic
10#11718881C2212yes—
11C2×#88074C2212yes—
12#11718647—21no—
13#11718611—22no—
14#11718608—22no—
15#11718607—22no—
16#11718590—21no—
17C13×#339—21no—
18#11718118—22no—
19C22×D4×C13C2311yescharacteristic
20C23×Dic13D412yes—
21C22×Dic26—21no—
22C2×C13×M16—21no—
23C4×D4×C13—41no—
24C4×D4×C13—41no—
25C13×#117—21no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13D412yes—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×#6101—42no—
36C13×#107—41no—
37C13×#106—41no—
38C13×#100—21no—
39C13×#100Q812yescomplemented
40#88074—22no—
41#88074Q814yescomplemented
42#88071—22no—
43#88071—21no—
44#88071—22no—
45#88071—22no—
46#88071—42no—
47#13463—131nomaximal, Sylow
48C24×C13C2×D412yes—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13C2×Q811yescharacteristic
52C2×D4×C13C2×Q812yes—
53C2×D4×C13#4111yescharacteristic
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13C2×D411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—42no—
62C22×Dic13—42no—
63C22×Dic13—82no—
64C2×Dic26—42no—
65C2×Dic26—81no—
66C2×Dic26—81no—
67C13×M16—22no—
68C13×M16—41no—
69C2×C8×C13—41no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—44no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—41no—
76C42×C13—41no—
77C42×C13—41no—
78C22⋊Dic13—24no—
79C22⋊Dic13—42no—
80C22⋊Dic13—42no—
81C22⋊Dic13—82no—
82C4⋊Dic13—81no—
83C4⋊Dic13—81no—
84#6101—84no—
85#2804—131no—
86#1867—132no—
87#1856D1311yescharacteristic
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—
97D4×C13—41no—
98D4×C13—42no—
99D4×C13—41no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—82no—
110C2×C4×C13—82no—
111C2×C4×C13C22⋊Q811yescharacteristic
112C2×C4×C13C4⋊Q811yescharacteristic
113C2×Dic13—42no—
114C2×Dic13—44no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—44no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—82no—
122C2×Dic13—82no—
123C2×Dic13—82no—
124Dic26—84no—
125C8×C13—42no—
126#518C2×D1311yescharacteristic
127#428—21no—
128C2×#100C2×D1311yescharacteristic
129C2×#99—132no—
130#400—261no—
131#393—262no—
132#391—261no—
133#390C2×D1311yescharacteristic
134#386—132no—
135#385—262no—
136#385—262no—
137#342—262no—
138#339—21no—
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—81no—
155C4×C13—81no—
156C4×C13—81no—
157Dic13—82no—
158Dic13—84no—
159Dic13—82no—
160C22×Q8—261no—
161C22×D4C22×D1311yescharacteristic
162C23×C4—132no—
163C2×M16—21no—
164C4×D4—41no—
165C4×D4—41no—
166#117—21no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—522no—
170C2×C4⋊C4C22⋊D1311yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—262no—
175C2×C22⋊C4—262no—
176C2×C42C22⋊D1311yescharacteristic
177#107—41no—
178#106—41no—
179#100—21no—
180#100Dic2612yescomplemented
181#99—134no—
182#99—262no—
183#95—262no—
184#95—262no—
185#95—261no—
186#95—262no—
187#95—522no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13—42no—
192C2×C13#206211yescharacteristic
193C2×C13#219811yescharacteristic
194C2×C13#219911yescharacteristic
195C24D4×D1312yes—
196C2×Q8—522no—
197C2×Q8—1041no—
198C2×Q8—1041no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4C2×Dic2611yescharacteristic
202C2×D4#612711yescharacteristic
203C2×D4Q8×D1312yes—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—262no—
209C22×C4—262no—
210C22×C4—522no—
211C22×C4—522no—
212C22×C4—1042no—
213C22×C4C2×C22⋊D1311yescharacteristic
214M16—22no—
215M16—41no—
216C2×C8—41no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—1041no—
221C4⋊C4—1041no—
222C4⋊C4—1044no—
223C22⋊C4—44no—
224C22⋊C4—42no—
225C22⋊C4—41no—
226C22⋊C4—264no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C22⋊C4—1042no—
230C42—41no—
231C42—41no—
232C13#1346311yescharacteristic, complemented, Sylow
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23#8814212yes—
238C23#8815012yes—
239C23#8819111yescharacteristic
240Q8—1044no—
241D4—41no—
242D4—41no—
243D4—42no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—524no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4—524no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—1042no—
264C2×C4—1042no—
265C2×C4—1042no—
266C2×C4#8817811yescharacteristic
267C2×C4#8819811yescharacteristic
268C8—42no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22#1171864011yescharacteristic
279C22#1171869311yescharacteristic
280C22#1171871411yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—1042no—
288C4—1044no—
289C4—1042no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2#1311618911yescharacteristic
295C2#1311683111yescharacteristic
296C2#1311683611yescharacteristic
subgroupG/H
centerC22#11718693
commutator, prime radical, cosocleC22×D4×C13C23
FrattiniC22×D4C22×D13
FittingC13×#1856C2
socleC22×C13B(4,𝔽2)
hypercenter#1856D13
hypocenterC13#13463
LCSG ▷ C22×D4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1856

Complements

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

NH ≅ G/Ntype
39. C13×#100Q8semidirect
41. #88074Q8semidirect
180. #100Dic26semidirect
232. C13#13463semidirect

Maximal subgroups

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

subgroupindex
#131227822
#131151172
#131129612
#131129552
C13×#18562
#1346313