Finite Group Databasebeta

← #15778924

Subgroups — #15778924

Order 3328.

480 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 101 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#13117549C211yesmaximal, characteristic
2C2×#11718134C211yesmaximal, characteristic
3#13114830C212yesmaximal, complemented
4#13112962C212yesmaximal, complemented
5C2×C13×#355C211yesmaximal, characteristic
6C2×C13×#124C2211yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C2×D4×Dic13C411yescharacteristic
9C2×C13×#101C2212yes—
10#11718891C2211yescharacteristic
11C2×#88076C2212yes—
12#11718882C411yescharacteristic
13#11718779—22no—
14#11718612—22no—
15#11718611—22no—
16#11718596C411yescharacteristic
17#11718593C411yescharacteristic
18C13×#355—22no—
19#11718146—22no—
20#11718134—22no—
21C22×Q8×C13C2311yescharacteristic
22C22×D4×C13C2×C411yescharacteristic
23C23×Dic13—21no—
24C2×C13×M16—22no—
25C13×#124—22no—
26C13×#124D412yes—
27C13×#124Q812yes—
28C2×C13×C22⋊C4—22no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—22no—
32Q8×Dic13—42no—
33D4×Dic13—42no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13D412yes—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D412yes—
41C2×#6099—22no—
42C13×#101—22no—
43C13×#101—22no—
44#88076—22no—
45#88076—22no—
46#88071—22no—
47#88071—21no—
48#88071—21no—
49#88054—44no—
50#12803—131nomaximal, Sylow
51C24×C13—21no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13C2×D411yescharacteristic
55C2×Q8×C13C2×Q811yescharacteristic
56C2×Q8×C13#4112yes—
57C2×D4×C13—21no—
58C2×D4×C13—41no—
59C2×D4×C13—41no—
60C2×D4×C13C4⋊C412yes—
61C22×C4×C13—21no—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D412yes—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—42no—
67C22×Dic13—82no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C412yes—
70C22×Dic13C22⋊C411yescharacteristic
71C13×M16—42no—
72C13×M16—42no—
73C2×C8×C13—42no—
74C13×C22⋊C4—24no—
75C13×C22⋊C4—24no—
76C42×C13—21no—
77C42×C13C4⋊C412yes—
78C22⋊Dic13—42no—
79C22⋊Dic13—82no—
80C4⋊Dic13—41no—
81C4⋊Dic13—42no—
82C4⋊Dic13—41no—
83C4⋊Dic13—82no—
84C4×Dic13—22no—
85C4×Dic13—24no—
86C4×Dic13—41no—
87#6099—42no—
88#6099—42no—
89C2×#1055—42no—
90#2326—131no—
91C2×#355—131no—
92C2×#355D1311yescharacteristic
93#1801—132no—
94#1394—132no—
95C23×C13—22no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13C2×C22⋊C411yescharacteristic
101Q8×C13—41no—
102Q8×C13—41no—
103Q8×C13—42no—
104D4×C13—42no—
105D4×C13—42no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13C2×C4⋊C411yescharacteristic
114C2×C4×C13#11711yescharacteristic
115C2×C4×C13#12112yes—
116C2×C4×C13C22⋊Q812yes—
117C2×Dic13—21no—
118C2×Dic13—22no—
119C2×Dic13—41no—
120C2×Dic13—42no—
121C2×Dic13—41no—
122C2×Dic13—42no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—84no—
128C2×Dic13#9912yes—
129C8×C13—82no—
130#1055—82no—
131C2×#124C2×D1311yescharacteristic
132C2×C4×Q8—131no—
133C2×C4×D4—131no—
134#423—262no—
135C2×#101—132no—
136C2×#101C2×D1312yes—
137#391—131no—
138#390—131no—
139#388—262no—
140#385—262no—
141#384—131no—
142#376—131no—
143#355—22no—
144#355—262no—
145#343—262no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—44no—
149C22×C13—42no—
150C22×C13—82no—
151C22×C13—81no—
152C22×C13—81no—
153C22×C13#38011yescharacteristic
154C22×C13C2×#9911yescharacteristic
155C22×C13#41011yescharacteristic
156C4×C13—22no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—22no—
160C4×C13—42no—
161Dic13—22no—
162Dic13—42no—
163Dic13—41no—
164Dic13—81no—
165Dic13—81no—
166C22×Q8C22×D1311yescharacteristic
167C22×D4C4×D1311yescharacteristic
168C23×C4—261no—
169C2×M16—22no—
170C2×M16—262no—
171#124—22no—
172#124Dic2612yes—
173#124C22⋊D1312yes—
174C4×Q8—522no—
175C4×D4—522no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—132no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—262no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—261no—
182C2×C22⋊C4—262no—
183C2×C42—131no—
184C2×C42—132no—
185C2×C42—131no—
186C2×C42C4×D1311yescharacteristic
187C4⋊C8—524no—
188#101—22no—
189#101—22no—
190#101—262no—
191#101—262no—
192#95—261no—
193#95—261no—
194#95—262no—
195C2×C13—21no—
196C2×C13—21no—
197C2×C13—82no—
198C2×C13#179911yescharacteristic
199C2×C13#213311yescharacteristic
200C2×C13#213411yescharacteristic
201C24—21no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8C2×Dic2611yescharacteristic
205C2×Q8#612912yes—
206C2×Q8C2×C22⋊D1311yescharacteristic
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4#610112yes—
211C22×C4—21no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—132no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—522no—
218C22×C4—1042no—
219C22×C4C2×C4×D1311yescharacteristic
220C22×C4D4×D1312yes—
221M16—42no—
222M16—42no—
223M16—522no—
224M16—522no—
225C2×C8—42no—
226C2×C8—522no—
227C4⋊C4—521no—
228C4⋊C4—522no—
229C4⋊C4—521no—
230C4⋊C4—1042no—
231C22⋊C4—24no—
232C22⋊C4—24no—
233C22⋊C4—522no—
234C22⋊C4—1042no—
235C42—21no—
236C42—264no—
237C42—262no—
238C42—521no—
239C42#610112yes—
240C13#1280311yescharacteristic, complemented, Sylow
241C23—22no—
242C23—42no—
243C23—42no—
244C23—41no—
245C23—41no—
246C23C22⋊C4×D1311yescharacteristic
247Q8—41no—
248Q8—42no—
249Q8—41no—
250D4—42no—
251D4—42no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—132no—
260C2×C4—262no—
261C2×C4—261no—
262C2×C4—521no—
263C2×C4—522no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—522no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—1044no—
271C2×C4#8813111yescharacteristic
272C2×C4#8813212yes—
273C2×C4C2×#610111yescharacteristic
274C2×C4#8819312yes—
275C8—82no—
276C8—1042no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22—42no—
281C22—82no—
282C22—81no—
283C22—81no—
284C22#1171840111yescharacteristic
285C22D13×#9911yescharacteristic
286C22#1171860311yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—21no—
291C4—42no—
292C4—262no—
293C4—522no—
294C4—521no—
295C4—1041no—
296C4—1041no—
297C2—21no—
298C2—21no—
299C2—82no—
300C2#1311482211yescharacteristic
301C2#1311652211yescharacteristic
302C2#1311652611yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC2×C13×#355C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC22×Q8×C13C23
hypercenterC2×#355D13
hypocenterC13#12803
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
3. #13114830C2semidirect
4. #13112962C2semidirect
240. C13#12803semidirect

Maximal subgroups

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

subgroupindex
#131175492
C2×#117181342
#131148302
#131129622
C2×C13×#3552
#1280313