Finite Group Databasebeta

← #15778100

Subgroups — #15778100

Order 3328.

500 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 115 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#13117405C211yesmaximal, characteristic
2C2×#11718070C212yesmaximal
3#101×Dic13C212yesmaximal
4#13112963C211yesmaximal, characteristic
5C13×#1394C211yesmaximal, characteristic
6C2×Q8×Dic13C2211yescharacteristic
7C2×#88198C2211yescharacteristic
8C2×#88141C411yescharacteristic
9C2×C13×#101C2212yes—
10C13×#391C2211yescharacteristic
11C2×#88076C2212yes—
12M16×Dic13—22no—
13#11718637C411yescharacteristic
14C42×Dic13C411yescharacteristic
15#11718590C411yescharacteristic
16#11718310—22no—
17#11718308—22no—
18#11718146—22no—
19#11718070C418yescomplemented
20C22×Q8×C13C2311yescharacteristic
21C22×Dic26C2×C411yescharacteristic
22C2×C13×M16—22no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25Q8×Dic13—41no—
26Q8×Dic13—41no—
27#88198—21no—
28#88198—21no—
29#88198C2×C414yes—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13D412yes—
32C2×#6101—22no—
33C2×#6101—21no—
34C2×#6101—22no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D412yes—
41C2×#6099—22no—
42#88141—41no—
43#88141—41no—
44C13×#101—22no—
45C13×#101C2×C414yes—
46C13×#95—22no—
47#88076—22no—
48#88076C2×C414yes—
49#88071—22no—
50#88055—42no—
51C8×Dic13—42no—
52C4×#356—131nomaximal, Sylow
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13C22×C412yes—
56C2×Q8×C13#4111yescharacteristic
57C2×Q8×C13#4111yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D412yes—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C412yes—
66C22×Dic13C22⋊C411yescharacteristic
67C2×Dic26—21no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×Dic26C4212yes—
71C13×M16—24no—
72C13×M16—42no—
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C42×C13—41no—
76C4⋊Dic13—41no—
77C4⋊Dic13—42no—
78#6101—24no—
79#6101—24no—
80#6101—42no—
81#6101—44no—
82C4×Dic13—24no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—42no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13C4212yes—
92#6099—24no—
93#6099—42no—
94C2×#1055—42no—
95C4×C4⋊Q8—131no—
96C2×#356—132no—
97C4×#101—132no—
98#1394—131no—
99#1394D1311yescharacteristic
100C23×C13C2×C22⋊C411yescharacteristic
101Q8×C13—42no—
102Q8×C13—41no—
103Q8×C13—41no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13C2×C4211yescharacteristic
114C2×C4×C13#11711yescharacteristic
115C2×C4×C13C4×D412yes—
116C2×C4×C13C4×D412yes—
117C2×Dic13—22no—
118C2×Dic13—22no—
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—21no—
123C2×Dic13—22no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—42no—
128C2×Dic13#9911yescharacteristic
129C2×Dic13#9911yescharacteristic
130Dic26—42no—
131Dic26—42no—
132C8×C13—44no—
133#1055—44no—
134C2×C4⋊Q8—131no—
135C2×C4×Q8—131no—
136C2×C4×Q8—131no—
137C2×#101—132no—
138C2×#101C2×D1312yes—
139C4×M16—262no—
140#391—131no—
141#391C2×D1311yescharacteristic
142#389—262no—
143#384—131no—
144C4×C4⋊C4—262no—
145C43—131no—
146#356—138no—
147#343—262no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13C4×C22⋊C411yescharacteristic
151C22×C13C2×#9911yescharacteristic
152C22×C13#41011yescharacteristic
153C4×C13—22no—
154C4×C13—22no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—42no—
158C4×C13—81no—
159Dic13—24no—
160Dic13—21no—
161Dic13—41no—
162Dic13—42no—
163Dic13—42no—
164Dic13#35612yescomplemented
165C22×Q8—131no—
166C22×Q8C22×D1311yescharacteristic
167C2×M16—22no—
168C2×M16—262no—
169C4⋊Q8—134no—
170C4⋊Q8—261no—
171C4⋊Q8—261no—
172C4×Q8—521no—
173C4×Q8—521no—
174C4×Q8—521no—
175C4×Q8—521no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—132no—
178C2×C4⋊C4—262no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—262no—
181C2×C4⋊C4C4×D1311yescharacteristic
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—132no—
185C2×C42—261no—
186C2×C42—261no—
187C2×C42—261no—
188C2×C42C4×D1311yescharacteristic
189#101—22no—
190#101—134no—
191#101—262no—
192#101C4×D1314yes—
193#97—522no—
194C4×C8—522no—
195#95—22no—
196#95—262no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13C4×#9911yescharacteristic
200C2×C13C2×#35611yescharacteristic
201C2×C13#213211yescharacteristic
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—132no—
205C2×Q8—261no—
206C2×Q8—521no—
207C2×Q8—521no—
208C2×Q8C2×C4×D1312yes—
209C2×Q8#612911yescharacteristic
210C2×Q8#613111yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—131no—
214C22×C4—132no—
215C22×C4—131no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4C2×C4×D1311yescharacteristic
219C22×C4D4×D1312yes—
220M16—24no—
221M16—42no—
222M16—264no—
223M16—522no—
224C2×C8—42no—
225C2×C8—522no—
226C4⋊C4—41no—
227C4⋊C4—264no—
228C4⋊C4—264no—
229C4⋊C4—521no—
230C4⋊C4—522no—
231C4⋊C4—522no—
232C4⋊C4—524no—
233C42—41no—
234C42—132no—
235C42—262no—
236C42—262no—
237C42—261no—
238C42—261no—
239C42—264no—
240C42—261no—
241C42—521no—
242C42—521no—
243C42—522no—
244C13C4×#35611yescharacteristic, complemented, Sylow
245C23C22⋊C4×D1311yescharacteristic
246Q8—42no—
247Q8—41no—
248Q8—41no—
249Q8—522no—
250Q8—522no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—131no—
261C2×C4—131no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—261no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—522no—
273C2×C4C42×D1311yescharacteristic
274C2×C4#8813512yes—
275C2×C4#8814611yescharacteristic
276C2×C4#8814712yes—
277C8—44no—
278C8—524no—
279C22—21no—
280C22—21no—
281C22#1171832711yescharacteristic
282C22#1171840111yescharacteristic
283C22D13×#9911yescharacteristic
284C4—22no—
285C4—22no—
286C4—21no—
287C4—21no—
288C4—42no—
289C4—81no—
290C4—132no—
291C4—264no—
292C4—261no—
293C4—521no—
294C4—522no—
295C4—522no—
296C2—21no—
297C2—21no—
298C2#1311462311yescharacteristic
299C2D13×#35611yescharacteristic
300C2#1311651811yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C2×C42
FrattiniC22×Q8C22×D13
FittingC13×#1394C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1394D13
hypocenterC13C4×#356
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
19. #11718070C4semidirect
164. Dic13#356semidirect
244. C13C4×#356semidirect

Maximal subgroups

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

subgroupindex
#131174052
C2×#117180702
#101×Dic132
#131129632
C13×#13942
C4×#35613