Finite Group Databasebeta

← #15781245

Subgroups — #15781245

Order 3328.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#13119821C211yesmaximal, characteristic
2C2×#11718070C214yesmaximal
3#13114832C211yesmaximal, characteristic
4C4×C13×#101C211yesmaximal, characteristic
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88198C2212yes—
7C2×#88123C411yescharacteristic
8C2×C13×#101C2212yes—
9C4×C13×M16—21no—
10C2×#88076C2212yes—
11#11718644—21no—
12#11718644—21no—
13#11718635C412yes—
14C4×C4⋊Dic13C411yescharacteristic
15#11718589—21no—
16#11718589—21no—
17#11718585—21no—
18C13×#343—21no—
19#11718122—21no—
20#11718070—28no—
21C22×Q8×C13C2311yescharacteristic
22C22×Dic26C2×C412yes—
23C2×C13×M16—22no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32#88198—24no—
33#88198—24no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×#6101—22no—
38C2×#6101—22no—
39C2×C4×Dic13C2×C412yes—
40C2×#6099—22no—
41#88123—41no—
42#88123—41no—
43C13×#101—22no—
44C13×#101D414yes—
45C13×#97—41no—
46C4×C8×C13—41no—
47#88076—24no—
48#88071—22no—
49#88071—22no—
50#88071—21no—
51C4⋊#1055—41no—
52C4⋊#1055—41no—
53#13227—131nomaximal, Sylow
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13C2×D412yes—
57C2×Q8×C13#4112yes—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×Dic13—22no—
66C22×Dic13—22no—
67C2×Dic26—24no—
68C2×Dic26—42no—
69C2×Dic26—42no—
70C13×M16—24no—
71C13×M16—42no—
72C2×C8×C13—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C4⋊Dic13—24no—
83C4⋊Dic13—42no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86#6101—44no—
87#6101—42no—
88#6101—42no—
89C4×Dic13—24no—
90#6099—42no—
91#6099—42no—
92C2×#1055—42no—
93#2546—131no—
94C2×#356—134no—
95#1801—131no—
96C4×#101D1311yescharacteristic
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—42no—
99Q8×C13—42no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13C4×D412yes—
116C2×C4×C13#12112yes—
117C2×C4×C13#12411yescharacteristic
118C2×C4×C13#12711yescharacteristic
119C2×Dic13—24no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125Dic26—84no—
126C8×C13—44no—
127#1055—82no—
128C2×C4⋊Q8—132no—
129C2×C4⋊Q8—131no—
130C2×C4×Q8C2×D1311yescharacteristic
131#423—261no—
132C2×#101—132no—
133C2×#101C2×D1312yes—
134C4×M16—21no—
135#398—261no—
136#398—261no—
137#391—132no—
138#389—261no—
139#389—261no—
140C4×C4⋊C4—131no—
141#356—268no—
142#343—21no—
143#343—261no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13#39011yescharacteristic
147C22×C13C2×#9911yescharacteristic
148C22×C13#41011yescharacteristic
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13#35612yescomplemented
158Dic13—44no—
159Dic13—82no—
160C22×Q8—132no—
161C22×Q8C22×D1311yescharacteristic
162C2×M16—22no—
163C2×M16—262no—
164C4⋊Q8—264no—
165C4⋊Q8—264no—
166C4⋊Q8—521no—
167C4⋊Q8—521no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—262no—
174C2×C4⋊C4—262no—
175C2×C4⋊C4C4×D1311yescharacteristic
176C2×C4⋊C4D5211yescharacteristic
177C2×C4⋊C4C22⋊D1311yescharacteristic
178C2×C42—132no—
179C2×C42C4×D1311yescharacteristic
180C2×C42D5211yescharacteristic
181C2×C42C22⋊D1311yescharacteristic
182C4⋊C8—521no—
183C4⋊C8—521no—
184#101—22no—
185#101—264no—
186#101D5214yes—
187#97—41no—
188C4×C8—41no—
189#95—261no—
190#95—262no—
191#95—262no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13#196411yescharacteristic
195C2×C13C2×#35611yescharacteristic
196C2×C13#213511yescharacteristic
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—264no—
200C2×Q8—522no—
201C2×Q8—522no—
202C2×Q8C2×D5212yes—
203C2×Q8#612712yes—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4#610311yescharacteristic
207C22×C4#610311yescharacteristic
208C22×C4#610311yescharacteristic
209C22×C4#610311yescharacteristic
210C22×C4C2×C4×D1311yescharacteristic
211C22×C4C2×D5211yescharacteristic
212C22×C4C2×C22⋊D1311yescharacteristic
213M16—24no—
214M16—42no—
215M16—522no—
216M16—522no—
217C2×C8—42no—
218C2×C8—522no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—264no—
223C4⋊C4—522no—
224C4⋊C4—522no—
225C4⋊C4—522no—
226C4⋊C4—524no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—264no—
236C13#1322711yescharacteristic, complemented, Sylow
237C23C2×#610311yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—1044no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—264no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4#8804611yescharacteristic
261C2×C4#8804611yescharacteristic
262C2×C4C4×D5212yes—
263C2×C4#8812811yescharacteristic
264C2×C4#8812911yescharacteristic
265C2×C4#8818412yes—
266C8—44no—
267C8—1042no—
268C22—21no—
269C22—21no—
270C22#1171860011yescharacteristic
271C22C2×#8804611yescharacteristic
272C22#1171866711yescharacteristic
273C4—22no—
274C4—21no—
275C4—22no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—524no—
282C4—1042no—
283C4#1171807012yescomplemented
284C2—21no—
285C2—21no—
286C2#1311567211yescharacteristic
287C2C2×#1171807011yescharacteristic
288C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC4×C13×#101C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenterC4×#101D13
hypocenterC13#13227
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
157. C4×C13#356semidirect
236. C13#13227semidirect
283. C4#11718070semidirect

Maximal subgroups

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

subgroupindex
#131198212
C2×#117180702
#131148322
C4×C13×#1012
#1322713