Finite Group Databasebeta

← #15766544

Subgroups — #15766544

Order 3328.

408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#11718507C211yesmaximal, characteristic
2#13114825C211yesmaximal, characteristic
3#13113606C211yesmaximal, characteristic, complemented
4#13113522C211yesmaximal, characteristic, complemented
5#13113516C211yesmaximal, characteristic, complemented
6#13113228C211yesmaximal, characteristic
7C13×#1301C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×#88063—21no—
14C2×#88061—21no—
15C2×#88058—21no—
16#11718586C2211yescharacteristic
17#11718585C2211yescharacteristic
18#11718507—22no—
19#11718507—22no—
20#11718146—21no—
21#11718078—22no—
22#11718073—22no—
23#11718072—22no—
24#11718051—22no—
25C22×D52D411yescharacteristic
26C22×C4×D13—21no—
27C22×Dic26—21no—
28C2×C13×M16—21no—
29C22×C8×C13—21no—
30C2×C42×C13C2311yescharacteristic
31C2×#6103—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13D411yescharacteristic
35C2×#6099—21no—
36C4×D52—21no—
37C4×D52—21no—
38C4×D52—21no—
39C4×D52—21no—
40#88123—21no—
41#88123—21no—
42#88123—21no—
43#88123D412yes—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8D412yes—
49C13×C22⋊C8—21no—
50C4×C8×C13—21no—
51C22⋊#1055—21no—
52#88063—42no—
53#88061—24no—
54#88058—24no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055D412yes—
58C4×#1055—21no—
59#10448—131nomaximal, Sylow
60C23×D13—21no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13#4111yescharacteristic
63C22×C4×C13#4111yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—41no—
66C2×D52—21no—
67C2×D52—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52SD1612yes—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13—82no—
75C2×Dic26—22no—
76C2×Dic26—41no—
77C2×Dic26—82no—
78C13×M16—41no—
79C13×M16—41no—
80C2×C8×C13—22no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C42×C13C2×D411yescharacteristic
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13#4111yescharacteristic
89#6103—41no—
90#6103—41no—
91C4⋊Dic13—22no—
92C4⋊Dic13—21no—
93C4⋊Dic13—22no—
94C4⋊Dic13—21no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6099—41no—
98#6099—41no—
99C2×#1055—22no—
100C2×#1055—41no—
101C2×#474—131no—
102#1800—131no—
103#1570—131no—
104#1549—131no—
105#1548—131no—
106#1478—131no—
107#1301D1311yescharacteristic, complemented
108C23×C13#12311yescharacteristic
109C22×D13—22no—
110C22×D13—41no—
111C22×D13—41no—
112C22×D13—81no—
113C22×D13—81no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13#12111yescharacteristic
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12111yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13#12411yescharacteristic
122C2×C4×C13C2×SD1611yescharacteristic
123C2×C4×C13#13511yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×Dic13—42no—
127C2×Dic13—41no—
128C2×Dic13—82no—
129C2×Dic13—81no—
130D52—22no—
131D52—22no—
132D52—41no—
133D52—41no—
134C4×D13—82no—
135C4×D13—82no—
136Dic26—82no—
137Dic26—82no—
138C8×C13—42no—
139C8×C13—81no—
140C8×C13—81no—
141#1055—42no—
142#1055—81no—
143C2×C4⋊Q8—131no—
144C2×C4×D4—131no—
145#474—262no—
146#474—262no—
147#431—131no—
148#431C2×D1311yescharacteristic
149C2×#107—261no—
150#423—131no—
151#423C2×D1311yescharacteristic
152C2×C4⋊C8C2×D1311yescharacteristic
153C2×#102—261no—
154C2×#100—261no—
155#343—261no—
156#334—262no—
157#333—262no—
158#332—262no—
159D4⋊C8—262no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13#39411yescharacteristic
163C22×C13#48311yescharacteristic
164C22×C13#48511yescharacteristic
165C2×D13—42no—
166C2×D13—82no—
167C2×D13—81no—
168C2×D13—81no—
169C2×D13—82no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13#44811yescharacteristic
174C4×C13#45211yescharacteristic
175C4×C13#46511yescharacteristic
176C4×C13#47011yescharacteristic
177C4×C13#47212yes—
178Dic13—82no—
179Dic13—81no—
180C22×Q8—261no—
181C22×D4—131no—
182C23×C4—261no—
183C2×M16—21no—
184C2×M16—261no—
185C22×C8—21no—
186C4⋊Q8—132no—
187C4⋊Q8—261no—
188C4⋊Q8—261no—
189C4⋊Q8—261no—
190C4×D4—261no—
191C4×D4—261no—
192C4×D4—261no—
193C4×D4—261no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C22⋊C4—261no—
198C2×C42C22×D1311yescharacteristic
199#107—264no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—132no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8D5212yes—
208#102—264no—
209#100—522no—
210C22⋊C8—21no—
211C22⋊C8—261no—
212C4×C8—21no—
213C4×C8—261no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13#203511yescharacteristic
217C2×C13#204511yescharacteristic
218C2×C13#204911yescharacteristic
219D13—82no—
220C24—261no—
221C2×Q8—262no—
222C2×Q8—521no—
223C2×Q8—1042no—
224C2×D4—132no—
225C2×D4—261no—
226C2×D4—261no—
227C2×D4—261no—
228C2×D4—261no—
229C2×D4—261no—
230C22×C4—261no—
231C22×C4—521no—
232C22×C4—521no—
233C22×C4—521no—
234C22×C4—1042no—
235C22×C4#612711yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C22×C4#613111yescharacteristic
238M16—41no—
239M16—41no—
240M16—521no—
241M16—521no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—262no—
248C2×C8—521no—
249C4⋊C4—262no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—262no—
253C4⋊C4—521no—
254C4⋊C4—521no—
255C22⋊C4—521no—
256C22⋊C4—521no—
257C42C2×D5211yescharacteristic
258C42#612711yescharacteristic
259C42D4×D1311yescharacteristic
260C42D4×D1311yescharacteristic
261C13#1044811yescharacteristic, complemented, Sylow
262C23—262no—
263C23—521no—
264C23—521no—
265C23—1041no—
266C23—1041no—
267C23#8814811yescharacteristic
268Q8—1042no—
269Q8—1042no—
270D4—262no—
271D4—262no—
272D4—521no—
273D4—521no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—521no—
277C2×C4—522no—
278C2×C4—1042no—
279C2×C4—1042no—
280C2×C4—1042no—
281C2×C4—1041no—
282C2×C4#8812911yescharacteristic
283C2×C4#8813611yescharacteristic
284C2×C4#8813811yescharacteristic
285C2×C4#8813811yescharacteristic
286C2×C4#8814811yescharacteristic
287C2×C4#8814911yescharacteristic
288C2×C4#8816611yescharacteristic
289C2×C4SD16×D1311yescharacteristic
290C2×C4#8816911yescharacteristic
291C2×C4#8817211yescharacteristic
292C8—42no—
293C8—81no—
294C8—81no—
295C8—522no—
296C8—1041no—
297C22—21no—
298C22—21no—
299C22—522no—
300C22—1042no—
301C22—1042no—
302C22—1041no—
303C22—1041no—
304C22#1171833311yescharacteristic
305C22#1171852311yescharacteristic
306C22#1171854911yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—1041no—
311C4—1042no—
312C4#1171843911yescharacteristic
313C4#1171844411yescharacteristic
314C4#1171846711yescharacteristic
315C4#1171847711yescharacteristic
316C4#1171855812yes—
317C2—21no—
318C2—21no—
319C2—1042no—
320C2#1311603511yescharacteristic
321C2#1311609311yescharacteristic
322C2#1311611911yescharacteristic
subgroupG/H
centerC22#11718333
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1301C2
socleC22×C13#394
prime radicalC22×D52D4
hypercenter#1301D13
hypocenterC13#10448
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #13113606C2semidirect
4. #13113522C2semidirect
5. #13113516C2semidirect
7. C13×#1301C2semidirect
107. #1301D13semidirect
261. C13#10448semidirect

Maximal subgroups

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

subgroupindex
C2×#117185072
#131148252
#131136062
#131135222
#131135162
#131132282
C13×#13012
#1044813