Finite Group Databasebeta

← #15790177

Subgroups — #15790177

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718328C213yesmaximal
2C2×#11718648C213yesmaximal
3C2×D13×#95C211yesmaximal, characteristic
4#13113101C211yesmaximal, characteristic, complemented
5#13113100C213yesmaximal, complemented
6#13113099C213yesmaximal, complemented
7C13×#1444C211yesmaximal, characteristic, complemented
8C23×C4×D13C2213yes—
9C22×C13×C4⋊C4C2213yes—
10C22×#6103C2213yes—
11C22×#6103C2211yescharacteristic
12C22×C4⋊Dic13C2213yes—
13C22×#6101C2213yes—
14C22×#6101C2213yes—
15C2×C13×#95C2213yes—
16C2×C13×#95C2211yescharacteristic
17C2×#88071C2216yes—
18C2×#88071C2213yes—
19C2×#88071C2213yes—
20#11718648—212no—
21#11718328—212no—
22D13×#95C418yescomplemented
23C24×D13C2311yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C23×C4×C13C2313yes—
26C23×C4×C13C2313yes—
27C23×Dic13C2311yescharacteristic
28C23×Dic13C2313yes—
29C23×Dic13C2313yes—
30C22×C4×D13—46no—
31C22×C4×D13—46no—
32C22×C4×D13C2×C4112yes—
33C22×C4×D13D4112yes—
34C22×C4×D13Q8112yes—
35C2×C13×C4⋊C4—26no—
36C2×C13×C4⋊C4—46no—
37C2×#6103—26no—
38C2×#6103—26no—
39C2×#6103—212no—
40C2×C4⋊Dic13—26no—
41C2×C4⋊Dic13—46no—
42C2×#6101—26no—
43C2×#6101—26no—
44C2×#6101—46no—
45C2×#6101—46no—
46C13×#95—26no—
47C13×#95C2×C414yes—
48#88071—26no—
49#88071—212no—
50#88071C2×C4112yes—
51#14353—131nomaximal, Sylow
52C24×C13C2411yescharacteristic
53C23×D13—23no—
54C23×D13—23no—
55C23×D13—21no—
56C23×D13—21no—
57C23×D13C22×C412yes—
58C23×D13C2×D416yes—
59C23×D13C2×Q816yes—
60C22×C4×C13—26no—
61C22×C4×C13—26no—
62C22×C4×C13—26no—
63C22×C4×C13—23no—
64C22×C4×C13—23no—
65C22×C4×C13—23no—
66C22×C4×C13—26no—
67C22×C4×C13—23no—
68C22×C4×C13—21no—
69C22×C4×C13—23no—
70C22×C4×C13C22×C416yes—
71C22×C4×C13C2×D416yes—
72C22×C4×C13C2×Q816yes—
73C22×Dic13—26no—
74C22×Dic13—26no—
75C22×Dic13—23no—
76C22×Dic13—23no—
77C22×Dic13—26no—
78C22×Dic13—23no—
79C22×Dic13—26no—
80C22×Dic13—23no—
81C22×Dic13—23no—
82C22×Dic13—21no—
83C22×Dic13C22×C416yes—
84C22×Dic13C2×D416yes—
85C22×Dic13C2×Q816yes—
86C2×C4×D13—424no—
87C2×C4×D13—412no—
88C2×C4×D13—412no—
89C2×C4×D13—424no—
90C2×C4×D13C4⋊C4148yescomplemented
91C13×C4⋊C4—412no—
92#6103—44no—
93#6103—412no—
94C4⋊Dic13—412no—
95#6101—412no—
96#6101—412no—
97C2×#380—133no—
98C2×#380—133no—
99C22×#95—131no—
100#1444—133no—
101#1444—131no—
102#1444—133no—
103#1444D1311yescharacteristic, complemented
104C23×C13C23×C411yescharacteristic
105C23×C13C22×D413yes—
106C23×C13C22×Q813yes—
107C23×C13H(5,𝔽2)13yes—
108C23×C13H(5,𝔽2)13yes—
109C23×C132−1+411yescharacteristic
110C23×C132−1+411yescharacteristic
111C22×D13—26no—
112C22×D13—22no—
113C22×D13—26no—
114C22×D13—26no—
115C22×D13—26no—
116C22×D13—26no—
117C22×D13—212no—
118C22×D13—26no—
119C22×D13—26no—
120C22×D13C2×C4⋊C4112yes—
121C22×D13#12714yes—
122C22×D13C4⋊Q8112yes—
123C2×C4×C13—212no—
124C2×C4×C13—26no—
125C2×C4×C13—26no—
126C2×C4×C13—212no—
127C2×C4×C13—43no—
128C2×C4×C13—41no—
129C2×C4×C13—43no—
130C2×C4×C13—43no—
131C2×C4×C13—46no—
132C2×C4×C13—46no—
133C2×C4×C13—43no—
134C2×C4×C13—43no—
135C2×C4×C13C2×C4⋊C4112yes—
136C2×Dic13—212no—
137C2×Dic13—26no—
138C2×Dic13—26no—
139C2×Dic13—212no—
140C2×Dic13—41no—
141C2×Dic13—43no—
142C2×Dic13—43no—
143C2×Dic13—43no—
144C2×Dic13—46no—
145C2×Dic13—43no—
146C2×Dic13—43no—
147C2×Dic13—46no—
148C2×Dic13C2×C4⋊C4112yes—
149C4×D13—448no—
150C24×C4—133no—
151C22×C4⋊C4—133no—
152C22×C4⋊C4—133no—
153C22×C4⋊C4—133no—
154C22×C4⋊C4C2×D1313yes—
155C22×C22⋊C4—131no—
156C22×C22⋊C4—133no—
157#380—2612no—
158#380—2612no—
159C2×#95—133no—
160C2×#95—138no—
161C2×#95—136no—
162C2×#95—133no—
163C2×#95C2×D1313yes—
164C2×#95C2×D1311yescharacteristic
165C22×C13C22×C4⋊C413yes—
166C22×C13#51813yes—
167C22×C13#51911yescharacteristic
168C22×C13C2×#12711yescharacteristic
169C22×C13C2×C4⋊Q813yes—
170C22×C13#53413yes—
171C22×C13#53413yes—
172C22×C13#53713yes—
173C22×C13#53713yes—
174C22×C13#54316yes—
175C22×C13#54413yes—
176C22×C13#54413yes—
177C2×D13—212no—
178C2×D13—212no—
179C2×D13—24no—
180C2×D13—24no—
181C2×D13—212no—
182C2×D13—212no—
183C2×D13#38418yes—
184C4×C13—212no—
185C4×C13—83no—
186C4×C13—81no—
187Dic13—212no—
188Dic13—81no—
189Dic13—83no—
190C25—131no—
191C23×C4—133no—
192C23×C4—1312no—
193C23×C4—1312no—
194C23×C4—1312no—
195C23×C4—131no—
196C23×C4—133no—
197C23×C4—526no—
198C23×C4—526no—
199C23×C4C22×D1311yescharacteristic
200C23×C4C22×D1313yes—
201C23×C4C22×D1313yes—
202C2×C4⋊C4—26no—
203C2×C4⋊C4—46no—
204C2×C4⋊C4—266no—
205C2×C4⋊C4—266no—
206C2×C4⋊C4—266no—
207C2×C4⋊C4—526no—
208C2×C4⋊C4—526no—
209C2×C4⋊C4—526no—
210C2×C22⋊C4—266no—
211C2×C22⋊C4—266no—
212C2×C22⋊C4—2612no—
213#95—26no—
214#95—1312no—
215#95—2612no—
216#95—266no—
217#95C4×D1314yes—
218C2×C13C2×#38411yescharacteristic
219C2×C13#231513yes—
220C2×C13#231613yes—
221C2×C13#265611yescharacteristic
222C2×C13#265611yescharacteristic
223C2×C13#265913yes—
224C2×C13#265913yes—
225D13—28no—
226C24—132no—
227C24—136no—
228C24—136no—
229C24—263no—
230C24—261no—
231C24—263no—
232C24—261no—
233C24C23×D1311yescharacteristic
234C22×C4—26no—
235C22×C4—26no—
236C22×C4—23no—
237C22×C4—23no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—26no—
241C22×C4—21no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—136no—
245C22×C4—136no—
246C22×C4—136no—
247C22×C4—1348no—
248C22×C4—266no—
249C22×C4—266no—
250C22×C4—263no—
251C22×C4—266no—
252C22×C4—263no—
253C22×C4—263no—
254C22×C4—263no—
255C22×C4—266no—
256C22×C4—263no—
257C22×C4—261no—
258C22×C4—5224no—
259C22×C4—5212no—
260C22×C4—5224no—
261C22×C4—5212no—
262C22×C4C2×C4×D1316yes—
263C22×C4D4×D1316yes—
264C22×C4Q8×D1316yes—
265C4⋊C4—412no—
266C4⋊C4—5212no—
267C4⋊C4—5212no—
268C4⋊C4—5212no—
269C22⋊C4—5212no—
270C22⋊C4—524no—
271C13#1435311yescharacteristic, complemented, Sylow
272C23—1312no—
273C23—1312no—
274C23—134no—
275C23—266no—
276C23—266no—
277C23—262no—
278C23—266no—
279C23—266no—
280C23—266no—
281C23—2612no—
282C23—266no—
283C23—266no—
284C23C22×C4×D1311yescharacteristic
285C23C2×D4×D1313yes—
286C23#8825113yes—
287C23C2×Q8×D1313yes—
288C23#8825411yescharacteristic
289C23#8825613yes—
290C23#8825711yescharacteristic
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—26no—
295C2×C4—46no—
296C2×C4—43no—
297C2×C4—43no—
298C2×C4—46no—
299C2×C4—43no—
300C2×C4—43no—
301C2×C4—43no—
302C2×C4—41no—
303C2×C4—1312no—
304C2×C4—2612no—
305C2×C4—266no—
306C2×C4—2612no—
307C2×C4—266no—
308C2×C4—5248no—
309C2×C4—523no—
310C2×C4—523no—
311C2×C4—523no—
312C2×C4—526no—
313C2×C4—526no—
314C2×C4—523no—
315C2×C4—521no—
316C2×C4—523no—
317C2×C4C4⋊C4×D13112yes—
318C22—138no—
319C22—2612no—
320C22—2612no—
321C22—264no—
322C22—264no—
323C22—2612no—
324C22—2612no—
325C22C2×C4⋊C4×D1313yes—
326C22#1171925013yes—
327C22#1171927711yescharacteristic
328C22#1171929413yes—
329C22#1171931313yes—
330C22#1171933413yes—
331C22#1171933916yes—
332C22#1171935813yes—
333C22#1171939413yes—
334C22D13×#12711yescharacteristic
335C22D13×C4⋊Q813yes—
336C22#1171943413yes—
337C4—212no—
338C4—83no—
339C4—81no—
340C4—2612no—
341C4—1041no—
342C4—1043no—
343C2—268no—
344C2D13×#38411yescharacteristic
345C2#1311744713yes—
346C2#1311745113yes—
347C2#1312093711yescharacteristic
348C2#1312093911yescharacteristic
349C2#1312094913yes—
350C2#1312095113yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1444D13
hypocenterC13#14353
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. #13113101C2semidirect
5. #13113100C2semidirect
6. #13113099C2semidirect
7. C13×#1444C2semidirect
22. D13×#95C4semidirect
90. C2×C4×D13C4⋊C4semidirect
103. #1444D13semidirect
271. C13#14353semidirect

Maximal subgroups

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

subgroupindex
C2×#117183282
C2×#117186482
C2×D13×#952
#131131012
#131131002
#131130992
C13×#14442
#1435313