Finite Group Databasebeta

← #15789927

Subgroups — #15789927

Order 3328.

2174 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718882C213yesmaximal, complemented
2C2×#11718612C213yesmaximal, complemented
3#13113101C211yesmaximal, characteristic, complemented
4#13113081C213yesmaximal, complemented
5#13113077C213yesmaximal, complemented
6#95×Dic13C211yesmaximal, characteristic, complemented
7C2×C13×#392C211yesmaximal, characteristic
8C23×D4×C13C2213yes—
9C22×C13×C22⋊C4C2213yes—
10C22×C22⋊Dic13C2213yes—
11C22×C22⋊Dic13C2213yes—
12C22×C22⋊Dic13C2216yes—
13C22×C4⋊Dic13C2211yescharacteristic
14C22×C4⋊Dic13C2213yes—
15C22×C4×Dic13C2213yes—
16C13×#392C418yescomplemented
17C2×C13×#95C2211yescharacteristic
18#11718882—212no—
19C2×#88071C2213yes—
20C2×#88071C2213yes—
21C2×#88071C2213yes—
22#11718612—212no—
23C25×C13C2313yes—
24C22×D4×C13—26no—
25C22×D4×C13—26no—
26C22×D4×C13—46no—
27C22×D4×C13—46no—
28C22×D4×C13C2×C4112yes—
29C23×C4×C13C2311yescharacteristic
30C23×C4×C13C2313yes—
31C23×Dic13C2313yes—
32C23×Dic13C2311yescharacteristic
33C23×Dic13C2313yes—
34C23×Dic13C2311yescharacteristic
35C2×C13×C22⋊C4—26no—
36C2×C13×C22⋊C4—26no—
37C2×C13×C22⋊C4C2×C4112yes—
38C2×C22⋊Dic13—26no—
39C2×C22⋊Dic13—26no—
40C2×C22⋊Dic13—212no—
41C2×C22⋊Dic13—212no—
42C2×C22⋊Dic13—46no—
43C2×C22⋊Dic13—46no—
44C2×C22⋊Dic13—46no—
45C2×C4⋊Dic13—26no—
46C2×C4⋊Dic13—26no—
47C2×C4⋊Dic13—46no—
48C2×C4×Dic13—46no—
49C2×C4×Dic13D4112yescomplemented
50C13×#95C2×C414yes—
51#88071—26no—
52#88071—26no—
53#88071—26no—
54#14321—131nomaximal, Sylow
55C24×C13—23no—
56C24×C13—26no—
57C24×C13—23no—
58C24×C13—26no—
59C24×C13—23no—
60C24×C13—26no—
61C24×C13—26no—
62C24×C13—23no—
63C24×C13—23no—
64C24×C13—23no—
65C24×C13C22×C416yes—
66C24×C13C2411yescharacteristic
67C2×D4×C13—224no—
68C2×D4×C13—424no—
69C2×D4×C13—412no—
70C2×D4×C13—412no—
71C2×D4×C13—424no—
72C22×C4×C13—26no—
73C22×C4×C13—26no—
74C22×C4×C13—23no—
75C22×C4×C13—23no—
76C22×C4×C13C22×C412yes—
77C22×C4×C13C22×C416yes—
78C22×C4×C13C2×D416yes—
79C22×C4×C13#4116yes—
80C22×Dic13—23no—
81C22×Dic13—21no—
82C22×Dic13—26no—
83C22×Dic13—26no—
84C22×Dic13—23no—
85C22×Dic13—23no—
86C22×Dic13—23no—
87C22×Dic13—23no—
88C22×Dic13—26no—
89C22×Dic13—23no—
90C22×Dic13—26no—
91C22×Dic13—23no—
92C22×Dic13—23no—
93C22×Dic13—21no—
94C22×Dic13C2×D416yes—
95C22×Dic13C2×D416yes—
96C13×C22⋊C4—224no—
97C22⋊Dic13—412no—
98C22⋊Dic13—424no—
99C22⋊Dic13—412no—
100C4⋊Dic13—412no—
101C4⋊Dic13—44no—
102C4×Dic13—412no—
103C2×#392D1311yescharacteristic
104C2×#390—133no—
105C2×#388—133no—
106#1444—131no—
107#1439—133no—
108#1438—133no—
109C4×#95—131no—
110C23×C13—26no—
111C23×C13—212no—
112C23×C13—26no—
113C23×C13—212no—
114C23×C13—26no—
115C23×C13—43no—
116C23×C13—43no—
117C23×C13—46no—
118C23×C13—43no—
119C23×C13—46no—
120C23×C13—46no—
121C23×C13—46no—
122C23×C13—43no—
123C23×C13—43no—
124C23×C13—43no—
125C23×C13—46no—
126C23×C13—46no—
127C23×C13—46no—
128C23×C13—46no—
129C23×C13—43no—
130C23×C13—46no—
131C23×C13—43no—
132C23×C13—46no—
133C23×C13C23×C411yescharacteristic
134C23×C13C22×D413yes—
135C23×C13C2×#4113yes—
136C23×C13H(5,𝔽2)13yes—
137C23×C13H(5,𝔽2)13yes—
138C23×C13H(5,𝔽2)11yescharacteristic
139C23×C132−1+411yescharacteristic
140D4×C13—448no—
141C2×C4×C13—212no—
142C2×C4×C13—26no—
143C2×C4×C13—26no—
144C2×C4×C13—212no—
145C2×C4×C13—26no—
146C2×C4×C13—41no—
147C2×C4×C13—43no—
148C2×C4×C13C4×D4112yes—
149C2×Dic13—26no—
150C2×Dic13—26no—
151C2×Dic13—26no—
152C2×Dic13—26no—
153C2×Dic13—26no—
154C2×Dic13—46no—
155C2×Dic13—46no—
156C2×Dic13—41no—
157C2×Dic13—43no—
158C2×Dic13—43no—
159C2×Dic13—46no—
160C2×Dic13—46no—
161C2×Dic13—43no—
162C2×Dic13—43no—
163C2×Dic13—43no—
164C2×Dic13#12714yes—
165C23×D4C2×D1313yes—
166C22×C4⋊C4—131no—
167C22×C4⋊C4—133no—
168C22×C22⋊C4—133no—
169C22×C22⋊C4—133no—
170C22×C22⋊C4—136no—
171C22×C22⋊C4C2×D1313yes—
172C22×C42—133no—
173#392Dic1318yescomplemented
174#390—2612no—
175#388—2612no—
176C2×#95—133no—
177C2×#95—133no—
178C2×#95—133no—
179C2×#95C2×D1311yescharacteristic
180C22×C13—46no—
181C22×C13—412no—
182C22×C13—46no—
183C22×C13—46no—
184C22×C13—412no—
185C22×C13—83no—
186C22×C13—83no—
187C22×C13—83no—
188C22×C13—86no—
189C22×C13—86no—
190C22×C13—83no—
191C22×C13C2×C4×D413yes—
192C22×C13#51813yes—
193C22×C13#52011yescharacteristic
194C22×C13C2×#12711yescharacteristic
195C22×C13#53213yes—
196C22×C13#53413yes—
197C22×C13#53513yes—
198C22×C13#53513yes—
199C22×C13#53713yes—
200C22×C13#53816yes—
201C22×C13#54013yes—
202C22×C13#54213yes—
203C4×C13—212no—
204C4×C13—42no—
205Dic13—24no—
206Dic13—46no—
207Dic13—81no—
208Dic13—83no—
209C25C22×D1313yes—
210C22×D4—26no—
211C22×D4—26no—
212C22×D4—46no—
213C22×D4—46no—
214C22×D4C2×Dic13112yes—
215C23×C4—131no—
216C23×C4—133no—
217C23×C4—133no—
218C23×C4—131no—
219C23×C4C22×D1311yescharacteristic
220C23×C4C22×D1313yes—
221C2×C4⋊C4—266no—
222C2×C4⋊C4—266no—
223C2×C4⋊C4—526no—
224C2×C22⋊C4—26no—
225C2×C22⋊C4—26no—
226C2×C22⋊C4—266no—
227C2×C22⋊C4—266no—
228C2×C22⋊C4—2612no—
229C2×C22⋊C4—2612no—
230C2×C22⋊C4—526no—
231C2×C22⋊C4—526no—
232C2×C22⋊C4—526no—
233C2×C22⋊C4C2×Dic13112yes—
234C2×C42—1312no—
235C2×C42—526no—
236#95—266no—
237#95—266no—
238#95—266no—
239#95C2×Dic1314yes—
240C2×C13—86no—
241C2×C13C4×#12711yescharacteristic
242C2×C13#232113yes—
243C2×C13#232413yes—
244C2×C13#265611yescharacteristic
245C2×C13#265711yescharacteristic
246C2×C13#266113yes—
247C2×C13#266213yes—
248C24—23no—
249C24—26no—
250C24—23no—
251C24—26no—
252C24—26no—
253C24—26no—
254C24—23no—
255C24—23no—
256C24—23no—
257C24—23no—
258C24C22×Dic1316yes—
259C24C23×D1311yescharacteristic
260C2×D4—224no—
261C2×D4—424no—
262C2×D4—412no—
263C2×D4—412no—
264C2×D4—424no—
265C22×C4—26no—
266C22×C4—26no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—136no—
270C22×C4—136no—
271C22×C4—263no—
272C22×C4—261no—
273C22×C4—266no—
274C22×C4—266no—
275C22×C4—263no—
276C22×C4—263no—
277C22×C4—263no—
278C22×C4—263no—
279C22×C4—266no—
280C22×C4—263no—
281C22×C4—266no—
282C22×C4—263no—
283C22×C4—263no—
284C22×C4—261no—
285C22×C4D4×D1316yes—
286C22×C4#612916yes—
287C22×C4C22×Dic1312yes—
288C22×C4C22×Dic1316yes—
289C4⋊C4—5212no—
290C4⋊C4—524no—
291C22⋊C4—224no—
292C22⋊C4—5212no—
293C22⋊C4—5212no—
294C22⋊C4—5224no—
295C42—5212no—
296C13#1432111yescharacteristic, complemented, Sylow
297C23—26no—
298C23—212no—
299C23—26no—
300C23—212no—
301C23—26no—
302C23—43no—
303C23—46no—
304C23—46no—
305C23—43no—
306C23—46no—
307C23—46no—
308C23—46no—
309C23—43no—
310C23—46no—
311C23—46no—
312C23—43no—
313C23—43no—
314C23—46no—
315C23—43no—
316C23—46no—
317C23—43no—
318C23—43no—
319C23—46no—
320C23C2×D4×D1313yes—
321C23C2×#612913yes—
322C23#8825113yes—
323C23#8825113yes—
324C23#8825611yescharacteristic
325C23#8825711yescharacteristic
326C23C23×Dic1311yescharacteristic
327D4—448no—
328C2×C4—212no—
329C2×C4—26no—
330C2×C4—26no—
331C2×C4—212no—
332C2×C4—26no—
333C2×C4—41no—
334C2×C4—43no—
335C2×C4—134no—
336C2×C4—266no—
337C2×C4—266no—
338C2×C4—266no—
339C2×C4—266no—
340C2×C4—266no—
341C2×C4—526no—
342C2×C4—526no—
343C2×C4—523no—
344C2×C4—526no—
345C2×C4—523no—
346C2×C4—526no—
347C2×C4—523no—
348C2×C4—523no—
349C2×C4—523no—
350C2×C4—521no—
351C2×C4D4×Dic13112yes—
352C22—412no—
353C22—46no—
354C22—46no—
355C22—412no—
356C22—46no—
357C22—83no—
358C22—83no—
359C22—83no—
360C22—86no—
361C22—86no—
362C22—83no—
363C22#1171929413yes—
364C22#1171929713yes—
365C22#1171929816yes—
366C22#1171930813yes—
367C22#1171931213yes—
368C22#1171931313yes—
369C22#1171932413yes—
370C22D13×#12711yescharacteristic
371C22#1171942113yes—
372C22C2×D4×Dic1313yes—
373C22#1171950313yes—
374C22#1171953211yescharacteristic
375C4—212no—
376C4—42no—
377C4—264no—
378C4—526no—
379C4—1041no—
380C4—1043no—
381C2—86no—
382C2#127×Dic1311yescharacteristic
383C2#1311749713yes—
384C2#1311753113yes—
385C2#1312093711yescharacteristic
386C2#1312094111yescharacteristic
387C2#1312096713yes—
388C2#1312097813yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
Fitting, prime radicalC2×C13×#392C2
socle, cosocleC24×C13C24
hypercenterC2×#392D13
hypocenterC13#14321
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#11718882C2semidirect
2. C2×#11718612C2semidirect
3. #13113101C2semidirect
4. #13113081C2semidirect
5. #13113077C2semidirect
6. #95×Dic13C2semidirect
16. C13×#392C4semidirect
49. C2×C4×Dic13D4semidirect
173. #392Dic13semidirect
296. C13#14321semidirect

Maximal subgroups

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

subgroupindex
C2×#117188822
C2×#117186122
#131131012
#131130812
#131130772
#95×Dic132
C2×C13×#3922
#1432113