Finite Group Databasebeta

← #15752212

Subgroups — #15752212

Order 3328.

404 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 81 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#13121795C211yesmaximal, characteristic
2#13116398C211yesmaximal, characteristic, complemented
3#13116398C211yesmaximal, characteristic, complemented
4#13112660C211yesmaximal, characteristic, complemented
5#13112658C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2094C211yesmaximal, characteristic
8C2×#88133—21no—
9C2×C13×#106—21no—
10C2×C13×#102—21no—
11C13×#390C2211yescharacteristic
12C13×#384C2211yescharacteristic
13#11718883—21no—
14#11718633—21no—
15#11718612—21no—
16#11718610—21no—
17#11718609—21no—
18#11718589C2211yescharacteristic
19#11718589C2211yescharacteristic
20C13×#336C2211yescharacteristic
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C42×C13C2311yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×C4×Dic13—21no—
49C22×#1055—21no—
50C22×#1055—21no—
51#88133—42no—
52#88133—42no—
53C13×#106—42no—
54C13×#102—42no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#7828—131nomaximal, Sylow
59C24×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—41no—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C2×C8×C13—22no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C42×C13—41no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C22⋊Dic13—81no—
89C22⋊Dic13—81no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13SD1612yes—
96#6101—42no—
97#6101—41no—
98#6101—41no—
99#6101—41no—
100#6101—41no—
101#6101—81no—
102C4×Dic13—42no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109#2727—131no—
110#2100—131no—
111#2100—131no—
112#2094D1311yescharacteristic
113#1271—131no—
114#1271—131no—
115#1270—131no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13#12011yescharacteristic
124D4×C13—42no—
125D4×C13—81no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13#13511yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C8×C13—42no—
157#1055—81no—
158#1055—81no—
159C2×#126—261no—
160C2×#106—21no—
161C2×#102—21no—
162#399—261no—
163#396—261no—
164#394—261no—
165#390C2×D1311yescharacteristic
166#389—131no—
167#389—131no—
168#389—261no—
169#388—261no—
170#384C2×D1311yescharacteristic
171#340—261no—
172#340—261no—
173#340—261no—
174#340—261no—
175#336—131no—
176#336—131no—
177#336C2×D1311yescharacteristic
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13#45011yescharacteristic
186C22×C13#45211yescharacteristic
187C22×C13#45211yescharacteristic
188C22×C13#45311yescharacteristic
189C22×C13#45411yescharacteristic
190C22×C13#45411yescharacteristic
191C22×C13#45811yescharacteristic
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—81no—
199C4×C13—161no—
200Dic13—42no—
201Dic13—81no—
202Dic13—81no—
203Dic13—81no—
204C22×D4C22⋊D1311yescharacteristic
205C22×C8—21no—
206C22×C8—261no—
207C22×C8—261no—
208#126—522no—
209#126—522no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4C22⋊D1311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—261no—
225C2×C22⋊C4—261no—
226C2×C22⋊C4—261no—
227C2×C22⋊C4—261no—
228C2×C42—261no—
229C2×C42C22×D1311yescharacteristic
230#106—42no—
231#102—42no—
232#95—261no—
233#95—261no—
234#95—261no—
235C2×C13—161no—
236C2×C13#161511yescharacteristic
237C2×C13#161611yescharacteristic
238C2×C13#161811yescharacteristic
239C2×C13#163111yescharacteristic
240C2×C13#163511yescharacteristic
241C2×C13#163811yescharacteristic
242C2×C13#165711yescharacteristic
243C24—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4D4×D1311yescharacteristic
255C22×C4D4×D1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—132no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—522no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C4⋊C4—521no—
282C4⋊C4—1041no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—522no—
288C22⋊C4—522no—
289C22⋊C4—1041no—
290C22⋊C4—1041no—
291C42—41no—
292C42—522no—
293C13#782811yescharacteristic, complemented, Sylow
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#8819111yescharacteristic
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—262no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4SD16×D1311yescharacteristic
329C2×C4#8816811yescharacteristic
330C2×C4#8816911yescharacteristic
331C2×C4#8817011yescharacteristic
332C2×C4#8819611yescharacteristic
333C2×C4#8820411yescharacteristic
334C8—42no—
335C8—1041no—
336C8—1041no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22#1171870811yescharacteristic
345C22#1171871411yescharacteristic
346C22#1171873811yescharacteristic
347C22#1171883011yescharacteristic
348C22#1171883411yescharacteristic
349C22#1171886211yescharacteristic
350C22#1171886211yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—161no—
359C4—522no—
360C4—1041no—
361C4—1041no—
362C4—1041no—
363C2—161no—
364C2#1311386411yescharacteristic
365C2#1311387111yescharacteristic
366C2#1311388211yescharacteristic
367C2#1311396011yescharacteristic
368C2#1311398611yescharacteristic
369C2#1311400611yescharacteristic
370C2#1311413211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2094C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2094D13
hypocenterC13#7828
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
2. #13116398C2semidirect
3. #13116398C2semidirect
4. #13112660C2semidirect
5. #13112658C2semidirect
293. C13#7828semidirect

Maximal subgroups

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

subgroupindex
#131217952
#131163982
#131126602
#131126582
#131126572
C13×#20942
#782813