Finite Group Databasebeta

← #15752108

Subgroups — #15752108

Order 3328.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#13122816C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116245C211yesmaximal, characteristic, complemented
4#13112661C211yesmaximal, characteristic, complemented
5#13112660C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2071C211yesmaximal, characteristic
8C2×C13×#102—21no—
9C13×#390C2211yescharacteristic
10C13×#384C2211yescharacteristic
11#11718883—21no—
12#11718639—21no—
13C2×#88050—21no—
14#11718614—21no—
15#11718612—21no—
16#11718612—21no—
17#11718608—21no—
18#11718590C2211yescharacteristic
19#11718589C2211yescharacteristic
20C13×#340—21no—
21C13×#336C2211yescharacteristic
22#11718121—21no—
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C22×Dic26D411yescharacteristic
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C22×#1055—21no—
47C22×#1055—21no—
48C13×#102—42no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88050—42no—
56#7811—131nomaximal, Sylow
57C24×C13—21no—
58C2×D4×C13—21no—
59C2×D4×C13—21no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—41no—
74C2×Dic26—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—41no—
89C22⋊Dic13—81no—
90C22⋊Dic13—81no—
91C22⋊Dic13—81no—
92C22⋊Dic13—81no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6101—41no—
98#6101—41no—
99C4×Dic13—81no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106#2808—131no—
107#2099—131no—
108#2072—131no—
109#2071D1311yescharacteristic
110#1272—131no—
111#1271—131no—
112#1270—131no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#12011yescharacteristic
121D4×C13—42no—
122D4×C13—81no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13#13511yescharacteristic
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153Dic26—42no—
154Dic26—81no—
155C8×C13—81no—
156#1055—81no—
157#1055—81no—
158C2×#103—261no—
159C2×#102—21no—
160#397—261no—
161#394—261no—
162#393—261no—
163#391—131no—
164#390C2×D1311yescharacteristic
165#389—131no—
166#388—261no—
167#388—261no—
168#387—261no—
169#384C2×D1311yescharacteristic
170#340—21no—
171#340—261no—
172#340—261no—
173#340—261no—
174#336—131no—
175#336—131no—
176#336C2×D1311yescharacteristic
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13#44911yescharacteristic
185C22×C13#44911yescharacteristic
186C22×C13#45211yescharacteristic
187C22×C13#45411yescharacteristic
188C22×C13#45511yescharacteristic
189C22×C13#45511yescharacteristic
190C22×C13#45811yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—81no—
198C4×C13—161no—
199Dic13—81no—
200Dic13—81no—
201Dic13—81no—
202Dic13—81no—
203C22×Q8—131no—
204C22×D4C22⋊D1311yescharacteristic
205C22×C8—21no—
206C22×C8—261no—
207C22×C8—261no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4C22⋊D1311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C42—261no—
223C2×C42C22×D1311yescharacteristic
224#103—522no—
225#102—42no—
226#95—261no—
227#95—261no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13—161no—
233C2×C13#161211yescharacteristic
234C2×C13#161211yescharacteristic
235C2×C13#161511yescharacteristic
236C2×C13#162811yescharacteristic
237C2×C13#164011yescharacteristic
238C2×C13#164611yescharacteristic
239C2×C13#166211yescharacteristic
240C24—21no—
241C2×Q8—261no—
242C2×Q8—261no—
243C2×Q8—521no—
244C2×Q8—521no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4D4×D1311yescharacteristic
256C22×C4D4×D1311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C2×C8—521no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—1041no—
284C22⋊C4—1041no—
285C22⋊C4—1041no—
286C22⋊C4—1041no—
287C42—41no—
288C42—1041no—
289C13#781111yescharacteristic, complemented, Sylow
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#8819111yescharacteristic
298Q8—522no—
299Q8—1041no—
300D4—42no—
301D4—81no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
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#8816511yescharacteristic
327C2×C4#8816611yescharacteristic
328C2×C4#8816911yescharacteristic
329C2×C4#8817011yescharacteristic
330C2×C4#8818611yescharacteristic
331C2×C4#8820411yescharacteristic
332C8—81no—
333C8—1041no—
334C8—1041no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22#1171869811yescharacteristic
343C22#1171871411yescharacteristic
344C22#1171872211yescharacteristic
345C22#1171881911yescharacteristic
346C22#1171883411yescharacteristic
347C22#1171886211yescharacteristic
348C22#1171886311yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—161no—
357C4—1041no—
358C4—1041no—
359C4—1041no—
360C4—1041no—
361C2—161no—
362C2#1311384711yescharacteristic
363C2#1311384811yescharacteristic
364C2#1311386411yescharacteristic
365C2#1311394411yescharacteristic
366C2#1311401911yescharacteristic
367C2#1311406211yescharacteristic
368C2#1311415811yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2071C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2071D13
hypocenterC13#7811
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116245C2semidirect
4. #13112661C2semidirect
5. #13112660C2semidirect
289. C13#7811semidirect

Maximal subgroups

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

subgroupindex
#131228162
#131163932
#131162452
#131126612
#131126602
#131126572
C13×#20712
#781113