Finite Group Databasebeta

← #15751948

Subgroups — #15751948

Order 3328.

430 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 91 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#13116394C211yesmaximal, characteristic, complemented
2#13116244C211yesmaximal, characteristic, complemented
3#13116239C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic, complemented
5#13112659C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2732C211yesmaximal, characteristic
8C2×C13×C22⋊Q8—21no—
9C13×#399—21no—
10C13×#398—21no—
11C13×#396—21no—
12C13×#391C2211yescharacteristic
13C13×#390C2211yescharacteristic
14C13×#389C2211yescharacteristic
15C13×#386—21no—
16C13×#385—21no—
17C2×#88075—21no—
18C2×#88072—21no—
19#11718596C2211yescharacteristic
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C13×C22⋊Q8—42no—
31C13×C22⋊Q8—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C42×C13C2311yescharacteristic
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C22×#1055—21no—
50C22×#1055—21no—
51C22×#1055—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#88075—42no—
57#88072—42no—
58#7787—131nomaximal, Sylow
59C24×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13D812yes—
64C2×D4×C13—21no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C2×D4×C13SD1612yes—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—42no—
74C22×C4×C13—81no—
75C22×C4×C13—81no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—41no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—81no—
96C13×C22⋊C4—81no—
97C42×C13—41no—
98C4⋊Dic13—42no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112#2732D1311yescharacteristic
113#2099—131no—
114#2072—131no—
115#2071—131no—
116#1272—131no—
117#1271—131no—
118#1270—131no—
119C23×C13—22no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13#12011yescharacteristic
127Q8×C13—42no—
128Q8×C13—81no—
129D4×C13—42no—
130D4×C13—81no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—84no—
153C2×C4×C13C2×D811yescharacteristic
154C2×C4×C13C2×SD1611yescharacteristic
155C2×C4×C13#13511yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C13#13711yescharacteristic
158C2×C4×C13#13711yescharacteristic
159C2×Dic13—81no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162#1055—81no—
163#1055—81no—
164#1055—81no—
165C2×C22⋊Q8—21no—
166C2×#103—261no—
167C2×#102—261no—
168#399—21no—
169#398—21no—
170#396—21no—
171#391C2×D1311yescharacteristic
172#390C2×D1311yescharacteristic
173#389C2×D1311yescharacteristic
174#386—21no—
175#385—21no—
176#384—131no—
177#340—261no—
178#340—261no—
179#340—261no—
180#340—261no—
181#336—131no—
182#336—131no—
183#336—131no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13#44711yescharacteristic
192C22×C13#44811yescharacteristic
193C22×C13#45211yescharacteristic
194C22×C13#45411yescharacteristic
195C22×C13#45511yescharacteristic
196C22×C13#45511yescharacteristic
197C22×C13#45811yescharacteristic
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—42no—
205C4×C13—81no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13—81no—
209Dic13—161no—
210C22×Q8C22⋊D1311yescharacteristic
211C22×D4C22⋊D1311yescharacteristic
212C23×C4—21no—
213C22×C8—261no—
214C22×C8—261no—
215C22×C8—261no—
216C22⋊Q8—42no—
217C22⋊Q8—42no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4C22⋊D1311yescharacteristic
226C2×C4⋊C4C22⋊D1311yescharacteristic
227C2×C4⋊C4C22⋊D1311yescharacteristic
228C2×C4⋊C4C22⋊D1311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C42C22×D1311yescharacteristic
235#103—522no—
236#102—522no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C2×C13—82no—
242C2×C13#160711yescharacteristic
243C2×C13#160811yescharacteristic
244C2×C13#161511yescharacteristic
245C2×C13#162711yescharacteristic
246C2×C13#164111yescharacteristic
247C2×C13#164311yescharacteristic
248C2×C13#166211yescharacteristic
249C24—21no—
250C2×Q8—21no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8#610412yes—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4#610612yes—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—42no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4—521no—
267C22×C4C2×C22⋊D1311yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270C2×C8—521no—
271C2×C8—521no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8—521no—
277C2×C8—521no—
278C2×C8—521no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—81no—
289C4⋊C4—522no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C42—41no—
302C13#778711yescharacteristic, complemented, Sylow
303C23—22no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23#8820711yescharacteristic
311Q8—42no—
312Q8—81no—
313D4—42no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—84no—
337C2×C4—1041no—
338C2×C4—1041no—
339C2×C4—1041no—
340C2×C4C2×#610411yescharacteristic
341C2×C4#8818611yescharacteristic
342C2×C4C2×#610611yescharacteristic
343C2×C4#8819611yescharacteristic
344C2×C4#8820411yescharacteristic
345C2×C4#8820511yescharacteristic
346C8—1041no—
347C8—1041no—
348C8—1041no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1171887811yescharacteristic
357C22#1171888811yescharacteristic
358C22#1171890011yescharacteristic
359C22#1171890311yescharacteristic
360C22#1171890311yescharacteristic
361C22#1171890411yescharacteristic
362C22#1171890611yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—2081no—
375C2—82no—
376C2#1311382211yescharacteristic
377C2#1311382711yescharacteristic
378C2#1311386711yescharacteristic
379C2#1311393911yescharacteristic
380C2#1311402911yescharacteristic
381C2#1311404311yescharacteristic
382C2#1311415911yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2732C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2732D13
hypocenterC13#7787
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2732

Complements

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

NH ≅ G/Ntype
1. #13116394C2semidirect
2. #13116244C2semidirect
4. #13112662C2semidirect
5. #13112659C2semidirect
302. C13#7787semidirect

Maximal subgroups

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

subgroupindex
#131163942
#131162442
#131162392
#131126622
#131126592
#131126572
C13×#27322
#778713