Finite Group Databasebeta

← #15765568

Subgroups — #15765568

Order 3328.

626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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#13125964C211yesmaximal, characteristic
2#13125761C211yesmaximal, characteristic
3#13115664C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic, complemented
5#13113517C211yesmaximal, characteristic, complemented
6#13112669C211yesmaximal, characteristic, complemented
7C13×#2868C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8—22no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11#11719182C2211yescharacteristic
12C13×#384—22no—
13C13×#384—22no—
14C43×C13C2211yescharacteristic
15#11718888—22no—
16#11718749—21no—
17#11718746—21no—
18#11718745—22no—
19#11718744—22no—
20#11718742—21no—
21#11718740—21no—
22#11718629—22no—
23C2×#88045—22no—
24#11718586C2211yescharacteristic
25#11718586C2211yescharacteristic
26#11718585C2211yescharacteristic
27#11718139—22no—
28#11718138—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C2×#6127—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—48no—
41C2×C13×C4⋊C4—28no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D412yes—
46C2×C42×C13—21no—
47C2×C42×C13—21no—
48C2×C42×C13D412yes—
49C2×C42×C13C2311yescharacteristic
50C2×#6106—24no—
51#88184—21no—
52#88184—21no—
53C2×#6099—21no—
54#88129—21no—
55#88128D411yescharacteristic
56C4×D52—21no—
57C4×D52—21no—
58#88123D411yescharacteristic
59#88075—24no—
60C22⋊#1055—21no—
61C22⋊#1055—21no—
62#88049—24no—
63#88048—24no—
64#88045—44no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68C4⋊#1055D412yes—
69C4×#1055—21no—
70C4×#1055—21no—
71#10283—131nomaximal, Sylow
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—44no—
75C2×Q8×C13—44no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C2×C22⋊D13—41no—
85#6127—42no—
86#6127—42no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×C4×D13—41no—
91C2×Dic26—21no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—416no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C42×C13—24no—
102C42×C13—24no—
103C42×C13—22no—
104C42×C13SD1614yescomplemented
105C42×C13C2×D411yescharacteristic
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D411yescharacteristic
108C42×C13#4111yescharacteristic
109#6106—84no—
110#6103—41no—
111#6103—41no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114#6099—42no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—41no—
118#3227—131no—
119#3206—131no—
120#2868D1311yescharacteristic, complemented
121#1962—131no—
122#1549—131no—
123#1548—131no—
124#1276—131no—
125C23×C13#12011yescharacteristic
126C22×D13—41no—
127Q8×C13—44no—
128Q8×C13—82no—
129Q8×C13—82no—
130Q8×C13—82no—
131C2×C4×C13—24no—
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—44no—
137C2×C4×C13—44no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12711yescharacteristic
146C2×C4×C13C2×SD1612yes—
147C2×C4×C13#13712yes—
148C22⋊D13—82no—
149C2×Dic13—41no—
150D52—42no—
151D52—42no—
152D52—42no—
153C4×D13—81no—
154C4×D13—81no—
155Dic26—42no—
156#1055—42no—
157#1055—42no—
158#1055—81no—
159#532—131no—
160C2×C4⋊Q8—22no—
161C2×C4⋊Q8C2×D1311yescharacteristic
162C2×C4⋊Q8C2×D1311yescharacteristic
163#498—261no—
164#492—261no—
165#487—261no—
166#486—261no—
167#481—262no—
168#476—262no—
169#461—262no—
170#448—262no—
171#431—131no—
172#431—131no—
173#423—131no—
174C2×#104—262no—
175#384—22no—
176#384—22no—
177C43C2×D1311yescharacteristic
178#333—262no—
179#332—262no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13#39211yescharacteristic
183C22×C13#44812yes—
184C2×D13—81no—
185C2×D13—81no—
186C2×D13—81no—
187C4×C13—28no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—82no—
191C4×C13—82no—
192C4×C13#45312yes—
193C4×C13#45612yes—
194C4×C13#46112yes—
195C4×C13#49211yescharacteristic
196C4×C13#49711yescharacteristic
197Dic13—81no—
198C2×#41—261no—
199C22×Q8—21no—
200C22×Q8C22⋊D1312yes—
201C2×SD16—264no—
202C2×M16—261no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—48no—
212C4⋊Q8—131no—
213#127—131no—
214#124—261no—
215#121—261no—
216#121—261no—
217C4×D4—261no—
218C4×D4—261no—
219C2×C4⋊C4—28no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C22⋊D1312yes—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42C22⋊D1312yes—
227C2×C42C22×D1311yescharacteristic
228#106—264no—
229C4⋊C8—132no—
230C4⋊C8—132no—
231C4⋊C8—261no—
232C4⋊C8—261no—
233#104—524no—
234#103—264no—
235#102—264no—
236C22⋊C8—261no—
237C22⋊C8—261no—
238C4×C8—261no—
239C4×C8—261no—
240C2×C13—22no—
241C2×C13#200211yescharacteristic
242C2×C13#200511yescharacteristic
243C2×C13#201311yescharacteristic
244D13—161no—
245#41—522no—
246#41—522no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—44no—
250C2×Q8—44no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—261no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4—521no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—521no—
262C22×C4C2×C22⋊D1311yescharacteristic
263C22×C4C2×C22⋊D1311yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265SD16—1044no—
266M16—522no—
267C2×C8—262no—
268C2×C8—262no—
269C2×C8—521no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—416no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C22⋊C4—521no—
282C22⋊C4—521no—
283C42—24no—
284C42—24no—
285C42—22no—
286C42#610614yescomplemented
287C42D4×D1311yescharacteristic
288C42D4×D1311yescharacteristic
289C42D4×D1311yescharacteristic
290C42#612911yescharacteristic
291C13#1028311yescharacteristic, complemented, Sylow
292C23—521no—
293C23#8820711yescharacteristic
294Q8—44no—
295Q8—82no—
296Q8—82no—
297Q8—82no—
298Q8—522no—
299D4—522no—
300D4—522no—
301D4—522no—
302D4—1042no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—521no—
313C2×C4—1041no—
314C2×C4—1041no—
315C2×C4#8819111yescharacteristic
316C2×C4#8819111yescharacteristic
317C2×C4#8819211yescharacteristic
318C2×C4#8819311yescharacteristic
319C2×C4#8819311yescharacteristic
320C2×C4#8819411yescharacteristic
321C2×C4C2×#610612yes—
322C2×C4#8819612yes—
323C8—522no—
324C8—522no—
325C8—1041no—
326C22—21no—
327C22—21no—
328C22—1041no—
329C22—1041no—
330C22—1041no—
331C22#1171888411yescharacteristic
332C22#1171888812yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—82no—
338C4—1041no—
339C4#1171873812yes—
340C4#1171874412yes—
341C4#1171874611yescharacteristic
342C4#1171874711yescharacteristic
343C4#1171875612yes—
344C2—22no—
345C2—2081no—
346C2#1311585111yescharacteristic
347C2#1311587211yescharacteristic
348C2#1311591911yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2868C2
socleC22×C13#392
prime radical#11719182C22
hypercenter#2868D13
hypocenterC13#10283
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2868

Complements

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

NH ≅ G/Ntype
4. #13113521C2semidirect
5. #13113517C2semidirect
6. #13112669C2semidirect
7. C13×#2868C2semidirect
104. C42×C13SD16semidirect
120. #2868D13semidirect
286. C42#6106semidirect
291. C13#10283semidirect

Maximal subgroups

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

subgroupindex
#131259642
#131257612
#131156642
#131135212
#131135172
#131126692
C13×#28682
#1028313