Finite Group Databasebeta

← #15765630

Subgroups — #15765630

Order 3328.

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

normal subgroups only

This group has 588 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#13125987C211yesmaximal, characteristic
2#13125784C211yesmaximal, characteristic
3#13115813C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic
5#13113517C211yesmaximal, characteristic
6#13112669C211yesmaximal, characteristic
7C13×#2868C211yesmaximal, characteristic
8C2×C13×C4⋊Q8—22no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11#11719175C2211yescharacteristic
12C13×#384—22no—
13C13×#384—22no—
14C43×C13C2211yescharacteristic
15#11718889—22no—
16#11718754—21no—
17#11718753—21no—
18#11718752—22no—
19#11718751—22no—
20#11718742—21no—
21#11718739—21no—
22#11718631—22no—
23#11718586C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718585C2211yescharacteristic
26#11718139—22no—
27#11718138—22no—
28#11718115—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C13×C4⋊Q8—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—48no—
40C2×C13×C4⋊C4—28no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4D412yes—
45C2×C42×C13—21no—
46C2×C42×C13—21no—
47C2×C42×C13D412yes—
48C2×C42×C13C2311yescharacteristic
49C2×#6107—24no—
50#88180—21no—
51#88178—21no—
52#88178—21no—
53C2×#6099—21no—
54#88124—21no—
55#88123D411yescharacteristic
56#88123D411yescharacteristic
57C4×Dic26—21no—
58C4×Dic26—21no—
59#88075—24no—
60C22⋊#1055—21no—
61C22⋊#1055—21no—
62#88050—24no—
63#88047—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055D412yes—
67C4⋊#1055D412yes—
68C4×#1055—21no—
69C4×#1055—21no—
70#10293—131nomaximal, Sylow
71C2×Q8×C13—22no—
72C2×Q8×C13—22no—
73C2×Q8×C13—44no—
74C2×Q8×C13—44no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C2×Dic26—21no—
84C2×Dic26—21no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—416no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C42×C13—24no—
95C42×C13—24no—
96C42×C13—22no—
97C42×C13Q1614yescomplemented
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13#4111yescharacteristic
102C22⋊Dic13—41no—
103#6107—84no—
104C4⋊Dic13—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108#6101—41no—
109#6101—41no—
110C4×Dic13—41no—
111#6099—42no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055—41no—
115#3230—131no—
116#3209—131no—
117#2868D1311yescharacteristic
118#1994—131no—
119#1549—131no—
120#1548—131no—
121#1276—131no—
122C23×C13#12011yescharacteristic
123Q8×C13—44no—
124Q8×C13—82no—
125Q8×C13—82no—
126Q8×C13—82no—
127C2×C4×C13—24no—
128C2×C4×C13—24no—
129C2×C4×C13—24no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—44no—
133C2×C4×C13—44no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12711yescharacteristic
142C2×C4×C13C2×Q1612yes—
143C2×C4×C13#13712yes—
144C2×Dic13—41no—
145C2×Dic13—41no—
146Dic26—42no—
147Dic26—42no—
148#1055—42no—
149#1055—42no—
150#1055—81no—
151#533—131no—
152C2×C4⋊Q8—22no—
153C2×C4⋊Q8C2×D1311yescharacteristic
154C2×C4⋊Q8C2×D1311yescharacteristic
155#500—261no—
156#494—261no—
157#487—261no—
158#487—261no—
159#484—262no—
160#477—262no—
161#462—262no—
162#451—262no—
163#431—131no—
164#431—131no—
165#423—131no—
166#384—22no—
167#384—22no—
168C43C2×D1311yescharacteristic
169#339—262no—
170#333—262no—
171#332—262no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13#39211yescharacteristic
175C22×C13#45112yes—
176C4×C13—28no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—82no—
180C4×C13—82no—
181C4×C13#45312yes—
182C4×C13#45612yes—
183C4×C13#46212yes—
184C4×C13#49411yescharacteristic
185C4×C13#49711yescharacteristic
186Dic13—81no—
187Dic13—81no—
188C22×Q8—21no—
189C22×Q8C22⋊D1312yes—
190C2×Q16—264no—
191C2×M16—261no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—48no—
201C4⋊Q8—131no—
202C4⋊Q8—131no—
203#125—261no—
204C22⋊Q8—261no—
205C22⋊Q8—261no—
206C4×Q8—261no—
207C4×Q8—261no—
208#117—261no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C22⋊D1312yes—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42C22⋊D1312yes—
217C2×C42C22×D1311yescharacteristic
218#107—264no—
219C4⋊C8—132no—
220C4⋊C8—132no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223#103—264no—
224#103—264no—
225C22⋊C8—261no—
226C22⋊C8—261no—
227C4×C8—261no—
228C4×C8—261no—
229C2×C13—22no—
230C2×C13#200211yescharacteristic
231C2×C13#200511yescharacteristic
232C2×C13#201611yescharacteristic
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8—44no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—261no—
240C2×Q8—261no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×C22⋊D1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247Q16—1044no—
248M16—522no—
249C2×C8—262no—
250C2×C8—262no—
251C2×C8—521no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—416no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C22⋊C4—521no—
268C42—24no—
269C42—24no—
270C42—22no—
271C42—521no—
272C42#610714yescomplemented
273C42D4×D1311yescharacteristic
274C42D4×D1311yescharacteristic
275C42D4×D1311yescharacteristic
276C42#612911yescharacteristic
277C13#1029311yescharacteristic, complemented, Sylow
278C23#8820711yescharacteristic
279Q8—44no—
280Q8—82no—
281Q8—82no—
282Q8—82no—
283Q8—522no—
284Q8—522no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4#8819111yescharacteristic
297C2×C4#8819111yescharacteristic
298C2×C4#8819211yescharacteristic
299C2×C4#8819311yescharacteristic
300C2×C4#8819311yescharacteristic
301C2×C4#8819411yescharacteristic
302C2×C4#8819612yes—
303C2×C4C2×#610712yes—
304C8—522no—
305C8—522no—
306C8—1041no—
307C22—21no—
308C22—21no—
309C22#1171888411yescharacteristic
310C22#1171888912yes—
311C4—28no—
312C4—21no—
313C4—21no—
314C4—82no—
315C4—82no—
316C4—1041no—
317C4—1041no—
318C4#1171873812yes—
319C4#1171874711yescharacteristic
320C4#1171875112yes—
321C4#1171875311yescharacteristic
322C4#1171875612yes—
323C2—22no—
324C2#1311585111yescharacteristic
325C2#1311587211yescharacteristic
326C2#1311593611yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2868C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#2868D13
hypocenterC13#10293
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
97. C42×C13Q16semidirect
272. C42#6107semidirect
277. C13#10293semidirect

Maximal subgroups

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

subgroupindex
#131259872
#131257842
#131158132
#131135212
#131135172
#131126692
C13×#28682
#1029313