Finite Group Databasebeta

← #15765629

Subgroups — #15765629

Order 3328.

588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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#13125984C211yesmaximal, characteristic
2#13125781C211yesmaximal, characteristic
3#13123234C211yesmaximal, characteristic
4#13113522C211yesmaximal, characteristic
5#13113518C211yesmaximal, characteristic
6#13112669C211yesmaximal, characteristic
7C13×#1994C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88123—22no—
10C2×#88123C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C13×#423C2211yescharacteristic
13C43×C13C2211yescharacteristic
14#11718754—21no—
15#11718753—21no—
16#11718742—21no—
17#11718739—21no—
18#11718711—22no—
19#11718705—22no—
20#11718692—22no—
21#11718682—22no—
22#11718596—22no—
23#11718596—22no—
24#11718586C2211yescharacteristic
25#11718586C2211yescharacteristic
26C13×#339—22no—
27#11718078—22no—
28#11718073—22no—
29C22×Dic26—21no—
30C22×Dic26D412yes—
31C2×C13×M16—21no—
32C13×C4⋊Q8D411yescharacteristic
33C13×C4⋊Q8D411yescharacteristic
34C13×#125—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C13×#117—21no—
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13D412yes—
43C2×C42×C13C2311yescharacteristic
44C2×#6107—24no—
45C2×C4⋊Dic13—28no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13D412yes—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58#88123—48no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61#88075—24no—
62C22⋊#1055—21no—
63C22⋊#1055—21no—
64#88050—24no—
65#88047—24no—
66C4⋊#1055D412yes—
67C4⋊#1055D412yes—
68C4×#1055—21no—
69C4×#1055—21no—
70#10293—131nomaximal, Sylow
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C22×C4×C13—22no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—22no—
78C22×Dic13—22no—
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26—44no—
82C2×Dic26—44no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C13×M16—42no—
86C2×C8×C13—41no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C22⋊C4—41no—
94C42×C13—24no—
95C42×C13—24no—
96C42×C13—22no—
97C42×C13—41no—
98C42×C13Q1614yescomplemented
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103#6107—84no—
104C4⋊Dic13—22no—
105C4⋊Dic13—22no—
106C4⋊Dic13—416no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C2×#1055—22no—
114C2×#1055—22no—
115#3230—131no—
116#3209—131no—
117#2868—131no—
118#1994D1311yescharacteristic
119#1549—131no—
120#1548—131no—
121#1276—131no—
122C23×C13#12011yescharacteristic
123Q8×C13—42no—
124Q8×C13—42no—
125C2×C4×C13—24no—
126C2×C4×C13—24no—
127C2×C4×C13—24no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12711yescharacteristic
138C2×C4×C13C2×Q1612yes—
139C2×C4×C13#13712yes—
140C2×Dic13—44no—
141C2×Dic13—44no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144Dic26—44no—
145Dic26—82no—
146Dic26—82no—
147Dic26—82no—
148C8×C13—81no—
149#1055—42no—
150#1055—42no—
151#533C2×D1311yescharacteristic
152C2×C4⋊Q8—131no—
153C2×C4⋊Q8—131no—
154C2×C4⋊Q8—262no—
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#423C2×D1311yescharacteristic
166#384—262no—
167#384—262no—
168C43C2×D1311yescharacteristic
169#339—22no—
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—81no—
180C4×C13—81no—
181C4×C13#45312yes—
182C4×C13#45612yes—
183C4×C13#46212yes—
184C4×C13#49411yescharacteristic
185C4×C13#49711yescharacteristic
186Dic13—82no—
187Dic13—82no—
188C22×Q8—132no—
189C22×Q8—261no—
190C2×Q16—264no—
191C2×M16—21no—
192C4⋊Q8—261no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
198C4⋊Q8—261no—
199C4⋊Q8—261no—
200C4⋊Q8—528no—
201C4⋊Q8D5211yescharacteristic
202C4⋊Q8D5211yescharacteristic
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208#117—21no—
209C2×C4⋊C4—132no—
210C2×C4⋊C4—268no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42C22⋊D1312yes—
217C2×C42C22×D1311yescharacteristic
218#107—264no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—132no—
222C4⋊C8—132no—
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—21no—
234C2×Q8—21no—
235C2×Q8—262no—
236C2×Q8—262no—
237C2×Q8—524no—
238C2×Q8—524no—
239C2×Q8—521no—
240C2×Q8—521no—
241C22×C4—22no—
242C22×C4—262no—
243C22×C4—262no—
244C22×C4D4×D1311yescharacteristic
245C22×C4D4×D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247Q16—1044no—
248M16—42no—
249C2×C8—41no—
250C2×C8—262no—
251C2×C8—262no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—262no—
259C4⋊C4—262no—
260C4⋊C4—5216no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C22⋊C4—41no—
268C42—24no—
269C42—24no—
270C42—22no—
271C42—41no—
272C42#610714yescomplemented
273C42C2×D5211yescharacteristic
274C42#612711yescharacteristic
275C42D4×D1311yescharacteristic
276C42D4×D1311yescharacteristic
277C13#1029311yescharacteristic, complemented, Sylow
278C23#8819111yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—524no—
282Q8—1042no—
283Q8—1042no—
284Q8—1042no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—524no—
293C2×C4—524no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4#8813611yescharacteristic
297C2×C4#8813611yescharacteristic
298C2×C4#8813811yescharacteristic
299C2×C4#8813811yescharacteristic
300C2×C4#8818411yescharacteristic
301C2×C4#8819411yescharacteristic
302C2×C4C2×#610712yes—
303C2×C4#8820512yes—
304C8—81no—
305C8—522no—
306C8—522no—
307C22—21no—
308C22—21no—
309C22#1171862111yescharacteristic
310C22#1171871112yes—
311C4—28no—
312C4—21no—
313C4—21no—
314C4—81no—
315C4—81no—
316C4—1042no—
317C4—1042no—
318C4#1171848312yes—
319C4#1171848712yes—
320C4#1171869212yes—
321C4#1171872111yescharacteristic
322C4#1171875311yescharacteristic
323C2—22no—
324C2#1311585011yescharacteristic
325C2#1311587111yescharacteristic
326C2#1311593511yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1994C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#1994D13
hypocenterC13#10293
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
98. 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
#131259842
#131257812
#131232342
#131135222
#131135182
#131126692
C13×#19942
#1029313