Finite Group Databasebeta

← #15764858

Subgroups — #15764858

Order 3328.

476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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
2C2×#11718341C211yesmaximal, characteristic
3#13125218C211yesmaximal, characteristic
4#13115824C211yesmaximal, characteristic
5#13113509C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C13×#1493C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×#88057—22no—
14#11718754—21no—
15#11718754—21no—
16#11718742—21no—
17#11718739—21no—
18#11718730—22no—
19#11718705—22no—
20#11718682—22no—
21#11718665—22no—
22#11718586C2211yescharacteristic
23C4×#6099C2211yescharacteristic
24#11718341—22no—
25#11718341—22no—
26C13×Q8⋊C8—22no—
27#11718146—22no—
28#11718074—22no—
29C22×Dic26—21no—
30C22×Dic26—21no—
31C2×C13×M16—21no—
32C22×C8×C13—21no—
33C13×C4⋊Q8D411yescharacteristic
34C13×C4⋊Q8D411yescharacteristic
35C13×#125—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C13×#117—21no—
41C2×C42×C13C2311yescharacteristic
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13D412yes—
46C2×#6099D412yes—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123D412yes—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C4×C8×C13—21no—
58C4×C8×C13D412yes—
59#88075—24no—
60C22⋊#1055—21no—
61#88057—28no—
62#88050—24no—
63#88050—24no—
64#88047—24no—
65C4⋊#1055D412yes—
66#88043—21no—
67C4×#1055—21no—
68C4×#1055—21no—
69#10173—131nomaximal, Sylow
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4111yescharacteristic
75C22×Dic13—22no—
76C22×Dic13—41no—
77C2×Dic26—22no—
78C2×Dic26—42no—
79C2×Dic26—42no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—82no—
84C13×M16—42no—
85C2×C8×C13—24no—
86C2×C8×C13—22no—
87C2×C8×C13—41no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C22⋊C4—41no—
95C42×C13—41no—
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C4⋊Dic13—22no—
101C4⋊Dic13—22no—
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108#6099—22no—
109#6099—22no—
110C2×#1055—22no—
111C2×#1055—22no—
112#3230—131no—
113C2×#498—131no—
114#3139—131no—
115#1997—131no—
116#1546—131no—
117#1493D1311yescharacteristic
118#1278—131no—
119C23×C13#12111yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13#12011yescharacteristic
127C2×C4×C13#12011yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12711yescharacteristic
132C2×C4×C13#13512yes—
133C2×C4×C13#13712yes—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—82no—
137C2×Dic13—82no—
138Dic26—44no—
139Dic26—82no—
140Dic26—82no—
141Dic26—81no—
142Dic26—81no—
143C8×C13—24no—
144C8×C13—81no—
145#1055—42no—
146#1055—42no—
147#533C2×D1311yescharacteristic
148C2×C4⋊Q8—131no—
149C2×C4⋊Q8—131no—
150#500—261no—
151#498—262no—
152#498—262no—
153#491—262no—
154#487—261no—
155#487—261no—
156#487—261no—
157#484—262no—
158#477—262no—
159#431—131no—
160C2×#106—262no—
161#423C2×D1311yescharacteristic
162#419—262no—
163C4×M16—131no—
164C2×C4×C8C2×D1311yescharacteristic
165#343—262no—
166#332—262no—
167Q8⋊C8—22no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13#39211yescharacteristic
171C22×C13#46412yes—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—81no—
175C4×C13—81no—
176C4×C13#45212yes—
177C4×C13#45612yes—
178C4×C13#47112yes—
179C4×C13#49511yescharacteristic
180C4×C13#49711yescharacteristic
181Dic13—82no—
182Dic13—82no—
183C22×Q8—261no—
184C22×Q8—261no—
185C2×M16—21no—
186C2×M16—132no—
187C22×C8—21no—
188C4⋊Q8—132no—
189C4⋊Q8—261no—
190C4⋊Q8—261no—
191C4⋊Q8—261no—
192C4⋊Q8—261no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4⋊Q8D5211yescharacteristic
197C4⋊Q8D5211yescharacteristic
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203#117—21no—
204C2×C4⋊C4—132no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C42C22×D1311yescharacteristic
209#107—264no—
210#106—268no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—132no—
214#103—264no—
215#103—264no—
216#103—264no—
217C22⋊C8—261no—
218#97—261no—
219C4×C8—21no—
220C4×C8—261no—
221C4×C8—261no—
222C4×C8C22⋊D1312yes—
223C2×C13—22no—
224C2×C13#200511yescharacteristic
225C2×C13#201511yescharacteristic
226C2×C13#201911yescharacteristic
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—262no—
230C2×Q8—521no—
231C2×Q8—521no—
232C2×Q8—521no—
233C2×Q8—522no—
234C2×Q8—522no—
235C2×Q8—1042no—
236C22×C4—262no—
237C22×C4—521no—
238C22×C4#612711yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C22×C4D4×D1311yescharacteristic
241M16—42no—
242M16—262no—
243M16—262no—
244C2×C8—24no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—262no—
248C2×C8—262no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—262no—
256C4⋊C4—262no—
257C4⋊C4—262no—
258C4⋊C4—262no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C22⋊C4—41no—
264C42—41no—
265C42C2×D5211yescharacteristic
266C42D4×D1311yescharacteristic
267C42D4×D1311yescharacteristic
268C42C2×C22⋊D1311yescharacteristic
269C13#1017311yescharacteristic, complemented, Sylow
270C23#8813811yescharacteristic
271Q8—42no—
272Q8—42no—
273Q8—524no—
274Q8—1042no—
275Q8—1042no—
276Q8—1041no—
277Q8—1041no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—522no—
283C2×C4—522no—
284C2×C4—1042no—
285C2×C4—1042no—
286C2×C4#8813611yescharacteristic
287C2×C4#8813611yescharacteristic
288C2×C4#8813811yescharacteristic
289C2×C4#8817012yes—
290C2×C4#8817212yes—
291C2×C4#8818411yescharacteristic
292C2×C4#8819111yescharacteristic
293C2×C4#8819411yescharacteristic
294C8—24no—
295C8—81no—
296C8—522no—
297C8—522no—
298C22—21no—
299C22—21no—
300C22#1171845912yes—
301C22#1171862111yescharacteristic
302C4—21no—
303C4—21no—
304C4—81no—
305C4—81no—
306C4—1042no—
307C4—1042no—
308C4#1171847112yes—
309C4#1171848712yes—
310C4#1171880212yes—
311C4#1171882911yescharacteristic
312C4#1171885111yescharacteristic
313C2—22no—
314C2#1311587111yescharacteristic
315C2#1311593111yescharacteristic
316C2#1311595111yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1493C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenter#1493D13
hypocenterC13#10173
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
269. C13#10173semidirect

Maximal subgroups

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

subgroupindex
#131259842
C2×#117183412
#131252182
#131158242
#131135092
#131126732
C13×#14932
#1017313