Finite Group Databasebeta

← #15765191

Subgroups — #15765191

Order 3328.

462 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 101 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#13125784C211yesmaximal, characteristic
2#13125358C211yesmaximal, characteristic
3#13115810C211yesmaximal, characteristic
4#13113401C211yesmaximal, characteristic
5#13113400C211yesmaximal, characteristic
6#13112680C211yesmaximal, characteristic
7C13×#3230C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#500—21no—
12C13×#487—21no—
13C13×#484—22no—
14C13×#477—22no—
15C13×#431C2211yescharacteristic
16#11718889—22no—
17#11718753—21no—
18#11718751—22no—
19#11718742—21no—
20#11718741—21no—
21#11718741—21no—
22#11718726—21no—
23#11718726—21no—
24#11718659—22no—
25#11718597C2211yescharacteristic
26#11718586C2211yescharacteristic
27C2×#88043C2211yescharacteristic
28#11718130—22no—
29#11718121—22no—
30#11718059—22no—
31C22×Q8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D411yescharacteristic
36C13×C4⋊Q8D411yescharacteristic
37C13×C4⋊Q8D412yes—
38C13×#125—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C13×#117—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6107—24no—
48#88180—21no—
49C2×C4⋊Dic13—21no—
50#88178—21no—
51#88178—21no—
52C22×#1055D412yes—
53#88124—21no—
54#88123D411yescharacteristic
55#88123D411yescharacteristic
56C4×Dic26—21no—
57C4×Dic26—21no—
58C13×#107—24no—
59C13×C4⋊C8—21no—
60C13×#103—24no—
61C13×C22⋊C8D412yes—
62C4×C8×C13—21no—
63#88075—24no—
64#88071—21no—
65#88071—21no—
66C22⋊#1055D412yes—
67#88048—22no—
68#88048—22no—
69#88047—22no—
70#88047—22no—
71C4⋊#1055—21no—
72#88043—21no—
73#88043—21no—
74C4×#1055—21no—
75#10224—131nomaximal, Sylow
76C2×Q8×C13—22no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—41no—
80C2×Q8×C13—82no—
81C22×C4×C13—41no—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—41no—
86C2×Dic26—21no—
87C2×Dic26—21no—
88C2×C8×C13—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C22⋊C4—41no—
100C42×C13—41no—
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13#4111yescharacteristic
105C22⋊Dic13—41no—
106#6107—84no—
107C4⋊Dic13—21no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13—21no—
111C4⋊Dic13—42no—
112#6101—41no—
113#6101—41no—
114C4×Dic13—41no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055Q1614yescomplemented
119#3230D1311yescharacteristic
120#3209—131no—
121#3162—131no—
122#1993—131no—
123#1518—131no—
124#1518—131no—
125#1281—131no—
126C23×C13#12711yescharacteristic
127Q8×C13—44no—
128Q8×C13—42no—
129Q8×C13—82no—
130Q8×C13—81no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—82no—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12011yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13C2×Q1612yes—
144C2×C4×C13#13712yes—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150Dic26—42no—
151Dic26—81no—
152C8×C13—42no—
153#1055—24no—
154#1055—42no—
155#533—131no—
156#533C2×D1311yescharacteristic
157C2×C4⋊Q8C2×D1311yescharacteristic
158#501—261no—
159#501—261no—
160#501—261no—
161#501—261no—
162#500—21no—
163#494—261no—
164#487—21no—
165#487—261no—
166#484—22no—
167#477—22no—
168#462—262no—
169#451—262no—
170#431—131no—
171#431C2×D1311yescharacteristic
172#427—262no—
173C2×#97—131no—
174#382—131no—
175#340—262no—
176#328—262no—
177#328—262no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#39211yescharacteristic
181C22×C13#49411yescharacteristic
182C22×C13#49711yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—82no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13#45112yes—
191C4×C13#46212yes—
192Dic13—81no—
193Dic13—81no—
194Dic13—161no—
195C22×Q8—21no—
196C2×Q16—264no—
197C22×C8—132no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—131no—
202C4⋊Q8—131no—
203C4⋊Q8C22⋊D1312yes—
204C4⋊Q8C22⋊D1311yescharacteristic
205C4⋊Q8C22⋊D1311yescharacteristic
206#125—21no—
207#125—261no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—261no—
211C22⋊Q8—261no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—261no—
215C4×Q8—261no—
216#117—21no—
217#117—261no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—261no—
221C2×C42C22×D1311yescharacteristic
222#107—24no—
223#107—262no—
224#107—262no—
225#106—262no—
226#106—262no—
227C4⋊C8—21no—
228C4⋊C8—261no—
229#103—24no—
230#103—264no—
231C22⋊C8—132no—
232C22⋊C8C22⋊D1312yes—
233#97—261no—
234#97—261no—
235C4×C8—21no—
236C4×C8—261no—
237#95—261no—
238#95—261no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13#200811yescharacteristic
242C2×C13#200911yescharacteristic
243C2×C13#201611yescharacteristic
244C2×Q8—22no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—82no—
249C2×Q8—261no—
250C2×Q8—261no—
251C22×C4—41no—
252C22×C4—521no—
253C22×C4D4×D1311yescharacteristic
254C22×C4D4×D1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256Q16—1044no—
257C2×C8—22no—
258C2×C8—134no—
259C2×C8—262no—
260C2×C8—262no—
261C2×C8—262no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4—522no—
279C22⋊C4—41no—
280C22⋊C4—521no—
281C42—41no—
282C42—521no—
283C42D4×D1311yescharacteristic
284C42#612911yescharacteristic
285C42C2×C22⋊D1311yescharacteristic
286C42C2×C22⋊D1311yescharacteristic
287C13#1022411yescharacteristic, complemented, Sylow
288C23#8819411yescharacteristic
289Q8—44no—
290Q8—42no—
291Q8—81no—
292Q8—82no—
293Q8—522no—
294Q8—1041no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4Q16×D1312yes—
307C2×C4#8817212yes—
308C2×C4#8819111yescharacteristic
309C2×C4#8819111yescharacteristic
310C2×C4#8819211yescharacteristic
311C2×C4#8819311yescharacteristic
312C2×C4#8819311yescharacteristic
313C2×C4#8820711yescharacteristic
314C8—42no—
315C8—264no—
316C8—522no—
317C22—21no—
318C22—21no—
319C22#1171884211yescharacteristic
320C22#1171885111yescharacteristic
321C22#1171888411yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—1041no—
330C4—1041no—
331C4—2081no—
332C4#1171884312yes—
333C4#1171884712yes—
334C2—21no—
335C2—21no—
336C2#1311588711yescharacteristic
337C2#1311589611yescharacteristic
338C2#1311593411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3230C2
socleC22×C13#392
prime radicalC23×C13#127
hypercenter#3230D13
hypocenterC13#10224
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
118. C2×#1055Q16semidirect
287. C13#10224semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131253582
#131158102
#131134012
#131134002
#131126802
C13×#32302
#1022413