Finite Group Databasebeta

← #15765994

Subgroups — #15765994

Order 3328.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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#13123108C211yesmaximal, characteristic
2#13115810C211yesmaximal, characteristic
3#13115657C211yesmaximal, characteristic
4#13112718C211yesmaximal, characteristic
5#13112718C211yesmaximal, characteristic
6#13112717C211yesmaximal, characteristic
7C13×#1993C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11C2×#88075—21no—
12C2×#88075—21no—
13#11718647—21no—
14#11718640—21no—
15#11718597C2211yescharacteristic
16#11718597C2211yescharacteristic
17C2×#88043C2211yescharacteristic
18C2×#88043C2211yescharacteristic
19#11718321—21no—
20#11718321—21no—
21#11718317—21no—
22#11718317—21no—
23C13×#340—21no—
24C13×#340—21no—
25#11718121—21no—
26#11718121—21no—
27C22×Q8×C13—21no—
28C22×Dic26—21no—
29C22×C8×C13—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8Q812yescomplemented
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C42×C13C2311yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×#6101—21no—
45C2×#6101—21no—
46C22×#1055—21no—
47C22×#1055—21no—
48C13×#97—21no—
49C13×#97—21no—
50C13×#95—21no—
51C13×#95—21no—
52#88075—42no—
53#88075—42no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88043—21no—
63#88043—21no—
64#88043—21no—
65#88043—21no—
66#10359—131nomaximal, Sylow
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—41no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C2×Dic26—81no—
84C2×Dic26—81no—
85C2×Dic26—81no—
86C2×C8×C13—22no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C42×C13C2×Q811yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98C42×C13#4111yescharacteristic
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103C4⋊Dic13—81no—
104#6101—81no—
105#6101—81no—
106C2×#1055—22no—
107C2×#1055—22no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112#2844—131no—
113#1993—131no—
114#1993D1311yescharacteristic
115#1960—131no—
116#1295—131no—
117#1295—131no—
118#1295—131no—
119C23×C13#12011yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13—81no—
123Q8×C13—81no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13C22⋊Q811yescharacteristic
140C2×C4×C13C22⋊Q811yescharacteristic
141C2×C4×C13C22⋊Q811yescharacteristic
142C2×C4×C13#12411yescharacteristic
143C2×C4×C13#12411yescharacteristic
144C2×C4×C13#12411yescharacteristic
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157Dic26—84no—
158C8×C13—42no—
159#1055—42no—
160#1055—42no—
161C2×C4⋊Q8C2×D1311yescharacteristic
162C2×#103—261no—
163C2×#103—261no—
164C2×#97—131no—
165C2×#97—131no—
166C2×#97C2×D1311yescharacteristic
167#400—261no—
168#400—261no—
169#400—261no—
170#395—261no—
171#395—261no—
172#395—261no—
173#382—131no—
174#382—131no—
175#382C2×D1311yescharacteristic
176#340—21no—
177#340—21no—
178#340—261no—
179#340—261no—
180C22×C13#39311yescharacteristic
181C22×C13#45311yescharacteristic
182C22×C13#45411yescharacteristic
183C22×C13#45511yescharacteristic
184C22×C13#45511yescharacteristic
185C22×C13#45611yescharacteristic
186C22×C13#45611yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—81no—
194C4×C13—81no—
195C4×C13—82no—
196Dic13—81no—
197Dic13—81no—
198Dic13—81no—
199Dic13—81no—
200C22×Q8—21no—
201C22×Q8—261no—
202C22×C8—21no—
203C22×C8—261no—
204C22×C8—261no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8Dic2612yescomplemented
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4C22⋊D1311yescharacteristic
219C2×C4⋊C4C22⋊D1311yescharacteristic
220C2×C42C22×D1311yescharacteristic
221#103—522no—
222#103—522no—
223#97—21no—
224#97—21no—
225#97—261no—
226#97—261no—
227#97—261no—
228#97—261no—
229#95—21no—
230#95—21no—
231#95—261no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95—261no—
239C2×C13#165911yescharacteristic
240C2×C13#166011yescharacteristic
241C2×C13#166411yescharacteristic
242C2×C13#166411yescharacteristic
243C2×C13#202711yescharacteristic
244C2×C13#202811yescharacteristic
245C2×C13#202811yescharacteristic
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—1041no—
253C2×Q8—1041no—
254C2×Q8—1041no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4D4×D1311yescharacteristic
263C22×C4D4×D1311yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—262no—
269C2×C8—262no—
270C2×C8—521no—
271C2×C8—521no—
272C2×C8—521no—
273C2×C8—521no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—521no—
281C4⋊C4—521no—
282C4⋊C4—521no—
283C4⋊C4—521no—
284C4⋊C4—1041no—
285C4⋊C4—1041no—
286C4⋊C4—1041no—
287C42C2×Dic2611yescharacteristic
288C42#612711yescharacteristic
289C42#612911yescharacteristic
290C42#612911yescharacteristic
291C13#1035911yescharacteristic, complemented, Sylow
292C23#8819111yescharacteristic
293Q8—42no—
294Q8—42no—
295Q8—81no—
296Q8—81no—
297Q8—1044no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4#8813211yescharacteristic
326C2×C4#8813211yescharacteristic
327C2×C4#8813911yescharacteristic
328C2×C4#8813911yescharacteristic
329C2×C4#8817811yescharacteristic
330C2×C4#8819011yescharacteristic
331C8—42no—
332C8—522no—
333C8—522no—
334C22#1171860811yescharacteristic
335C22#1171872211yescharacteristic
336C22#1171875611yescharacteristic
337C22#1171885911yescharacteristic
338C22#1171886211yescharacteristic
339C22#1171886311yescharacteristic
340C22#1171886611yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—82no—
350C4—1041no—
351C4—1041no—
352C4—1041no—
353C4—1041no—
354C2#1311414111yescharacteristic
355C2#1311414611yescharacteristic
356C2#1311416811yescharacteristic
357C2#1311416911yescharacteristic
358C2#1311599011yescharacteristic
359C2#1311599511yescharacteristic
360C2#1311599711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1993C2
socle, prime radicalC23×C13#120
hypercenter#1993D13
hypocenterC13#10359
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
33. C13×C4⋊Q8Q8semidirect
208. C4⋊Q8Dic26semidirect
291. C13#10359semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131158102
#131156572
#131127182
#131127172
C13×#19932
#1035913