Finite Group Databasebeta

← #15766128

Subgroups — #15766128

Order 3328.

404 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 75 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#13121008C211yesmaximal, characteristic
2#13115822C211yesmaximal, characteristic
3#13113356C211yesmaximal, characteristic
4#13112743C211yesmaximal, characteristic
5#13112721C211yesmaximal, characteristic
6#13112688C211yesmaximal, characteristic
7C13×#1511C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C13×#407C2211yescharacteristic
10C13×#381C2211yescharacteristic
11#11718873C2211yescharacteristic
12C4×C22⋊Dic13C2211yescharacteristic
13C4×C22⋊Dic13C2211yescharacteristic
14#11718868C2211yescharacteristic
15#11718609—21no—
16#11718608—21no—
17#11718321—21no—
18#11718317—21no—
19#11718315—21no—
20#11718307—21no—
21C13×#328—21no—
22C13×#328—21no—
23#11718130—21no—
24#11718130—21no—
25#11718118—21no—
26#11718118—21no—
27C22×Q8×C13Q811yescharacteristic, complemented
28C23×C4×C13C2311yescharacteristic
29C22×Dic26—21no—
30C2×C13×M16—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4Q811yescharacteristic, complemented
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C22⋊Dic13D411yescharacteristic
42C2×C22⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×C4×Dic13—21no—
48C2×C4×Dic13—21no—
49C2×#6099—21no—
50C13×C22⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×#95—21no—
53C13×#95D411yescharacteristic
54C13×#95D411yescharacteristic
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071D411yescharacteristic
62#88071D411yescharacteristic
63C22⋊#1055—21no—
64C22⋊#1055—21no—
65#10383—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C2×Q8×C13—21no—
68C2×Q8×C13—21no—
69C2×Q8×C13—81no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—81no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×Q811yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—41no—
86C2×Dic26—42no—
87C2×Dic26—81no—
88C2×Dic26—81no—
89C13×M16—81no—
90C2×C8×C13—41no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—81no—
98C22⋊Dic13—22no—
99C22⋊Dic13—42no—
100C22⋊Dic13—41no—
101C22⋊Dic13—41no—
102C22⋊Dic13—41no—
103C4⋊Dic13—42no—
104C4⋊Dic13—81no—
105#6101—81no—
106#6101—81no—
107C4×Dic13—81no—
108C4×Dic13—81no—
109#6099—81no—
110C2×#1055—41no—
111#2665—131no—
112#1996—131no—
113#1511D1311yescharacteristic
114#1508—131no—
115#1305—131no—
116#1297—131no—
117#1284—131no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13#12011yescharacteristic
123C23×C13C22⋊Q811yescharacteristic
124C23×C13#12411yescharacteristic
125Q8×C13—81no—
126Q8×C13—81no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
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—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13C22⋊Q811yescharacteristic
144C2×C4×C13C22⋊Q811yescharacteristic
145C2×C4×C13#12411yescharacteristic
146C2×C4×C13#12411yescharacteristic
147C2×Dic13—22no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—42no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162Dic26—84no—
163C8×C13—81no—
164#1055—81no—
165C2×C22⋊Q8C2×D1311yescharacteristic
166#407—131no—
167#407C2×D1311yescharacteristic
168#400—261no—
169#396—261no—
170#395—261no—
171#393—261no—
172#391—261no—
173#387—261no—
174#381C2×D1311yescharacteristic
175#380—131no—
176C4×C22⋊C4—131no—
177C4×C22⋊C4—131no—
178#342—261no—
179#342—261no—
180#328—21no—
181#328—21no—
182#328—261no—
183#328—261no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13#39311yescharacteristic
195C22×C13#45511yescharacteristic
196C22×C13#45611yescharacteristic
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205Dic13—42no—
206Dic13—81no—
207Dic13—81no—
208Dic13—81no—
209Dic13—82no—
210C22×Q8—261no—
211C22×Q8Dic2611yescharacteristic, complemented
212C23×C4C22×D1311yescharacteristic
213C2×M16—21no—
214C2×M16—261no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4Dic2611yescharacteristic, complemented
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—131no—
228C2×C22⋊C4—131no—
229C2×C22⋊C4—261no—
230C2×C22⋊C4—261no—
231C2×C42—261no—
232C2×C42—261no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—261no—
236C22⋊C8—261no—
237#95—21no—
238#95—131no—
239#95—131no—
240#95—261no—
241#95—261no—
242#95—261no—
243#95—261no—
244#95—261no—
245#95—261no—
246#95C22⋊D1311yescharacteristic
247#95C22⋊D1311yescharacteristic
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—41no—
251C2×C13—41no—
252C2×C13#202811yescharacteristic
253C2×C13#203111yescharacteristic
254C2×C13#203211yescharacteristic
255C24D4×D1311yescharacteristic
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—81no—
259C2×Q8—522no—
260C2×Q8—1041no—
261C2×Q8—1041no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—81no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—521no—
272C22×C4C2×Dic2611yescharacteristic
273C22×C4#612711yescharacteristic
274C22×C4D4×D1311yescharacteristic
275C22×C4#612911yescharacteristic
276C22×C4#612911yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278M16—81no—
279M16—1041no—
280C2×C8—41no—
281C2×C8—521no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—522no—
287C4⋊C4—1041no—
288C4⋊C4—1041no—
289C4⋊C4—1041no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—81no—
293C22⋊C4—262no—
294C22⋊C4—522no—
295C22⋊C4—521no—
296C22⋊C4—521no—
297C22⋊C4—521no—
298C42—1041no—
299C42—1041no—
300C13#1038311yescharacteristic, complemented, Sylow
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23#8813211yescharacteristic
306C23#8813911yescharacteristic
307C23#8819111yescharacteristic
308Q8—81no—
309Q8—81no—
310Q8—1044no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—262no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—522no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—1041no—
341C2×C4—1041no—
342C2×C4#8813211yescharacteristic
343C2×C4#8813911yescharacteristic
344C2×C4#8817811yescharacteristic
345C2×C4#8819011yescharacteristic
346C8—81no—
347C8—1041no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22#1171860811yescharacteristic
359C22#1171886311yescharacteristic
360C22#1171886611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—522no—
370C4—1041no—
371C4—1041no—
372C4—1041no—
373C4—1042no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1311599511yescharacteristic
379C2#1311600611yescharacteristic
380C2#1311601311yescharacteristic
subgroupG/H
centerC22#11718608
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1511C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenter#1511D13
hypocenterC13#10383
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
27. C22×Q8×C13Q8semidirect
36. C2×C13×C4⋊C4Q8semidirect
211. C22×Q8Dic26semidirect
224. C2×C4⋊C4Dic26semidirect
300. C13#10383semidirect

Maximal subgroups

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

subgroupindex
#131210082
#131158222
#131133562
#131127432
#131127212
#131126882
C13×#15112
#1038313