Finite Group Databasebeta

← #15766127

Subgroups — #15766127

Order 3328.

404 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 77 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#13115820C211yesmaximal, characteristic
2#13113368C211yesmaximal, characteristic
3#13113355C211yesmaximal, characteristic
4#13112742C211yesmaximal, characteristic
5#13112722C211yesmaximal, characteristic
6#13112688C211yesmaximal, characteristic
7C13×#2665C211yesmaximal, characteristic
8C2×#88178C2211yescharacteristic
9C13×#400—21no—
10C13×#396—21no—
11C13×#395—21no—
12C13×#393—21no—
13C13×#391—21no—
14C13×#387—21no—
15C13×#381C2211yescharacteristic
16C13×#380C2211yescharacteristic
17C4×C13×C22⋊C4C2211yescharacteristic
18C4×C22⋊Dic13C2211yescharacteristic
19#11718868C2211yescharacteristic
20#11718868C2211yescharacteristic
21#11718119—21no—
22#11718119—21no—
23#11718044—21no—
24#11718044—21no—
25#11718044—21no—
26#11718044—21no—
27C22×Q8×C13—21no—
28C23×C4×C13C2311yescharacteristic
29C22×Dic26Q811yescharacteristic, complemented
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C42×C13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13Q811yescharacteristic, complemented
42#88178—21no—
43#88178—21no—
44#88178—21no—
45#88178—21no—
46C2×#6101—21no—
47C2×C4×Dic13—21no—
48C2×#6099—21no—
49C2×#6099—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95D411yescharacteristic
57C13×#95D411yescharacteristic
58C13×#95D411yescharacteristic
59C13×#95D411yescharacteristic
60#88071—21no—
61C22⋊#1055—21no—
62C22⋊#1055—21no—
63C22⋊#1055—21no—
64C22⋊#1055—21no—
65#10383—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C2×Q8×C13—42no—
68C2×Q8×C13—81no—
69C2×Q8×C13—81no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—81no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×Q811yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—41no—
86C2×Dic26—21no—
87C2×Dic26—21no—
88C2×Dic26—81no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—81no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—81no—
97C42×C13—81no—
98C22⋊Dic13—22no—
99C22⋊Dic13—41no—
100C22⋊Dic13—41no—
101C22⋊Dic13—41no—
102C4⋊Dic13—21no—
103C4⋊Dic13—21no—
104#6101—41no—
105#6101—41no—
106C4×Dic13—81no—
107#6099—81no—
108#6099—81no—
109C2×#1055—41no—
110C2×#1055—41no—
111#2665D1311yescharacteristic
112#1996—131no—
113#1511—131no—
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—84no—
126C2×C4×C13—22no—
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—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13C22⋊Q811yescharacteristic
151C2×C4×C13C22⋊Q811yescharacteristic
152C2×C4×C13#12411yescharacteristic
153C2×C4×C13#12411yescharacteristic
154C2×Dic13—42no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—81no—
158C2×Dic13—81no—
159C2×Dic13—81no—
160C2×Dic13—81no—
161Dic26—81no—
162Dic26—81no—
163#1055—81no—
164#1055—81no—
165C2×C22⋊Q8—131no—
166#407—131no—
167#407—131no—
168#400—21no—
169#396—21no—
170#395—21no—
171#393—21no—
172#391—21no—
173#387—21no—
174#381C2×D1311yescharacteristic
175#380C2×D1311yescharacteristic
176C4×C22⋊C4—131no—
177C4×C22⋊C4C2×D1311yescharacteristic
178#342—261no—
179#342—261no—
180#328—261no—
181#328—261no—
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—42no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205C4×C13—81no—
206C4×C13—81no—
207Dic13—82no—
208Dic13—81no—
209Dic13—81no—
210C22×Q8—21no—
211C22×Q8—131no—
212C23×C4C22×D1311yescharacteristic
213C2×M16—261no—
214C2×M16—261no—
215C22⋊Q8—261no—
216C22⋊Q8—261no—
217C22⋊Q8—261no—
218C22⋊Q8—261no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—261no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—261no—
228C2×C22⋊C4—261no—
229C2×C22⋊C4C22⋊D1311yescharacteristic
230C2×C22⋊C4C22⋊D1311yescharacteristic
231C2×C42—21no—
232C2×C42—261no—
233C22⋊C8—261no—
234C22⋊C8—261no—
235C22⋊C8—261no—
236C22⋊C8—261no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—261no—
244#95C22⋊D1311yescharacteristic
245#95C22⋊D1311yescharacteristic
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
255C24C2×C22⋊D1311yescharacteristic
256C2×Q8—42no—
257C2×Q8—81no—
258C2×Q8—81no—
259C2×Q8—261no—
260C2×Q8—261no—
261C2×Q8—1041no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—81no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—521no—
272C22×C4Q8×D1311yescharacteristic
273C22×C4#613111yescharacteristic
274C22×C4#613111yescharacteristic
275C22×C4#613111yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278M16—1041no—
279M16—1041no—
280C2×C8—521no—
281C2×C8—521no—
282C4⋊C4—42no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—261no—
287C4⋊C4—261no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—81no—
294C22⋊C4—262no—
295C22⋊C4—521no—
296C22⋊C4—521no—
297C22⋊C4—521no—
298C42—81no—
299C42—1041no—
300C13#1038311yescharacteristic, complemented, Sylow
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23#8820011yescharacteristic
306C23#8820111yescharacteristic
307C23#8820711yescharacteristic
308Q8—84no—
309Q8—1041no—
310Q8—1041no—
311C2×C4—22no—
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—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—522no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—1041no—
339C2×C4—1041no—
340C2×C4—1041no—
341C2×C4—1041no—
342C2×C4#8820011yescharacteristic
343C2×C4#8820011yescharacteristic
344C2×C4#8820111yescharacteristic
345C2×C4#8820111yescharacteristic
346C8—1041no—
347C8—1041no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22#1171889211yescharacteristic
359C22#1171890311yescharacteristic
360C22#1171890711yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4—1042no—
372C4—1041no—
373C4—1041no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1311599411yescharacteristic
379C2#1311600511yescharacteristic
380C2#1311601211yescharacteristic
subgroupG/H
centerC22#11718892
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2665C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenter#2665D13
hypocenterC13#10383
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2665

Complements

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

NH ≅ G/Ntype
29. C22×Dic26Q8semidirect
41. C2×C4⋊Dic13Q8semidirect
300. C13#10383semidirect

Maximal subgroups

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

subgroupindex
#131158202
#131133682
#131133552
#131127422
#131127222
#131126882
C13×#26652
#1038313