Finite Group Databasebeta

← #15766085

Subgroups — #15766085

Order 3328.

422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115821C211yesmaximal, characteristic
2#13113407C211yesmaximal, characteristic
3C2×#11718044C211yesmaximal, characteristic
4#13112715C211yesmaximal, characteristic
5#13112703C211yesmaximal, characteristic
6#13112684C211yesmaximal, characteristic
7C13×#2569C211yesmaximal, characteristic
8C2×#88178C2211yescharacteristic
9C13×#400—21no—
10C13×#398—21no—
11C13×#387—21no—
12C13×#387—21no—
13C13×#385—21no—
14C13×#380—21no—
15C13×#380C2211yescharacteristic
16C4×C13×C22⋊C4C2211yescharacteristic
17C2×C13×#95C2211yescharacteristic
18#11718873C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20C2×C22⋊#1055C2211yescharacteristic
21#11718119—21no—
22#11718119—21no—
23#11718044—21no—
24#11718044—21no—
25#11718044—21no—
26#11718044—21no—
27C23×C4×C13—21no—
28C23×C4×C13C2311yescharacteristic
29C22×Dic26Q811yescharacteristic
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊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⋊Dic13—21no—
42C2×C4⋊Dic13Q811yescharacteristic
43#88178—21no—
44#88178—21no—
45#88178—21no—
46#88178—21no—
47C2×#6101—21no—
48C22×#1055—21no—
49C22×#1055—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#10377—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—42no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×Q811yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—41no—
87C2×Dic26—21no—
88C2×Dic26—21no—
89C2×Dic26—81no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—81no—
93C13×C4⋊C4—81no—
94C13×C4⋊C4—81no—
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C42×C13—81no—
102C22⋊Dic13—41no—
103C22⋊Dic13—41no—
104C22⋊Dic13—41no—
105C22⋊Dic13—41no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13—81no—
109#6101—41no—
110#6101—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055—81no—
114C2×#1055—81no—
115#2569D1311yescharacteristic
116#1996—131no—
117#1520—131no—
118C2×#328—131no—
119#1294—131no—
120#1289—131no—
121#1282—131no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13#12011yescharacteristic
125C23×C13C22⋊Q811yescharacteristic
126C23×C13#12411yescharacteristic
127C23×C13#13511yescharacteristic
128C23×C13#13511yescharacteristic
129C23×C13#13711yescharacteristic
130C23×C13#13711yescharacteristic
131C2×C4×C13—22no—
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×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—82no—
156C2×C4×C13—82no—
157C2×C4×C13C22⋊Q811yescharacteristic
158C2×C4×C13C22⋊Q811yescharacteristic
159C2×C4×C13#12411yescharacteristic
160C2×C4×C13#12411yescharacteristic
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—81no—
164C2×Dic13—81no—
165C2×Dic13—81no—
166C2×Dic13—81no—
167C2×Dic13—81no—
168Dic26—81no—
169Dic26—81no—
170#1055—81no—
171#1055—81no—
172C2×C22⋊Q8—131no—
173C2×C22⋊C8—131no—
174C2×C22⋊C8—131no—
175#400—21no—
176#398—21no—
177#387—21no—
178#387—21no—
179#385—21no—
180#380—21no—
181#380—131no—
182#380C2×D1311yescharacteristic
183C4×C22⋊C4C2×D1311yescharacteristic
184C2×#95C2×D1311yescharacteristic
185#342—261no—
186#342—261no—
187#328—261no—
188#328—261no—
189#328—261no—
190#328—261no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13#39311yescharacteristic
202C22×C13#45211yescharacteristic
203C22×C13#45211yescharacteristic
204C22×C13#47911yescharacteristic
205C22×C13#47911yescharacteristic
206C22×C13#48811yescharacteristic
207C22×C13#49111yescharacteristic
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—42no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218Dic13—81no—
219Dic13—81no—
220Dic13—161no—
221C22×Q8—131no—
222C23×C4—21no—
223C23×C4C22×D1311yescharacteristic
224C22×C8—261no—
225C22×C8—261no—
226C22⋊Q8—261no—
227C22⋊Q8—261no—
228C22⋊Q8—261no—
229C22⋊Q8—261no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—261no—
240C2×C22⋊C4—261no—
241C2×C22⋊C4C22⋊D1311yescharacteristic
242C2×C22⋊C4C22⋊D1311yescharacteristic
243C2×C42—21no—
244C22⋊C8—261no—
245C22⋊C8—261no—
246C22⋊C8—261no—
247C22⋊C8—261no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—261no—
255#95C22⋊D1311yescharacteristic
256#95C22⋊D1311yescharacteristic
257#95C22⋊D1311yescharacteristic
258#95C22⋊D1311yescharacteristic
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—21no—
265C2×C13#202611yescharacteristic
266C2×C13#203111yescharacteristic
267C2×C13#203211yescharacteristic
268C24C2×C22⋊D1311yescharacteristic
269C2×Q8—261no—
270C2×Q8—261no—
271C2×Q8—1041no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—81no—
282C22×C4—81no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—521no—
286C22×C4Q8×D1311yescharacteristic
287C22×C4#613111yescharacteristic
288C22×C4#613111yescharacteristic
289C22×C4#613111yescharacteristic
290C22×C4C2×C22⋊D1311yescharacteristic
291C22×C4C2×C22⋊D1311yescharacteristic
292C2×C8—521no—
293C2×C8—521no—
294C2×C8—1041no—
295C2×C8—1041no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—81no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4—521no—
304C4⋊C4—521no—
305C4⋊C4—1041no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—521no—
313C22⋊C4—521no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C42—81no—
317C13#1037711yescharacteristic, complemented, Sylow
318C23—41no—
319C23—41no—
320C23#8820011yescharacteristic
321C23#8820111yescharacteristic
322C23#8820411yescharacteristic
323C23#8820411yescharacteristic
324C23#8820511yescharacteristic
325C23#8820511yescharacteristic
326C23#8820711yescharacteristic
327Q8—1041no—
328Q8—1041no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4—1041no—
360C2×C4—1041no—
361C2×C4—1041no—
362C2×C4#8820011yescharacteristic
363C2×C4#8820011yescharacteristic
364C2×C4#8820111yescharacteristic
365C2×C4#8820111yescharacteristic
366C8—1041no—
367C8—1041no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1171872411yescharacteristic
379C22#1171872411yescharacteristic
380C22#1171872911yescharacteristic
381C22#1171873011yescharacteristic
382C22#1171889211yescharacteristic
383C22#1171890011yescharacteristic
384C22#1171890011yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—1041no—
396C4—1041no—
397C4—2081no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#1311598411yescharacteristic
405C2#1311600511yescharacteristic
406C2#1311601211yescharacteristic
subgroupG/H
centerC22#11718892
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2569C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenter#2569D13
hypocenterC13#10377
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2569

Complements

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

NH ≅ G/Ntype
317. C13#10377semidirect

Maximal subgroups

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

subgroupindex
#131158212
#131134072
C2×#117180442
#131127152
#131127032
#131126842
C13×#25692
#1037713