Finite Group Databasebeta

← #15766091

Subgroups — #15766091

Order 3328.

422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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#13120060C211yesmaximal, characteristic
2#13115820C211yesmaximal, characteristic
3#13113409C211yesmaximal, characteristic
4C2×#11718044C211yesmaximal, characteristic
5#13112703C211yesmaximal, characteristic
6#13112683C211yesmaximal, characteristic
7C13×#1294C211yesmaximal, characteristic
8C2×#88178C2211yescharacteristic
9C2×C13×C22⋊C8C2211yescharacteristic
10C13×#380C2211yescharacteristic
11C2×C13×#95C2211yescharacteristic
12#11718873—21no—
13#11718873C2211yescharacteristic
14#11718871—21no—
15C4×C22⋊Dic13C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17#11718322—21no—
18#11718321—21no—
19#11718316—21no—
20#11718315—21no—
21#11718119—21no—
22#11718119—21no—
23#11718059—21no—
24#11718059—21no—
25#11718044—21no—
26#11718044—21no—
27C23×C4×C13—21no—
28C23×C4×C13C2311yescharacteristic
29C22×Dic26Q811yescharacteristic
30C22×C8×C13—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C22⋊C4—21no—
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13D411yescharacteristic
36C2×C22⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13Q811yescharacteristic
41#88178—21no—
42#88178—21no—
43#88178—21no—
44#88178—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×C4×Dic13—21no—
49C22×#1055—21no—
50C13×C22⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95D411yescharacteristic
55C13×#95D411yescharacteristic
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#10377—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—42no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—81no—
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—21no—
86C22×Dic13—21no—
87C2×Dic26—21no—
88C2×Dic26—21no—
89C2×Dic26—81no—
90C2×C8×C13—41no—
91C2×C8×C13—81no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—41no—
100C22⋊Dic13—41no—
101C22⋊Dic13—41no—
102C22⋊Dic13—41no—
103C4⋊Dic13—21no—
104C4⋊Dic13—21no—
105C4⋊Dic13—42no—
106C4⋊Dic13—81no—
107C4⋊Dic13—81no—
108#6101—42no—
109#6101—41no—
110#6101—41no—
111#6101—81no—
112C4×Dic13—81no—
113C2×#1055—41no—
114C2×#1055—81no—
115#2569—131no—
116#1996—131no—
117#1520—131no—
118C2×#328—131no—
119#1294D1311yescharacteristic
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—82no—
144C2×C4×C13—82no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13C22⋊Q811yescharacteristic
149C2×C4×C13C22⋊Q811yescharacteristic
150C2×C4×C13#12411yescharacteristic
151C2×C4×C13#12411yescharacteristic
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—81no—
167C2×Dic13—81no—
168Dic26—81no—
169Dic26—81no—
170C8×C13—81no—
171#1055—81no—
172C2×C22⋊Q8—131no—
173C2×C22⋊C8—131no—
174C2×C22⋊C8C2×D1311yescharacteristic
175#400—261no—
176#398—261no—
177#387—261no—
178#387—261no—
179#385—261no—
180#380—131no—
181#380—261no—
182#380C2×D1311yescharacteristic
183C4×C22⋊C4—131no—
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—161no—
215Dic13—81no—
216Dic13—81no—
217Dic13—81no—
218Dic13—81no—
219Dic13—81no—
220Dic13—81no—
221C22×Q8—131no—
222C23×C4—21no—
223C23×C4C22×D1311yescharacteristic
224C22×C8—21no—
225C22×C8—261no—
226C22⋊Q8—261no—
227C22⋊Q8—261no—
228C22⋊Q8—261no—
229C22⋊Q8—261no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—131no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—131no—
240C2×C22⋊C4—131no—
241C2×C22⋊C4—261no—
242C2×C22⋊C4—261no—
243C2×C42—261no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—261no—
247C22⋊C8—261no—
248#95—21no—
249#95—21no—
250#95—131no—
251#95—131no—
252#95—261no—
253#95—261no—
254#95—261no—
255#95—261no—
256#95—261no—
257#95D5211yescharacteristic
258#95D5211yescharacteristic
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
268C24D4×D1311yescharacteristic
269C2×Q8—261no—
270C2×Q8—261no—
271C2×Q8—1041no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4C2×D5211yescharacteristic
287C22×C4#612711yescharacteristic
288C22×C4#612711yescharacteristic
289C22×C4D4×D1311yescharacteristic
290C22×C4#612911yescharacteristic
291C22×C4Q8×D1311yescharacteristic
292C2×C8—41no—
293C2×C8—81no—
294C2×C8—521no—
295C2×C8—1041no—
296C4⋊C4—81no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4—522no—
300C4⋊C4—522no—
301C4⋊C4—521no—
302C4⋊C4—521no—
303C4⋊C4—1041no—
304C4⋊C4—1041no—
305C4⋊C4—1041no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C22⋊C4—261no—
312C22⋊C4—521no—
313C22⋊C4—521no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C42—1041no—
317C13#1037711yescharacteristic, complemented, Sylow
318C23—41no—
319C23—41no—
320C23#8813611yescharacteristic
321C23#8813911yescharacteristic
322C23#8815011yescharacteristic
323C23#8816611yescharacteristic
324C23#8816911yescharacteristic
325C23#8817011yescharacteristic
326C23#8817211yescharacteristic
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—82no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—1041no—
361C2×C4—1041no—
362C2×C4#8812911yescharacteristic
363C2×C4#8813911yescharacteristic
364C2×C4#8815011yescharacteristic
365C2×C4#8815111yescharacteristic
366C8—81no—
367C8—1041no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1171833411yescharacteristic
379C22#1171842911yescharacteristic
380C22#1171844411yescharacteristic
381C22#1171845811yescharacteristic
382C22#1171847111yescharacteristic
383C22#1171851811yescharacteristic
384C22#1171853811yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—161no—
392C4—1041no—
393C4—1041no—
394C4—1041no—
395C4—1041no—
396C4—1041no—
397C4—1041no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#1311598611yescharacteristic
405C2#1311600911yescharacteristic
406C2#1311601411yescharacteristic
subgroupG/H
centerC22#11718334
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1294C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenter#1294D13
hypocenterC13#10377
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

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
#131200602
#131158202
#131134092
C2×#117180442
#131127032
#131126832
C13×#12942
#1037713