Finite Group Databasebeta

← #15773805

Subgroups — #15773805

Order 3328.

506 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 83 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#13119994C211yesmaximal, characteristic
2C2×#11718117C211yesmaximal, characteristic
3#13112856C212yesmaximal, complemented
4#13112835C212yesmaximal, complemented
5C13×#1819C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C2×#88178C411yescharacteristic, complemented
8C13×#379—21no—
9#11718908—21no—
10#11718872—21no—
11C4×C22⋊Dic13C411yescharacteristic, complemented
12C2×C22⋊#1055—21no—
13#11718614C411yescharacteristic, complemented
14#11718614C2211yescharacteristic
15#11718608C411yescharacteristic, complemented
16#11718608C2211yescharacteristic
17#11718606—21no—
18#11718606—21no—
19C13×#342—21no—
20C13×#342C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—41no—
29C2×C13×C22⋊C4—41no—
30C2×C13×C22⋊C4—41no—
31C2×C13×C22⋊C4—41no—
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C13×C22⋊C4C2311yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C22⋊Dic13—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43#88178—41no—
44#88178—41no—
45C2×#6101—21no—
46C2×C4×Dic13—21no—
47C22×#1055—41no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56#11845—131nomaximal, Sylow
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—22no—
60C24×C13—41no—
61C24×C13—42no—
62C24×C13—81no—
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13—81no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C2×Dic26—41no—
82C2×Dic26—81no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—82no—
90C13×C22⋊C4—82no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95C22⋊Dic13—42no—
96C22⋊Dic13—81no—
97C22⋊Dic13—81no—
98C4⋊Dic13—41no—
99#6101—42no—
100C4×Dic13—81no—
101C2×#1055—42no—
102C2×#1055—82no—
103#2561—131no—
104#1819D1311yescharacteristic
105C2×#323—131no—
106#1351—132no—
107#1344—132no—
108C23×C13—22no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—81no—
126C23×C13—81no—
127C23×C13—84no—
128C23×C13—84no—
129C23×C13#9911yescharacteristic
130C23×C13#9911yescharacteristic
131C23×C13C2×C22⋊C411yescharacteristic
132C23×C13#13512yes—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—82no—
146C2×C4×C13—82no—
147C2×C4×C13—82no—
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—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160Dic26—82no—
161#1055—82no—
162C2×C22⋊Q8—131no—
163C22×C22⋊C4C2×D1311yescharacteristic
164C2×C22⋊C8—261no—
165#397—131no—
166#397—131no—
167#393—131no—
168#393—131no—
169#388—261no—
170#388—261no—
171#381—261no—
172#379—21no—
173#379—261no—
174C4×C22⋊C4—131no—
175#342—21no—
176#342C2×D1312yes—
177#323—132no—
178#323—261no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—22no—
186C22×C13—21no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—81no—
197C22×C13—84no—
198C22×C13—81no—
199C22×C13—84no—
200C22×C13#35412yes—
201C22×C13C2×#9911yescharacteristic
202C22×C13#41611yescharacteristic
203C22×C13#42111yescharacteristic
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—162no—
209Dic13—81no—
210Dic13—81no—
211Dic13—81no—
212Dic13—81no—
213C25C22⋊D1311yescharacteristic
214C22×Q8—131no—
215C23×C4C4×D1311yescharacteristic
216C23×C4D5211yescharacteristic
217C22×C8—521no—
218C22⋊Q8—521no—
219C22⋊Q8—521no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—261no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—41no—
224C2×C22⋊C4—41no—
225C2×C22⋊C4—41no—
226C2×C22⋊C4—41no—
227C2×C22⋊C4—261no—
228C2×C22⋊C4—261no—
229C2×C22⋊C4—261no—
230C2×C22⋊C4—261no—
231C2×C22⋊C4—261no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4C4×D1311yescharacteristic
234C2×C22⋊C4D5211yescharacteristic
235C2×C22⋊C4C22⋊D1311yescharacteristic
236C2×C22⋊C4C22×D1311yescharacteristic
237C2×C42—261no—
238C22⋊C8—262no—
239C22⋊C8—521no—
240#95—131no—
241#95—131no—
242#95—261no—
243#95—261no—
244#95—261no—
245#95—261no—
246C2×C13—21no—
247C2×C13—21no—
248C2×C13—22no—
249C2×C13—42no—
250C2×C13—41no—
251C2×C13—81no—
252C2×C13#151611yescharacteristic
253C2×C13#212111yescharacteristic
254C2×C13C2×#35411yescharacteristic
255C24—21no—
256C24—21no—
257C24—22no—
258C24—41no—
259C24—42no—
260C24—81no—
261C24#610311yescharacteristic
262C24#610311yescharacteristic
263C24C2×C22⋊D1311yescharacteristic
264C2×Q8—521no—
265C2×Q8—1041no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—81no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4#610311yescharacteristic
278C22×C4#610311yescharacteristic
279C22×C4C2×C4×D1311yescharacteristic
280C22×C4C2×D5211yescharacteristic
281C2×C8—522no—
282C2×C8—1042no—
283C4⋊C4—521no—
284C4⋊C4—522no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—82no—
292C22⋊C4—82no—
293C22⋊C4—522no—
294C22⋊C4—522no—
295C22⋊C4—522no—
296C22⋊C4—521no—
297C22⋊C4—521no—
298C22⋊C4—1041no—
299C22⋊C4—1041no—
300C42—1041no—
301C13#1184511yescharacteristic, complemented, Sylow
302C23—21no—
303C23—21no—
304C23—22no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—81no—
321C23—84no—
322C23—84no—
323C23#8804611yescharacteristic
324C23#8804611yescharacteristic
325C23C2×#610311yescharacteristic
326C23#8820412yes—
327Q8—1042no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
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—
355C8—1042no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—84no—
375C22—81no—
376C22—84no—
377C22#1171806512yes—
378C22C2×#8804611yescharacteristic
379C22#1171866311yescharacteristic
380C22#1171866611yescharacteristic
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—162no—
386C4—1041no—
387C4—1041no—
388C4—1041no—
389C4—1041no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—42no—
394C2—41no—
395C2—81no—
396C2#1311339011yescharacteristic
397C2#1311648011yescharacteristic
398C2C2×#1171806511yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1819C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1819D13
hypocenterC13#11845
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1819

Complements

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

NH ≅ G/Ntype
3. #13112856C2semidirect
4. #13112835C2semidirect
7. C2×#88178C4semidirect
11. C4×C22⋊Dic13C4semidirect
13. #11718614C4semidirect
15. #11718608C4semidirect
301. C13#11845semidirect

Maximal subgroups

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

subgroupindex
#131199942
C2×#117181172
#131128562
#131128352
C13×#18192
#1184513