Finite Group Databasebeta

← #15773502

Subgroups — #15773502

Order 3328.

768 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#88073C211yesmaximal, characteristic, complemented
2#13113174C211yesmaximal, characteristic, complemented
3#13112839C214yesmaximal, complemented
4C13×#2408C211yesmaximal, characteristic
5C23×D4×C13C411yescharacteristic
6C2×C13×#121—21no—
7C2×C13×#120—21no—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#394C2212yes—
10C13×#392C412yes—
11C13×#390—21no—
12C13×#380C411yescharacteristic
13C13×#379—21no—
14C2×#88073—21no—
15#11718868—21no—
16C4×#6099—21no—
17#11718122C2212yescomplemented
18#11718120C2212yescomplemented
19#11718117—21no—
20C25×C13—21no—
21C22×D4×C13—22no—
22C22×D4×C13—21no—
23C22×D4×C13—41no—
24C22×D4×C13—41no—
25C22×D4×C13—44no—
26C22×D4×C13C2×C412yes—
27C22×D4×C13D411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C13×#121—44no—
31C13×#120—44no—
32C4×D4×C13—41no—
33C4×D4×C13—41no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×#6099—22no—
44C2×#6099—41no—
45C13×#95C2×C412yes—
46#88073—24no—
47C22⋊#1055—22no—
48C22⋊#1055—41no—
49#88043—41no—
50C4×#1055—41no—
51#11779—131nomaximal, Sylow
52C24×C13—22no—
53C24×C13—42no—
54C24×C13—44no—
55C24×C13—42no—
56C24×C13—42no—
57C24×C13—82no—
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22⋊C411yescharacteristic
60C2×D4×C13—24no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C2×D4×C13—42no—
65C2×D4×C13—42no—
66C2×D4×C13—48no—
67C2×D4×C13—44no—
68C2×D4×C13—44no—
69C2×D4×C13—44no—
70C2×D4×C13—44no—
71C2×D4×C13—44no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—82no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—22no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C13×C4⋊C4—41no—
88C13×C4⋊C4—42no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—44no—
94C13×C22⋊C4—82no—
95C42×C13—21no—
96C42×C13—21no—
97#6099—24no—
98#6099—42no—
99#6099—82no—
100C2×#1055—42no—
101C2×#1055—42no—
102#2408D1311yescharacteristic
103C4×#100—131no—
104#1465—131no—
105#1345—134no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—24no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—48no—
120C23×C13—42no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13—84no—
124C23×C13—88no—
125C23×C13—88no—
126C23×C13—84no—
127C23×C13#10412yes—
128C23×C13C2×C22⋊C411yescharacteristic
129D4×C13—44no—
130D4×C13—44no—
131D4×C13—44no—
132D4×C13—44no—
133D4×C13—44no—
134D4×C13—88no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—81no—
151C2×C4×C13#9911yescharacteristic
152C2×C4×C13#9911yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)12yes—
154#1055—44no—
155#1055—82no—
156C23×D4Dic1311yescharacteristic
157C2×#121—21no—
158C2×#120—21no—
159C2×C4×D4C2×D1311yescharacteristic
160C2×#100—261no—
161#407—261no—
162C4×M16—261no—
163#394C2×D1312yes—
164#392Dic1312yes—
165#390—21no—
166#380Dic1311yescharacteristic
167#379—21no—
168#343—132no—
169#324—132no—
170#323—261no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—22no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—44no—
178C22×C13—44no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—44no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13—816no—
189C22×C13—82no—
190C22×C13—82no—
191C22×C13C2×#9911yescharacteristic
192C22×C13#41811yescharacteristic
193C22×C13C2×#10411yescharacteristic
194C4×C13—21no—
195C4×C13—22no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—82no—
200C4×C13AΣL(1,𝔽16)12yes—
201C25—21no—
202C22×D4—22no—
203C22×D4—21no—
204C22×D4—41no—
205C22×D4—41no—
206C22×D4—44no—
207C22×D4C2×Dic1312yes—
208C22×D4C22⋊D1311yescharacteristic
209C23×C4C2×Dic1311yescharacteristic
210C23×C4C22⋊D1311yescharacteristic
211C2×M16—262no—
212C2×M16—521no—
213#121—44no—
214#120—44no—
215C4×D4—41no—
216C4×D4—41no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C22×D1311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4C2×Dic1311yescharacteristic
224C2×C22⋊C4C22⋊D1311yescharacteristic
225C2×C42C22⋊D1311yescharacteristic
226#100—264no—
227C22⋊C8—262no—
228C22⋊C8—521no—
229#97—521no—
230C4×C8—521no—
231#95C2×Dic1312yes—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—42no—
235C2×C13—81no—
236C2×C13—84no—
237C2×C13#150711yescharacteristic
238C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
239C2×C13#213411yescharacteristic
240C24—22no—
241C24—42no—
242C24—44no—
243C24—42no—
244C24—42no—
245C24—82no—
246C24C22⋊Dic1311yescharacteristic
247C24C22⋊Dic1311yescharacteristic
248C2×D4—24no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—48no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—44no—
258C2×D4—44no—
259C2×D4—44no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—82no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4C22⋊Dic1311yescharacteristic
271C22×C4C22⋊Dic1311yescharacteristic
272C22×C4C22×Dic1311yescharacteristic
273C22×C4C2×C22⋊D1311yescharacteristic
274C22×C4C2×C22⋊D1311yescharacteristic
275M16—264no—
276M16—522no—
277M16—1042no—
278C2×C8—522no—
279C2×C8—522no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—82no—
288C42—21no—
289C42—21no—
290C13#1177911yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—24no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—84no—
309C23—88no—
310C23—88no—
311C23—84no—
312C23#8807712yes—
313C23C2×C22⋊Dic1311yescharacteristic
314D4—44no—
315D4—44no—
316D4—44no—
317D4—44no—
318D4—44no—
319D4—88no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4#8807411yescharacteristic
337C2×C4#8807411yescharacteristic
338C2×C4#8818612yes—
339C8—524no—
340C8—1042no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—44no—
348C22—44no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—44no—
354C22—41no—
355C22—81no—
356C22—82no—
357C22—82no—
358C22—816no—
359C22—82no—
360C22—82no—
361C22#1171887611yescharacteristic
362C22C2×#8807411yescharacteristic
363C22C2×#8807711yescharacteristic
364C4—22no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—82no—
370C4#1171812812yes—
371C2—21no—
372C2—21no—
373C2—42no—
374C2—81no—
375C2—84no—
376C2#1311335211yescharacteristic
377C2C2×#1171812811yescharacteristic
378C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
Fitting, prime radicalC13×#2408C2
socleC22×C13C2×#99
cosocleC2×C13×C4⋊C4C23
hypercenter#2408D13
hypocenterC13#11779
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C4×#88073C2semidirect
2. #13113174C2semidirect
3. #13112839C2semidirect
17. #11718122C22semidirect
18. #11718120C22semidirect
290. C13#11779semidirect

Maximal subgroups

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

subgroupindex
C4×#880732
#131131742
#131128392
C13×#24082
#1177913