Finite Group Databasebeta

← #15773489

Subgroups — #15773489

Order 3328.

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

normal subgroups only

This group has 652 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×#88074C211yesmaximal, characteristic, complemented
2#13113174C211yesmaximal, characteristic, complemented
3#13112833C214yesmaximal, complemented
4C13×#2541C211yesmaximal, characteristic
5C2×C13×#127—21no—
6C2×C13×#127C411yescharacteristic, complemented
7C2×C13×#121—21no—
8C2×C13×#121—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#392C412yescomplemented
11C13×#392C2212yes—
12C13×#390—21no—
13C4×C13×C4⋊C4C411yescharacteristic, complemented
14C2×#88074—21no—
15C4×C22⋊Dic13—21no—
16#11718868—21no—
17#11718120—21no—
18#11718118C2212yes—
19#11718117C2212yes—
20C22×D4×C13—22no—
21C22×D4×C13—22no—
22C22×D4×C13—21no—
23C22×D4×C13—21no—
24C22×D4×C13C2×C412yes—
25C22×D4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#127—41no—
29C13×#127—41no—
30C13×#127—44no—
31C13×#121—44no—
32C13×#121—44no—
33C4×D4×C13—41no—
34C4×D4×C13—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4C2311yescharacteristic
41C2×C42×C13—21no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C4×Dic13—41no—
45C2×#6099—41no—
46C13×#95C2×C412yes—
47#88074—24no—
48#88071—41no—
49C22⋊#1055—22no—
50C22⋊#1055—41no—
51#11776—131nomaximal, Sylow
52C24×C13—22no—
53C24×C13C22⋊C411yescharacteristic
54C24×C13C2×D411yescharacteristic
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—44no—
62C2×D4×C13—44no—
63C2×D4×C13—42no—
64C2×D4×C13—42no—
65C2×D4×C13—44no—
66C2×D4×C13—44no—
67C2×D4×C13—41no—
68C2×D4×C13—41no—
69C2×D4×C13—42no—
70C2×D4×C13—82no—
71C2×D4×C13—82no—
72C2×D4×C13—82no—
73C22×C4×C13—22no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—42no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—44no—
91C13×C22⋊C4—44no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—42no—
95C22⋊Dic13—24no—
96C22⋊Dic13—42no—
97C4×Dic13—82no—
98#6099—82no—
99C2×#1055—42no—
100#2541D1311yescharacteristic
101C4×#99—131no—
102#1465—131no—
103#1343—134no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—42no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13AGL(1,ℤ/8)12yes—
122D4×C13—44no—
123D4×C13—82no—
124D4×C13—84no—
125D4×C13—88no—
126D4×C13—88no—
127D4×C13—84no—
128D4×C13—82no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—22no—
132C2×C4×C13—24no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#10412yes—
148C2×Dic13—44no—
149C2×Dic13—82no—
150C2×Dic13—82no—
151#1055—82no—
152C2×#127—21no—
153C2×#127Dic1311yescharacteristic, complemented
154C2×#121—21no—
155C2×#121—21no—
156C2×C4×D4C2×D1311yescharacteristic
157C2×#99—261no—
158#407—261no—
159#392Dic1312yescomplemented
160#392C2×D1312yes—
161#390—21no—
162C4×C4⋊C4Dic1311yescharacteristic, complemented
163C4×C22⋊C4—261no—
164#342—132no—
165#324—261no—
166#323—132no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—82no—
180C22×C13—82no—
181C22×C13—82no—
182C22×C13—82no—
183C22×C13—82no—
184C22×C13—82no—
185C22×C13—82no—
186C22×C13C2×#9911yescharacteristic
187C22×C13#41811yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C4×C13—21no—
190C4×C13—22no—
191C4×C13—44no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13#35312yes—
196Dic13—84no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4C2×Dic1312yes—
202C22×D4C22⋊D1311yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C2×M16—521no—
206#127—41no—
207#127—41no—
208#127—44no—
209#121—44no—
210#121—44no—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C22⋊D1311yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—262no—
218C2×C22⋊C4C2×Dic1311yescharacteristic
219C2×C22⋊C4C22×D1311yescharacteristic
220C2×C42—21no—
221C2×C42—521no—
222C2×C42C2×Dic1311yescharacteristic
223#99—264no—
224C22⋊C8—262no—
225C22⋊C8—521no—
226#95—521no—
227#95C2×Dic1312yes—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—42no—
231C2×C13—81no—
232C2×C13—162no—
233C2×C13#150711yescharacteristic
234C2×C13#212211yescharacteristic
235C2×C13C2×#35311yescharacteristic
236C24—22no—
237C24C22⋊Dic1311yescharacteristic
238C24C2×C22⋊D1311yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—44no—
250C2×D4—44no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4—82no—
255C2×D4—82no—
256C2×D4—82no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—522no—
265C22×C4C22⋊Dic1311yescharacteristic
266C22×C4C22⋊Dic1311yescharacteristic
267C22×C4C22⋊Dic1311yescharacteristic
268C22×C4C22×Dic1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270M16—1042no—
271C2×C8—522no—
272C4⋊C4—24no—
273C4⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—44no—
277C22⋊C4—44no—
278C22⋊C4—264no—
279C22⋊C4—522no—
280C42—21no—
281C42—21no—
282C42—42no—
283C42—1042no—
284C13#1177611yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23#8818612yes—
302C23C2×C22⋊Dic1311yescharacteristic
303D4—44no—
304D4—84no—
305D4—82no—
306D4—88no—
307D4—88no—
308D4—84no—
309D4—82no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—524no—
327C2×C4—1042no—
328C2×C4—1042no—
329C2×C4#8807411yescharacteristic
330C2×C4#8807411yescharacteristic
331C2×C4#8807712yes—
332C8—1042no—
333C22—21no—
334C22—21no—
335C22—22no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—82no—
346C22—82no—
347C22—82no—
348C22—82no—
349C22—82no—
350C22—82no—
351C22—82no—
352C22#1171887611yescharacteristic
353C22C2×#8807411yescharacteristic
354C22C2×#8807711yescharacteristic
355C4—22no—
356C4—21no—
357C4—44no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—1044no—
362C4#1171813712yes—
363C2—21no—
364C2—21no—
365C2—42no—
366C2—81no—
367C2—162no—
368C2#1311335211yescharacteristic
369C2#1311648611yescharacteristic
370C2C2×#1171813711yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2541C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2541D13
hypocenterC13#11776
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C4×#88074C2semidirect
2. #13113174C2semidirect
3. #13112833C2semidirect
6. C2×C13×#127C4semidirect
10. C13×#392C4semidirect
13. C4×C13×C4⋊C4C4semidirect
153. C2×#127Dic13semidirect
159. #392Dic13semidirect
162. C4×C4⋊C4Dic13semidirect
284. C13#11776semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131742
#131128332
C13×#25412
#1177613