Finite Group Databasebeta

← #15773690

Subgroups — #15773690

Order 3328.

434 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114824C211yesmaximal, characteristic
2#13113177C211yesmaximal, characteristic
3#13112860C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2395C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C13×#117C411yescharacteristic, complemented
8C13×#400C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#398C411yescharacteristic, complemented
11C13×#397—21no—
12C13×#397C2211yescharacteristic
13C13×#394—21no—
14C4×C13×C4⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074—21no—
18#11718873—21no—
19#11718587—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C13×#117—41no—
29C13×#117—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4C2311yescharacteristic
41C2×C42×C13—21no—
42C2×C42×C13—21no—
43C2×C42×C13D411yescharacteristic
44C2×C22⋊Dic13—22no—
45C2×C4⋊Dic13—41no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88074—42no—
53#88071—41no—
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56#88043—41no—
57#11822—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—42no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—42no—
95C42×C13—41no—
96C42×C13—41no—
97C22⋊Dic13—42no—
98C22⋊Dic13—42no—
99C4⋊Dic13—82no—
100C2×#1055—42no—
101#2395D1311yescharacteristic
102#1799—131no—
103#1466—131no—
104#1352—132no—
105#1344—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13AGL(1,ℤ/8)11yescharacteristic
117C23×C13#13711yescharacteristic
118D4×C13—42no—
119D4×C13—42no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
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—81no—
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#9911yescharacteristic
148C2×Dic13—82no—
149C2×Dic13—82no—
150C2×Dic13—82no—
151#1055—82no—
152C2×C4×D4C2×D1311yescharacteristic
153C2×#117Dic1311yescharacteristic, complemented
154#432—261no—
155C2×#99—261no—
156#400Dic1311yescharacteristic, complemented
157#399C2×D1311yescharacteristic
158#398Dic1311yescharacteristic, complemented
159#397—21no—
160#397C2×D1311yescharacteristic
161#394—21no—
162#380—261no—
163C4×C4⋊C4—21no—
164C4×C22⋊C4—21no—
165C4×C22⋊C4Dic1311yescharacteristic, complemented
166#342—132no—
167#323—132no—
168#323—261no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13C2×#9911yescharacteristic
184C22×C13#41711yescharacteristic
185C22×C13#42111yescharacteristic
186C4×C13—21no—
187C4×C13—42no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195C4×C13#35212yes—
196Dic13—162no—
197C22×D4C22⋊D1311yescharacteristic
198C23×C4C2×Dic1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C4×D4—41no—
201C4×D4—41no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—521no—
207C2×C4⋊C4C2×Dic1311yescharacteristic
208C2×C4⋊C4C2×Dic1311yescharacteristic
209C2×C4⋊C4C2×Dic1311yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—262no—
215C2×C22⋊C4C22⋊D1311yescharacteristic
216C2×C22⋊C4C22×D1311yescharacteristic
217C2×C42—21no—
218C2×C42—21no—
219C2×C42C22⋊D1311yescharacteristic
220C4⋊C8—521no—
221#99—522no—
222C22⋊C8—262no—
223#97—521no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—521no—
229#95C2×Dic1311yescharacteristic
230#95C2×Dic1311yescharacteristic
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—41no—
234C2×C13—41no—
235C2×C13—81no—
236C2×C13#151311yescharacteristic
237C2×C13C2×#35211yescharacteristic
238C2×C13#212611yescharacteristic
239C24C22⋊Dic1311yescharacteristic
240C24C2×C22⋊D1311yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—522no—
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22⋊Dic1311yescharacteristic
259C22×C4C22×Dic1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261C2×C8—522no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—1042no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—522no—
276C22⋊C4—522no—
277C42—21no—
278C42—21no—
279C42—42no—
280C42—41no—
281C42—41no—
282C13#1182211yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23#8820311yescharacteristic
293C23#8820511yescharacteristic
294C23C2×C22⋊Dic1311yescharacteristic
295D4—42no—
296D4—42no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—1042no—
324C2×C4—1042no—
325C2×C4—1042no—
326C2×C4#8807411yescharacteristic
327C2×C4#8807411yescharacteristic
328C8—1042no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C2×#8807411yescharacteristic
344C22#1171889311yescharacteristic
345C22#1171889711yescharacteristic
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4—2082no—
356C4#1171813112yes—
357C2—21no—
358C2—21no—
359C2—41no—
360C2—41no—
361C2—81no—
362C2#1311337911yescharacteristic
363C2C2×#1171813111yescharacteristic
364C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2395C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2395D13
hypocenterC13#11822
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2395

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112836C2semidirect
7. C2×C13×#117C4semidirect
8. C13×#400C4semidirect
10. C13×#398C4semidirect
16. C4×C13×C22⋊C4C4semidirect
153. C2×#117Dic13semidirect
156. #400Dic13semidirect
158. #398Dic13semidirect
165. C4×C22⋊C4Dic13semidirect
282. C13#11822semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131772
#131128602
#131128362
C13×#23952
#1182213