Finite Group Databasebeta

← #15773695

Subgroups — #15773695

Order 3328.

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

normal subgroups only

This group has 446 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#13113174C211yesmaximal, characteristic
3#13112857C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2398C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400—21no—
9C13×#397C411yescharacteristic, complemented
10C13×#397C2211yescharacteristic
11C13×#394—21no—
12C13×#393C411yescharacteristic, complemented
13C13×#393C2211yescharacteristic
14C4×C13×C22⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C13×#376C411yescharacteristic, complemented
17C2×#88074—21no—
18#11718873—21no—
19#11718868—21no—
20#11718120—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4C2311yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C4⋊Dic13—41no—
45C2×#6099—41no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88074—42no—
54#88071—41no—
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57#11823—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—42no—
61C2×Q8×C13—41no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
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—21no—
73C22×C4×C13—21no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
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—
100#6099—82no—
101C2×#1055—42no—
102#2398D1311yescharacteristic
103#1799—131no—
104#1465—131no—
105#1351—132no—
106#1344—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13C2×C22⋊C411yescharacteristic
117C23×C13AGL(1,ℤ/8)11yescharacteristic
118C23×C13#13711yescharacteristic
119Q8×C13—42no—
120Q8×C13—42no—
121D4×C13—42no—
122D4×C13—42no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
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—41no—
146C2×C4×C13—41no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13#9911yescharacteristic
150C2×C4×C13#9911yescharacteristic
151C2×Dic13—82no—
152C2×Dic13—82no—
153C2×Dic13—82no—
154#1055—82no—
155C2×C4×Q8Dic1311yescharacteristic, complemented
156C2×C4×D4C2×D1311yescharacteristic
157C2×#99—261no—
158#407—261no—
159#400—21no—
160#397Dic1311yescharacteristic, complemented
161#397C2×D1311yescharacteristic
162#394—21no—
163#393Dic1311yescharacteristic, complemented
164#393C2×D1311yescharacteristic
165#380—261no—
166C4×C22⋊C4—21no—
167C4×C22⋊C4—21no—
168#376Dic1311yescharacteristic, complemented
169#342—132no—
170#324—261no—
171#323—132no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—42no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13C2×#9911yescharacteristic
187C22×C13#41711yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—21no—
190C4×C13—42no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13#35412yes—
199Dic13—162no—
200C22×Q8C2×Dic1311yescharacteristic
201C22×D4C22⋊D1311yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C2×M16—521no—
205C4×Q8—41no—
206C4×Q8—41no—
207C4×D4—41no—
208C4×D4—41no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—521no—
211C2×C4⋊C4C2×Dic1311yescharacteristic
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—262no—
218C2×C22⋊C4C2×Dic1311yescharacteristic
219C2×C22⋊C4C22×D1311yescharacteristic
220C2×C42—21no—
221C2×C42—21no—
222C2×C42C2×Dic1311yescharacteristic
223#99—522no—
224C22⋊C8—262no—
225C22⋊C8—521no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—521no—
232#95C2×Dic1311yescharacteristic
233#95C2×Dic1311yescharacteristic
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—41no—
237C2×C13—41no—
238C2×C13—81no—
239C2×C13#151311yescharacteristic
240C2×C13#212011yescharacteristic
241C2×C13C2×#35411yescharacteristic
242C24C22⋊Dic1311yescharacteristic
243C24C2×C22⋊D1311yescharacteristic
244C2×Q8—42no—
245C2×Q8—41no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—41no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—522no—
261C22×C4C22⋊Dic1311yescharacteristic
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22×Dic1311yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266M16—1042no—
267C2×C8—522no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—1042no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C42—21no—
282C42—21no—
283C42—42no—
284C42—41no—
285C42—41no—
286C13#1182311yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#8820311yescharacteristic
297C23#8820511yescharacteristic
298C23C2×C22⋊Dic1311yescharacteristic
299Q8—42no—
300Q8—42no—
301D4—42no—
302D4—42no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—1042no—
330C2×C4—1042no—
331C2×C4—1042no—
332C2×C4#8807411yescharacteristic
333C2×C4#8807411yescharacteristic
334C8—1042no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22—81no—
349C22C2×#8807411yescharacteristic
350C22#1171889311yescharacteristic
351C22#1171889711yescharacteristic
352C4—21no—
353C4—41no—
354C4—42no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—2082no—
362C4#1171813312yes—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—41no—
367C2—81no—
368C2#1311337911yescharacteristic
369C2#1311647711yescharacteristic
370C2C2×#1171813311yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2398C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2398D13
hypocenterC13#11823
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2398

Complements

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

NH ≅ G/Ntype
3. #13112857C2semidirect
4. #13112836C2semidirect
6. C2×C4×Q8×C13C4semidirect
9. C13×#397C4semidirect
12. C13×#393C4semidirect
16. C13×#376C4semidirect
155. C2×C4×Q8Dic13semidirect
160. #397Dic13semidirect
163. #393Dic13semidirect
168. #376Dic13semidirect
286. C13#11823semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131742
#131128572
#131128362
C13×#23982
#1182313