Finite Group Databasebeta

← #15773258

Subgroups — #15773258

Order 3328.

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

normal subgroups only

This group has 470 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
2#13113154C211yesmaximal, 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—
18C4×C22⋊Dic13—21no—
19C2×C22⋊#1055—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—
45C22×#1055—41no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88074—24no—
54#88071—41no—
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57#11728—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—42no—
61C2×Q8×C13—41no—
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—41no—
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—21no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—42no—
93C42×C13—41no—
94C42×C13—41no—
95C22⋊Dic13—24no—
96C22⋊Dic13—42no—
97C4×Dic13—82no—
98C2×#1055—42no—
99C2×#1055—82no—
100#2398D1311yescharacteristic
101C4×#99—131no—
102#1459—131no—
103#1351—132no—
104#1344—132no—
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#10412yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C23×C13#13512yes—
116Q8×C13—42no—
117Q8×C13—42no—
118D4×C13—44no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
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—81no—
144C2×C4×C13—81no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×Dic13—44no—
148C2×Dic13—82no—
149C2×Dic13—82no—
150#1055—82no—
151C2×C4×Q8Dic1311yescharacteristic, complemented
152C2×C4×D4C2×D1311yescharacteristic
153C2×#99—261no—
154C2×C22⋊C8—261no—
155#400—21no—
156#397Dic1311yescharacteristic, complemented
157#397C2×D1311yescharacteristic
158#394—21no—
159#393Dic1311yescharacteristic, complemented
160#393C2×D1311yescharacteristic
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—261no—
164#376Dic1311yescharacteristic, complemented
165#342—132no—
166#324—261no—
167#323—132no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—42no—
173C22×C13—42no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13C2×#9911yescharacteristic
181C22×C13#41611yescharacteristic
182C22×C13C2×#10411yescharacteristic
183C4×C13—21no—
184C4×C13—42no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13#35412yes—
193Dic13—84no—
194C22×Q8C2×Dic1311yescharacteristic
195C22×D4C22⋊D1311yescharacteristic
196C23×C4C22⋊D1311yescharacteristic
197C23×C4C22⋊D1311yescharacteristic
198C22×C8—521no—
199C4×Q8—41no—
200C4×Q8—41no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×Dic1311yescharacteristic
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—262no—
211C2×C22⋊C4C2×Dic1311yescharacteristic
212C2×C22⋊C4C22×D1311yescharacteristic
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—521no—
216C2×C42C2×Dic1311yescharacteristic
217#99—264no—
218C22⋊C8—262no—
219C22⋊C8—521no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—521no—
226#95C2×Dic1311yescharacteristic
227#95C2×Dic1311yescharacteristic
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—42no—
231C2×C13—42no—
232C2×C13#150111yescharacteristic
233C2×C13#212011yescharacteristic
234C2×C13C2×#35411yescharacteristic
235C24C22⋊Dic1311yescharacteristic
236C24C2×C22⋊D1311yescharacteristic
237C2×Q8—42no—
238C2×Q8—41no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—522no—
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22×Dic1311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258C2×C8—522no—
259C2×C8—1042no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—264no—
270C22⋊C4—522no—
271C42—21no—
272C42—21no—
273C42—42no—
274C42—41no—
275C42—41no—
276C42—1042no—
277C13#1172811yescharacteristic, complemented, Sylow
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#8807712yes—
287C23#8820412yes—
288C23C2×C22⋊Dic1311yescharacteristic
289Q8—42no—
290Q8—42no—
291D4—44no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—524no—
319C2×C4—1042no—
320C2×C4—1042no—
321C2×C4#8807411yescharacteristic
322C2×C4#8807411yescharacteristic
323C8—1042no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22C2×#8807411yescharacteristic
337C22#1171889411yescharacteristic
338C22C2×#8807711yescharacteristic
339C4—21no—
340C4—42no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—1044no—
349C4#1171813312yes—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—42no—
354C2#1311332711yescharacteristic
355C2#1311647711yescharacteristic
356C2C2×#1171813311yescharacteristic
subgroupG/H
centerC2×C4#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#11728
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ 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
151. C2×C4×Q8Dic13semidirect
156. #397Dic13semidirect
159. #393Dic13semidirect
164. #376Dic13semidirect
277. C13#11728semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131542
#131128572
#131128362
C13×#23982
#1172813