Finite Group Databasebeta

← #15773956

Subgroups — #15773956

Order 3328.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#13113154C211yesmaximal, characteristic
3#13112836C214yesmaximal, complemented
4C13×#2547C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×#124—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C13×#397C412yescomplemented
9C13×#397C2212yes—
10C13×#391—21no—
11C13×#380—21no—
12C13×#380—21no—
13C4×C13×C4⋊C4C411yescharacteristic, complemented
14C2×#88074—21no—
15#11718873—21no—
16C2×C22⋊#1055—21no—
17#11718120—21no—
18#11718118C2212yes—
19#11718117C2212yes—
20C22×Q8×C13—21no—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×C4⋊Q8—41no—
25C13×C4⋊Q8—41no—
26C13×#124—42no—
27C13×#124—42no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4C2311yescharacteristic
38C2×C42×C13—21no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C22⋊Dic13—22no—
41C2×C4⋊Dic13—41no—
42C22×#1055—41no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95C2×C412yes—
46#88074—42no—
47#88071—41no—
48C22⋊#1055—22no—
49C22⋊#1055—41no—
50#11878—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C2×Q8×C13—42no—
54C2×Q8×C13—42no—
55C2×Q8×C13—42no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13D812yes—
59C2×D4×C13SD1612yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—44no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—42no—
87C22⋊Dic13—42no—
88C22⋊Dic13—42no—
89C4⋊Dic13—82no—
90C2×#1055—42no—
91C2×#1055—82no—
92#2547D1311yescharacteristic
93#1799—131no—
94#1459—131no—
95#1344—134no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13#10212yes—
105C23×C13C2×C22⋊C411yescharacteristic
106C23×C13C2×D811yescharacteristic
107C23×C13C2×SD1611yescharacteristic
108Q8×C13—84no—
109D4×C13—42no—
110D4×C13—42no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#10212yes—
133C2×Dic13—82no—
134C2×Dic13—82no—
135C2×Dic13—82no—
136#1055—82no—
137C2×C4⋊Q8Dic1311yescharacteristic, complemented
138C2×#124—21no—
139C2×C4×D4C2×D1311yescharacteristic
140C2×#99—261no—
141C2×C22⋊C8—261no—
142#397Dic1312yescomplemented
143#397C2×D1312yes—
144#391—21no—
145#380—21no—
146#380—21no—
147#380—261no—
148C4×C4⋊C4Dic1311yescharacteristic, complemented
149#342—132no—
150#324—261no—
151#323—132no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—22no—
156C22×C13—21no—
157C22×C13—42no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13C2×#9911yescharacteristic
167C22×C13C2×#10211yescharacteristic
168C22×C13#42111yescharacteristic
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—82no—
175C4×C13—82no—
176C4×C13#35412yes—
177Dic13—162no—
178C22×Q8—21no—
179C22×D4C22⋊D1311yescharacteristic
180C23×C4C22⋊D1311yescharacteristic
181C23×C4C22⋊D1311yescharacteristic
182C22×C8—521no—
183C4⋊Q8—41no—
184C4⋊Q8—41no—
185#124—42no—
186#124—42no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—521no—
192C2×C4⋊C4C2×Dic1312yes—
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4C2×Dic1311yescharacteristic
198C2×C22⋊C4C22×D1311yescharacteristic
199C2×C42—21no—
200C2×C42C2×Dic1311yescharacteristic
201#99—522no—
202C22⋊C8—262no—
203C22⋊C8—521no—
204#95—22no—
205#95—22no—
206#95—521no—
207#95C2×Dic1312yes—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—41no—
211C2×C13—42no—
212C2×C13—41no—
213C2×C13#151911yescharacteristic
214C2×C13#212311yescharacteristic
215C2×C13C2×#35411yescharacteristic
216C24C22⋊Dic1311yescharacteristic
217C24C2×C22⋊D1311yescharacteristic
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4#610412yes—
224C2×D4#610512yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—522no—
234C22×C4C22⋊Dic1311yescharacteristic
235C22×C4C22⋊Dic1311yescharacteristic
236C22×C4C22⋊Dic1311yescharacteristic
237C22×C4C22×Dic1311yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239C2×C8—522no—
240C2×C8—1042no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—1042no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—522no—
253C22⋊C4—522no—
254C42—21no—
255C42—21no—
256C42—42no—
257C13#1187811yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23#8807212yes—
267C23C2×#610411yescharacteristic
268C23C2×#610511yescharacteristic
269C23C2×C22⋊Dic1311yescharacteristic
270Q8—84no—
271D4—42no—
272D4—42no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—1042no—
293C2×C4—1042no—
294C2×C4—1042no—
295C2×C4#8807212yes—
296C2×C4#8807411yescharacteristic
297C2×C4#8807411yescharacteristic
298C8—1042no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—22no—
303C22—21no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—81no—
312C22—81no—
313C22C2×#8807211yescharacteristic
314C22C2×#8807411yescharacteristic
315C22#1171889711yescharacteristic
316C4—22no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—82no—
322C4—82no—
323C4—2082no—
324C4#1171813312yes—
325C2—21no—
326C2—21no—
327C2—41no—
328C2—42no—
329C2—41no—
330C2#1311340411yescharacteristic
331C2#1311649011yescharacteristic
332C2C2×#1171813311yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2547C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2547D13
hypocenterC13#11878
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
3. #13112836C2semidirect
5. C2×C13×C4⋊Q8C4semidirect
8. C13×#397C4semidirect
13. C4×C13×C4⋊C4C4semidirect
137. C2×C4⋊Q8Dic13semidirect
142. #397Dic13semidirect
148. C4×C4⋊C4Dic13semidirect
257. C13#11878semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131542
#131128362
C13×#25472
#1187813