Finite Group Databasebeta

← #15779161

Subgroups — #15779161

Order 3328.

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

normal subgroups only

This group has 656 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#13114764C211yesmaximal, characteristic
2#13114754C211yesmaximal, characteristic
3#13112954C214yesmaximal, complemented
4C13×#2297C211yesmaximal, characteristic
5C22×C13×#41C2211yescharacteristic
6C2×C13×#117C411yescharacteristic, complemented
7C22×C42×C13C411yescharacteristic, complemented
8C13×#391—21no—
9C13×#390—21no—
10C13×#386C412yescomplemented
11C13×#386C2212yes—
12C4×C13×C22⋊C4—21no—
13C4×C13×C22⋊C4—21no—
14C2×#88076—21no—
15C2×#88074—21no—
16C2×#88074C2212yes—
17C2×#88073C2212yes—
18#11718872—21no—
19#11718868—21no—
20C2×C13×#41—24no—
21C2×C13×#41—42no—
22C2×C13×#41—42no—
23C22×Q8×C13D411yescharacteristic
24C22×D4×C13C2×C411yescharacteristic
25C22×D4×C13D411yescharacteristic
26C22×D4×C13C2311yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C412yes—
29C23×C4×C13D411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C13×#117—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4C2×C412yes—
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13—21no—
39C2×C42×C13—42no—
40C2×C22⋊Dic13—22no—
41C2×#6099—22no—
42C13×#95—22no—
43C13×#95—22no—
44#88076—42no—
45#88074—24no—
46#88074—42no—
47#88073—24no—
48#88071—42no—
49C22⋊#1055—42no—
50#12853—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C22×C411yescharacteristic
53C24×C13C2×D411yescharacteristic
54C13×#41—416no—
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13#4114yes—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—44no—
79C22×C4×C13—42no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—42no—
85C13×C4⋊C4—42no—
86C13×C22⋊C4—44no—
87C13×C22⋊C4—44no—
88C13×C22⋊C4—42no—
89C42×C13—42no—
90C42×C13—42no—
91C42×C13—42no—
92C22⋊Dic13—42no—
93C22⋊Dic13—42no—
94#6099—42no—
95#6099—42no—
96C2×#1055—42no—
97#2297D1311yescharacteristic
98#1785—131no—
99#1782—131no—
100#1390—134no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13#11712yes—
113C23×C13#12312yes—
114Q8×C13—44no—
115D4×C13—44no—
116D4×C13—44no—
117D4×C13—44no—
118C2×C4×C13—28no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—24no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—44no—
130C2×C4×C13—44no—
131C2×C4×C13—42no—
132C2×C4×C13—44no—
133C2×C4×C13—42no—
134C2×C4×C13—44no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13#9912yes—
139C2×C4×C13#9912yes—
140C2×C4×C13#12312yes—
141C2×Dic13—82no—
142C2×Dic13—84no—
143#1055—82no—
144C22×#41C2×D1311yescharacteristic
145C2×#117Dic1311yescharacteristic, complemented
146C22×C42Dic1311yescharacteristic, complemented
147C2×#101—261no—
148C2×#100—132no—
149C2×#99—132no—
150C2×#99—261no—
151#407—261no—
152#391—21no—
153#390—21no—
154#386Dic1312yescomplemented
155#386C2×D1312yes—
156#381—261no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4—21no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—42no—
165C22×C13—42no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—41no—
169C22×C13—42no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13#38111yescharacteristic
173C22×C13C2×#9911yescharacteristic
174C22×C13C2×#9911yescharacteristic
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—41no—
179C4×C13—44no—
180C4×C13—82no—
181Dic13—162no—
182C2×#41—24no—
183C2×#41—42no—
184C2×#41—42no—
185C22×Q8C22⋊D1311yescharacteristic
186C22×D4C2×Dic1311yescharacteristic
187C22×D4C22⋊D1311yescharacteristic
188C22×D4C22×D1311yescharacteristic
189C23×C4C2×Dic1311yescharacteristic
190C23×C4C2×Dic1312yes—
191C23×C4C22⋊D1311yescharacteristic
192C23×C4C22⋊D1311yescharacteristic
193C2×M16—262no—
194#117—42no—
195C2×C4⋊C4—21no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—262no—
199C2×C22⋊C4C2×Dic1312yes—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—42no—
204#101—522no—
205#100—264no—
206#99—264no—
207#99—522no—
208C22⋊C8—522no—
209#95—22no—
210#95—22no—
211#95—522no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—42no—
215C2×C13—42no—
216C2×C13—81no—
217C2×C13#181911yescharacteristic
218C2×C13#212012yes—
219C24C22⋊Dic1311yescharacteristic
220C24C22×Dic1311yescharacteristic
221C24C2×C22⋊D1311yescharacteristic
222#41—416no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4#612714yes—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—44no—
247C22×C4—42no—
248C22×C4—522no—
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C2×C22⋊D1311yescharacteristic
253M16—522no—
254M16—522no—
255C2×C8—522no—
256C4⋊C4—42no—
257C22⋊C4—44no—
258C22⋊C4—44no—
259C22⋊C4—42no—
260C22⋊C4—522no—
261C22⋊C4—522no—
262C42—42no—
263C42—42no—
264C42—42no—
265C13#1285311yescharacteristic, complemented, Sylow
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—42no—
274C23—42no—
275C23—42no—
276C23#8818012yes—
277C23#8818312yes—
278C23C2×C22⋊Dic1311yescharacteristic
279Q8—44no—
280D4—44no—
281D4—44no—
282D4—44no—
283C2×C4—28no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—1042no—
304C2×C4—1044no—
305C2×C4#8807412yes—
306C2×C4#8807412yes—
307C2×C4#8818312yes—
308C8—1042no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—42no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—42no—
320C22—81no—
321C22—81no—
322C22#1171887211yescharacteristic
323C22C2×#8807411yescharacteristic
324C22C2×#8807411yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—44no—
330C4—82no—
331C4—2082no—
332C2—21no—
333C2—21no—
334C2—42no—
335C2—42no—
336C2—81no—
337C2#1311491011yescharacteristic
338C2#1311647712yes—
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2297C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×D4×C13C23
hypercenter#2297D13
hypocenterC13#12853
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2297

Complements

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

NH ≅ G/Ntype
3. #13112954C2semidirect
6. C2×C13×#117C4semidirect
7. C22×C42×C13C4semidirect
10. C13×#386C4semidirect
145. C2×#117Dic13semidirect
146. C22×C42Dic13semidirect
154. #386Dic13semidirect
265. C13#12853semidirect

Maximal subgroups

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

subgroupindex
#131147642
#131147542
#131129542
C13×#22972
#1285313