Finite Group Databasebeta

← #16786744

Subgroups — #16786744

Order 3328.

602 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 104 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#13130067C212yesmaximal, complemented
2#13129767C212yesmaximal, complemented
3#13129765C212yesmaximal, complemented
4#13117326C211yesmaximal, characteristic
5C22×#6127C411yescharacteristic
6C22×C42×C13C411yescharacteristic
7C2×#88180C2211yescharacteristic
8#11719119—22no—
9#11718874—22no—
10#11718600C411yescharacteristic
11#11718600C2211yescharacteristic
12C4×#6103—22no—
13#11718590C411yescharacteristic
14#11718590C2211yescharacteristic
15#11718305—22no—
16#11718285C2214yes—
17C23×C4×C13—21no—
18C23×C4×C13C2×C411yescharacteristic
19C22×C22⋊D13—21no—
20C2×#6127—22no—
21C2×#6127—41no—
22C2×#6127—41no—
23C2×#6127—42no—
24C2×#6127C814yescomplemented
25C22×D52C2×C411yescharacteristic
26C22×C4×D13—21no—
27C22×Dic26C2×C411yescharacteristic
28C2×C42×C13—21no—
29C2×C42×C13—42no—
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C22⋊Dic13D412yes—
33C2×#6103—22no—
34C2×#6103—22no—
35#88180—41no—
36#88180—41no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13C2311yescharacteristic
39C2×C4×Dic13D412yes—
40C22⋊#1057—24no—
41C4⋊#1057—42no—
42C4×#1057—42no—
43#88071—22no—
44#88071—22no—
45#11431—131nomaximal, Sylow
46C24×C13C22⋊C411yescharacteristic
47C23×D13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—42no—
54C22×C4×C13—42no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C2×C812yes—
58C22×C4×C13M1612yes—
59C22×C4×C13C22×C411yescharacteristic
60C2×C22⋊D13—24no—
61C2×C22⋊D13—42no—
62C2×C22⋊D13—42no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C412yes—
65C22×Dic13C2×D412yes—
66#6127—44no—
67#6127—44no—
68#6127—44no—
69#6127—44no—
70C2×D52—21no—
71C2×D52—41no—
72C2×D52—41no—
73C2×D52C2×C812yes—
74C2×C4×D13—24no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13—42no—
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26C2×C812yes—
82C2×#1057—44no—
83C42×C13—41no—
84C42×C13—41no—
85C42×C13—42no—
86C22⋊Dic13—42no—
87#6103—44no—
88#6103—44no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4×Dic13—22no—
92C4×Dic13—22no—
93#2297—131no—
94#1458—132no—
95#1319—132no—
96#1318—132no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13C22⋊C812yes—
102C23×C13C2×C22⋊C411yescharacteristic
103C22×D13—22no—
104C22×D13—42no—
105C22×D13—42no—
106C22×D13—41no—
107C22×D13—41no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—48no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13C22⋊C812yes—
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#10012yes—
125C2×C4×C13C22×C811yescharacteristic
126C2×C4×C13C2×M1611yescharacteristic
127C22⋊D13—48no—
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135D52—42no—
136D52—42no—
137C4×D13—44no—
138C4×D13—44no—
139Dic26—42no—
140Dic26—42no—
141#1057—84no—
142C22×#41—131no—
143C2×#117—131no—
144C22×C42#26111yescharacteristic
145#431—262no—
146#391—131no—
147#391—131no—
148#390—131no—
149#390—131no—
150#386—262no—
151C4×C22⋊C4—262no—
152#324—134no—
153#323—262no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—22no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C2×C22⋊C811yescharacteristic
162C22×C13C2×#9911yescharacteristic
163C22×C13C2×#10011yescharacteristic
164C2×D13—44no—
165C2×D13—42no—
166C2×D13—82no—
167C2×D13—81no—
168C2×D13—81no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—42no—
172C4×C13—42no—
173C4×C13#32312yes—
174C4×C13#32312yes—
175Dic13—42no—
176Dic13—42no—
177Dic13—42no—
178C2×#41—134no—
179C2×#41—262no—
180C2×#41—521no—
181C2×#41—521no—
182C2×#41—522no—
183C22×Q8—131no—
184C22×D4—131no—
185C22×D4—261no—
186C23×C4—21no—
187C23×C4—261no—
188C23×C4C2×#26111yescharacteristic
189#117—521no—
190#117—521no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C22⋊C4—132no—
194C2×C22⋊C4—262no—
195C2×C22⋊C4—262no—
196C2×C42—21no—
197C2×C42—42no—
198C2×C42—132no—
199C2×C42C2×#26111yescharacteristic
200C2×C42C2×#26111yescharacteristic
201C4⋊C8—522no—
202C22⋊C8—264no—
203C4×C8—522no—
204#95—262no—
205#95—262no—
206C2×C13—21no—
207C2×C13—21no—
208C2×C13—42no—
209C2×C13C2×#32311yescharacteristic
210C2×C13#212611yescharacteristic
211C2×C13#213211yescharacteristic
212D13—82no—
213C24—261no—
214C24C22⋊#26111yescharacteristic
215#41—524no—
216#41—524no—
217#41—524no—
218#41—524no—
219C2×Q8—132no—
220C2×Q8—261no—
221C2×Q8—521no—
222C2×Q8—521no—
223C2×D4—132no—
224C2×D4—264no—
225C2×D4—261no—
226C2×D4—521no—
227C2×D4—521no—
228C2×D4—522no—
229C2×D4—522no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—132no—
239C22×C4—132no—
240C22×C4—261no—
241C22×C4—264no—
242C22×C4—521no—
243C22×C4—521no—
244C22×C4—522no—
245C22×C4D13⋊C812yes—
246C22×C4#611812yes—
247C22×C4C22⋊#26111yescharacteristic
248C22×C4C22×#26111yescharacteristic
249C2×C8—524no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C22⋊C4—524no—
253C22⋊C4—524no—
254C22⋊C4—522no—
255C42—41no—
256C42—41no—
257C42—42no—
258C42—262no—
259C42—262no—
260C13#1143111yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—262no—
266C23—522no—
267C23—522no—
268C23—521no—
269C23—521no—
270C23#8811112yes—
271C23C2×C22⋊#26111yescharacteristic
272Q8—522no—
273Q8—522no—
274D4—522no—
275D4—522no—
276D4—528no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—48no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—262no—
291C2×C4—262no—
292C2×C4—262no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—524no—
296C2×C4—524no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4#8810711yescharacteristic
300C2×C4#8810711yescharacteristic
301C2×C4#8811112yes—
302C2×C4#8812112yes—
303C2×C4C2×D13⋊C811yescharacteristic
304C2×C4C2×#611811yescharacteristic
305C8—1044no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—524no—
314C22—522no—
315C22—1042no—
316C22—1041no—
317C22—1041no—
318C22C2×#8810711yescharacteristic
319C22C2×#8811111yescharacteristic
320C22C2×#8812111yescharacteristic
321C4—21no—
322C4—21no—
323C4—42no—
324C4—42no—
325C4—522no—
326C4—522no—
327C4—522no—
328C4#1171828712yes—
329C4#1171828712yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—1042no—
334C2C2×#1171828711yescharacteristic
335C2#1313110911yescharacteristic
336C2#1313112911yescharacteristic
subgroupG/H
centerC2×C4#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC22×C42×C13C4
socleC22×C13C2×#99
prime radicalC22×#6127C4
cosocleC2×C4⋊Dic13C23
hypercenterC22×C42#261
hypocenterC13#11431
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #13130067C2semidirect
2. #13129767C2semidirect
3. #13129765C2semidirect
24. C2×#6127C8semidirect
260. C13#11431semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297672
#131297652
#131173262
#1143113