Finite Group Databasebeta

← #16786742

Subgroups — #16786742

Order 3328.

602 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 112 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#13129766C212yesmaximal, complemented
3#13129764C212yesmaximal, complemented
4#13117327C211yesmaximal, characteristic
5C22×C13×#41C411yescharacteristic
6C2×#88180C2211yescharacteristic
7C22×C4×Dic13C411yescharacteristic
8#11719119—22no—
9#11718891C411yescharacteristic
10#11718891C2211yescharacteristic
11#11718882C411yescharacteristic
12#11718882C2211yescharacteristic
13#11718881—22no—
14C4×C22⋊Dic13—22no—
15#11718305—22no—
16#11718285C2214yes—
17C2×C13×#41—22no—
18C2×C13×#41—41no—
19C2×C13×#41—41no—
20C2×C13×#41—42no—
21C2×C13×#41C814yescomplemented
22C22×Q8×C13C2×C411yescharacteristic
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13—21no—
26C23×C4×C13C2×C411yescharacteristic
27C23×Dic13—21no—
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13—22no—
30C2×C22⋊Dic13D412yes—
31#88180—41no—
32#88180—41no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2311yescharacteristic
35C2×C4×Dic13—21no—
36C2×C4×Dic13—42no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D412yes—
40C22⋊#1057—24no—
41C4⋊#1057—42no—
42C4×#1057—42no—
43#88071—22no—
44#88071—22no—
45#11431—131nomaximal, Sylow
46C24×C13—21no—
47C24×C13C22⋊C411yescharacteristic
48C13×#41—44no—
49C13×#41—44no—
50C13×#41—44no—
51C13×#41—44no—
52C2×Q8×C13—21no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13C2×C812yes—
56C2×D4×C13—24no—
57C2×D4×C13—21no—
58C2×D4×C13—41no—
59C2×D4×C13—41no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C2×D4×C13C2×C812yes—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—24no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C2×C812yes—
73C22×C4×C13M1612yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—42no—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C22×Dic13C22⋊C412yes—
81C22×Dic13C2×D412yes—
82C2×#1057—44no—
83C22⋊Dic13—42no—
84C22⋊Dic13—44no—
85C22⋊Dic13—44no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—42no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93#2297—131no—
94#1458—132no—
95#1319—132no—
96#1318—132no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—22no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13C22⋊C812yes—
107C23×C13C2×C22⋊C411yescharacteristic
108Q8×C13—42no—
109Q8×C13—42no—
110D4×C13—42no—
111D4×C13—42no—
112D4×C13—48no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—44no—
123C2×C4×C13—44no—
124C2×C4×C13C22⋊C812yes—
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#10012yes—
128C2×C4×C13C22×C811yescharacteristic
129C2×C4×C13C2×M1611yescharacteristic
130C2×Dic13—22no—
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—22no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—48no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141#1057—84no—
142C22×#41#26111yescharacteristic
143C2×#117—131no—
144C22×C42—131no—
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—44no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—42no—
163C22×C13—82no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13C2×C22⋊C811yescharacteristic
167C22×C13C2×#9911yescharacteristic
168C22×C13C2×#10011yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—42no—
172C4×C13#32312yes—
173C4×C13#32312yes—
174Dic13—42no—
175Dic13—42no—
176Dic13—42no—
177Dic13—42no—
178C2×#41—22no—
179C2×#41—41no—
180C2×#41—41no—
181C2×#41—42no—
182C2×#41#105714yescomplemented
183C22×Q8C2×#26111yescharacteristic
184C22×D4—21no—
185C22×D4C2×#26111yescharacteristic
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—132no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—261no—
200C2×C42—522no—
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×C13—82no—
210C2×C13C2×#32311yescharacteristic
211C2×C13#212611yescharacteristic
212C2×C13#213211yescharacteristic
213C24—21no—
214C24C22⋊#26111yescharacteristic
215#41—44no—
216#41—44no—
217#41—44no—
218#41—44no—
219C2×Q8—21no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8C2×#105712yes—
223C2×D4—24no—
224C2×D4—21no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4C2×#105712yes—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—24no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—42no—
238C22×C4—132no—
239C22×C4—132no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—522no—
243C22×C4—522no—
244C22×C4—522no—
245C22×C4C2×#105712yes—
246C22×C4#612212yes—
247C22×C4C22⋊#26111yescharacteristic
248C22×C4C22×#26111yescharacteristic
249C2×C8—524no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C22⋊C4—522no—
253C22⋊C4—524no—
254C22⋊C4—524no—
255C42—262no—
256C42—262no—
257C42—521no—
258C42—521no—
259C42—522no—
260C13#1143111yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—22no—
264C23—41no—
265C23—41no—
266C23—42no—
267C23—42no—
268C23—41no—
269C23—41no—
270C23C22⋊#105712yes—
271C23C2×C22⋊#26111yescharacteristic
272Q8—42no—
273Q8—42no—
274D4—42no—
275D4—42no—
276D4—48no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—262no—
289C2×C4—262no—
290C2×C4—262no—
291C2×C4—262no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—528no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4#8811911yescharacteristic
300C2×C4#8811911yescharacteristic
301C2×C4C22⋊#105712yes—
302C2×C4#8812112yes—
303C2×C4C22×#105711yescharacteristic
304C2×C4C2×#612211yescharacteristic
305C8—1044no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—44no—
312C22—41no—
313C22—41no—
314C22—42no—
315C22—82no—
316C22—81no—
317C22—81no—
318C22C2×#8811911yescharacteristic
319C22C2×C22⋊#105711yescharacteristic
320C22C2×#8812111yescharacteristic
321C4—21no—
322C4—21no—
323C4—42no—
324C4—522no—
325C4—522no—
326C4—522no—
327C4—522no—
328C4#1171830512yes—
329C4#1171830512yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—82no—
334C2C2×#1171830511yescharacteristic
335C2#1313110711yescharacteristic
336C2#1313112711yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC22×C13×#41C4
socleC22×C13C2×#99
cosocleC2×C4⋊Dic13C23
hypercenterC22×#41#261
hypocenterC13#11431
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #13130067C2semidirect
2. #13129766C2semidirect
3. #13129764C2semidirect
21. C2×C13×#41C8semidirect
182. C2×#41#1057semidirect
260. C13#11431semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297662
#131297642
#131173272
#1143113