Finite Group Databasebeta

← #16778754

Subgroups — #16778754

Order 3328.

426 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130751C211yesmaximal, characteristic, complemented
2#13130553C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129652C212yesmaximal
5#13123200C211yesmaximal, characteristic
6C2×#88133—21no—
7C2×#88110—21no—
8C2×C4⋊#1057—21no—
9C13×#390C411yescharacteristic
10#11718882C411yescharacteristic
11#11718882C2211yescharacteristic
12#11718646C411yescharacteristic
13#11718634C2211yescharacteristic
14#11718612—21no—
15#11718606—21no—
16#11718605—21no—
17C42×Dic13C2211yescharacteristic
18#11718589C411yescharacteristic
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4—21no—
28C2×C13×C22⋊C4—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88133—44no—
46#88110—24no—
47C4⋊#1057—42no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#7706—131nomaximal, Sylow
52C24×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C22×C4×C13—21no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C2×#1057—24no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C42×C13—22no—
76C22⋊Dic13—42no—
77C22⋊Dic13—42no—
78C22⋊Dic13—42no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81C4⋊Dic13—22no—
82C4⋊Dic13—42no—
83C4⋊Dic13—41no—
84#6101—42no—
85#6101—42no—
86C4×Dic13—22no—
87C4×Dic13—21no—
88C4×Dic13—22no—
89C4×Dic13—21no—
90C4×Dic13—41no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93#2860—131no—
94#1831—131no—
95#1745—131no—
96#1271—132no—
97#1270—132no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13C2×C22⋊C411yescharacteristic
106D4×C13—82no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#10412yes—
118C2×C4×C13#13112yes—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13AGL(1,ℤ/8)11yescharacteristic
136C2×Dic13AGL(1,ℤ/8)12yes—
137C2×Dic13#13711yescharacteristic
138#1057—44no—
139#1057—82no—
140C2×#126—261no—
141C2×C4⋊C8—261no—
142C2×#97—261no—
143#390—131no—
144#390—131no—
145#390#26111yescharacteristic
146#389—131no—
147#389—131no—
148#389—131no—
149#388—261no—
150#388—261no—
151#388—261no—
152C43—131no—
153#336—132no—
154#336—132no—
155#336—261no—
156#336—261no—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13#40811yescharacteristic
165C22×C13#41011yescharacteristic
166C22×C13#41311yescharacteristic
167C22×C13#41711yescharacteristic
168C22×C13#41811yescharacteristic
169C22×C13C2×#10411yescharacteristic
170C22×C13#42111yescharacteristic
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13—81no—
175Dic13—22no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180Dic13—81no—
181Dic13—81no—
182C22×D4C2×#26111yescharacteristic
183C22×C8—262no—
184C22×C8—262no—
185#126—524no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4C2×#26111yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—261no—
195C2×C22⋊C4—261no—
196C2×C22⋊C4—261no—
197C2×C22⋊C4—261no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42—131no—
204C2×C42C2×#26111yescharacteristic
205C4⋊C8—522no—
206#97—264no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13—161no—
211C2×C13#147311yescharacteristic
212C2×C13#148311yescharacteristic
213C2×C13#149611yescharacteristic
214C2×C13#150511yescharacteristic
215C2×C13#151211yescharacteristic
216C2×C13#152911yescharacteristic
217C2×C13#155711yescharacteristic
218C24—21no—
219C2×D4—22no—
220C2×D4—41no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—264no—
233C2×C8—522no—
234C2×C8—522no—
235C2×C8—522no—
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—262no—
240C4⋊C4—521no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—522no—
247C22⋊C4—521no—
248C22⋊C4—521no—
249C22⋊C4—522no—
250C22⋊C4—522no—
251C42—22no—
252C42—261no—
253C42—262no—
254C42—261no—
255C42—262no—
256C42—521no—
257C42—521no—
258C42—521no—
259C13#770611yescharacteristic, complemented, Sylow
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23C2×C22⋊#26111yescharacteristic
268D4—82no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—132no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4#8811612yes—
299C2×C4#8823812yes—
300C8—524no—
301C8—1042no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1171913211yescharacteristic
310C22#1171913811yescharacteristic
311C22C2×#8811611yescharacteristic
312C22#1171914211yescharacteristic
313C22#1171914611yescharacteristic
314C22#1171916411yescharacteristic
315C22#1171916611yescharacteristic
316C4—22no—
317C4—22no—
318C4—41no—
319C4—81no—
320C4—261no—
321C4—261no—
322C4—262no—
323C4—521no—
324C4—521no—
325C4—1041no—
326C4—1041no—
327C2—161no—
328C2#1313011811yescharacteristic
329C2#1313015111yescharacteristic
330C2#1313019511yescharacteristic
331C2#1313022511yescharacteristic
332C2#1313024811yescharacteristic
333C2#1313030111yescharacteristic
334C2#1313036711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#390C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenter#390#261
hypocenterC13#7706
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #13130751C2semidirect
2. #13130553C2semidirect
3. #13129655C2semidirect
259. C13#7706semidirect

Maximal subgroups

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

subgroupindex
#131307512
#131305532
#131296552
#131296522
#131232002
#770613