Finite Group Databasebeta

← #16778261

Subgroups — #16778261

Order 3328.

596 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88111C211yesmaximal, characteristic
2#13130497C211yesmaximal, characteristic
3#13129656C212yesmaximal, complemented
4#13129655C212yesmaximal, complemented
5C4×#88200C211yesmaximal, characteristic
6C22×D13⋊C8—21no—
7C2×C4×Q8×C13C411yescharacteristic
8C2×#88200C411yescharacteristic
9C2×C42×D13C2211yescharacteristic
10C2×#88111—21no—
11C2×C4×#1057—21no—
12#11718891C2211yescharacteristic
13#11718650—21no—
14#11718648C411yescharacteristic
15#11718639—21no—
16#11718634C2211yescharacteristic
17C4×#6103—21no—
18C4×C4⋊Dic13C411yescharacteristic
19C4×#6101—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×C4×D13C2×C411yescharacteristic
25C22×C4×D13D411yescharacteristic
26C22×C4×D13D411yescharacteristic
27C22×#1057—22no—
28C22×#1057—22no—
29C2×D13⋊C8—24no—
30C2×D13⋊C8—42no—
31C2×D13⋊C8—42no—
32C4×Q8×C13—42no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13C2×C411yescharacteristic
37#88200—22no—
38#88200C814yescomplemented
39C2×#6103—21no—
40C2×#6103—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13C2311yescharacteristic
49C42×D13—42no—
50#88111—24no—
51C4×#1057—42no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#7566—131nomaximal, Sylow
58C23×D13C22⋊C411yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2×C812yescomplemented
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C2×D411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C2×C4×D13—22no—
74C2×C4×D13—22no—
75C2×C4×D13—22no—
76C2×C4×D13—22no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C4×D13C2×C812yes—
81C2×C4×D13M1612yes—
82C2×C4×D13SD1612yes—
83C2×C4×D13Q1612yes—
84C2×#1057—24no—
85C2×#1057—24no—
86C2×#1057—42no—
87C2×#1057—42no—
88C2×#1057—42no—
89C2×#1057—42no—
90D13⋊C8—48no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—42no—
93C42×C13—22no—
94C42×C13—42no—
95#6103—24no—
96#6103—42no—
97C4⋊Dic13—21no—
98C4⋊Dic13—41no—
99C4⋊Dic13C2×C812yescomplemented
100#6101—24no—
101#6101—42no—
102C4×Dic13—22no—
103C4×Dic13—41no—
104C4×Dic13—41no—
105C4×Dic13—42no—
106C4×C22⋊Q8—131no—
107C4×C22⋊C8—131no—
108C2×#336—131no—
109#1272—132no—
110#1271—132no—
111C23×C13C2×C22⋊C411yescharacteristic
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13C22⋊C812yes—
117C22×D13#10312yes—
118C22×D13#10412yes—
119Q8×C13—42no—
120Q8×C13—42no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—22no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#9912yes—
133C2×C4×C13#10312yes—
134C2×C4×C13#10412yes—
135C2×C4×C13C22×C811yescharacteristic
136C2×C4×C13C2×M1611yescharacteristic
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—22no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13C22⋊C812yes—
150C2×Dic13C2×SD1611yescharacteristic
151C2×Dic13C2×Q1611yescharacteristic
152C2×Dic13#13512yes—
153C4×D13—24no—
154C4×D13—24no—
155C4×D13—42no—
156C4×D13—42no—
157C4×D13—44no—
158#1057—44no—
159#1057—44no—
160C23×C8—261no—
161C2×C22⋊Q8—131no—
162C2×C4×Q8#26111yescharacteristic
163C22×C42—131no—
164C2×C22⋊C8—261no—
165C2×C4×C8—261no—
166#391—131no—
167#389—131no—
168#387—261no—
169#385—261no—
170#380—131no—
171C4×C4⋊C4—131no—
172C4×C4⋊C4—261no—
173C4×C22⋊C4—261no—
174#336—132no—
175#336—132no—
176#336—261no—
177C22×C13C2×C22⋊C811yescharacteristic
178C22×C13C2×#9911yescharacteristic
179C22×C13#41311yescharacteristic
180C22×C13C2×#10311yescharacteristic
181C22×C13#41611yescharacteristic
182C22×C13C2×#10411yescharacteristic
183C22×C13C2×#10411yescharacteristic
184C2×D13—22no—
185C2×D13—22no—
186C2×D13—22no—
187C2×D13—22no—
188C2×D13—22no—
189C2×D13—22no—
190C2×D13Q8⋊C814yes—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—42no—
194C4×C13—41no—
195C4×C13—81no—
196C4×C13#32814yes—
197Dic13—22no—
198Dic13—21no—
199Dic13—21no—
200Dic13—22no—
201Dic13—42no—
202Dic13—81no—
203C22×Q8C2×#26111yescharacteristic
204C23×C4—131no—
205C23×C4—131no—
206C23×C4—131no—
207C22×C8—262no—
208C22×C8—262no—
209C22×C8—264no—
210C22×C8—522no—
211C22×C8—522no—
212C22⋊Q8—134no—
213C22⋊Q8—262no—
214C4×Q8—42no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4C2×#26111yescharacteristic
221C2×C22⋊C4—261no—
222C2×C22⋊C4—261no—
223C2×C42—21no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—261no—
228C2×C42—522no—
229C2×C42C2×#26111yescharacteristic
230C22⋊C8—264no—
231C4×C8—522no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237C2×C13#145911yescharacteristic
238C2×C13C2×Q8⋊C811yescharacteristic
239C2×C13#147611yescharacteristic
240C2×C13C2×#32811yescharacteristic
241C2×C13#150111yescharacteristic
242C2×C13#152411yescharacteristic
243C2×C13#154211yescharacteristic
244D13—24no—
245C24—131no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8D13⋊C812yescomplemented
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—132no—
256C22×C4—132no—
257C22×C4—132no—
258C22×C4—132no—
259C22×C4—262no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4C22⋊#26111yescharacteristic
269C22×C4C22⋊#26111yescharacteristic
270C22×C4C22×#26111yescharacteristic
271C2×C8—264no—
272C2×C8—264no—
273C2×C8—522no—
274C2×C8—522no—
275C2×C8—522no—
276C2×C8—528no—
277C2×C8—522no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—132no—
281C4⋊C4—264no—
282C4⋊C4—261no—
283C4⋊C4—521no—
284C4⋊C4—522no—
285C22⋊C4—264no—
286C22⋊C4—522no—
287C42—22no—
288C42—42no—
289C42—262no—
290C42—521no—
291C42—521no—
292C42—522no—
293C13#756611yescharacteristic, complemented, Sylow
294C23—132no—
295C23—132no—
296C23—132no—
297C23—261no—
298C23—261no—
299C23—261no—
300C23—261no—
301C23C2×C22⋊#26111yescharacteristic
302Q8—42no—
303Q8—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—132no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—132no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—264no—
326C2×C4—264no—
327C2×C4—262no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—524no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4#8811712yes—
337C2×C4#8811812yes—
338C2×C4#8811912yes—
339C2×C4C2×D13⋊C811yescharacteristic
340C2×C4D13⋊M1611yescharacteristic
341C8—524no—
342C8—524no—
343C22—134no—
344C22—262no—
345C22—262no—
346C22—262no—
347C22—262no—
348C22—262no—
349C22—262no—
350C22D13⋊(C22⋊C8)11yescharacteristic
351C22#1171913211yescharacteristic
352C22C2×#8811711yescharacteristic
353C22C2×#8811811yescharacteristic
354C22D13⋊#10411yescharacteristic
355C22#1171916511yescharacteristic
356C22C2×#8811911yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—41no—
361C4—81no—
362C4—262no—
363C4—261no—
364C4—261no—
365C4—262no—
366C4—522no—
367C4—1041no—
368C4#1171829814yes—
369C2—264no—
370C2#1313007111yescharacteristic
371C2D13⋊(Q8⋊C8)11yescharacteristic
372C2#1313013011yescharacteristic
373C2C2×#1171829811yescharacteristic
374C2#1313021111yescharacteristic
375C2#1313028811yescharacteristic
376C2#1313033711yescharacteristic
subgroupG/H
centerC22×C4C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#7566
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #13129656C2semidirect
4. #13129655C2semidirect
38. #88200C8semidirect
62. C2×Q8×C13C2×C8semidirect
99. C4⋊Dic13C2×C8semidirect
249. C2×Q8D13⋊C8semidirect
293. C13#7566semidirect

Maximal subgroups

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

subgroupindex
C4×#881112
#131304972
#131296562
#131296552
C4×#882002
#756613