Finite Group Databasebeta

← #16778303

Subgroups — #16778303

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130726C211yesmaximal, characteristic
2C2×#11718290C211yesmaximal, characteristic
3#13129654C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5#13117320C211yesmaximal, characteristic
6C23×#1057—21no—
7C2×C13×#117C411yescharacteristic
8C2×#88180C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057—21no—
11#11718646C411yescharacteristic
12#11718646C411yescharacteristic
13#11718646C2211yescharacteristic
14#11718646C2211yescharacteristic
15#11718611—21no—
16#11718611—21no—
17C4×C4⋊Dic13—21no—
18C4×C4⋊Dic13—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×#1057—24no—
27C22×#1057—22no—
28C22×#1057—22no—
29C22×#1057—42no—
30C22×#1057—42no—
31C13×#117—22no—
32C13×#117C814yescomplemented
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C42×C13—21no—
37C2×C22⋊Dic13—21no—
38#88180—42no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×C4⋊Dic13C2×C411yescharacteristic
45C2×C4×Dic13—21no—
46C2×C4×Dic13—42no—
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13C2311yescharacteristic
51C22⋊#1057—42no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#7579—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C2×C812yes—
64C22×C4×C13M1612yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—41no—
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78C22×Dic13C2×D411yescharacteristic
79C2×#1057—24no—
80C2×#1057—48no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4C2×C812yescomplemented
89C13×C4⋊C4C2×C812yescomplemented
90C13×C22⋊C4—24no—
91C42×C13—24no—
92C22⋊Dic13—42no—
93C4⋊Dic13—42no—
94C4⋊Dic13—42no—
95C4⋊Dic13—42no—
96C4⋊Dic13—41no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4×Dic13—41no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104C4×Dic13—42no—
105#2296—131no—
106#1817—131no—
107C2×#336—131no—
108#1271—132no—
109#1271—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13C22⋊C812yes—
115C23×C13#9912yes—
116C23×C13#10112yes—
117C23×C13C2×C22⋊C411yescharacteristic
118C2×C4×C13—24no—
119C2×C4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13C22⋊C812yes—
131C2×C4×C13C22×C811yescharacteristic
132C2×C4×C13C2×M1611yescharacteristic
133C2×Dic13—24no—
134C2×Dic13—24no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—44no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13#10412yes—
152C2×Dic13#13512yes—
153C2×Dic13AGL(1,ℤ/8)11yescharacteristic
154C2×Dic13#13711yescharacteristic
155#1057—44no—
156#1057—82no—
157C23×C8—261no—
158C2×#117—131no—
159C2×#117#26111yescharacteristic
160C22×C42—131no—
161C2×C22⋊C8—261no—
162#389—131no—
163#389—131no—
164#389—131no—
165#389—131no—
166#385—261no—
167#385—261no—
168C4×C4⋊C4—261no—
169C4×C4⋊C4—261no—
170#336—132no—
171#336—132no—
172#336—261no—
173#336—261no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13#32414yes—
181C22×C13C2×C22⋊C811yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13C2×#10111yescharacteristic
184C22×C13#41611yescharacteristic
185C22×C13#41711yescharacteristic
186C22×C13C2×#10411yescharacteristic
187C22×C13#42111yescharacteristic
188C4×C13—22no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—42no—
193Dic13—21no—
194Dic13—22no—
195Dic13—21no—
196Dic13—22no—
197Dic13—41no—
198Dic13—81no—
199Dic13—81no—
200C23×C4—131no—
201C23×C4—131no—
202C23×C4C2×#26111yescharacteristic
203C22×C8—262no—
204C22×C8—264no—
205C22×C8—262no—
206C22×C8—522no—
207C22×C8—522no—
208#117—22no—
209#117—522no—
210#117#105714yescomplemented
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4C2×#26111yescharacteristic
218C2×C4⋊C4C2×#26111yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—261no—
221C2×C42—21no—
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—261no—
227C2×C42—522no—
228C22⋊C8—522no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233C2×C13—24no—
234C2×C13C2×#32411yescharacteristic
235C2×C13#147611yescharacteristic
236C2×C13#147711yescharacteristic
237C2×C13#150411yescharacteristic
238C2×C13#151611yescharacteristic
239C2×C13#153111yescharacteristic
240C2×C13#155211yescharacteristic
241C24C22⋊#26111yescharacteristic
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—262no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—262no—
254C22×C4—262no—
255C22×C4—262no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—521no—
259C22×C4C2×#105712yes—
260C22×C4#612212yes—
261C22×C4C22⋊#26111yescharacteristic
262C22×C4C22×#26111yescharacteristic
263C2×C8—264no—
264C2×C8—522no—
265C2×C8—528no—
266C2×C8—522no—
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—522no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—522no—
278C4⋊C4—522no—
279C4⋊C4C2×#105712yescomplemented
280C4⋊C4C2×#105712yescomplemented
281C22⋊C4—24no—
282C22⋊C4—522no—
283C42—24no—
284C42—521no—
285C42—521no—
286C42—521no—
287C42—521no—
288C42—522no—
289C13#757911yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#8810712yes—
295C23#8811312yes—
296C23C22⋊#105712yes—
297C23C2×C22⋊#26111yescharacteristic
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—132no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—132no—
314C2×C4—264no—
315C2×C4—264no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—524no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4C22⋊#105712yes—
333C2×C4C22×#105711yescharacteristic
334C2×C4C2×#612211yescharacteristic
335C8—524no—
336C8—1042no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22#1171828514yes—
344C22C2×#8810711yescharacteristic
345C22C2×#8811311yescharacteristic
346C22D13⋊#10411yescharacteristic
347C22#1171916411yescharacteristic
348C22#1171916511yescharacteristic
349C22#1171916611yescharacteristic
350C22C2×C22⋊#105711yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—262no—
357C4—261no—
358C4—262no—
359C4—261no—
360C4—521no—
361C4—1041no—
362C4—1041no—
363C2—24no—
364C2C2×#1171828511yescharacteristic
365C2#1313012711yescharacteristic
366C2#1313013111yescharacteristic
367C2#1313022411yescharacteristic
368C2#1313026411yescharacteristic
369C2#1313030811yescharacteristic
370C2#1313035711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#7579
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #13129654C2semidirect
4. #13129654C2semidirect
32. C13×#117C8semidirect
88. C13×C4⋊C4C2×C8semidirect
89. C13×C4⋊C4C2×C8semidirect
210. #117#1057semidirect
279. C4⋊C4C2×#1057semidirect
280. C4⋊C4C2×#1057semidirect
289. C13#7579semidirect

Maximal subgroups

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

subgroupindex
#131307262
C2×#117182902
#131296542
#131173202
#757913