Finite Group Databasebeta

← #16779255

Subgroups — #16779255

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719130C211yesmaximal, characteristic
2C2×#11719130C211yesmaximal, characteristic
3#13129679C214yesmaximal
4C4×#88131C211yesmaximal, characteristic
5C22×C4×Dic13C2211yescharacteristic
6C2×#88131C412yes—
7C2×C22⋊#1057C2212yes—
8C2×C22⋊#1057C2212yes—
9#11719130—21no—
10#11719130—21no—
11#11719130—21no—
12#11719130—21no—
13#11719130—21no—
14#11719130—21no—
15#11719130C412yescomplemented
16#11719130C412yescomplemented
17C2×#88110—21no—
18C2×#88110C412yescomplemented
19C2×C4⋊#1057—21no—
20C2×C4⋊#1057C412yescomplemented
21C4×C13×C22⋊C4C411yescharacteristic
22C4×C22⋊Dic13C411yescharacteristic
23C22⋊C4×Dic13C2212yes—
24C4×#6101—21no—
25C42×Dic13—21no—
26#11718310—21no—
27#11718309—21no—
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2311yescharacteristic
31C22×#1057—22no—
32C22×#1057C2×C414yes—
33C2×C13×C22⋊C4C2×C412yes—
34C2×C42×C13—21no—
35C2×C22⋊Dic13C2×C412yes—
36C2×#6101—22no—
37C2×C4×Dic13—22no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—22no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13Q811yescharacteristic
51C2×C4×Dic13Q811yescharacteristic
52#88131—24no—
53#88131—24no—
54C22⋊#1057—22no—
55C22⋊#1057—22no—
56C22⋊#1057—22no—
57C22⋊#1057C2×C414yes—
58#88110—22no—
59#88110—22no—
60#88110—22no—
61#88110—22no—
62C4⋊#1057—22no—
63C4⋊#1057—22no—
64C4⋊#1057—22no—
65C4⋊#1057—22no—
66C13×#95—21no—
67#88071—21no—
68#88071—22no—
69#7930—131nomaximal, Sylow
70C24×C13C22×C411yescharacteristic
71C22×C4×C13—22no—
72C22×C4×C13—42no—
73C22×C4×C13C4211yescharacteristic
74C22×C4×C13C4211yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C4⋊C411yescharacteristic
78C22×C4×C13C4⋊C411yescharacteristic
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—42no—
83C22×Dic13C4211yescharacteristic
84C22×Dic13C4211yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C4⋊C411yescharacteristic
88C22×Dic13C4⋊C411yescharacteristic
89C22×Dic13C22×C411yescharacteristic
90C22×Dic13C22×C411yescharacteristic
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13C2×D411yescharacteristic
93C22×Dic13C2×D411yescharacteristic
94C22×Dic13C2×Q811yescharacteristic
95C2×#1057—24no—
96C2×#1057—24no—
97C2×#1057—44no—
98C2×#1057—44no—
99C13×C22⋊C4—22no—
100C13×C22⋊C4M1614yes—
101C42×C13—42no—
102C22⋊Dic13—22no—
103C22⋊Dic13M1614yes—
104#6101—28no—
105C4×Dic13—28no—
106C4×Dic13—44no—
107C4×Dic13—42no—
108C4×Dic13C22⋊C411yescharacteristic
109C4×Dic13C22⋊C411yescharacteristic
110C4×Dic13C22⋊C411yescharacteristic
111C4×Dic13C22⋊C411yescharacteristic
112C4×Dic13C22⋊C411yescharacteristic
113C4×Dic13C22⋊C411yescharacteristic
114C4×Dic13C22⋊C411yescharacteristic
115C4×Dic13C22⋊C411yescharacteristic
116C4×Dic13C4⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121C4×Dic13C4⋊C411yescharacteristic
122C4×Dic13C4⋊C411yescharacteristic
123C4×Dic13C4⋊C411yescharacteristic
124C2×#432—131no—
125C2×#432—131no—
126C4×#117—131no—
127#1282—134no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13C2×C4211yescharacteristic
131C23×C13C2×C22⋊C411yescharacteristic
132C23×C13C2×C4⋊C411yescharacteristic
133C23×C13C2×M1612yes—
134C23×C13C2×M1612yes—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—24no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13#9511yescharacteristic
145C2×C4×C13#9511yescharacteristic
146C2×C4×C13#9511yescharacteristic
147C2×C4×C13#9511yescharacteristic
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—22no—
157C2×Dic13—22no—
158C2×Dic13—22no—
159C2×Dic13—24no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13#9511yescharacteristic
166C2×Dic13#9511yescharacteristic
167C2×Dic13#9511yescharacteristic
168C2×Dic13#9511yescharacteristic
169C2×Dic13C2×C22⋊C411yescharacteristic
170C2×Dic13C2×C22⋊C411yescharacteristic
171C2×Dic13C2×C4⋊C411yescharacteristic
172C2×Dic13C2×C4⋊C411yescharacteristic
173#1057—44no—
174#1057—44no—
175C2×#117—132no—
176C22×C42—131no—
177#432—132no—
178#432—132no—
179#432—261no—
180#432—261no—
181#432—261no—
182#432—261no—
183#432—261no—
184#432—261no—
185C2×C4⋊C8—132no—
186C2×C4⋊C8—261no—
187C2×C22⋊C8—132no—
188C2×C22⋊C8—132no—
189C2×#97—132no—
190C2×#97—261no—
191C4×C4⋊C4—261no—
192C4×C4⋊C4—261no—
193C4×C22⋊C4—131no—
194C4×C22⋊C4—132no—
195C4×C22⋊C4#26111yescharacteristic
196#376—261no—
197C43—261no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13C2×#9511yescharacteristic
207C22×C13C4×M1612yes—
208C22×C13#40712yes—
209C22×C13#42311yescharacteristic
210C22×C13#42311yescharacteristic
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—44no—
215C4×C13#34412yes—
216Dic13—21no—
217Dic13—21no—
218Dic13—21no—
219Dic13—21no—
220Dic13—21no—
221Dic13—21no—
222Dic13—21no—
223Dic13—44no—
224Dic13#41012yes—
225C23×C4—131no—
226C23×C4—131no—
227C23×C4C2×#26111yescharacteristic
228C22×C8—134no—
229C22×C8—262no—
230#117—264no—
231#117—264no—
232C2×C4⋊C4—262no—
233C2×C22⋊C4—132no—
234C2×C22⋊C4C2×#26112yes—
235C2×C42—21no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—131no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—262no—
249C2×C42—262no—
250C2×C42—261no—
251C4⋊C8—262no—
252C4⋊C8—262no—
253C4⋊C8—262no—
254C4⋊C8—262no—
255C22⋊C8—134no—
256C22⋊C8—262no—
257C22⋊C8—262no—
258C22⋊C8—262no—
259#97—262no—
260#97—262no—
261#97—262no—
262#97—262no—
263#95—21no—
264#95—262no—
265#95—261no—
266C2×C13—22no—
267C2×C13—22no—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13#172811yescharacteristic
271C2×C13#174011yescharacteristic
272C2×C13C2×#34411yescharacteristic
273C24C22×#26111yescharacteristic
274C22×C4—22no—
275C22×C4—42no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—262no—
289C22×C4—262no—
290C22×C4—262no—
291C22×C4—522no—
292C22×C4C4×#26111yescharacteristic
293C22×C4C4×#26111yescharacteristic
294C22×C4C4⋊#26111yescharacteristic
295C22×C4C4⋊#26111yescharacteristic
296C22×C4C22⋊#26111yescharacteristic
297C22×C4C22⋊#26111yescharacteristic
298C2×C8—264no—
299C2×C8—264no—
300C2×C8—524no—
301C2×C8—524no—
302C4⋊C4—268no—
303C22⋊C4—22no—
304C22⋊C4—134no—
305C22⋊C4—262no—
306C22⋊C4#611814yes—
307C42—42no—
308C42—131no—
309C42—131no—
310C42—131no—
311C42—131no—
312C42—131no—
313C42—131no—
314C42—131no—
315C42—131no—
316C42—131no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—131no—
321C42—131no—
322C42—131no—
323C42—131no—
324C42—268no—
325C42—522no—
326C42—524no—
327C13#793011yescharacteristic, complemented, Sylow
328C23—41no—
329C23—41no—
330C23C2×#611812yes—
331C23D13⋊M1612yes—
332C23C2×C4×#26111yescharacteristic
333C23C2×C4⋊#26111yescharacteristic
334C23C2×C22⋊#26111yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—262no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—262no—
362C2×C4—262no—
363C2×C4—264no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4(C2×#261)⋊C411yescharacteristic
370C2×C4(C2×#261)⋊C411yescharacteristic
371C2×C4(C2×#261)⋊C411yescharacteristic
372C2×C4(C2×#261)⋊C411yescharacteristic
373C8—524no—
374C8—524no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22C4×#611812yes—
384C22#1171905211yescharacteristic
385C22#1171905311yescharacteristic
386C22#1171912712yes—
387C22C2×(C2×#261)⋊C411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—132no—
393C4—261no—
394C4—261no—
395C4—261no—
396C4—261no—
397C4—261no—
398C4—261no—
399C4—261no—
400C4—524no—
401C4#1171823912yes—
402C2—22no—
403C2—22no—
404C2—21no—
405C2—21no—
406C2#1313050011yescharacteristic
407C2#1313053411yescharacteristic
408C2C2×#1171823911yescharacteristic
subgroupG/H
centerC22C2×(C2×#261)⋊C4
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC4×C13×C22⋊C4C4
socleC22×C13C2×#95
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC4×C22⋊C4#261
hypocenterC13#7930
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
15. #11719130C4semidirect
16. #11719130C4semidirect
18. C2×#88110C4semidirect
20. C2×C4⋊#1057C4semidirect
327. C13#7930semidirect

Maximal subgroups

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

subgroupindex
C2×#117191302
#131296792
C4×#881312
#793013