Finite Group Databasebeta

← #11808480

Subgroups — #11808480

Order 1152.

2025 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63921C212yesmaximal
3C2×#63921C211yesmaximal, characteristic
4C2×#63883C212yesmaximal, complemented
5C3×#4993C212yesmaximal, complemented
6#10591370C211yesmaximal, characteristic, complemented
7#10591317C212yesmaximal, complemented
8#10591303C214yesmaximal, complemented
9D3×#399—32nomaximal
10C23×D32C2211yescharacteristic
11C22×C4×C3⋊D3C2212yes—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C22×#624C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic, complemented
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
17C2×#3750C2212yescomplemented
18C4⋊C4×C3⋊D3—24no—
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2214yescomplemented
22C2×Dic3⋊Dic3C2214yescomplemented
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2214yes—
25#63921—24no—
26#63921—28no—
27#63883—28no—
28C3×C3⋊#95C2212yescomplemented
29#63579C2212yescomplemented
30C2×D3×C4⋊C4—32no—
31C2×D3×C4⋊C4—34no—
32C2×D3×C4⋊C4—61no—
33C2×D3×C22⋊C4—34no—
34C2×D3×C22⋊C4—32no—
35C3×#399—32no—
36#4993—34no—
37#4993D312yescomplemented
38#4949—34no—
39#4949—32no—
40#4677—32no—
41D3×#95—32no—
42C23×C3⋊D3C2311yescharacteristic
43C23×C3×D3C2312yes—
44C22×D32—24no—
45C22×D32—22no—
46C22×D32—22no—
47C22×D32—24no—
48C22×D32Q814yes—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2311yescharacteristic
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—24no—
56C2×C4×C3⋊D3—24no—
57C2×C4×C3⋊D3D414yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2314yes—
60C2×#624—24no—
61C2×#624—24no—
62C2×#624—24no—
63C2×#624—22no—
64C2×#624D418yes—
65C32×C4⋊C4—22no—
66C4⋊(C3⋊Dic3)—22no—
67#3750—24no—
68C3×(C2×D3)⋊C4—24no—
69C3×(C2×D3)⋊C4—28no—
70C3×Dic3⋊C4—28no—
71Dic3⋊Dic3—28no—
72(C2×D3)⋊Dic3—24no—
73(C2×D3)⋊Dic3—28no—
74C2×#399—91noSylow
75C24×D3—32no—
76C22×C4×D3—32no—
77C22×C4×D3—34no—
78C22×C4×D3—34no—
79C22×C4×D3—32no—
80C22×C4×D3—61no—
81C22×C4×D3—62no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—34no—
84C2×C3×C4⋊C4C2×D312yescomplemented
85C2×C3×C22⋊C4—34no—
86C2×C3×C22⋊C4—32no—
87C2×#217—32no—
88C2×#217—34no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4C2×D312yes—
92C2×(C2×D3)⋊C4C2×D314yes—
93C2×C4⋊Dic3—32no—
94C2×C4⋊Dic3—34no—
95C2×C4⋊Dic3—61no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—62no—
99C2×Dic3⋊C4C2×D314yescomplemented
100D3×C4⋊C4—616no—
101D3×C4⋊C4—68no—
102D3×C4⋊C4—68no—
103D3×C22⋊C4—68no—
104D3×C22⋊C4—616no—
105C3×#95—32no—
106C3⋊#95—34no—
107C3⋊#95C2×D312yescomplemented
108C23×C32C2411yescharacteristic
109C22×C3⋊D3C2×D414yes—
110C22×C3⋊D3C2×D412yes—
111C22×C3⋊D3C2×Q812yes—
112C22×C3⋊D3#4112yes—
113C22×C3⋊D3#4114yes—
114C22×C3×D3—24no—
115C22×C3×D3—22no—
116C22×C3×D3—22no—
117C22×C3×D3—24no—
118C22×C3×D3C2×Q814yes—
119C2×D32—216no—
120C2×D32—28no—
121C2×D32—48no—
122C2×D32—44no—
123C2×D32—44no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4C2×D412yes—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3C2×D412yes—
134C4×C3⋊D3—28no—
135C4×C3⋊D3—48no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—24no—
140C2×C3×Dic3C2×D418yes—
141#624—216no—
142#624—44no—
143C22×C4⋊C4—92no—
144C22×C4⋊C4—91no—
145C22×C22⋊C4—92no—
146C22×C22⋊C4—91no—
147#399—32no—
148#399—92no—
149#399—94no—
150C2×#95—91no—
151C24×C3—32no—
152C23×D3—32no—
153C23×D3—38no—
154C23×D3—61no—
155C23×D3—68no—
156C23×D3—64no—
157C23×D3—68no—
158C23×D3—64no—
159C23×D3C22×D312yes—
160C22×C3×C4—21no—
161C22×C3×C4—22no—
162C22×C3×C4—34no—
163C22×C3×C4—32no—
164C22×C3×C4C22×D314yes—
165C22×C3×C4C22×D312yes—
166C22×Dic3—32no—
167C22×Dic3—34no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D314yes—
172C2×C4×D3—38no—
173C2×C4×D3—316no—
174C2×C4×D3—64no—
175C2×C4×D3—68no—
176C2×C4×D3—68no—
177C2×C4×D3—68no—
178C2×C4×D3—68no—
179C2×C4×D3—64no—
180C2×C4×D3—68no—
181C2×C4×D3—68no—
182C2×C4×D3—68no—
183C2×C4×D3—68no—
184C2×C4×D3—68no—
185C2×C4×D3—124no—
186C2×C4×D3—124no—
187C3×C4⋊C4—24no—
188C3×C4⋊C4—24no—
189C3×C4⋊C4—68no—
190C3×C22⋊C4—68no—
191C3×C22⋊C4—64no—
192#217—64no—
193#217—68no—
194(C2×D3)⋊C4—24no—
195(C2×D3)⋊C4—28no—
196(C2×D3)⋊C4—64no—
197(C2×D3)⋊C4—68no—
198C4⋊Dic3—68no—
199C4⋊Dic3—64no—
200C4⋊Dic3—64no—
201Dic3⋊C4—28no—
202Dic3⋊C4—68no—
203Dic3⋊C4—68no—
204Dic3⋊C4—68no—
205C22×C32C22×D412yes—
206C22×C32C22×D411yescharacteristic
207C22×C32C22×Q811yescharacteristic
208C22×C32C2×#4111yescharacteristic
209C22×C32C2×#4112yes—
210C2×C3⋊D3C22⋊Q818yes—
211C2×C3⋊D3C22⋊Q814yes—
212C2×C3⋊D3#12318yes—
213C2×C3⋊D3#12314yes—
214C2×C3⋊D3#12714yes—
215C2×C3×D3—28no—
216C2×C3×D3—24no—
217C2×C3×D3—44no—
218C2×C3×D3—42no—
219C2×C3×D3—42no—
220D32—416no—
221C32×C4—22no—
222C32×C4—42no—
223C3⋊Dic3—22no—
224C3⋊Dic3—42no—
225C3×Dic3—28no—
226C3×Dic3—42no—
227C25—91no—
228C23×C4—92no—
229C23×C4—91no—
230C23×C4—91no—
231C23×C4—92no—
232C2×C4⋊C4—34no—
233C2×C4⋊C4—94no—
234C2×C4⋊C4—92no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—184no—
237C2×C4⋊C4—188no—
238C2×C4⋊C4D3211yescharacteristic, complemented
239C2×C22⋊C4—34no—
240C2×C22⋊C4—32no—
241C2×C22⋊C4—94no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—188no—
244C2×C22⋊C4—184no—
245#95—32no—
246#95—92no—
247C23×C3—21no—
248C23×C3—34no—
249C23×C3—64no—
250C23×C3—62no—
251C23×C3—64no—
252C23×C3—62no—
253C23×C3C23×D312yes—
254C22×D3—24no—
255C22×D3—22no—
256C22×D3—24no—
257C22×D3—22no—
258C22×D3—38no—
259C22×D3—34no—
260C22×D3—34no—
261C22×D3—38no—
262C22×D3—34no—
263C22×D3—62no—
264C22×D3—64no—
265C22×D3—62no—
266C22×D3—64no—
267C22×D3—62no—
268C22×D3—632no—
269C22×D3—616no—
270C22×D3—128no—
271C22×D3—1216no—
272C22×D3—128no—
273C22×D3D3×Q814yes—
274C2×C3×C4—24no—
275C2×C3×C4—24no—
276C2×C3×C4—24no—
277C2×C3×C4—24no—
278C2×C3×C4—24no—
279C2×C3×C4—24no—
280C2×C3×C4—22no—
281C2×C3×C4—38no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—64no—
285C2×C3×C4—64no—
286C2×C3×C4—64no—
287C2×C3×C4—62no—
288C2×C3×C4D3×D414yes—
289C2×Dic3—24no—
290C2×Dic3—24no—
291C2×Dic3—24no—
292C2×Dic3—22no—
293C2×Dic3—34no—
294C2×Dic3—62no—
295C2×Dic3—64no—
296C2×Dic3—64no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3D3×D418yes—
304C4×D3—632no—
305C4×D3—616no—
306C4×D3—616no—
307C4×D3—128no—
308C4×D3—1216no—
309C4×D3—1216no—
310C2×C32C2×C22⋊Q812yes—
311C2×C32C2×C22⋊Q811yescharacteristic
312C2×C32C2×#12312yes—
313C2×C32C2×#12311yescharacteristic
314C2×C32C2×#12711yescharacteristic
315C3⋊D3#39918yescomplemented
316C3×D3—44no—
317C24—32no—
318C24—94no—
319C24—91no—
320C24—184no—
321C24—182no—
322C24—184no—
323C24—182no—
324C22×C4—34no—
325C22×C4—32no—
326C22×C4—98no—
327C22×C4—91no—
328C22×C4—94no—
329C22×C4—92no—
330C22×C4—184no—
331C22×C4—184no—
332C22×C4—184no—
333C22×C4—184no—
334C22×C4—184no—
335C22×C4—184no—
336C22×C4—182no—
337C22×C4—184no—
338C22×C4C2×D3212yes—
339C22×C4C2×D3211yescharacteristic
340C4⋊C4—22no—
341C4⋊C4—68no—
342C4⋊C4—184no—
343C4⋊C4—188no—
344C4⋊C4—182no—
345C22⋊C4—68no—
346C22⋊C4—64no—
347C22⋊C4—188no—
348C22⋊C4—184no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—68no—
355C22×C3—64no—
356C22×C3—122no—
357C22×C3—124no—
358C22×C3—122no—
359C22×C3C2×D3×D414yes—
360C22×C3C2×D3×D412yes—
361C22×C3C2×D3×Q812yes—
362C22×C3D3×#4114yes—
363C22×C3D3×#4112yes—
364C2×D3—28no—
365C2×D3—24no—
366C2×D3—38no—
367C2×D3—316no—
368C2×D3—38no—
369C2×D3—316no—
370C2×D3—38no—
371C2×D3—42no—
372C2×D3—44no—
373C2×D3—42no—
374C2×D3—64no—
375C2×D3—64no—
376C2×D3—68no—
377C2×D3—64no—
378C2×D3—68no—
379C2×D3—1232no—
380C3×C4—24no—
381C3×C4—24no—
382C3×C4—44no—
383C3×C4—44no—
384C3×C4—68no—
385C3×C4—122no—
386Dic3—28no—
387Dic3—42no—
388Dic3—64no—
389Dic3—64no—
390Dic3—124no—
391Dic3—124no—
392C32C2×#39911yescharacteristic, complemented, Sylow
393C23—34no—
394C23—64no—
395C23—64no—
396C23—62no—
397C23—62no—
398C23—94no—
399C23—94no—
400C23—92no—
401C23—92no—
402C23—92no—
403C23—1816no—
404C23—188no—
405C23—364no—
406C23—368no—
407C23—364no—
408C23C22×D3211yescharacteristic
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—38no—
414C2×C4—64no—
415C2×C4—64no—
416C2×C4—64no—
417C2×C4—62no—
418C2×C4—92no—
419C2×C4—188no—
420C2×C4—1816no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—368no—
426C2×C4—364no—
427C2×C4#381112yes—
428C2×C3—21no—
429C2×C3—22no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—124no—
434C2×C3D3×C22⋊Q814yes—
435C2×C3D3×C22⋊Q812yes—
436C2×C3D3×#12312yes—
437C2×C3D3×#12314yes—
438C2×C3D3×#12712yes—
439D3—316no—
440D3—44no—
441D3—68no—
442C22—68no—
443C22—64no—
444C22—94no—
445C22—98no—
446C22—98no—
447C22—94no—
448C22—94no—
449C22—122no—
450C22—124no—
451C22—122no—
452C22—3616no—
453C22#6430612yes—
454C22D32×D412yes—
455C22D32×Q811yescharacteristic
456C22#6431911yescharacteristic
457C22C2×#381111yescharacteristic
458C4—22no—
459C4—42no—
460C4—68no—
461C4—122no—
462C4—182no—
463C4—362no—
464C3—21no—
465C3D3×#39912yescomplemented
466C2—98no—
467C2—124no—
468C2#1059460812yes—
469C2#1059462412yes—
470C2#1059507911yescharacteristic
471C2#1059530011yescharacteristic
472C2#1059542911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
4. C2×#63883C2semidirect
5. C3×#4993C2semidirect
6. #10591370C2semidirect
7. #10591317C2semidirect
8. #10591303C2semidirect
15. C2×C32×C4⋊C4C22semidirect
16. C2×C4⋊(C3⋊Dic3)C22semidirect
17. C2×#3750C22semidirect
21. C2×C3×Dic3⋊C4C22semidirect
22. C2×Dic3⋊Dic3C22semidirect
28. C3×C3⋊#95C22semidirect
29. #63579C22semidirect
37. #4993D3semidirect
84. C2×C3×C4⋊C4C2×D3semidirect
99. C2×Dic3⋊C4C2×D3semidirect
107. C3⋊#95C2×D3semidirect
238. C2×C4⋊C4D32semidirect
315. C3⋊D3#399semidirect
392. C32C2×#399semidirect
465. C3D3×#399semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#639212
C2×#638832
C3×#49932
#105913702
#105913172
#105913032
D3×#3993