Finite Group Databasebeta

← #11802780

Subgroups — #11802780

Order 1152.

1597 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#217C211yesmaximal, characteristic
2#10592946C211yesmaximal, characteristic
3C3×#5247C211yesmaximal, characteristic
4#10591716C212yesmaximal, complemented
5#10591702C214yesmaximal, complemented
6#10591701C214yesmaximal, complemented
7Dic3×#217C212yesmaximal, complemented
8#82093—31nomaximal
9#73820—31nomaximal
10C25×C32C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2211yescharacteristic
13C2×#3757C2212yes—
14C2×#3757C2212yes—
15C2×#3757C2212yes—
16C2×C3×#217C418yescomplemented
17C2×C3×#217C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×Dic3⋊Dic3C2214yescomplemented
23C2×Dic32C2214yescomplemented
24#63579C2214yescomplemented
25#63579C2214yescomplemented
26C22×C3×C22⋊C4—31no—
27C22×#217D311yescharacteristic
28C3×#379—31no—
29#5247—31no—
30#5247—31no—
31#5247—61no—
32#5247D311yescharacteristic
33#5212—32no—
34C4×#217—32no—
35#4951—34no—
36#4951—34no—
37#4945—34no—
38#4944—34no—
39#4942—32no—
40Dic3×C22⋊C4—32no—
41C24×C32—24no—
42C24×C32—42no—
43C24×C32—42no—
44C24×C32C2×C414yes—
45C24×C32C2311yescharacteristic
46C24×C32C2311yescharacteristic
47C24×C32C2311yescharacteristic
48C22×C3⋊Dic3C2314yes—
49C22×C3×Dic3—42no—
50C22×C3×Dic3—42no—
51C22×C3×Dic3C2×C414yes—
52C22×C3×Dic3C2×C414yes—
53C22×C3×Dic3C2314yes—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56#3757—24no—
57#3757—42no—
58#3757—42no—
59C3×#217—24no—
60C3×#217—42no—
61C3×#217—42no—
62C3×#217C2×C418yes—
63C3×#217C2×C418yes—
64Dic3⋊Dic3—44no—
65Dic32—44no—
66#2312—91noSylow
67C25×C3—21no—
68C25×C3C2×D311yescharacteristic
69C25×C3C2×D311yescharacteristic
70C23×C3×C4—31no—
71C23×C3×C4—31no—
72C23×Dic3C2×D311yescharacteristic
73C23×Dic3C2×D311yescharacteristic
74C2×C3×C22⋊C4—38no—
75C2×C3×C22⋊C4—32no—
76C2×C3×C22⋊C4—32no—
77C2×C3×C22⋊C4—32no—
78C2×C3×C22⋊C4—32no—
79C2×C3×C22⋊C4—32no—
80C2×#217—32no—
81C2×#217—32no—
82C2×#217—32no—
83C2×#217—32no—
84C2×#217—32no—
85C2×#217—32no—
86C2×#217—62no—
87C2×#217—62no—
88C2×#217—62no—
89C2×#217Dic318yescomplemented
90C2×#217C2×D312yes—
91C2×#217C2×D312yes—
92C2×#217C2×D312yes—
93C2×#217C2×D312yes—
94C2×#217C2×D312yes—
95C2×C4⋊Dic3—34no—
96C2×Dic3⋊C4—34no—
97C2×C4×Dic3—34no—
98C2×C4×Dic3—34no—
99C3⋊#95—34no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C23×C32—22no—
104C23×C32—22no—
105C23×C32—22no—
106C23×C32—22no—
107C23×C32—28no—
108C23×C32—22no—
109C23×C32—22no—
110C23×C32—22no—
111C23×C32—22no—
112C23×C32—44no—
113C23×C32—44no—
114C23×C32—416no—
115C23×C32C22×C412yes—
116C23×C32C22×C412yes—
117C23×C32C22×C412yes—
118C23×C32#4114yes—
119C23×C32C2411yescharacteristic
120C2×C3⋊Dic3—24no—
121C2×C3⋊Dic3—24no—
122C2×C3⋊Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—44no—
129C2×C3×Dic3—44no—
130C2×C3×Dic3C22×C414yes—
131C2×C3×Dic3C22×C414yes—
132C22×C22⋊C4—31no—
133#388—94no—
134#388—94no—
135#380—92no—
136#379—31no—
137#379—91no—
138C4×C22⋊C4—92no—
139C24×C3—24no—
140C24×C3—24no—
141C24×C3—24no—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—21no—
145C24×C3—44no—
146C24×C3—42no—
147C24×C3—42no—
148C24×C3—42no—
149C24×C3—42no—
150C24×C3—44no—
151C24×C3—44no—
152C24×C3C4×D314yes—
153C24×C3C2×Dic314yes—
154C24×C3C22×D311yescharacteristic
155C24×C3C22×D311yescharacteristic
156C24×C3C22×D311yescharacteristic
157C24×C3C22×D311yescharacteristic
158C24×C3C22×D311yescharacteristic
159C24×C3C22×D311yescharacteristic
160C22×C3×C4—32no—
161C22×C3×C4—32no—
162C22×C3×C4—34no—
163C22×C3×C4—34no—
164C22×C3×C4—34no—
165C22×C3×C4—122no—
166C22×C3×C4—122no—
167C22×Dic3—34no—
168C22×Dic3—34no—
169C22×Dic3—42no—
170C22×Dic3—42no—
171C22×Dic3—64no—
172C22×Dic3C2×Dic314yes—
173C22×Dic3C2×Dic314yes—
174C22×Dic3C22×D314yes—
175C22×Dic3C22×D312yes—
176C22×Dic3C22×D312yes—
177C3×C22⋊C4—38no—
178C3×C22⋊C4—38no—
179C3×C22⋊C4—64no—
180C3×C22⋊C4—122no—
181C3×C22⋊C4—122no—
182#217—24no—
183#217—42no—
184#217—42no—
185#217—64no—
186#217—64no—
187#217—124no—
188#217—122no—
189#217—122no—
190#217—122no—
191#217—122no—
192#217—124no—
193#217—124no—
194#217C2×Dic318yes—
195#217C2×Dic318yes—
196C4⋊Dic3—124no—
197Dic3⋊C4—124no—
198C4×Dic3—124no—
199C4×Dic3—124no—
200C22×C32—22no—
201C22×C32—22no—
202C22×C32—22no—
203C22×C32—22no—
204C22×C32—28no—
205C22×C32—22no—
206C22×C32—22no—
207C22×C32—22no—
208C22×C32—22no—
209C22×C32—416no—
210C22×C32—44no—
211C22×C32—44no—
212C22×C32#11714yes—
213C22×C32C23×C411yescharacteristic
214C22×C32C2×#4112yes—
215C22×C32H(5,𝔽2)12yes—
216C22×C32H(5,𝔽2)12yes—
217C3⋊Dic3—44no—
218C3×Dic3—24no—
219C3×Dic3—24no—
220C3×Dic3—44no—
221C25D3211yescharacteristic
222C23×C4—31no—
223C23×C4—31no—
224C2×C4⋊C4—94no—
225C2×C22⋊C4—38no—
226C2×C22⋊C4—32no—
227C2×C22⋊C4—32no—
228C2×C22⋊C4—32no—
229C2×C22⋊C4—32no—
230C2×C22⋊C4—32no—
231C2×C22⋊C4—92no—
232C2×C22⋊C4—92no—
233C2×C22⋊C4—92no—
234C2×C42—94no—
235#95—94no—
236#95—94no—
237C23×C3—22no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—22no—
241C23×C3—24no—
242C23×C3—24no—
243C23×C3—28no—
244C23×C3—28no—
245C23×C3—22no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3—22no—
253C23×C3—22no—
254C23×C3—22no—
255C23×C3—22no—
256C23×C3—22no—
257C23×C3—21no—
258C23×C3—22no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—24no—
262C23×C3—42no—
263C23×C3—42no—
264C23×C3—42no—
265C23×C3—42no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—48no—
269C23×C3—44no—
270C23×C3—44no—
271C23×C3—44no—
272C23×C3—44no—
273C23×C3—48no—
274C23×C3—48no—
275C23×C3—416no—
276C23×C3—416no—
277C23×C3—432no—
278C23×C3C2×C4×D312yes—
279C23×C3C2×C4×D312yes—
280C23×C3C2×C4×D312yes—
281C23×C3#23514yes—
282C23×C3#23714yes—
283C23×C3C22×Dic312yes—
284C23×C3C22×Dic312yes—
285C23×C3C22×Dic312yes—
286C23×C3C23×D311yescharacteristic
287C23×C3C23×D311yescharacteristic
288C2×C3×C4—34no—
289C2×C3×C4—34no—
290C2×C3×C4—64no—
291C2×C3×C4—64no—
292C2×C3×C4—64no—
293C2×C3×C4—64no—
294C2×C3×C4—64no—
295C2×C3×C4—124no—
296C2×C3×C4—124no—
297C2×Dic3—24no—
298C2×Dic3—24no—
299C2×Dic3—24no—
300C2×Dic3—24no—
301C2×Dic3—24no—
302C2×Dic3—44no—
303C2×Dic3—44no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—64no—
310C2×Dic3—124no—
311C2×Dic3—124no—
312C2×Dic3—124no—
313C2×Dic3C22×Dic314yes—
314C2×Dic3C22×Dic314yes—
315C2×C32—24no—
316C2×C32—42no—
317C2×C32—42no—
318C2×C32C2×#11711yescharacteristic
319C2×C32#51811yescharacteristic
320C2×C32#51811yescharacteristic
321C2×C32#53814yes—
322C24—24no—
323C24—42no—
324C24—42no—
325C24D3×Dic314yes—
326C24C2×D3211yescharacteristic
327C24C2×D3211yescharacteristic
328C24C2×D3211yescharacteristic
329C22×C4—32no—
330C22×C4—32no—
331C22×C4—34no—
332C22×C4—34no—
333C22×C4—34no—
334C22×C4—94no—
335C22×C4—122no—
336C22×C4—122no—
337C4⋊C4—364no—
338C22⋊C4—38no—
339C22⋊C4—38no—
340C22⋊C4—64no—
341C22⋊C4—122no—
342C22⋊C4—122no—
343C22⋊C4—184no—
344C22⋊C4—362no—
345C22⋊C4—362no—
346C42—364no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—28no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—28no—
353C22×C3—24no—
354C22×C3—24no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—24no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—48no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—416no—
380C22×C3—416no—
381C22×C3—48no—
382C22×C3—48no—
383C22×C3—432no—
384C22×C3—44no—
385C22×C3—44no—
386C22×C3—44no—
387C22×C3—44no—
388C22×C3#87714yes—
389C22×C3#92614yes—
390C22×C3C22×C4×D311yescharacteristic
391C22×C3C2×#23512yes—
392C22×C3C2×#23712yes—
393C22×C3#100412yes—
394C22×C3#100412yes—
395C22×C3#100412yes—
396C22×C3#100412yes—
397C22×C3C23×Dic311yescharacteristic
398C3×C4—64no—
399C3×C4—64no—
400C3×C4—124no—
401Dic3—24no—
402Dic3—24no—
403Dic3—44no—
404Dic3—124no—
405Dic3—124no—
406Dic3—244no—
407C32#231211yescharacteristic, complemented, Sylow
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—28no—
417C23—44no—
418C23—44no—
419C23—416no—
420C23C2×D3×Dic312yes—
421C23C2×D3×Dic312yes—
422C23C2×D3×Dic312yes—
423C23#380414yes—
424C23C22×D3211yescharacteristic
425C2×C4—34no—
426C2×C4—34no—
427C2×C4—64no—
428C2×C4—64no—
429C2×C4—64no—
430C2×C4—64no—
431C2×C4—64no—
432C2×C4—124no—
433C2×C4—124no—
434C2×C4—184no—
435C2×C4—184no—
436C2×C4—184no—
437C2×C3—24no—
438C2×C3—24no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—24no—
443C2×C3—44no—
444C2×C3—44no—
445C2×C3—44no—
446C2×C3—42no—
447C2×C3—42no—
448C2×C3—42no—
449C2×C3—42no—
450C2×C3C2×#87711yescharacteristic
451C2×C3#548611yescharacteristic
452C2×C3#548611yescharacteristic
453C2×C3#549414yes—
454C2×C3#559314yes—
455C2×C3C2×#92611yescharacteristic
456C2×C3#579811yescharacteristic
457C2×C3#579811yescharacteristic
458C22—22no—
459C22—22no—
460C22—28no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—416no—
468C22—44no—
469C22—44no—
470C22#6395514yes—
471C22C22×D3×Dic311yescharacteristic
472C22C2×#380412yes—
473C22#6433012yes—
474C22#6433012yes—
475C4—64no—
476C4—64no—
477C4—124no—
478C4—364no—
479C3—21no—
480C3#7382011yescharacteristic, complemented
481C3#8209311yescharacteristic, complemented
482C2—24no—
483C2—42no—
484C2—42no—
485C2C2×#6395511yescharacteristic
486C2#1059550611yescharacteristic
487C2#1059550611yescharacteristic
488C2#1059550714yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC25×C32C22
socle, cosocleC23×C32C24
hypercenterC25D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
4. #10591716C2semidirect
5. #10591702C2semidirect
6. #10591701C2semidirect
7. Dic3×#217C2semidirect
16. C2×C3×#217C4semidirect
22. C2×Dic3⋊Dic3C22semidirect
23. C2×Dic32C22semidirect
24. #63579C22semidirect
25. #63579C22semidirect
89. C2×#217Dic3semidirect
407. C32#2312semidirect
480. C3#73820semidirect
481. C3#82093semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2172
#105929462
C3×#52472
#105917162
#105917022
#105917012
Dic3×#2172
#820933
#738203