Finite Group Databasebeta

← #11801954

Subgroups — #11801954

Order 1152.

1213 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C3×#4951C212yesmaximal
3#10591705C211yesmaximal, characteristic
4#10591705C211yesmaximal, characteristic
5#10591703C212yesmaximal
6#10591274C211yesmaximal, characteristic, complemented
7#10591263C212yesmaximal, complemented
8#10591257C211yesmaximal, characteristic, complemented
9#10591252C211yesmaximal, characteristic, complemented
10C4×Dic32C211yesmaximal, characteristic, complemented
11#10591197C212yesmaximal, complemented
12#75451—32nomaximal
13C23×C3⋊Dic3C2211yescharacteristic
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64086C418yescomplemented
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×#3724C2212yes—
26C2×Dic32C2211yescharacteristic
27C2×Dic32C2212yes—
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30C2×Dic32C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#877—32no—
38C2×#877—61no—
39C3×#388—32no—
40#4978—32no—
41Dic3×C4⋊C4—32no—
42#4951D312yes—
43#4945—32no—
44#4944—32no—
45Dic3×C22⋊C4—32no—
46Dic3×C22⋊C4—32no—
47#4933—32no—
48C42×Dic3—32no—
49#4655—32no—
50#4652—32no—
51#4649—32no—
52#4648—32no—
53C24×C32C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—22no—
57C22×C3⋊Dic3—22no—
58C22×C3⋊Dic3C2×C414yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C32×C22⋊C4C2×C414yes—
68#3757C2×C414yes—
69#3750C2×C414yes—
70#3750C2×C414yes—
71C4×C3⋊Dic3C2×C414yes—
72C4×C3⋊Dic3C2×C414yes—
73C3×#217—24no—
74C3×#217—24no—
75C3×C4⋊Dic3—24no—
76C3×C4×Dic3—24no—
77#3724—24no—
78Dic32—22no—
79Dic32—22no—
80Dic32—22no—
81Dic32—22no—
82Dic32—24no—
83#2298—91noSylow
84C23×Dic3—32no—
85C23×Dic3—61no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C22⋊C4—21no—
88C2×C3×C22⋊C4—32no—
89C2×C3×C22⋊C4—32no—
90C2×C3×C22⋊C4C2×D312yes—
91C2×C3×C42—32no—
92C2×#217—32no—
93C2×#217—61no—
94C2×#217C2×D312yes—
95C2×#217C2×D312yes—
96C2×C4⋊Dic3C2×D312yes—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—32no—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—61no—
113C2×C4×Dic3C2×D312yes—
114#877—316no—
115#877—68no—
116C3×#95—32no—
117C3×#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C23×C32—21no—
129C23×C32—21no—
130C23×C32—22no—
131C23×C32—22no—
132C23×C32C22×C412yes—
133C23×C32C2411yescharacteristic
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4C22×C412yes—
137C2×C32×C4C22×C412yes—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—28no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C22×C412yes—
145C2×C3⋊Dic3C22×C412yes—
146C2×C3⋊Dic3C22×C412yes—
147C2×C3⋊Dic3#4112yes—
148C2×C3⋊Dic3#4112yes—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3#4114yes—
160C2×C3×Dic3#4114yes—
161C2×#117—91no—
162#388—32no—
163#388—92no—
164#387—92no—
165#387—92no—
166C4×C4⋊C4—91no—
167C4×C4⋊C4—91no—
168C4×C22⋊C4—91no—
169C4×C22⋊C4—91no—
170#376—91no—
171C43—91no—
172C24×C3—21no—
173C24×C3C22×D312yes—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4C22×D312yes—
181C22×C3×C4C22×D312yes—
182C22×Dic3—32no—
183C22×Dic3—38no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—32no—
187C22×Dic3—64no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—64no—
193C22×Dic3—64no—
194C22×Dic3—64no—
195C22×Dic3—64no—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C3×C4⋊C4—64no—
201C3×C22⋊C4—24no—
202C3×C22⋊C4—64no—
203C3×C22⋊C4—64no—
204C3×C22⋊C4C4×D318yes—
205C3×C42—64no—
206#217—24no—
207#217—24no—
208#217—38no—
209#217—64no—
210C4⋊Dic3—24no—
211Dic3⋊C4—38no—
212Dic3⋊C4—38no—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216Dic3⋊C4—64no—
217C4×Dic3—24no—
218C4×Dic3—38no—
219C4×Dic3—38no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C4×Dic3—64no—
225C4×Dic3—64no—
226C4×Dic3—64no—
227C4×Dic3—64no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—22no—
231C22×C32—42no—
232C22×C32—42no—
233C22×C32C23×C411yescharacteristic
234C22×C32C2×#4112yes—
235C22×C32C2×#4112yes—
236C22×C32C2×#4111yescharacteristic
237C22×C32C2×#4111yescharacteristic
238C32×C4—22no—
239C32×C4—22no—
240C3⋊Dic3—22no—
241C3⋊Dic3—22no—
242C3⋊Dic3—22no—
243C3⋊Dic3#11714yes—
244C3×Dic3—24no—
245C3×Dic3—24no—
246C3×Dic3—42no—
247C3×Dic3—42no—
248C23×C4—91no—
249#117—98no—
250C2×C4⋊C4—32no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—92no—
254C2×C22⋊C4—32no—
255C2×C22⋊C4—32no—
256C2×C22⋊C4—91no—
257C2×C22⋊C4D3211yescharacteristic
258C2×C42—32no—
259C2×C42—91no—
260C2×C42—91no—
261C2×C42—91no—
262C2×C42—91no—
263C2×C42—92no—
264C2×C42—91no—
265C2×C42—91no—
266#95—32no—
267#95—32no—
268#95—92no—
269#95—92no—
270#95—92no—
271#95—92no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—21no—
281C23×C3—22no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3C2×C4×D314yes—
285C23×C3C23×D312yes—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—34no—
293C2×C3×C4—34no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4C2×C4×D314yes—
307C2×C3×C4C2×C4×D314yes—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—34no—
319C2×Dic3—34no—
320C2×Dic3—34no—
321C2×Dic3—34no—
322C2×Dic3—34no—
323C2×Dic3—34no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—616no—
331C2×Dic3—616no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3#23714yes—
343C2×Dic3#23714yes—
344C2×C32—42no—
345C2×C32C2×#11711yescharacteristic
346C2×C32C4×#4111yescharacteristic
347C2×C32C4×#4111yescharacteristic
348C2×C32#52912yes—
349C2×C32#52912yes—
350C24C2×D3211yescharacteristic
351C22×C4—32no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—94no—
360C22×C4—182no—
361C22×C4—182no—
362C22×C4C2×D3211yescharacteristic
363C22×C4C2×D3211yescharacteristic
364C4⋊C4—64no—
365C4⋊C4—94no—
366C4⋊C4—94no—
367C4⋊C4—184no—
368C22⋊C4—64no—
369C22⋊C4—64no—
370C22⋊C4—94no—
371C22⋊C4#62414yes—
372C42—64no—
373C42—94no—
374C42—94no—
375C42—184no—
376C42—182no—
377C42—182no—
378C42—182no—
379C42—182no—
380C22×C3—24no—
381C22×C3—24no—
382C22×C3—24no—
383C22×C3—24no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—44no—
392C22×C3—44no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3C22×C4×D312yes—
398C22×C3C2×#23712yes—
399C22×C3C2×#23712yes—
400C22×C3D3×#4112yes—
401C22×C3D3×#4112yes—
402C22×C3D3×#4112yes—
403C22×C3D3×#4112yes—
404C3×C4—24no—
405C3×C4—24no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—64no—
409C3×C4—64no—
410C3×C4—122no—
411C3×C4—122no—
412Dic3—24no—
413Dic3—24no—
414Dic3—38no—
415Dic3—42no—
416Dic3—42no—
417Dic3—64no—
418Dic3—64no—
419Dic3—64no—
420Dic3—64no—
421Dic3—64no—
422Dic3—122no—
423Dic3—122no—
424C32#229811yescharacteristic, complemented, Sylow
425C23—21no—
426C23—21no—
427C23—22no—
428C23—22no—
429C23C2×#62412yes—
430C23C22×D3211yescharacteristic
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—34no—
434C2×C4—34no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—92no—
446C2×C4—92no—
447C2×C4—92no—
448C2×C4—92no—
449C2×C4—92no—
450C2×C4—92no—
451C2×C4—188no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4—182no—
455C2×C4—182no—
456C2×C4C2×#62412yes—
457C2×C4C2×#62412yes—
458C2×C3—22no—
459C2×C3—22no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—44no—
464C2×C3—44no—
465C2×C3D3×#11712yes—
466C2×C3C4×#23712yes—
467C2×C3C4×#23712yes—
468C2×C3#560012yes—
469C2×C3#564912yes—
470C2×C3#568012yes—
471C2×C3#570612yes—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—42no—
476C22—42no—
477C22#6430611yescharacteristic
478C22#6430611yescharacteristic
479C22D3×#23712yes—
480C22D3×#23712yes—
481C22C22×#62411yescharacteristic
482C4—22no—
483C4—22no—
484C4—64no—
485C4—64no—
486C4—94no—
487C4—122no—
488C4—122no—
489C4—182no—
490C4—182no—
491C4—182no—
492C3—21no—
493C3#7545112yescomplemented
494C2—42no—
495C2#1059411112yes—
496C2#1059411212yes—
497C2#1059496911yescharacteristic
498C2#1059519011yescharacteristic
499C2#1059519011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10591274C2semidirect
7. #10591263C2semidirect
8. #10591257C2semidirect
9. #10591252C2semidirect
10. C4×Dic32C2semidirect
11. #10591197C2semidirect
20. #64086C4semidirect
424. C32#2298semidirect
493. C3#75451semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C3×#49512
#105917052
#105917032
#105912742
#105912632
#105912572
#105912522
C4×Dic322
#105911972
#754513