Finite Group Databasebeta

← #11805536

Subgroups — #11805536

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63902C211yesmaximal, characteristic
2C2×#63879C212yesmaximal
3#10592349C211yesmaximal, characteristic, complemented
4C3×#4668C212yesmaximal, complemented
5#10591377C212yesmaximal, complemented
6#10591366C212yesmaximal, complemented
7D3×C3⋊#95C212yesmaximal, complemented
8#10591274C211yesmaximal, characteristic, complemented
9#10591256C212yesmaximal, complemented
10#74394—32nomaximal
11C22×C3×C4×D3C2212yes—
12C22×#625C2211yescharacteristic
13C22×D3×Dic3C2212yes—
14C22×D3×Dic3C2212yes—
15C2×#3750C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×Dic32C2212yes—
25#63902C418yescomplemented
26#63879—28no—
27C32×#95C2211yescharacteristic
28#63658C2212yes—
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2211yescharacteristic
33#63579C2211yescharacteristic
34C2×C4×#67—32no—
35C2×#67⋊C4—32no—
36C2×#67⋊C4—32no—
37C3×#385—32no—
38C2×C3⋊#95—32no—
39#4989—32no—
40#4987—32no—
41#4976—32no—
42Dic3×C4⋊C4—32no—
43#4950—32no—
44#4942—32no—
45#4668D312yescomplemented
46D3×#95—32no—
47#4650—32no—
48#4650—61no—
49#4647—32no—
50C23×C3×D3C2312yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3—24no—
61C2×C3×C4×D3—42no—
62C2×#625C2×C414yes—
63C2×#625D414yes—
64C2×#625Q814yes—
65C2×D3×Dic3—24no—
66C2×D3×Dic3—24no—
67C2×D3×Dic3—42no—
68C2×D3×Dic3—42no—
69C2×D3×Dic3—42no—
70C2×D3×Dic3C2×C418yescomplemented
71#3750—24no—
72C4×C3⋊Dic3C2×C414yescomplemented
73C3×(C2×D3)⋊C4—24no—
74C3×(C2×D3)⋊C4C2×C418yescomplemented
75C3×C4⋊Dic3—24no—
76C3×Dic3⋊C4—42no—
77#3724C2×C414yescomplemented
78Dic3⋊Dic3—42no—
79(C2×D3)⋊Dic3—24no—
80Dic32—24no—
81#2349—91noSylow
82C23×C3×C4—32no—
83C22×#67—32no—
84C23×Dic3—32no—
85C23×Dic3—32no—
86C22×C4×D3—32no—
87C22×C4×D3—32no—
88C22×C4×D3C2×D312yes—
89C2×C3×C4⋊C4—32no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C22⋊C4—32no—
92C2×C3×C22⋊C4—32no—
93C2×#217—32no—
94C4×#67—68no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4C2×D312yes—
97C2×(C2×D3)⋊C4C2×D312yes—
98C2×C4⋊Dic3—32no—
99C2×C4⋊Dic3C2×D312yes—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—62no—
105C2×Dic3⋊C4C2×D312yes—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—61no—
110#67⋊C4—316no—
111#67⋊C4—68no—
112C3×#95—21no—
113C3×#95—32no—
114C3×#95C2×D312yes—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—62no—
123C3⋊#95—61no—
124C3⋊#95C2×D312yes—
125C23×C32C2411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3C22×C414yes—
131C22×C3×D3C2×D414yes—
132C22×C3×D3C2×Q814yes—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4C22×C412yes—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C2×D412yes—
145C2×C3⋊Dic3C2×Q812yes—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C22×C414yes—
154C2×C3×Dic3#4114yes—
155C3×C4×D3—48no—
156#625C4⋊C4116yescomplemented
157D3×Dic3—48no—
158D3×Dic3—48no—
159C2×C4×D4—91no—
160C2×C4×D4—92no—
161#389—92no—
162#385—32no—
163#385—92no—
164#382—91no—
165#380—92no—
166C4×C4⋊C4—91no—
167C2×#95—92no—
168C24×C3—32no—
169C23×D3C22×D312yes—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—64no—
176C22×C3×C4—64no—
177C22×C3×C4—122no—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C2×#67—38no—
182C2×#67—38no—
183C2×#67—38no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—38no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—62no—
192C22×Dic3—64no—
193C22×Dic3—64no—
194C22×Dic3—122no—
195C22×Dic3—122no—
196C22×Dic3—122no—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C2×C4×D3—24no—
201C2×C4×D3—24no—
202C2×C4×D3—38no—
203C2×C4×D3—42no—
204C2×C4×D3—64no—
205C2×C4×D3—64no—
206C2×C4×D3—122no—
207C2×C4×D3—122no—
208C2×C4×D3—122no—
209C3×C4⋊C4—64no—
210C3×C4⋊C4—122no—
211C3×C22⋊C4—38no—
212C3×C22⋊C4—64no—
213#217—64no—
214(C2×D3)⋊C4—24no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4C4×D318yescomplemented
217C4⋊Dic3—24no—
218C4⋊Dic3—122no—
219Dic3⋊C4—38no—
220Dic3⋊C4—42no—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223Dic3⋊C4—124no—
224Dic3⋊C4—122no—
225C4×Dic3—38no—
226C4×Dic3—64no—
227C4×Dic3—64no—
228C4×Dic3—64no—
229C22×C32C23×C411yescharacteristic
230C22×C32C22×D411yescharacteristic
231C22×C32C22×Q811yescharacteristic
232C22×C32C2×#4112yes—
233C22×C32H(5,𝔽2)12yes—
234C2×C3×D3—24no—
235C2×C3×D3—24no—
236C2×C3×D3—24no—
237C2×C3×D3—24no—
238C2×C3×D3—24no—
239C2×C3×D3—24no—
240C2×C3×D3C2×C4⋊C418yes—
241C32×C4—22no—
242C32×C4—42no—
243C3⋊Dic3—22no—
244C3⋊Dic3—42no—
245C3⋊Dic3C2×C4⋊C414yes—
246C3×Dic3—24no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C22×D4—91no—
250C23×C4—32no—
251C23×C4—92no—
252C23×C4—92no—
253C4×D4—98no—
254C4×D4—188no—
255C2×C4⋊C4—32no—
256C2×C4⋊C4—32no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—92no—
260C2×C22⋊C4—32no—
261C2×C22⋊C4—32no—
262C2×C22⋊C4—92no—
263C2×C42—91no—
264C2×C42—92no—
265#95—32no—
266#95—91no—
267#95—92no—
268#95—91no—
269#95—92no—
270#95—91no—
271#95D3211yescharacteristic
272C23×C3—21no—
273C23×C3—34no—
274C23×C3—34no—
275C23×C3—34no—
276C23×C3—62no—
277C23×C3—62no—
278C23×C3—62no—
279C23×C3—62no—
280C23×C3C23×D312yes—
281C22×D3—22no—
282C22×D3—22no—
283C22×D3—22no—
284C22×D3—22no—
285C22×D3C2×C4×D314yes—
286C22×D3D3×D414yes—
287C22×D3D3×Q814yes—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—34no—
298C2×C3×C4—34no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—128no—
311C2×C3×C4C2×C4×D314yes—
312#67—332no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—22no—
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—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337C2×Dic3—122no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—128no—
341C2×Dic3—128no—
342C2×Dic3C2×C4×D314yes—
343C2×Dic3#23714yes—
344C4×D3—48no—
345C4×D3—128no—
346C4×D3—128no—
347C2×C32C22×C4⋊C411yescharacteristic
348C2×C32C4×#4111yescharacteristic
349C2×C32#51811yescharacteristic
350C2×C32#54612yes—
351C2×C32#55412yes—
352C3×D3—28no—
353C24—32no—
354C2×D4—94no—
355C2×D4—94no—
356C2×D4—94no—
357C22×C4—32no—
358C22×C4—32no—
359C22×C4—32no—
360C22×C4—64no—
361C22×C4—64no—
362C22×C4—98no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—92no—
366C22×C4—122no—
367C22×C4—184no—
368C22×C4—184no—
369C22×C4—362no—
370C22×C4—362no—
371C22×C4—362no—
372C22×C4C2×D3212yes—
373C22×C4C2×D3211yescharacteristic
374C4⋊C4—64no—
375C4⋊C4—94no—
376C4⋊C4—122no—
377C4⋊C4—184no—
378C4⋊C4—362no—
379C22⋊C4—38no—
380C22⋊C4—64no—
381C22⋊C4—184no—
382C42—94no—
383C42—184no—
384C22×C3—21no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—38no—
390C22×C3—64no—
391C22×C3—64no—
392C22×C3—64no—
393C22×C3—64no—
394C22×C3—64no—
395C22×C3—64no—
396C22×C3C22×C4×D312yes—
397C22×C3C2×D3×D412yes—
398C22×C3C2×#23712yes—
399C22×C3#100412yes—
400C22×C3C2×D3×Q812yes—
401C22×C3D3×#4112yes—
402C22×C3#100912yes—
403C2×D3—24no—
404C2×D3—24no—
405C2×D3—24no—
406C2×D3—24no—
407C2×D3—24no—
408C2×D3—24no—
409C2×D3D3×C4⋊C418yes—
410C3×C4—24no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—64no—
415C3×C4—64no—
416C3×C4—82no—
417C3×C4—122no—
418Dic3—24no—
419Dic3—24no—
420Dic3—38no—
421Dic3—42no—
422Dic3—64no—
423Dic3—64no—
424Dic3—122no—
425Dic3—122no—
426Dic3—122no—
427Dic3—242no—
428C32#234911yescharacteristic, complemented, Sylow
429C23—34no—
430C23—34no—
431C23—34no—
432C23—62no—
433C23—62no—
434C23—62no—
435C23—62no—
436C23C22×D3211yescharacteristic
437D4—916no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—34no—
443C2×C4—34no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—92no—
454C2×C4—92no—
455C2×C4—128no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—368no—
461C2×C4—368no—
462C2×C4C4×D3212yes—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—22no—
467C2×C3—22no—
468C2×C3—68no—
469C2×C3C2×D3×C4⋊C412yes—
470C2×C3C4×#23712yes—
471C2×C3#554512yes—
472C2×C3#559112yes—
473C2×C3#563512yes—
474C2×C3#563612yes—
475C2×C3#565412yes—
476D3—28no—
477C22—38no—
478C22—64no—
479C22—64no—
480C22—64no—
481C22—64no—
482C22—64no—
483C22—64no—
484C22C2×C4×D3211yescharacteristic
485C22#6430712yes—
486C22D32×D411yescharacteristic
487C22D3×#23712yes—
488C22D32×Q811yescharacteristic
489C4—22no—
490C4—42no—
491C4—64no—
492C4—64no—
493C4—94no—
494C4—122no—
495C4—182no—
496C4—362no—
497C3—21no—
498C3#7439412yescomplemented
499C2—68no—
500C2#1059399611yescharacteristic
501C2#1059405011yescharacteristic
502C2#1059427412yes—
503C2#1059453512yes—
504C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #10592349C2semidirect
4. C3×#4668C2semidirect
5. #10591377C2semidirect
6. #10591366C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591274C2semidirect
9. #10591256C2semidirect
25. #63902C4semidirect
45. #4668D3semidirect
70. C2×D3×Dic3C2×C4semidirect
72. C4×C3⋊Dic3C2×C4semidirect
74. C3×(C2×D3)⋊C4C2×C4semidirect
77. #3724C2×C4semidirect
156. #625C4⋊C4semidirect
216. (C2×D3)⋊C4C4×D3semidirect
428. C32#2349semidirect
498. C3#74394semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
C2×#638792
#105923492
C3×#46682
#105913772
#105913662
D3×C3⋊#952
#105912742
#105912562
#743943