Finite Group Databasebeta

← #11802883

Subgroups — #11802883

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C3×#4980C212yesmaximal, complemented
3#10591360C211yesmaximal, characteristic, complemented
4#10591359C211yesmaximal, characteristic, complemented
5#10591355C211yesmaximal, characteristic
6#10591355C211yesmaximal, characteristic
7C4×#3724C211yesmaximal, characteristic, complemented
8#10591271C212yesmaximal, complemented
9#10591266C212yesmaximal
10#10591257C211yesmaximal, characteristic, complemented
11#10591202C212yesmaximal
12#74944—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752C2211yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64101C418yescomplemented
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×#3724C2211yescharacteristic
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×#3724C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C2×Dic32C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#892—32no—
38C2×#892—61no—
39C3×#387—32no—
40#4990—32no—
41#4980D312yescomplemented
42#4975—32no—
43#4940—32no—
44C4×Dic3⋊C4—32no—
45#4670—32no—
46#4669—32no—
47#4667—32no—
48#4667—32no—
49#4654—32no—
50#4653—32no—
51#4650—32no—
52#4649—32no—
53C23×C3⋊D3C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3C2×C414yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C32×C4⋊C4C2×C414yes—
68#3752C2×C414yes—
69#3752C2×C414yes—
70C4⋊(C3⋊Dic3)C2×C414yes—
71C4×C3⋊Dic3C2×C414yes—
72C4×C3⋊Dic3C2×C414yes—
73C3×C4⋊Dic3—42no—
74C3×C4×Dic3—42no—
75#3724—22no—
76#3724—22no—
77#3724—22no—
78#3724—22no—
79#3724—42no—
80#3722—42no—
81#3722—42no—
82Dic32—42no—
83#2314—91noSylow
84C22×C4×D3—32no—
85C22×C4×D3—61no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—32no—
88C2×C3×C4⋊C4C2×D312yes—
89C2×C3×C42—32no—
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4—32no—
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—32no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D312yes—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—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#892—316no—
115#892—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⋊#95C2×D312yes—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C23×C32C2411yescharacteristic
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—21no—
133C22×C3⋊D3—21no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3C22×C412yes—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C22×C412yes—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3C22×C412yes—
150C2×C3⋊Dic3C22×C412yes—
151C2×C3⋊Dic3C22×C412yes—
152C2×C3⋊Dic3#4112yes—
153C2×C3⋊Dic3#4112yes—
154C4×C3⋊D3—28no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×#117—91no—
168#388—92no—
169#388—92no—
170#387—32no—
171#387—92no—
172#384—91no—
173#382—91no—
174#380—91no—
175#380—91no—
176C4×C4⋊C4—91no—
177C4×C4⋊C4—91no—
178C23×D3—32no—
179C23×D3—61no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D312yes—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C2×C4×D3—38no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—64no—
205C2×C4×D3—64no—
206C3×C4⋊C4—24no—
207C3×C4⋊C4—122no—
208C3×C4⋊C4C4×D318yes—
209C3×C42—122no—
210(C2×D3)⋊C4—38no—
211(C2×D3)⋊C4—38no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—122no—
215(C2×D3)⋊C4—122no—
216(C2×D3)⋊C4—122no—
217(C2×D3)⋊C4—122no—
218C4⋊Dic3—38no—
219C4⋊Dic3—42no—
220C4⋊Dic3—64no—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223Dic3⋊C4—64no—
224Dic3⋊C4—64no—
225Dic3⋊C4—122no—
226Dic3⋊C4—122no—
227C4×Dic3—38no—
228C4×Dic3—38no—
229C4×Dic3—42no—
230C4×Dic3—64no—
231C4×Dic3—64no—
232C4×Dic3—122no—
233C4×Dic3—122no—
234C22×C32C23×C411yescharacteristic
235C22×C32C2×#4111yescharacteristic
236C22×C32C2×#4111yescharacteristic
237C22×C32H(5,𝔽2)11yescharacteristic
238C22×C32H(5,𝔽2)11yescharacteristic
239C22×C322−1+411yescharacteristic
240C22×C322−1+411yescharacteristic
241C2×C3⋊D3—22no—
242C2×C3⋊D3—22no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—41no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C32×C4—22no—
249C32×C4—22no—
250C32×C4—22no—
251C3⋊Dic3—22no—
252C3⋊Dic3—22no—
253C3⋊Dic3#11714yes—
254C3×Dic3—42no—
255C3×Dic3—42no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C23×C4—91no—
259#117—98no—
260C2×C4⋊C4—32no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—91no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—92no—
267C2×C4⋊C4D3211yescharacteristic
268C2×C22⋊C4—91no—
269C2×C22⋊C4—91no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4—92no—
272C2×C42—32no—
273C2×C42—91no—
274C2×C42—91no—
275C2×C42—92no—
276#95—32no—
277#95—32no—
278#95—32no—
279#95—32no—
280#95—92no—
281#95—92no—
282C23×C3—21no—
283C23×C3C23×D312yes—
284C22×D3—34no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—121no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4C2×C4×D314yes—
326C2×C3×C4C2×C4×D314yes—
327C2×C3×C4C2×C4×D314yes—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—34no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C4×D3—616no—
359C4×D3—616no—
360C2×C32C2×#11711yescharacteristic
361C2×C32#52011yescharacteristic
362C2×C32#52011yescharacteristic
363C2×C32#54011yescharacteristic
364C2×C32#54111yescharacteristic
365C2×C32#54211yescharacteristic
366C2×C32#54211yescharacteristic
367C3⋊D3—42no—
368C24—91no—
369C22×C4—32no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—32no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—94no—
377C22×C4—182no—
378C22×C4—182no—
379C22×C4C2×D3211yescharacteristic
380C22×C4C2×D3211yescharacteristic
381C22×C4C2×D3211yescharacteristic
382C4⋊C4—94no—
383C4⋊C4—122no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C4⋊C4—182no—
387C4⋊C4—182no—
388C4⋊C4—362no—
389C4⋊C4#62414yes—
390C22⋊C4—94no—
391C22⋊C4—94no—
392C22⋊C4—362no—
393C22⋊C4—362no—
394C42—94no—
395C42—94no—
396C42—122no—
397C42—362no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3C22×C4×D312yes—
406C22×C3#100412yes—
407C22×C3#100712yes—
408C22×C3D3×#4112yes—
409C22×C3D3×#4112yes—
410C22×C3#100912yes—
411C22×C3#101012yes—
412C2×D3—64no—
413C2×D3—64no—
414C2×D3—64no—
415C2×D3—64no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—122no—
426C3×C4—24no—
427C3×C4—24no—
428C3×C4—24no—
429C3×C4—24no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—122no—
433C3×C4—122no—
434C3×C4—122no—
435C3×C4—122no—
436Dic3—38no—
437Dic3—42no—
438Dic3—42no—
439Dic3—42no—
440Dic3—42no—
441Dic3—64no—
442Dic3—64no—
443Dic3—64no—
444Dic3—122no—
445Dic3—122no—
446C32#231411yescharacteristic, complemented, Sylow
447C23—92no—
448C23—181no—
449C23—181no—
450C23—181no—
451C23—181no—
452C23—181no—
453C23—181no—
454C23C22×D3211yescharacteristic
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—92no—
474C2×C4—92no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—188no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4C2×#62412yes—
484C2×C4C2×#62412yes—
485C2×C4C2×#62412yes—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3D3×#11712yes—
494C2×C3#554612yes—
495C2×C3#557412yes—
496C2×C3#564012yes—
497C2×C3#566312yes—
498C2×C3#569612yes—
499C2×C3#571012yes—
500D3—124no—
501D3—124no—
502C22—182no—
503C22—182no—
504C22—182no—
505C22—361no—
506C22—361no—
507C22—361no—
508C22—361no—
509C22#6430611yescharacteristic
510C22#6430611yescharacteristic
511C22#6430911yescharacteristic
512C22#6431311yescharacteristic
513C22#6431611yescharacteristic
514C22#6432011yescharacteristic
515C22C22×#62411yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—94no—
520C4—122no—
521C4—122no—
522C4—122no—
523C4—122no—
524C4—182no—
525C4—182no—
526C3—21no—
527C3#7494412yescomplemented
528C2—362no—
529C2#1059456811yescharacteristic
530C2#1059456911yescharacteristic
531C2#1059457111yescharacteristic
532C2#1059459911yescharacteristic
533C2#1059496911yescharacteristic
534C2#1059521911yescharacteristic
535C2#1059535311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2314
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4980C2semidirect
3. #10591360C2semidirect
4. #10591359C2semidirect
7. C4×#3724C2semidirect
8. #10591271C2semidirect
10. #10591257C2semidirect
20. #64101C4semidirect
41. #4980D3semidirect
446. C32#2314semidirect
527. C3#74944semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C3×#49802
#105913602
#105913592
#105913552
C4×#37242
#105912712
#105912662
#105912572
#105912022
#749443