Finite Group Databasebeta

← #11805376

Subgroups — #11805376

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic
3C3×#4651C211yesmaximal, characteristic, complemented
4C3×#4649C211yesmaximal, characteristic, complemented
5#10591260C211yesmaximal, characteristic
6#10591258C212yesmaximal
7#10591256C212yesmaximal, complemented
8#10591243C212yesmaximal, complemented
9#10591242C211yesmaximal, characteristic, complemented
10#10591223C211yesmaximal, characteristic, complemented
11#10591194C212yesmaximal
12#74263—31nomaximal
13#73635—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×#3752C2212yes—
16C2×#3750C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×#3724C2211yescharacteristic
22C2×#3724C2211yescharacteristic
23C2×Dic3⋊Dic3C2212yes—
24C2×#3722C2212yes—
25C2×#3722C2211yescharacteristic
26C2×#3722C2211yescharacteristic
27C2×Dic32C2212yes—
28C2×Dic32C2212yes—
29#63874C418yescomplemented
30C32×#95C2211yescharacteristic
31#63658C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×#872—31no—
39C2×#872—31no—
40C3×#383—31no—
41C3×C4×C4⋊C4—31no—
42#4990—32no—
43#4976—32no—
44#4940—32no—
45#4937—31no—
46C4×C4⋊Dic3—31no—
47C4×Dic3⋊C4—32no—
48#4670—32no—
49#4669—32no—
50#4667—31no—
51#4667—31no—
52#4667—61no—
53#4666—31no—
54#4666—31no—
55#4651—31no—
56#4651D311yescharacteristic, complemented
57#4649—31no—
58#4649—32no—
59#4649D311yescharacteristic, complemented
60#4647—32no—
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4×C3⋊D3—24no—
67C2×C4×C3⋊D3C2×C414yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74#3752—42no—
75#3750—24no—
76C3×Dic3⋊C4—24no—
77C3×C4×Dic3—42no—
78C3×C4×Dic3C2×C414yes—
79C3×C4×Dic3C2×C414yes—
80#3724C2×C414yes—
81#3724C2×C414yes—
82Dic3⋊Dic3—24no—
83#3722—24no—
84#3722C2×C414yes—
85#3722C2×C414yes—
86Dic32—24no—
87Dic32—42no—
88#2347—91noSylow
89C22×C4×D3—31no—
90C22×C4×D3—31no—
91C22×C4×D3—61no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C42—31no—
94C2×C3×C42—31no—
95C2×C3×C42—32no—
96C2×(C2×D3)⋊C4—31no—
97C2×(C2×D3)⋊C4—31no—
98C2×(C2×D3)⋊C4—31no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—62no—
105C2×C4⋊Dic3—32no—
106C2×Dic3⋊C4—31no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—62no—
114C2×Dic3⋊C4C2×D312yes—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3C2×D312yes—
120C2×C4×Dic3C2×D311yescharacteristic
121C2×C4×Dic3C2×D311yescharacteristic
122#872—38no—
123#872—38no—
124C3×#95—21no—
125C3×#95—32no—
126C3×#95—31no—
127C3×#95—32no—
128C3×#95—31no—
129C3×#95C2×D311yescharacteristic
130C3×#95C2×D311yescharacteristic
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—61no—
138C3⋊#95C2×D311yescharacteristic
139C3⋊#95C2×D311yescharacteristic
140C3⋊#95C2×D312yes—
141C3⋊#95C2×D312yes—
142C23×C32C2411yescharacteristic
143C22×C3⋊D3—21no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3C22×C412yes—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4C22×C412yes—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3C22×C412yes—
157C2×C3⋊Dic3#4114yes—
158C4×C3⋊D3—28no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3#4114yes—
175C2×#117—91no—
176#389—92no—
177#388—92no—
178#388—92no—
179#383—31no—
180#383—91no—
181#380—91no—
182C4×C4⋊C4—31no—
183C4×C4⋊C4—92no—
184C4×C4⋊C4—91no—
185C4×C22⋊C4—91no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4C22×D312yes—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—61no—
206C22×Dic3—62no—
207C22×Dic3C22×D312yes—
208C22×Dic3C22×D311yescharacteristic
209C22×Dic3C22×D311yescharacteristic
210C22×Dic3C22×D311yescharacteristic
211C22×Dic3C22×D311yescharacteristic
212C22×Dic3C22×D312yes—
213C2×C4×D3—34no—
214C2×C4×D3—34no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×C4×D3—124no—
219C3×C4⋊C4—64no—
220C3×C42—34no—
221C3×C42—34no—
222C3×C42—122no—
223(C2×D3)⋊C4—34no—
224(C2×D3)⋊C4—34no—
225(C2×D3)⋊C4—34no—
226(C2×D3)⋊C4—34no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—122no—
230(C2×D3)⋊C4—122no—
231(C2×D3)⋊C4—124no—
232C4⋊Dic3—64no—
233Dic3⋊C4—24no—
234Dic3⋊C4—34no—
235Dic3⋊C4—34no—
236Dic3⋊C4—34no—
237Dic3⋊C4—34no—
238Dic3⋊C4—64no—
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241Dic3⋊C4—124no—
242C4×Dic3—42no—
243C4×Dic3—64no—
244C4×Dic3—64no—
245C4×Dic3—122no—
246C4×Dic3—122no—
247C4×Dic3C4×D314yes—
248C4×Dic3C4×D314yes—
249C22×C32C23×C411yescharacteristic
250C22×C32C2×#4112yes—
251C22×C32C2×#4112yes—
252C22×C32H(5,𝔽2)11yescharacteristic
253C22×C322−1+411yescharacteristic
254C2×C3⋊D3—22no—
255C2×C3⋊D3—22no—
256C2×C3⋊D3—22no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C32×C4—22no—
260C32×C4—42no—
261C3⋊Dic3—42no—
262C3⋊Dic3#11714yes—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—24no—
268C3×Dic3—42no—
269C23×C4—91no—
270#117—98no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—92no—
275C2×C4⋊C4—92no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—92no—
279C2×C22⋊C4—92no—
280C2×C42—31no—
281C2×C42—31no—
282C2×C42—32no—
283C2×C42—92no—
284C2×C42—92no—
285#95—31no—
286#95—31no—
287#95—32no—
288#95—32no—
289#95—92no—
290#95—92no—
291#95—91no—
292#95D3211yescharacteristic
293C23×C3—21no—
294C23×C3C23×D311yescharacteristic
295C23×C3C23×D311yescharacteristic
296C22×D3—32no—
297C22×D3—32no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—61no—
308C22×D3—61no—
309C22×D3—122no—
310C22×D3—122no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—34no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4C2×C4×D312yes—
342C2×Dic3—22no—
343C2×Dic3—21no—
344C2×Dic3—22no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—34no—
356C2×Dic3—34no—
357C2×Dic3—62no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3C2×C4×D312yes—
369C2×Dic3C2×C4×D312yes—
370C2×Dic3C2×C4×D312yes—
371C2×Dic3C2×C4×D312yes—
372C2×Dic3#23514yes—
373C4×D3—68no—
374C4×D3—68no—
375C4×D3—128no—
376C2×C32C2×#11711yescharacteristic
377C2×C32C4×#4111yescharacteristic
378C2×C32#52011yescharacteristic
379C2×C32#55312yes—
380C2×C32#55612yes—
381C3⋊D3—42no—
382C24—91no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—32no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4—91no—
390C22×C4—94no—
391C22×C4—92no—
392C22×C4—184no—
393C22×C4C2×D3212yes—
394C22×C4C2×D3211yescharacteristic
395C4⋊C4—64no—
396C4⋊C4—94no—
397C4⋊C4—94no—
398C4⋊C4—184no—
399C4⋊C4—184no—
400C22⋊C4—94no—
401C22⋊C4—94no—
402C22⋊C4—184no—
403C22⋊C4—362no—
404C42—34no—
405C42—34no—
406C42—122no—
407C42—184no—
408C42—362no—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3C22×C4×D311yescharacteristic
415C22×C3C22×C4×D311yescharacteristic
416C22×C3C2×#23512yes—
417C22×C3#100411yescharacteristic
418C22×C3#100711yescharacteristic
419C22×C3D3×#4112yes—
420C22×C3D3×#4112yes—
421C22×C3D3×#4112yes—
422C22×C3#100911yescharacteristic
423C22×C3#101011yescharacteristic
424C2×D3—64no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—64no—
445C3×C4—62no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—62no—
449C3×C4—82no—
450C3×C4—122no—
451Dic3—22no—
452Dic3—22no—
453Dic3—22no—
454Dic3—22no—
455Dic3—24no—
456Dic3—34no—
457Dic3—34no—
458Dic3—42no—
459Dic3—64no—
460Dic3—122no—
461Dic3—122no—
462Dic3—242no—
463C32#234711yescharacteristic, complemented, Sylow
464C23—92no—
465C23—182no—
466C23—182no—
467C23—181no—
468C23—181no—
469C23C22×D3211yescharacteristic
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—34no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—92no—
491C2×C4—94no—
492C2×C4—188no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4C4×D3212yes—
497C2×C3—21no—
498C2×C3—22no—
499C2×C3—22no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3C4×#23511yescharacteristic
503C2×C3#550411yescharacteristic
504C2×C3D3×#11711yescharacteristic
505C2×C3D3×#11711yescharacteristic
506C2×C3#552211yescharacteristic
507C2×C3#552311yescharacteristic
508C2×C3#554012yes—
509C2×C3#556812yes—
510C2×C3#570212yes—
511C2×C3#570912yes—
512D3—124no—
513D3—122no—
514D3—122no—
515C22—182no—
516C22—182no—
517C22—182no—
518C22—362no—
519C22—362no—
520C22C2×C4×D3211yescharacteristic
521C22D3×#23512yes—
522C22#6431212yes—
523C22#6431411yescharacteristic
524C22#6431511yescharacteristic
525C4—22no—
526C4—42no—
527C4—64no—
528C4—62no—
529C4—62no—
530C4—62no—
531C4—62no—
532C4—94no—
533C4—122no—
534C4—362no—
535C3—21no—
536C3#7363511yescharacteristic, complemented
537C3#7426311yescharacteristic, complemented
538C2—362no—
539C2#1059396511yescharacteristic
540C2#1059405211yescharacteristic
541C2#1059409712yes—
542C2#1059442412yes—
543C2#1059451011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2347
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4651C2semidirect
4. C3×#4649C2semidirect
7. #10591256C2semidirect
8. #10591243C2semidirect
9. #10591242C2semidirect
10. #10591223C2semidirect
29. #63874C4semidirect
56. #4651D3semidirect
59. #4649D3semidirect
463. C32#2347semidirect
536. C3#73635semidirect
537. C3#74263semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
#105923662
C3×#46512
C3×#46492
#105912602
#105912582
#105912562
#105912432
#105912422
#105912232
#105911942
#742633
#736353