Finite Group Databasebeta

← #11805240

Subgroups — #11805240

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4#10591720C211yesmaximal, characteristic
5#10591720C211yesmaximal, characteristic
6#10591705C211yesmaximal, characteristic
7#10591705C211yesmaximal, characteristic
8#10591264C212yesmaximal, complemented
9#10591263C212yesmaximal, complemented
10#10591243C212yesmaximal, complemented
11#10591197C212yesmaximal, complemented
12#73880—31nomaximal
13#73458—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C2×#3750C418yescomplemented
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×#3724C2212yes—
29C2×#3724C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C22×Dic3⋊C4—31no—
39C22×Dic3⋊C4—31no—
40C22×Dic3⋊C4—61no—
41C3×#380—31no—
42C3×C4×C22⋊C4—31no—
43#5212D311yescharacteristic
44C4×#217D311yescharacteristic
45#4978—32no—
46#4976—32no—
47#4942—31no—
48#4942—31no—
49#4942—31no—
50#4942—31no—
51Dic3×C22⋊C4—31no—
52Dic3×C22⋊C4—31no—
53Dic3×C22⋊C4—31no—
54Dic3×C22⋊C4—31no—
55#4933—32no—
56C4×Dic3⋊C4—32no—
57#4655—32no—
58#4652—32no—
59#4649—32no—
60#4647—32no—
61C24×C32C2311yescharacteristic
62C22×C32×C4—42no—
63C22×C32×C4C2×C414yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3—24no—
67C22×C3⋊Dic3—42no—
68C22×C3⋊Dic3C2×C414yes—
69C22×C3⋊Dic3C2×C414yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78#3750C2×C414yes—
79#3750C2×C414yes—
80#3750C2×C414yes—
81#3750C2×C414yes—
82C3×#217—22no—
83C3×#217—22no—
84C3×#217—22no—
85C3×#217Q814yes—
86C3×C4⋊Dic3—42no—
87C3×C4×Dic3—42no—
88#3724—24no—
89#3724—42no—
90Dic32—24no—
91Dic32—42no—
92#2345—91noSylow
93C23×C3×C4—21no—
94C23×C3×C4C2×D311yescharacteristic
95C23×C3×C4C2×D311yescharacteristic
96C23×Dic3—31no—
97C23×Dic3—31no—
98C23×Dic3—31no—
99C23×Dic3—31no—
100C23×Dic3—61no—
101C23×Dic3—61no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C42—32no—
108C2×#217C2×D311yescharacteristic
109C2×#217C2×D311yescharacteristic
110C2×#217C2×D311yescharacteristic
111C2×#217C2×D311yescharacteristic
112C2×C4⋊Dic3C2×D312yes—
113C2×Dic3⋊C4—38no—
114C2×Dic3⋊C4—38no—
115C2×Dic3⋊C4—31no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—68no—
128C2×Dic3⋊C4—61no—
129C2×Dic3⋊C4—61no—
130C2×Dic3⋊C4—61no—
131C2×Dic3⋊C4—61no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3C2×D312yes—
137C3×#95—32no—
138C3×#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95C2×D312yes—
148C3⋊#95C2×D312yes—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32C22×C412yes—
152C23×C32C2×Q812yes—
153C23×C32#4112yes—
154C23×C32C2411yescharacteristic
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—44no—
158C2×C32×C4C22×C412yes—
159C2×C32×C4C22×C412yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—28no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—44no—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3⋊Dic3C22×C412yes—
167C2×C3⋊Dic3C22×C412yes—
168C2×C3⋊Dic3C22×C412yes—
169C2×C3⋊Dic3#4114yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×Q814yes—
182C22×C4⋊C4—91no—
183#389—92no—
184#387—92no—
185#387—92no—
186#380—31no—
187#380—91no—
188#380—91no—
189C4×C4⋊C4—92no—
190C4×C22⋊C4—31no—
191C4×C22⋊C4—91no—
192C4×C22⋊C4—91no—
193C24×C3—21no—
194C24×C3C22×D311yescharacteristic
195C24×C3C22×D311yescharacteristic
196C22×C3×C4—24no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—42no—
204C22×C3×C4—42no—
205C22×C3×C4—44no—
206C22×C3×C4C4×D314yes—
207C22×C3×C4C4×D314yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—34no—
215C22×Dic3—34no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—34no—
223C22×Dic3—34no—
224C22×Dic3—64no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—64no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—64no—
231C22×Dic3—64no—
232C22×Dic3—68no—
233C22×Dic3—122no—
234C22×Dic3—122no—
235C22×Dic3—124no—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C3×C4⋊C4—122no—
241C3×C22⋊C4—34no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—62no—
245C3×C42—122no—
246#217—22no—
247#217—22no—
248#217—22no—
249#217Dic614yes—
250C4⋊Dic3—42no—
251Dic3⋊C4—34no—
252Dic3⋊C4—34no—
253Dic3⋊C4—34no—
254Dic3⋊C4—34no—
255Dic3⋊C4—34no—
256Dic3⋊C4—34no—
257Dic3⋊C4—34no—
258Dic3⋊C4—34no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—122no—
266Dic3⋊C4—122no—
267C4×Dic3—42no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—122no—
271C4×Dic3—122no—
272C22×C32—22no—
273C22×C32—22no—
274C22×C32—24no—
275C22×C32—24no—
276C22×C32C4×Q814yes—
277C22×C32C23×C411yescharacteristic
278C22×C32C22×Q811yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4112yes—
281C22×C32H(5,𝔽2)12yes—
282C32×C4—22no—
283C32×C4—22no—
284C3⋊Dic3—22no—
285C3⋊Dic3—22no—
286C3⋊Dic3—22no—
287C3⋊Dic3#11714yes—
288C3×Dic3—24no—
289C3×Dic3—42no—
290C3×Dic3—42no—
291C3×Dic3—42no—
292C23×C4—91no—
293C23×C4—91no—
294C23×C4D3211yescharacteristic
295C2×C4⋊C4—32no—
296C2×C4⋊C4—98no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—92no—
302C2×C4⋊C4—92no—
303C2×C22⋊C4—31no—
304C2×C22⋊C4—31no—
305C2×C22⋊C4—31no—
306C2×C22⋊C4—31no—
307C2×C42—32no—
308C2×C42—92no—
309C2×C42—92no—
310#95—32no—
311#95—32no—
312#95—92no—
313#95—92no—
314#95—92no—
315#95—92no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3C2×Dic612yes—
327C23×C3C2×C4×D312yes—
328C23×C3C2×C4×D312yes—
329C23×C3#23512yes—
330C23×C3#23712yes—
331C23×C3D3×Q812yes—
332C23×C3C23×D311yescharacteristic
333C23×C3C23×D311yescharacteristic
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—34no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—44no—
344C2×C3×C4—44no—
345C2×C3×C4—48no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4C2×C4×D312yes—
358C2×C3×C4C2×C4×D312yes—
359C2×C3×C4C2×C4×D312yes—
360C2×C3×C4C2×C4×D312yes—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—32no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—64no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—68no—
388C2×Dic3—68no—
389C2×Dic3—616no—
390C2×Dic3—64no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—124no—
400C2×Dic3—124no—
401C2×Dic3—128no—
402C2×Dic3C2×Dic614yes—
403C2×C32—24no—
404C2×C32C2×#11711yescharacteristic
405C2×C32C2×C4×Q811yescharacteristic
406C2×C32#51811yescharacteristic
407C2×C32#55312yes—
408C2×C32#55412yes—
409C24C2×D3211yescharacteristic
410C22×C4—32no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—42no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—94no—
420C22×C4—94no—
421C22×C4—184no—
422C22×C4—362no—
423C22×C4#62414yes—
424C22×C4C2×D3211yescharacteristic
425C22×C4C2×D3211yescharacteristic
426C4⋊C4—94no—
427C4⋊C4—94no—
428C4⋊C4—94no—
429C4⋊C4—94no—
430C4⋊C4—122no—
431C4⋊C4—184no—
432C4⋊C4—362no—
433C22⋊C4—34no—
434C22⋊C4—62no—
435C22⋊C4—62no—
436C22⋊C4—62no—
437C42—122no—
438C42—184no—
439C42—362no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—28no—
443C22×C3—28no—
444C22×C3—24no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—22no—
457C22×C3—24no—
458C22×C3C4×Dic614yes—
459C22×C3#88714yes—
460C22×C3C22×Dic611yescharacteristic
461C22×C3C22×C4×D311yescharacteristic
462C22×C3C22×C4×D311yescharacteristic
463C22×C3C2×#23511yescharacteristic
464C22×C3C2×#23711yescharacteristic
465C22×C3#100412yes—
466C22×C3#100412yes—
467C22×C3C2×D3×Q811yescharacteristic
468C22×C3D3×#4112yes—
469C22×C3D3×#4112yes—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—64no—
477C3×C4—122no—
478C3×C4—122no—
479C3×C4—122no—
480Dic3—24no—
481Dic3—34no—
482Dic3—34no—
483Dic3—42no—
484Dic3—42no—
485Dic3—42no—
486Dic3—64no—
487Dic3—64no—
488Dic3—62no—
489Dic3—62no—
490Dic3—62no—
491Dic3—62no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495Dic3—122no—
496C32#234511yescharacteristic, complemented, Sylow
497C23—22no—
498C23—22no—
499C23D3×Dic612yes—
500C23#379512yes—
501C23C2×#62412yes—
502C23C22×D3211yescharacteristic
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—34no—
506C2×C4—44no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—94no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—188no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4—182no—
527C2×C4—364no—
528C2×C4C2×#62412yes—
529C2×C4C2×#62412yes—
530C2×C3—28no—
531C2×C3—24no—
532C2×C3—24no—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3C2×C4×Dic611yescharacteristic
539C2×C3#548611yescharacteristic
540C2×C3#548611yescharacteristic
541C2×C3C2×#88711yescharacteristic
542C2×C3D3×#11711yescharacteristic
543C2×C3D3×#11711yescharacteristic
544C2×C3#553912yes—
545C2×C3#554012yes—
546C2×C3#560112yes—
547C2×C3#563612yes—
548C22—24no—
549C22—24no—
550C22—22no—
551C22—22no—
552C22#6384414yes—
553C22C2×D3×Dic611yescharacteristic
554C22C2×#379511yescharacteristic
555C22#6430612yes—
556C22C22×#62411yescharacteristic
557C22#6433012yes—
558C4—22no—
559C4—22no—
560C4—64no—
561C4—94no—
562C4—122no—
563C4—122no—
564C4—122no—
565C4—182no—
566C4—182no—
567C4—182no—
568C3—21no—
569C3#7345811yescharacteristic, complemented
570C3#7388011yescharacteristic, complemented
571C2—24no—
572C2C2×#6384411yescharacteristic
573C2#1059495912yes—
574C2#1059496212yes—
575C2#1059496911yescharacteristic
576C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591264C2semidirect
9. #10591263C2semidirect
10. #10591243C2semidirect
11. #10591197C2semidirect
17. C2×#3750C4semidirect
496. C32#2345semidirect
569. C3#73458semidirect
570. C3#73880semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C3×#52122
C3×C4×#2172
#105917202
#105917052
#105912642
#105912632
#105912432
#105911972
#738803
#734583