Finite Group Databasebeta

← #11805104

Subgroups — #11805104

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C3×#5211C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4Dic3×#217C212yesmaximal
5#10591693C212yesmaximal
6#10591360C211yesmaximal, characteristic, complemented
7#10591271C212yesmaximal, complemented
8#10591271C212yesmaximal, complemented
9#10591257C211yesmaximal, characteristic, complemented
10#10591252C211yesmaximal, characteristic, complemented
11#10591229C211yesmaximal, characteristic, complemented
12#74059—31nomaximal
13#73335—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C2×#3757C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18#64135C418yescomplemented
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×#3724C2212yes—
25C2×#3724C2212yes—
26C2×Dic32C2212yes—
27C2×Dic32C2212yes—
28C3×C3⋊#95C2211yescharacteristic
29C3×C3⋊#95C2211yescharacteristic
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#926—31no—
39C2×#926—31no—
40C2×#926—61no—
41C3×#381—31no—
42C2×C3×#95—31no—
43#5211D311yescharacteristic
44#5210—32no—
45C4×#217—32no—
46C2×C3⋊#95D311yescharacteristic
47#4946—32no—
48Dic3×C22⋊C4—32no—
49#4654—32no—
50#4654—32no—
51#4653—32no—
52#4653—32no—
53#4651—31no—
54#4651—31no—
55#4650—31no—
56#4650—31no—
57#4649—31no—
58#4649—31no—
59#4648—31no—
60#4648—31no—
61C24×C32C2311yescharacteristic
62C22×C32×C4—24no—
63C22×C32×C4C2×C414yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3×Dic3—24no—
71C22×C3×Dic3—24no—
72C22×C3×Dic3—42no—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77#3757C2×C414yes—
78#3757C2×C414yes—
79C4⋊(C3⋊Dic3)C2×C414yescomplemented
80C4⋊(C3⋊Dic3)C2×C414yescomplemented
81C4×C3⋊Dic3C2×C414yescomplemented
82C4×C3⋊Dic3C2×C414yescomplemented
83C3×#217—24no—
84#3724—24no—
85#3724—42no—
86Dic32—24no—
87Dic32—42no—
88#2343—91noSylow
89C23×C3×C4—21no—
90C23×C3×C4—32no—
91C23×C3×C4C2×D311yescharacteristic
92C23×C3×C4C2×D311yescharacteristic
93C23×Dic3C2×D312yes—
94C2×C3×C22⋊C4—32no—
95C2×#217—31no—
96C2×#217—31no—
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—61no—
100C2×#217—61no—
101C2×#217C2×D312yes—
102#926—38no—
103#926—38no—
104#926—68no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3—61no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3—61no—
125C3×#95—31no—
126C3×#95—31no—
127C3×#95—31no—
128C3×#95—31no—
129C3×#95—32no—
130C3×#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95C2×D311yescharacteristic
140C3⋊#95C2×D311yescharacteristic
141C3⋊#95C2×D311yescharacteristic
142C3⋊#95C2×D311yescharacteristic
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32—22no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32C22×C412yes—
149C23×C32#4114yes—
150C23×C32C2411yescharacteristic
151C2×C32×C4—28no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C22×C412yes—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3C22×C412yes—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C22×C412yes—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
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—48no—
178C2×C3×Dic3#4114yes—
179C2×#117—91no—
180#387—92no—
181#387—92no—
182#385—92no—
183#383—91no—
184#382—91no—
185#381—31no—
186C4×C4⋊C4—91no—
187C4×C22⋊C4—92no—
188#376—91no—
189C2×#95—31no—
190C24×C3—21no—
191C24×C3C22×D311yescharacteristic
192C24×C3C22×D311yescharacteristic
193C22×C3×C4—28no—
194C22×C3×C4—24no—
195C22×C3×C4—24no—
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—64no—
204C22×C3×C4—64no—
205C22×C3×C4—122no—
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—24no—
213C22×Dic3—24no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—42no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C3×C22⋊C4—64no—
232#217—24no—
233#217—34no—
234#217—34no—
235#217—34no—
236#217—34no—
237#217—64no—
238#217—64no—
239C4⋊Dic3—34no—
240C4⋊Dic3—34no—
241C4⋊Dic3—34no—
242C4⋊Dic3—34no—
243C4⋊Dic3—64no—
244C4⋊Dic3—64no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—122no—
248Dic3⋊C4—122no—
249C4×Dic3—34no—
250C4×Dic3—34no—
251C4×Dic3—34no—
252C4×Dic3—34no—
253C4×Dic3—64no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C4×Dic3—122no—
258C4×Dic3—122no—
259C22×C32—22no—
260C22×C32—22no—
261C22×C32—24no—
262C22×C32—24no—
263C22×C32#11714yes—
264C22×C32C23×C411yescharacteristic
265C22×C32C2×#4112yes—
266C22×C32C2×#4112yes—
267C22×C32H(5,𝔽2)11yescharacteristic
268C22×C322−1+411yescharacteristic
269C32×C4—22no—
270C32×C4—22no—
271C3⋊Dic3—22no—
272C3⋊Dic3—22no—
273C3⋊Dic3—22no—
274C3⋊Dic3—22no—
275C3×Dic3—24no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C23×C4—32no—
280C23×C4D3211yescharacteristic
281#117—98no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—92no—
285C2×C4⋊C4—92no—
286C2×C22⋊C4—32no—
287C2×C22⋊C4—91no—
288C2×C22⋊C4—91no—
289C2×C42—91no—
290C2×C42—91no—
291C2×C42—92no—
292C2×C42—92no—
293#95—31no—
294#95—31no—
295#95—32no—
296#95—31no—
297#95—31no—
298#95—32no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—24no—
311C23×C3—22no—
312C23×C3—41no—
313C23×C3—42no—
314C23×C3—41no—
315C23×C3C2×C4×D312yes—
316C23×C3C2×C4×D312yes—
317C23×C3#23714yes—
318C23×C3#23714yes—
319C23×C3C23×D311yescharacteristic
320C23×C3C23×D311yescharacteristic
321C2×C3×C4—24no—
322C2×C3×C4—24no—
323C2×C3×C4—216no—
324C2×C3×C4—28no—
325C2×C3×C4—28no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—34no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—128no—
345C2×C3×C4C2×C4×D312yes—
346C2×C3×C4C2×C4×D312yes—
347C2×C3×C4C2×C4×D312yes—
348C2×C3×C4C2×C4×D312yes—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—48no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3#23514yes—
392C2×C32—24no—
393C2×C32C2×#11711yescharacteristic
394C2×C32C4×#4111yescharacteristic
395C2×C32#52011yescharacteristic
396C2×C32#55112yes—
397C2×C32#55212yes—
398C24C2×D3211yescharacteristic
399C22×C4—24no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—32no—
404C22×C4—64no—
405C22×C4—64no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—122no—
411C22×C4#62414yes—
412C22×C4C2×D3211yescharacteristic
413C22×C4C2×D3211yescharacteristic
414C4⋊C4—94no—
415C4⋊C4—94no—
416C4⋊C4—184no—
417C4⋊C4—362no—
418C22⋊C4—64no—
419C22⋊C4—94no—
420C22⋊C4—94no—
421C42—94no—
422C42—94no—
423C42—184no—
424C42—362no—
425C22×C3—24no—
426C22×C3—24no—
427C22×C3—22no—
428C22×C3—24no—
429C22×C3—22no—
430C22×C3—24no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—22no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—24no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3#87714yes—
444C22×C3#87714yes—
445C22×C3C22×C4×D311yescharacteristic
446C22×C3C22×C4×D311yescharacteristic
447C22×C3C2×#23512yes—
448C22×C3C2×#23712yes—
449C22×C3C2×#23712yes—
450C22×C3#100411yescharacteristic
451C22×C3#100711yescharacteristic
452C22×C3D3×#4112yes—
453C22×C3#100911yescharacteristic
454C22×C3#101011yescharacteristic
455C3×C4—24no—
456C3×C4—24no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—64no—
462C3×C4—122no—
463C3×C4—122no—
464C3×C4—122no—
465Dic3—24no—
466Dic3—42no—
467Dic3—42no—
468Dic3—42no—
469Dic3—62no—
470Dic3—62no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478Dic3—122no—
479Dic3—122no—
480Dic3—122no—
481C32#234311yescharacteristic, complemented, Sylow
482C23—21no—
483C23—22no—
484C23—21no—
485C23#380514yes—
486C23C2×#62412yes—
487C23C22×D3211yescharacteristic
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—28no—
491C2×C4—34no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—92no—
504C2×C4—92no—
505C2×C4—92no—
506C2×C4—92no—
507C2×C4—128no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4C2×#62412yes—
515C2×C4C2×#62412yes—
516C2×C3—24no—
517C2×C3—24no—
518C2×C3—22no—
519C2×C3—22no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—44no—
524C2×C3C4×#23511yescharacteristic
525C2×C3C2×#87711yescharacteristic
526C2×C3C2×#87711yescharacteristic
527C2×C3#549512yes—
528C2×C3#550411yescharacteristic
529C2×C3#551312yes—
530C2×C3#552211yescharacteristic
531C2×C3#552311yescharacteristic
532C2×C3#565012yes—
533C2×C3#565812yes—
534C22—24no—
535C22—24no—
536C22—22no—
537C22—22no—
538C22#6395714yes—
539C22#6429711yescharacteristic
540C22D3×#23512yes—
541C22#6430711yescharacteristic
542C22C2×#380512yes—
543C22C22×#62411yescharacteristic
544C4—22no—
545C4—22no—
546C4—64no—
547C4—122no—
548C4—122no—
549C4—122no—
550C4—182no—
551C4—182no—
552C4—182no—
553C4—182no—
554C3—21no—
555C3#7333511yescharacteristic, complemented
556C3#7405911yescharacteristic, complemented
557C2—24no—
558C2#1059494012yes—
559C2#1059495212yes—
560C2#1059495411yescharacteristic
561C2#1059499011yescharacteristic
562C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591360C2semidirect
7. #10591271C2semidirect
8. #10591271C2semidirect
9. #10591257C2semidirect
10. #10591252C2semidirect
11. #10591229C2semidirect
18. #64135C4semidirect
79. C4⋊(C3⋊Dic3)C2×C4semidirect
80. C4⋊(C3⋊Dic3)C2×C4semidirect
81. C4×C3⋊Dic3C2×C4semidirect
82. C4×C3⋊Dic3C2×C4semidirect
481. C32#2343semidirect
555. C3#73335semidirect
556. C3#74059semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C3×#52112
C2×C3×C3⋊#952
Dic3×#2172
#105916932
#105913602
#105912712
#105912572
#105912522
#105912292
#740593
#733353