Finite Group Databasebeta

← #11805093

Subgroups — #11805093

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×#64081C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10591378C212yesmaximal
5#10591370C211yesmaximal, characteristic
6#10591360C211yesmaximal, characteristic, complemented
7#10591263C212yesmaximal, complemented
8#10591252C211yesmaximal, characteristic, complemented
9#10591233C212yesmaximal
10#10591219C211yesmaximal, characteristic
11#10591197C212yesmaximal, complemented
12#74296—31nomaximal
13#73766—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#624C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64081C418yescomplemented
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×#3724C2212yes—
26C2×#3722C2212yes—
27C2×Dic32C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2211yescharacteristic
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#872—31no—
39C2×#872—31no—
40C2×#872—61no—
41C3×#383—31no—
42C3×C4×C4⋊C4—31no—
43#4989—32no—
44#4978—32no—
45C4×(C2×D3)⋊C4—32no—
46#4937D311yescharacteristic, complemented
47C4×C4⋊Dic3D311yescharacteristic, complemented
48#4933—32no—
49#4668—32no—
50#4666—32no—
51#4664—31no—
52#4664—31no—
53D3×#95—31no—
54D3×#95—31no—
55#4655—32no—
56#4652—32no—
57#4650—31no—
58#4650—31no—
59#4648—31no—
60#4648—31no—
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3C2×C414yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C2×#624—24no—
75C2×#624—24no—
76C2×#624—42no—
77C32×C42C2×C414yescomplemented
78#3752C2×C414yes—
79#3752C2×C414yes—
80#3750C2×C414yescomplemented
81#3750C2×C414yescomplemented
82C4×C3⋊Dic3C2×C414yescomplemented
83C3×C4⋊Dic3—24no—
84C3×C4×Dic3—42no—
85#3724—42no—
86#3722—24no—
87Dic32—24no—
88#2343—91noSylow
89C22×C4×D3—31no—
90C22×C4×D3—31no—
91C22×C4×D3—32no—
92C22×C4×D3—32no—
93C22×C4×D3—61no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C42—21no—
96C2×C3×C42—32no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—31no—
102C2×(C2×D3)⋊C4—31no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3C2×D312yes—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—61no—
115C2×Dic3⋊C4—61no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—61no—
121C2×C4×Dic3C2×D312yes—
122#872—38no—
123#872—38no—
124#872—68no—
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×C32C2411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3C22×C412yes—
150C22×C3⋊D3#4114yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C22×C412yes—
156C2×C32×C4C22×C412yes—
157C2×C32×C4C22×C412yes—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3C22×C412yes—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C22×C412yes—
165C4×C3⋊D3—28no—
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#4114yes—
178#624—48no—
179C2×#117—91no—
180#387—92no—
181#387—92no—
182#385—92no—
183#383—31no—
184#382—91no—
185#381—91no—
186C4×C4⋊C4—31no—
187C4×C22⋊C4—92no—
188#376—91no—
189C2×#95—91no—
190C23×D3—31no—
191C23×D3—31no—
192C23×D3—61no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C2×C4×D3—34no—
220C2×C4×D3—34no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—68no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—122no—
230C2×C4×D3—122no—
231C3×C4⋊C4—64no—
232C3×C42—24no—
233C3×C42—122no—
234C3×C42C4×D314yescomplemented
235C3×C42C4×D314yescomplemented
236(C2×D3)⋊C4—34no—
237(C2×D3)⋊C4—34no—
238(C2×D3)⋊C4—34no—
239(C2×D3)⋊C4—34no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—24no—
245Dic3⋊C4—34no—
246Dic3⋊C4—34no—
247Dic3⋊C4—34no—
248Dic3⋊C4—34no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—122no—
252Dic3⋊C4—122no—
253C4×Dic3—34no—
254C4×Dic3—34no—
255C4×Dic3—42no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C22×C32C23×C411yescharacteristic
260C22×C32C2×#4112yes—
261C22×C32C2×#4112yes—
262C22×C32H(5,𝔽2)11yescharacteristic
263C22×C322−1+411yescharacteristic
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—24no—
267C2×C3⋊D3—24no—
268C2×C3⋊D3#11714yes—
269C32×C4—22no—
270C32×C4—22no—
271C32×C4—22no—
272C3⋊Dic3—22no—
273C3⋊Dic3—22no—
274C3⋊Dic3—22no—
275C3×Dic3—24no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C23×C4—92no—
280C23×C4—91no—
281#117—98no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—92no—
286C2×C22⋊C4—91no—
287C2×C22⋊C4—91no—
288C2×C22⋊C4—92no—
289C2×C42—32no—
290C2×C42—91no—
291C2×C42—92no—
292C2×C42D3211yescharacteristic
293#95—31no—
294#95—31no—
295#95—31no—
296#95—32no—
297#95—31no—
298#95—32no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303C23×C3—21no—
304C23×C3C23×D311yescharacteristic
305C23×C3C23×D311yescharacteristic
306C22×D3—32no—
307C22×D3—32no—
308C22×D3—34no—
309C22×D3—34no—
310C22×D3—62no—
311C22×D3—64no—
312C22×D3—62no—
313C22×D3—61no—
314C22×D3—61no—
315C22×D3—62no—
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—121no—
319C22×D3—122no—
320C22×D3—121no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—34no—
334C2×C3×C4—41no—
335C2×C3×C4—42no—
336C2×C3×C4—41no—
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—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4C2×C4×D312yes—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4C2×C4×D312yes—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—64no—
375C2×Dic3—62no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—121no—
384C2×Dic3—122no—
385C2×Dic3—121no—
386C2×Dic3#23514yes—
387C4×D3—68no—
388C4×D3—68no—
389C4×D3—616no—
390C4×D3—128no—
391C4×D3—128no—
392C2×C32C2×#11711yescharacteristic
393C2×C32C4×#4111yescharacteristic
394C2×C32#52011yescharacteristic
395C2×C32#55112yes—
396C2×C32#55212yes—
397C3⋊D3—24no—
398C24—91no—
399C22×C4—32no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—94no—
407C22×C4—184no—
408C22×C4—184no—
409C22×C4—184no—
410C22×C4—362no—
411C22×C4C2×D3211yescharacteristic
412C22×C4C2×D3211yescharacteristic
413C22×C4C2×D3211yescharacteristic
414C4⋊C4—64no—
415C4⋊C4—94no—
416C4⋊C4—94no—
417C4⋊C4—362no—
418C22⋊C4—94no—
419C22⋊C4—94no—
420C22⋊C4—184no—
421C42—94no—
422C42—122no—
423C42—184no—
424C42#62414yescomplemented
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3C22×C4×D311yescharacteristic
431C22×C3C22×C4×D311yescharacteristic
432C22×C3C2×#23512yes—
433C22×C3#100411yescharacteristic
434C22×C3#100711yescharacteristic
435C22×C3D3×#4112yes—
436C22×C3D3×#4112yes—
437C22×C3D3×#4112yes—
438C22×C3#100911yescharacteristic
439C22×C3#101011yescharacteristic
440C2×D3—34no—
441C2×D3—34no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—64no—
450C2×D3—64no—
451C2×D3—122no—
452C2×D3—124no—
453C2×D3—122no—
454C2×D3—124no—
455C3×C4—24no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—64no—
465C3×C4—122no—
466C3×C4—122no—
467C3×C4—122no—
468Dic3—24no—
469Dic3—42no—
470Dic3—42no—
471Dic3—42no—
472Dic3—64no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—62no—
478Dic3—62no—
479Dic3—122no—
480Dic3—122no—
481C32#234311yescharacteristic, complemented, Sylow
482C23—94no—
483C23—92no—
484C23—181no—
485C23—182no—
486C23—181no—
487C23C22×D3211yescharacteristic
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—34no—
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—62no—
504C2×C4—92no—
505C2×C4—92no—
506C2×C4—92no—
507C2×C4—188no—
508C2×C4—181no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—181no—
512C2×C4—368no—
513C2×C4C2×#62412yes—
514C2×C4C2×#62412yes—
515C2×C4C2×#62412yes—
516C2×C3—21no—
517C2×C3—22no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3C4×#23511yescharacteristic
522C2×C3#550411yescharacteristic
523C2×C3D3×#11711yescharacteristic
524C2×C3D3×#11711yescharacteristic
525C2×C3#552211yescharacteristic
526C2×C3#552311yescharacteristic
527C2×C3#555612yes—
528C2×C3#558112yes—
529C2×C3#570512yes—
530C2×C3#570812yes—
531D3—64no—
532D3—64no—
533D3—124no—
534C22—94no—
535C22—182no—
536C22—184no—
537C22—182no—
538C22—184no—
539C22#6429711yescharacteristic
540C22D3×#23512yes—
541C22#6430612yes—
542C22#6430711yescharacteristic
543C22C22×#62411yescharacteristic
544C4—22no—
545C4—22no—
546C4—22no—
547C4—64no—
548C4—122no—
549C4—122no—
550C4—122no—
551C4—182no—
552C4—182no—
553C4—182no—
554C3—21no—
555C3#7376611yescharacteristic, complemented
556C3#7429611yescharacteristic, complemented
557C2—184no—
558C2#1059393312yes—
559C2#1059401812yes—
560C2#1059495411yescharacteristic
561C2#1059496911yescharacteristic
562C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4937C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
6. #10591360C2semidirect
7. #10591263C2semidirect
8. #10591252C2semidirect
11. #10591197C2semidirect
22. #64081C4semidirect
46. #4937D3semidirect
47. C4×C4⋊Dic3D3semidirect
77. C32×C42C2×C4semidirect
80. #3750C2×C4semidirect
81. #3750C2×C4semidirect
82. C4×C3⋊Dic3C2×C4semidirect
234. C3×C42C4×D3semidirect
235. C3×C42C4×D3semidirect
424. C42#624semidirect
481. C32#2343semidirect
555. C3#73766semidirect
556. C3#74296semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×#49372
C3×C4×C4⋊Dic32
#105913782
#105913702
#105913602
#105912632
#105912522
#105912332
#105912192
#105911972
#742963
#737663