Finite Group Databasebeta

← #11805087

Subgroups — #11805087

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic
2#10592363C211yesmaximal, characteristic
3C3×#4650C211yesmaximal, characteristic, complemented
4C3×#4649C211yesmaximal, characteristic, complemented
5#10591374C212yesmaximal
6#10591370C211yesmaximal, characteristic
7#10591255C212yesmaximal, complemented
8#10591239C211yesmaximal, characteristic, complemented
9#10591233C212yesmaximal
10#10591223C211yesmaximal, characteristic, complemented
11#10591193C212yesmaximal, complemented
12#74227—31nomaximal
13#73766—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#624C2212yes—
16C2×#3752C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×#3724C2211yescharacteristic
23C2×#3724C2211yescharacteristic
24C2×#3722C2211yescharacteristic
25C2×#3722C2211yescharacteristic
26C2×Dic32C2212yes—
27#63874C418yescomplemented
28C32×#95C2211yescharacteristic
29#63658C2211yescharacteristic
30#63658C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#872—31no—
39C2×#872—31no—
40C3×#382—31no—
41C3×C4×C4⋊C4—31no—
42#4989—32no—
43#4989—32no—
44#4978—32no—
45#4978—32no—
46C4×(C2×D3)⋊C4—32no—
47#4937—31no—
48#4933—32no—
49#4932—31no—
50#4666—32no—
51#4664—31no—
52#4664—31no—
53#4664—61no—
54D3×#95—31no—
55D3×#95—31no—
56#4652—32no—
57#4651—31no—
58#4650D311yescharacteristic, complemented
59#4649D311yescharacteristic, complemented
60#4648—31no—
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—
74C2×#624—24no—
75C2×#624—24no—
76C2×#624—42no—
77#3752—24no—
78C3×Dic3⋊C4—24no—
79C3×Dic3⋊C4—42no—
80C3×C4×Dic3—42no—
81C3×C4×Dic3C2×C414yescomplemented
82C3×C4×Dic3C2×C414yescomplemented
83#3724C2×C414yescomplemented
84#3724C2×C414yescomplemented
85#3722C2×C414yes—
86#3722C2×C414yes—
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×C4⋊C4—32no—
96C2×C3×C42—31no—
97C2×C3×C42—31no—
98C2×C3×C42—32no—
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—62no—
106C2×Dic3⋊C4—31no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4C2×D312yes—
111C2×Dic3⋊C4C2×D312yes—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3C2×D312yes—
115C2×C4×Dic3C2×D311yescharacteristic
116C2×C4×Dic3C2×D311yescharacteristic
117#872—38no—
118#872—38no—
119C3×#95—21no—
120C3×#95—31no—
121C3×#95—31no—
122C3×#95—32no—
123C3×#95C2×D311yescharacteristic
124C3×#95C2×D311yescharacteristic
125C3⋊#95—31no—
126C3⋊#95—31no—
127C3⋊#95—32no—
128C3⋊#95—32no—
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—61no—
138C3⋊#95—62no—
139C3⋊#95C2×D311yescharacteristic
140C3⋊#95C2×D311yescharacteristic
141C3⋊#95C2×D312yes—
142C23×C32C2411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3C22×C412yes—
147C22×C3⋊D3#4114yes—
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⋊Dic3—22no—
157C2×C3⋊Dic3C22×C412yes—
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—
175#624—48no—
176C2×#117—91no—
177#387—92no—
178#387—92no—
179#385—92no—
180#383—91no—
181#382—31no—
182#381—91no—
183C4×C4⋊C4—31no—
184C4×C22⋊C4—92no—
185#376—91no—
186C2×#95—91no—
187C23×D3—31no—
188C23×D3—31no—
189C23×D3—61no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—32no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—32no—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—61no—
207C22×Dic3—62no—
208C22×Dic3C22×D312yes—
209C22×Dic3C22×D311yescharacteristic
210C22×Dic3C22×D311yescharacteristic
211C22×Dic3C22×D311yescharacteristic
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D312yes—
214C2×C4×D3—34no—
215C2×C4×D3—34no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—124no—
224C2×C4×D3—122no—
225C2×C4×D3—122no—
226C3×C4⋊C4—64no—
227C3×C4⋊C4—122no—
228C3×C42—34no—
229C3×C42—34no—
230C3×C42—122no—
231(C2×D3)⋊C4—34no—
232(C2×D3)⋊C4—34no—
233(C2×D3)⋊C4—34no—
234(C2×D3)⋊C4—34no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—124no—
238Dic3⋊C4—24no—
239Dic3⋊C4—34no—
240Dic3⋊C4—34no—
241Dic3⋊C4—34no—
242Dic3⋊C4—34no—
243Dic3⋊C4—42no—
244C4×Dic3—42no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C4×Dic3C4×D314yescomplemented
248C4×Dic3C4×D314yescomplemented
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—24no—
257C2×C3⋊D3—24no—
258C2×C3⋊D3#11714yes—
259C32×C4—22no—
260C32×C4—42no—
261C3⋊Dic3—22no—
262C3⋊Dic3—42no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—24no—
268C3×Dic3—42no—
269C23×C4—92no—
270C23×C4—91no—
271#117—98no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—92no—
279C2×C42—31no—
280C2×C42—31no—
281C2×C42—32no—
282C2×C42—92no—
283#95—31no—
284#95—31no—
285#95—32no—
286#95—92no—
287#95—92no—
288#95—92no—
289#95—92no—
290#95—91no—
291#95—92no—
292#95D3211yescharacteristic
293C23×C3—21no—
294C23×C3C23×D311yescharacteristic
295C23×C3C23×D311yescharacteristic
296C22×D3—32no—
297C22×D3—32no—
298C22×D3—34no—
299C22×D3—34no—
300C22×D3—62no—
301C22×D3—64no—
302C22×D3—62no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—61no—
307C22×D3—62no—
308C22×D3—122no—
309C22×D3—121no—
310C22×D3—121no—
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—62no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
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—21no—
347C2×Dic3—21no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—122no—
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—
376C4×D3—128no—
377C4×D3—128no—
378C2×C32C2×#11711yescharacteristic
379C2×C32C4×#4111yescharacteristic
380C2×C32#52011yescharacteristic
381C2×C32#55112yes—
382C2×C32#55212yes—
383C3⋊D3—24no—
384C24—91no—
385C22×C4—31no—
386C22×C4—32no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—32no—
391C22×C4—91no—
392C22×C4—94no—
393C22×C4—92no—
394C22×C4—184no—
395C22×C4—184no—
396C22×C4—184no—
397C22×C4—362no—
398C22×C4C2×D3212yes—
399C22×C4C2×D3211yescharacteristic
400C4⋊C4—64no—
401C4⋊C4—94no—
402C4⋊C4—94no—
403C4⋊C4—122no—
404C22⋊C4—94no—
405C22⋊C4—94no—
406C22⋊C4—184no—
407C42—34no—
408C42—34no—
409C42—122no—
410C42—184no—
411C22×C3—21no—
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3C22×C4×D311yescharacteristic
417C22×C3C22×C4×D311yescharacteristic
418C22×C3C2×#23512yes—
419C22×C3#100411yescharacteristic
420C22×C3#100411yescharacteristic
421C22×C3#100711yescharacteristic
422C22×C3#100711yescharacteristic
423C22×C3D3×#4112yes—
424C22×C3D3×#4112yes—
425C22×C3D3×#4112yes—
426C2×D3—34no—
427C2×D3—34no—
428C2×D3—64no—
429C2×D3—64no—
430C2×D3—64no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—64no—
436C2×D3—64no—
437C2×D3—124no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—124no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—64no—
447C3×C4—62no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—62no—
451C3×C4—82no—
452C3×C4—122no—
453Dic3—22no—
454Dic3—22no—
455Dic3—22no—
456Dic3—22no—
457Dic3—24no—
458Dic3—42no—
459Dic3—62no—
460Dic3—62no—
461Dic3—122no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465C32#234311yescharacteristic, complemented, Sylow
466C23—92no—
467C23—94no—
468C23—182no—
469C23—181no—
470C23—181no—
471C23C22×D3211yescharacteristic
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—34no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—92no—
493C2×C4—188no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—368no—
499C2×C4C4×D3212yes—
500C2×C3—21no—
501C2×C3—22no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—22no—
505C2×C3C4×#23511yescharacteristic
506C2×C3#550411yescharacteristic
507C2×C3#550411yescharacteristic
508C2×C3D3×#11711yescharacteristic
509C2×C3D3×#11711yescharacteristic
510C2×C3#552211yescharacteristic
511C2×C3#555612yes—
512C2×C3#558112yes—
513C2×C3#567912yes—
514C2×C3#569312yes—
515D3—64no—
516D3—64no—
517D3—124no—
518C22—94no—
519C22—184no—
520C22—182no—
521C22—182no—
522C22—184no—
523C22C2×C4×D3211yescharacteristic
524C22D3×#23512yes—
525C22#6431212yes—
526C22#6431311yescharacteristic
527C22#6431611yescharacteristic
528C4—22no—
529C4—42no—
530C4—62no—
531C4—62no—
532C4—62no—
533C4—62no—
534C4—64no—
535C4—122no—
536C4—182no—
537C4—362no—
538C3—21no—
539C3#7376611yescharacteristic, complemented
540C3#7422711yescharacteristic, complemented
541C2—184no—
542C2#1059396511yescharacteristic
543C2#1059405211yescharacteristic
544C2#1059430012yes—
545C2#1059434912yes—
546C2#1059450911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4650C2semidirect
4. C3×#4649C2semidirect
7. #10591255C2semidirect
8. #10591239C2semidirect
10. #10591223C2semidirect
11. #10591193C2semidirect
27. #63874C4semidirect
58. #4650D3semidirect
59. #4649D3semidirect
81. C3×C4×Dic3C2×C4semidirect
82. C3×C4×Dic3C2×C4semidirect
83. #3724C2×C4semidirect
84. #3724C2×C4semidirect
247. C4×Dic3C4×D3semidirect
248. C4×Dic3C4×D3semidirect
465. C32#2343semidirect
539. C3#73766semidirect
540. C3#74227semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
#105923632
C3×#46502
C3×#46492
#105913742
#105913702
#105912552
#105912392
#105912332
#105912232
#105911932
#742273
#737663