Finite Group Databasebeta

← #11805086

Subgroups — #11805086

Order 1152.

1141 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63855C211yesmaximal, characteristic
2#10592349C211yesmaximal, characteristic, complemented
3C3×#4664C211yesmaximal, characteristic
4C3×#4649C211yesmaximal, characteristic, complemented
5#10591372C212yesmaximal
6Dic3×(C2×D3)⋊C4C212yesmaximal
7D3×C3⋊#95C211yesmaximal, characteristic
8#10591332C212yesmaximal, complemented
9#10591254C212yesmaximal, complemented
10#10591252C211yesmaximal, characteristic, complemented
11#10591223C211yesmaximal, characteristic, complemented
12#74059—31nomaximal
13#73766—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×#3750C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×Dic3⋊Dic3C2211yescharacteristic
23C2×Dic3⋊Dic3C2211yescharacteristic
24C2×(C2×D3)⋊Dic3C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2211yescharacteristic
26C2×Dic32C2212yes—
27#63855C418yescomplemented
28C32×#95C2211yescharacteristic
29#63658C2212yes—
30#63658C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#926—31no—
39C2×#872—31no—
40C3×#381—31no—
41C3×C4×C4⋊C4—31no—
42C2×C3⋊#95—31no—
43#4989—32no—
44#4978—32no—
45#4946—32no—
46Dic3×C22⋊C4—32no—
47C4×(C2×D3)⋊C4—32no—
48#4937—31no—
49#4933—32no—
50#4664D311yescharacteristic
51D3×#95—31no—
52#4654—32no—
53#4653—32no—
54#4651—31no—
55#4650—31no—
56#4650—31no—
57#4650—61no—
58#4649D311yescharacteristic, complemented
59#4648—31no—
60#4648—31no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3C2×C414yes—
74C2×D3×Dic3—24no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—42no—
77#3750—42no—
78C4×C3⋊Dic3C2×C414yescomplemented
79C3×(C2×D3)⋊C4—24no—
80C3×Dic3⋊C4—24no—
81C3×C4×Dic3—42no—
82C3×C4×Dic3C2×C414yescomplemented
83Dic3⋊Dic3C2×C414yescomplemented
84Dic3⋊Dic3C2×C414yescomplemented
85(C2×D3)⋊Dic3C2×C414yes—
86(C2×D3)⋊Dic3C2×C414yes—
87Dic32—24no—
88#2343—91noSylow
89C23×C3×C4—31no—
90C23×Dic3—32no—
91C22×C4×D3—32no—
92C22×C4×D3C2×D311yescharacteristic
93C2×C3×C4⋊C4—32no—
94C2×C3×C22⋊C4—32no—
95C2×C3×C42—31no—
96C2×C3×C42—32no—
97C2×#217—31no—
98C2×#217—31no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4C2×D312yes—
102#926—38no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×Dic3⋊C4—31no—
106C2×Dic3⋊C4—31no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4—62no—
110C2×Dic3⋊C4C2×D312yes—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3C2×D312yes—
117C2×C4×Dic3C2×D311yescharacteristic
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—32no—
127C3⋊#95—31no—
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—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C22×C412yes—
160C2×C3⋊Dic3C22×C412yes—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—22no—
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×Dic3#4114yes—
174C3×C4×D3—28no—
175D3×Dic3—48no—
176C2×#117—91no—
177#387—92no—
178#387—92no—
179#385—92no—
180#383—91no—
181#382—91no—
182#381—31no—
183C4×C4⋊C4—31no—
184C4×C22⋊C4—92no—
185#376—91no—
186C2×#95—91no—
187C24×C3—31no—
188C23×D3C22×D311yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—31no—
192C22×C3×C4—32no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—34no—
196C22×C3×C4—32no—
197C22×C3×C4—64no—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—62no—
211C22×Dic3—64no—
212C22×Dic3—64no—
213C22×Dic3—122no—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D311yescharacteristic
216C22×Dic3C22×D311yescharacteristic
217C22×Dic3C22×D311yescharacteristic
218C22×Dic3C22×D312yes—
219C2×C4×D3—24no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—122no—
223C2×C4×D3C4×D314yes—
224C3×C4⋊C4—64no—
225C3×C22⋊C4—64no—
226C3×C42—34no—
227C3×C42—122no—
228#217—34no—
229#217—34no—
230(C2×D3)⋊C4—24no—
231(C2×D3)⋊C4—34no—
232(C2×D3)⋊C4—34no—
233C4⋊Dic3—34no—
234C4⋊Dic3—34no—
235Dic3⋊C4—24no—
236Dic3⋊C4—34no—
237Dic3⋊C4—34no—
238Dic3⋊C4—122no—
239Dic3⋊C4—122no—
240Dic3⋊C4—124no—
241C4×Dic3—34no—
242C4×Dic3—34no—
243C4×Dic3—42no—
244C4×Dic3—64no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C4×Dic3C4×D314yescomplemented
248C22×C32C23×C411yescharacteristic
249C22×C32C2×#4112yes—
250C22×C32C2×#4112yes—
251C22×C32H(5,𝔽2)11yescharacteristic
252C22×C322−1+411yescharacteristic
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—24no—
256C2×C3×D3—24no—
257C2×C3×D3#11714yes—
258C32×C4—22no—
259C32×C4—42no—
260C3⋊Dic3—22no—
261C3⋊Dic3—22no—
262C3⋊Dic3—42no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—24no—
267C3×Dic3—42no—
268C23×C4—31no—
269C23×C4—92no—
270#117—98no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—92no—
275C2×C22⋊C4—32no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C42—31no—
279C2×C42—32no—
280C2×C42—91no—
281C2×C42—92no—
282#95—31no—
283#95—31no—
284#95—32no—
285#95—92no—
286#95—92no—
287#95—92no—
288#95—92no—
289#95—91no—
290#95—92no—
291#95D3211yescharacteristic
292C23×C3—21no—
293C23×C3—32no—
294C23×C3—34no—
295C23×C3—62no—
296C23×C3—61no—
297C23×C3—61no—
298C23×C3C23×D311yescharacteristic
299C23×C3C23×D311yescharacteristic
300C22×D3—22no—
301C22×D3—21no—
302C22×D3—21no—
303C22×D3C2×C4×D312yes—
304C22×D3#23714yes—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—32no—
317C2×C3×C4—34no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—68no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—61no—
327C2×C3×C4—62no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4C2×C4×D312yes—
333C2×C3×C4C2×C4×D312yes—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—21no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—62no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—128no—
368C2×Dic3C2×C4×D312yes—
369C2×Dic3C2×C4×D312yes—
370C2×Dic3C2×C4×D312yes—
371C2×Dic3#23514yes—
372C4×D3—28no—
373C4×D3—128no—
374C2×C32C2×#11711yescharacteristic
375C2×C32C4×#4111yescharacteristic
376C2×C32#52011yescharacteristic
377C2×C32#55112yes—
378C2×C32#55212yes—
379C3×D3—24no—
380C24—31no—
381C22×C4—31no—
382C22×C4—32no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—34no—
386C22×C4—32no—
387C22×C4—64no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—92no—
391C22×C4—184no—
392C22×C4—184no—
393C22×C4—362no—
394C22×C4C2×D3212yes—
395C22×C4C2×D3211yescharacteristic
396C4⋊C4—64no—
397C4⋊C4—94no—
398C4⋊C4—94no—
399C4⋊C4—362no—
400C22⋊C4—64no—
401C22⋊C4—94no—
402C22⋊C4—94no—
403C42—34no—
404C42—94no—
405C42—122no—
406C42—184no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—34no—
413C22×C3—62no—
414C22×C3—62no—
415C22×C3—64no—
416C22×C3—64no—
417C22×C3C22×C4×D311yescharacteristic
418C22×C3C22×C4×D311yescharacteristic
419C22×C3C2×#23512yes—
420C22×C3C2×#23712yes—
421C22×C3#100411yescharacteristic
422C22×C3#100711yescharacteristic
423C22×C3D3×#4112yes—
424C22×C3D3×#4112yes—
425C22×C3#100911yescharacteristic
426C22×C3#101011yescharacteristic
427C2×D3—24no—
428C2×D3—24no—
429C2×D3—22no—
430C2×D3—22no—
431C2×D3#87714yes—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—42no—
437C3×C4—64no—
438C3×C4—62no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4—82no—
442C3×C4—122no—
443Dic3—22no—
444Dic3—22no—
445Dic3—22no—
446Dic3—24no—
447Dic3—42no—
448Dic3—64no—
449Dic3—62no—
450Dic3—62no—
451Dic3—62no—
452Dic3—62no—
453Dic3—122no—
454Dic3—122no—
455Dic3—122no—
456Dic3—242no—
457C32#234311yescharacteristic, complemented, Sylow
458C23—32no—
459C23—34no—
460C23—62no—
461C23—61no—
462C23—61no—
463C23C22×D3211yescharacteristic
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—34no—
472C2×C4—68no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—62no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—182no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4—182no—
490C2×C4—368no—
491C2×C4C4×D3212yes—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—64no—
498C2×C3C4×#23511yescharacteristic
499C2×C3C2×#87711yescharacteristic
500C2×C3#550411yescharacteristic
501C2×C3D3×#11711yescharacteristic
502C2×C3#552211yescharacteristic
503C2×C3#552311yescharacteristic
504C2×C3#555612yes—
505C2×C3#558112yes—
506C2×C3#565012yes—
507C2×C3#565812yes—
508D3—24no—
509C22—34no—
510C22—64no—
511C22—62no—
512C22—62no—
513C22—64no—
514C22C2×C4×D3211yescharacteristic
515C22D3×#23512yes—
516C22D3×#23712yes—
517C22#6431411yescharacteristic
518C22#6431511yescharacteristic
519C4—22no—
520C4—42no—
521C4—62no—
522C4—62no—
523C4—64no—
524C4—62no—
525C4—122no—
526C4—182no—
527C4—182no—
528C4—362no—
529C3—21no—
530C3#7376611yescharacteristic, complemented
531C3#7405911yescharacteristic, complemented
532C2—64no—
533C2#1059396511yescharacteristic
534C2D3×#87711yescharacteristic
535C2#1059429912yes—
536C2#1059442012yes—
537C2#1059451011yescharacteristic
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
2. #10592349C2semidirect
4. C3×#4649C2semidirect
8. #10591332C2semidirect
9. #10591254C2semidirect
10. #10591252C2semidirect
11. #10591223C2semidirect
27. #63855C4semidirect
58. #4649D3semidirect
78. C4×C3⋊Dic3C2×C4semidirect
82. C3×C4×Dic3C2×C4semidirect
83. Dic3⋊Dic3C2×C4semidirect
84. Dic3⋊Dic3C2×C4semidirect
247. C4×Dic3C4×D3semidirect
457. C32#2343semidirect
530. C3#73766semidirect
531. C3#74059semidirect

Maximal subgroups

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

subgroupindex
C2×#638552
#105923492
C3×#46642
C3×#46492
#105913722
Dic3×(C2×D3)⋊C42
D3×C3⋊#952
#105913322
#105912542
#105912522
#105912232
#740593
#737663