Finite Group Databasebeta

← #11803071

Subgroups — #11803071

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2#10592350C211yesmaximal, characteristic, complemented
3C3×#4667C211yesmaximal, characteristic, complemented
4C3×D3×#95C211yesmaximal, characteristic, complemented
5#10591381C212yesmaximal
6#10591360C211yesmaximal, characteristic, complemented
7#10591294C211yesmaximal, characteristic, complemented
8#10591282C212yesmaximal, complemented
9#10591277C212yesmaximal, complemented
10#10591255C212yesmaximal, complemented
11#10591237C211yesmaximal, characteristic, complemented
12#74006—31nomaximal
13#73367—31nomaximal
14C22×C3×C4×D3C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#625C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×#3724C2212yes—
22C2×#3724C2211yescharacteristic
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2211yescharacteristic
27C2×Dic32C2212yes—
28C4×#625C418yescomplemented
29C32×#95C2211yescharacteristic
30#63658C2211yescharacteristic
31#63658C2212yes—
32#63658C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×#67—31no—
40C3×#380—31no—
41C2×C3×#95—31no—
42#5213—32no—
43#5211—31no—
44#5210—32no—
45C4×#217—31no—
46#4989—32no—
47#4978—32no—
48#4956—32no—
49#4945—32no—
50#4669—32no—
51#4667D311yescharacteristic, complemented
52#4666—31no—
53#4664—31no—
54D3×#95D311yescharacteristic, complemented
55#4652—32no—
56#4651—31no—
57#4651—31no—
58#4651—61no—
59#4650—31no—
60#4650—31no—
61C23×C3×D3C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3—42no—
74C2×C3×C4×D3—42no—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3—42no—
77C2×C3×C4×D3C2×C414yes—
78C2×C3×C4×D3C2×C414yescomplemented
79C2×#625—24no—
80C2×#625C2×C414yes—
81C4×C3⋊Dic3C2×C414yescomplemented
82C3×(C2×D3)⋊C4—42no—
83C3×Dic3⋊C4—42no—
84#3724—42no—
85#3724C2×C414yescomplemented
86(C2×D3)⋊Dic3—24no—
87(C2×D3)⋊Dic3—42no—
88(C2×D3)⋊Dic3C2×C414yes—
89(C2×D3)⋊Dic3C2×C414yescomplemented
90Dic32—42no—
91#2318—91noSylow
92C23×C3×C4—31no—
93C23×C3×C4—31no—
94C23×C3×C4—32no—
95C22×#67—31no—
96C22×#67—31no—
97C22×C4×D3C2×D312yes—
98C22×C4×D3C2×D311yescharacteristic
99C22×C4×D3C2×D311yescharacteristic
100C2×C3×C4⋊C4—32no—
101C2×C3×C22⋊C4—32no—
102C2×#217—31no—
103C2×#217—31no—
104C2×#217—32no—
105C2×#217—32no—
106C4×#67—38no—
107C4×#67—38no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4C2×D312yes—
113C2×Dic3⋊C4—31no—
114C2×Dic3⋊C4—31no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4C2×D312yes—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—61no—
123C3×#95—21no—
124C3×#95—31no—
125C3×#95—31no—
126C3×#95—32no—
127C3×#95C2×D311yescharacteristic
128C3×#95C2×D311yescharacteristic
129C3⋊#95—32no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—61no—
140C3⋊#95—62no—
141C3⋊#95—62no—
142C3⋊#95C2×D311yescharacteristic
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—21no—
152C22×C3×D3—21no—
153C22×C3×D3C22×C412yes—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4114yes—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C22×C412yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C22×C412yes—
168C2×C3⋊Dic3C22×C412yes—
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×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C3×C4×D3—44no—
180C3×C4×D3—44no—
181C3×C4×D3—48no—
182#625—28no—
183C2×C4×D4—91no—
184#388—92no—
185#387—92no—
186#386—92no—
187#385—92no—
188#383—91no—
189#382—91no—
190#381—91no—
191#380—31no—
192C4×C22⋊C4—91no—
193C2×#95—31no—
194C24×C3—31no—
195C24×C3—31no—
196C23×D3C22×D311yescharacteristic
197C23×D3C22×D311yescharacteristic
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—34no—
203C22×C3×C4—34no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—64no—
207C22×C3×C4—122no—
208C22×C3×C4—122no—
209C22×C3×C4—122no—
210C22×C3×C4—122no—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—34no—
216C2×#67—34no—
217C2×#67—64no—
218C2×#67—64no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—62no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D311yescharacteristic
232C2×C4×D3—24no—
233C2×C4×D3—42no—
234C2×C4×D3—42no—
235C2×C4×D3—42no—
236C2×C4×D3—42no—
237C2×C4×D3C4×D314yes—
238C2×C4×D3C4×D314yescomplemented
239C3×C4⋊C4—122no—
240C3×C22⋊C4—122no—
241#217—34no—
242#217—34no—
243#217—64no—
244#217—122no—
245(C2×D3)⋊C4—34no—
246(C2×D3)⋊C4—34no—
247(C2×D3)⋊C4—42no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—122no—
250Dic3⋊C4—34no—
251Dic3⋊C4—34no—
252Dic3⋊C4—42no—
253Dic3⋊C4—122no—
254Dic3⋊C4—122no—
255C4×Dic3—34no—
256C4×Dic3—34no—
257C4×Dic3—64no—
258C4×Dic3—122no—
259C4×Dic3—122no—
260C22×C32C23×C411yescharacteristic
261C22×C32C2×#4112yes—
262C22×C32H(5,𝔽2)12yes—
263C22×C32H(5,𝔽2)11yescharacteristic
264C22×C322−1+411yescharacteristic
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—24no—
268C2×C3×D3—24no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3#11714yes—
275C32×C4—22no—
276C32×C4—42no—
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—42no—
283C3×Dic3—42no—
284C22×D4—91no—
285C23×C4—31no—
286C23×C4—31no—
287C23×C4—32no—
288C4×D4—98no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—92no—
292C2×C22⋊C4—32no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—92no—
297C2×C42—91no—
298C2×C42—92no—
299#95—31no—
300#95—32no—
301#95—31no—
302#95—92no—
303#95—92no—
304#95—91no—
305#95—92no—
306#95—92no—
307#95D3211yescharacteristic
308C23×C3—21no—
309C23×C3—32no—
310C23×C3—34no—
311C23×C3—32no—
312C23×C3—62no—
313C23×C3—61no—
314C23×C3—61no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—61no—
318C23×C3—61no—
319C23×C3C23×D311yescharacteristic
320C23×C3C23×D311yescharacteristic
321C22×D3—22no—
322C22×D3—21no—
323C22×D3—21no—
324C22×D3—21no—
325C22×D3—22no—
326C22×D3—21no—
327C22×D3—22no—
328C22×D3C2×C4×D312yes—
329C22×D3C2×C4×D312yes—
330C22×D3#23514yes—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
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—32no—
341C2×C3×C4—32no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
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—124no—
355C2×C3×C4—124no—
356C2×C3×C4—128no—
357C2×C3×C4C2×C4×D312yes—
358C2×C3×C4C2×C4×D312yes—
359#67—68no—
360#67—68no—
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—32no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—122no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3C2×C4×D312yes—
394C2×Dic3C2×C4×D312yes—
395C4×D3—44no—
396C4×D3—44no—
397C4×D3—48no—
398C2×C32C2×#11711yescharacteristic
399C2×C32#51811yescharacteristic
400C2×C32#52011yescharacteristic
401C2×C32#53812yes—
402C2×C32#53912yes—
403C3×D3—24no—
404C3×D3—42no—
405C24—31no—
406C24—31no—
407C2×D4—94no—
408C2×D4—184no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—34no—
412C22×C4—34no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—64no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—92no—
419C22×C4—122no—
420C22×C4—122no—
421C22×C4—122no—
422C22×C4—122no—
423C22×C4C2×D3212yes—
424C22×C4C2×D3211yescharacteristic
425C4⋊C4—94no—
426C4⋊C4—122no—
427C4⋊C4—362no—
428C22⋊C4—94no—
429C22⋊C4—94no—
430C22⋊C4—122no—
431C22⋊C4—184no—
432C22⋊C4—362no—
433C42—94no—
434C42—362no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—34no—
441C22×C3—64no—
442C22×C3—62no—
443C22×C3—62no—
444C22×C3—64no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3C22×C4×D311yescharacteristic
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C2×#23512yes—
453C22×C3#100412yes—
454C22×C3#100412yes—
455C22×C3#100411yescharacteristic
456C22×C3#100411yescharacteristic
457C22×C3#100711yescharacteristic
458C22×C3#100711yescharacteristic
459C22×C3D3×#4112yes—
460C2×D3—22no—
461C2×D3—24no—
462C2×D3—22no—
463C2×D3—24no—
464C2×D3—22no—
465C2×D3—22no—
466C2×D3—22no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3#87214yes—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—62no—
476C3×C4—62no—
477C3×C4—82no—
478C3×C4—122no—
479C3×C4—122no—
480Dic3—22no—
481Dic3—22no—
482Dic3—42no—
483Dic3—42no—
484Dic3—62no—
485Dic3—62no—
486Dic3—62no—
487Dic3—62no—
488Dic3—122no—
489Dic3—122no—
490Dic3—122no—
491Dic3—122no—
492Dic3—242no—
493C32#231811yescharacteristic, complemented, Sylow
494C23—32no—
495C23—34no—
496C23—32no—
497C23—62no—
498C23—61no—
499C23—61no—
500C23—62no—
501C23—61no—
502C23—62no—
503C23—61no—
504C23C22×D3211yescharacteristic
505D4—188no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—32no—
511C2×C4—32no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—124no—
523C2×C4—124no—
524C2×C4—128no—
525C2×C4—182no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4C4×D3212yes—
532C2×C3—21no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—64no—
538C2×C3—122no—
539C2×C3C2×#87211yescharacteristic
540C2×C3#548611yescharacteristic
541C2×C3#548611yescharacteristic
542C2×C3#549412yes—
543C2×C3#550411yescharacteristic
544C2×C3#550411yescharacteristic
545C2×C3#551512yes—
546C2×C3D3×#11711yescharacteristic
547C2×C3#561312yes—
548C2×C3#563812yes—
549D3—24no—
550D3—42no—
551C22—34no—
552C22—62no—
553C22—64no—
554C22—62no—
555C22—64no—
556C22—62no—
557C22—62no—
558C22—62no—
559C22—122no—
560C22—122no—
561C22C2×C4×D3211yescharacteristic
562C22D3×#23512yes—
563C22#6431312yes—
564C22#6431311yescharacteristic
565C22#6431611yescharacteristic
566C4—22no—
567C4—42no—
568C4—62no—
569C4—62no—
570C4—122no—
571C4—122no—
572C4—182no—
573C4—182no—
574C4—362no—
575C3—21no—
576C3#7336711yescharacteristic, complemented
577C3#7400611yescharacteristic, complemented
578C2—64no—
579C2—122no—
580C2D3×#87211yescharacteristic
581C2#1059418111yescharacteristic
582C2#1059419512yes—
583C2#1059450911yescharacteristic
584C2#1059454012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592350C2semidirect
3. C3×#4667C2semidirect
4. C3×D3×#95C2semidirect
6. #10591360C2semidirect
7. #10591294C2semidirect
8. #10591282C2semidirect
9. #10591277C2semidirect
10. #10591255C2semidirect
11. #10591237C2semidirect
28. C4×#625C4semidirect
51. #4667D3semidirect
54. D3×#95D3semidirect
78. C2×C3×C4×D3C2×C4semidirect
81. C4×C3⋊Dic3C2×C4semidirect
85. #3724C2×C4semidirect
89. (C2×D3)⋊Dic3C2×C4semidirect
238. C2×C4×D3C4×D3semidirect
493. C32#2318semidirect
576. C3#73367semidirect
577. C3#74006semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
#105923502
C3×#46672
C3×D3×#952
#105913812
#105913602
#105912942
#105912822
#105912772
#105912552
#105912372
#740063
#733673