Finite Group Databasebeta

← #11806055

Subgroups — #11806055

Order 1152.

1197 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2#10592349C211yesmaximal, characteristic, complemented
3C3×#4666C211yesmaximal, characteristic, complemented
4C3×#4664C211yesmaximal, characteristic, complemented
5#10591386C212yesmaximal
6#10591294C211yesmaximal, characteristic, complemented
7#10591282C212yesmaximal, complemented
8#10591279C212yesmaximal, complemented
9#10591257C211yesmaximal, characteristic, complemented
10#10591243C212yesmaximal, complemented
11#10591237C211yesmaximal, characteristic, complemented
12#74061—31nomaximal
13#73463—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#625C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2212yes—
23C2×#3724C2211yescharacteristic
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30C4×#625C418yescomplemented
31C32×#95C2211yescharacteristic
32#63658C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×#67—31no—
40C3×#381—31no—
41C3×C4×C22⋊C4—31no—
42#5211—31no—
43C4×#217—31no—
44#4957—32no—
45#4957—32no—
46#4945—32no—
47#4944—32no—
48#4940—32no—
49C4×Dic3⋊C4—32no—
50#4669—32no—
51#4666—31no—
52#4666D311yescharacteristic, complemented
53#4664—31no—
54#4664D311yescharacteristic, complemented
55#4650—31no—
56#4650—31no—
57#4650—61no—
58#4649—32no—
59#4649—31no—
60#4649—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×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—42no—
73C2×C3×C4×D3—42no—
74C2×C3×C4×D3C2×C414yes—
75C2×C3×C4×D3C2×C414yes—
76C2×#625—22no—
77C2×#625—22no—
78C2×#625C2×C414yes—
79#3750—24no—
80C4×C3⋊Dic3C2×C414yes—
81C3×(C2×D3)⋊C4—24no—
82C3×(C2×D3)⋊C4—42no—
83C3×C4×Dic3—42no—
84#3724—24no—
85#3724C2×C414yes—
86(C2×D3)⋊Dic3—24no—
87(C2×D3)⋊Dic3—42no—
88(C2×D3)⋊Dic3C2×C414yes—
89(C2×D3)⋊Dic3C2×C414yes—
90Dic32—24no—
91Dic32—42no—
92#2357—91noSylow
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C22×#67—31no—
96C22×#67—31no—
97C22×C4×D3C2×D311yescharacteristic
98C22×C4×D3C2×D311yescharacteristic
99C2×C3×C22⋊C4—32no—
100C2×C3×C22⋊C4—32no—
101C2×C3×C42—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×(C2×D3)⋊C4C2×D312yes—
114C2×Dic3⋊C4—31no—
115C2×Dic3⋊C4—31no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—62no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—61no—
128C2×C4×Dic3C2×D312yes—
129C3×#95—21no—
130C3×#95—31no—
131C3×#95—31no—
132C3×#95—32no—
133C3×#95C2×D311yescharacteristic
134C3×#95C2×D311yescharacteristic
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—61no—
142C3⋊#95—62no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D312yes—
146C23×C32C2411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—21no—
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—21no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3C22×C412yes—
156C22×C3×D3C22×C412yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C22×C412yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C22×C412yes—
167C2×C3⋊Dic3C22×C412yes—
168C2×C3⋊Dic3#4112yes—
169C2×C3⋊Dic3#4112yes—
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—
179C2×C3×Dic3#4114yes—
180C3×C4×D3—44no—
181C3×C4×D3—44no—
182#625—28no—
183C2×C4×D4—91no—
184#390—92no—
185#388—92no—
186#388—92no—
187#382—91no—
188#381—31no—
189#381—91no—
190C4×C4⋊C4—91no—
191C4×C4⋊C4—92no—
192C4×C22⋊C4—31no—
193C4×C22⋊C4—91no—
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—32no—
203C22×C3×C4—34no—
204C22×C3×C4—34no—
205C22×C3×C4—32no—
206C22×C3×C4—122no—
207C22×C3×C4—122no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—34no—
213C2×#67—34no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—62no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—62no—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D312yes—
231C2×C4×D3—42no—
232C2×C4×D3—42no—
233C2×C4×D3C4×D314yes—
234C2×C4×D3C4×D314yes—
235C3×C22⋊C4—64no—
236C3×C22⋊C4—122no—
237C3×C42—122no—
238#217—34no—
239#217—34no—
240#217—64no—
241#217—122no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—34no—
244(C2×D3)⋊C4—34no—
245(C2×D3)⋊C4—42no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—122no—
248Dic3⋊C4—34no—
249Dic3⋊C4—34no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—124no—
255C4×Dic3—34no—
256C4×Dic3—34no—
257C4×Dic3—42no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—122no—
262C4×Dic3—122no—
263C22×C32C23×C411yescharacteristic
264C22×C32C2×#4112yes—
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32H(5,𝔽2)12yes—
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3—22no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C32×C4—22no—
279C32×C4—42no—
280C3⋊Dic3—22no—
281C3⋊Dic3—42no—
282C3⋊Dic3#11714yes—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—24no—
286C3×Dic3—42no—
287C22×D4—91no—
288C23×C4—31no—
289C23×C4—31no—
290C4×D4—98no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—92no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—32no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C42—32no—
301C2×C42—91no—
302C2×C42—92no—
303C2×C42—92no—
304#95—31no—
305#95—31no—
306#95—32no—
307#95—92no—
308#95—91no—
309#95—92no—
310#95D3211yescharacteristic
311C23×C3—21no—
312C23×C3—32no—
313C23×C3—32no—
314C23×C3—62no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—61no—
319C23×C3—61no—
320C23×C3—61no—
321C23×C3—61no—
322C23×C3C23×D311yescharacteristic
323C23×C3C23×D311yescharacteristic
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—21no—
329C22×D3—21no—
330C22×D3—21no—
331C22×D3—21no—
332C22×D3C2×C4×D312yes—
333C22×D3C2×C4×D312yes—
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—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—34no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—124no—
358C2×C3×C4—124no—
359C2×C3×C4C2×C4×D312yes—
360C2×C3×C4C2×C4×D312yes—
361#67—68no—
362#67—68no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3C2×C4×D312yes—
395C2×Dic3C2×C4×D312yes—
396C2×Dic3#23514yes—
397C4×D3—44no—
398C4×D3—44no—
399C2×C32C2×#11711yescharacteristic
400C2×C32C4×#4111yescharacteristic
401C2×C32#51811yescharacteristic
402C2×C32#55312yes—
403C2×C32#55912yes—
404C3×D3—42no—
405C3×D3—42no—
406C24—31no—
407C24—31no—
408C2×D4—94no—
409C2×D4—182no—
410C2×D4—182no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—31no—
414C22×C4—34no—
415C22×C4—34no—
416C22×C4—32no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—92no—
420C22×C4—122no—
421C22×C4—122no—
422C22×C4C2×D3212yes—
423C22×C4C2×D3211yescharacteristic
424C4⋊C4—94no—
425C4⋊C4—184no—
426C4⋊C4—184no—
427C22⋊C4—64no—
428C22⋊C4—94no—
429C22⋊C4—94no—
430C22⋊C4—122no—
431C22⋊C4—184no—
432C22⋊C4—362no—
433C42—94no—
434C42—122no—
435C42—184no—
436C42—362no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—62no—
443C22×C3—62no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3C22×C4×D311yescharacteristic
453C22×C3C22×C4×D311yescharacteristic
454C22×C3C2×#23512yes—
455C22×C3#100412yes—
456C22×C3#100412yes—
457C22×C3D3×#4112yes—
458C22×C3D3×#4111yescharacteristic
459C22×C3D3×#4111yescharacteristic
460C22×C3D3×#4111yescharacteristic
461C22×C3D3×#4111yescharacteristic
462C2×D3—22no—
463C2×D3—22no—
464C2×D3—22no—
465C2×D3—22no—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—42no—
471C2×D3—42no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—64no—
478C3×C4—62no—
479C3×C4—62no—
480C3×C4—82no—
481C3×C4—122no—
482Dic3—22no—
483Dic3—22no—
484Dic3—24no—
485Dic3—34no—
486Dic3—34no—
487Dic3—42no—
488Dic3—64no—
489Dic3—62no—
490Dic3—62no—
491Dic3—122no—
492Dic3—122no—
493Dic3—122no—
494Dic3—242no—
495C32#235711yescharacteristic, complemented, Sylow
496C23—32no—
497C23—32no—
498C23—62no—
499C23—62no—
500C23—61no—
501C23—61no—
502C23—62no—
503C23—62no—
504C23—61no—
505C23—61no—
506C23C22×D3211yescharacteristic
507D4—188no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—34no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—124no—
527C2×C4—124no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4C4×D3212yes—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3—122no—
539C2×C3—122no—
540C2×C3C4×#23511yescharacteristic
541C2×C3#548611yescharacteristic
542C2×C3#548611yescharacteristic
543C2×C3D3×#11711yescharacteristic
544C2×C3D3×#11711yescharacteristic
545C2×C3#552211yescharacteristic
546C2×C3#554012yes—
547C2×C3#555912yes—
548C2×C3#566112yes—
549C2×C3#566412yes—
550D3—42no—
551D3—42no—
552C22—62no—
553C22—62no—
554C22—62no—
555C22—62no—
556C22—62no—
557C22—62no—
558C22—122no—
559C22—122no—
560C22—122no—
561C22—122no—
562C22C2×C4×D3211yescharacteristic
563C22D3×#23512yes—
564C22#6431211yescharacteristic
565C22#6431312yes—
566C22#6431911yescharacteristic
567C4—22no—
568C4—42no—
569C4—64no—
570C4—62no—
571C4—62no—
572C4—94no—
573C4—122no—
574C4—182no—
575C4—362no—
576C3—21no—
577C3#7346311yescharacteristic, complemented
578C3#7406111yescharacteristic, complemented
579C2—122no—
580C2—122no—
581C2#1059396511yescharacteristic
582C2#1059418111yescharacteristic
583C2#1059420812yes—
584C2#1059441312yes—
585C2#1059460211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592349C2semidirect
3. C3×#4666C2semidirect
4. C3×#4664C2semidirect
6. #10591294C2semidirect
7. #10591282C2semidirect
8. #10591279C2semidirect
9. #10591257C2semidirect
10. #10591243C2semidirect
11. #10591237C2semidirect
30. C4×#625C4semidirect
52. #4666D3semidirect
54. #4664D3semidirect
495. C32#2357semidirect
577. C3#73463semidirect
578. C3#74061semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
#105923492
C3×#46662
C3×#46642
#105913862
#105912942
#105912822
#105912792
#105912572
#105912432
#105912372
#740613
#734633