Finite Group Databasebeta

← #11778219

Subgroups — #11778219

Order 1152.

695 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 695 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5605C211yesmaximal, characteristic
2#10592739C211yesmaximal, characteristic, complemented
3#10591322C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71846—31nomaximal
9#68286—31nomaximal
10C22×#634C2211yescharacteristic, complemented
11C2×C3×D3×D4—21no—
12C32×#121C2211yescharacteristic
13C2×#3754—21no—
14C3×#939—21no—
15C3×#937—21no—
16C3×#930C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C3×#894—21no—
19C3×#883—21no—
20C3×#882—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×#3716—21no—
23#63657C2211yescharacteristic, complemented
24#63637—21no—
25C3×C3⋊#95C2211yescharacteristic, complemented
26C3×#830C2211yescharacteristic, complemented
27#63579—21no—
28#63567—21no—
29C3×#534—31no—
30#5605D311yescharacteristic
31#5040—31no—
32#5040—31no—
33#5040—31no—
34#5040—61no—
35#4947—31no—
36#4738—31no—
37#4673—31no—
38C3×#327—31no—
39#4537—31no—
40#4537D311yescharacteristic, complemented
41#4525—31no—
42#4468—31no—
43#4451—31no—
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—42no—
53C2×C3×#67—21no—
54C2×C3×#67—21no—
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C3×D3×D4—42no—
59C3×D3×D4—42no—
60C2×C3×D12—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C32×C4⋊C4D411yescharacteristic
64C32×C22⋊C4—21no—
65#3754—42no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#217—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×C4⋊Dic3D411yescharacteristic
73C3×Dic3⋊C4—21no—
74C2×C3×C3⋊C8—21no—
75(C2×D3)⋊Dic3—42no—
76#3716—42no—
77#1601—91noSylow
78C22×C3×D4—61no—
79C2×D3×D4—21no—
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C3×#123—61no—
84C3×#123—61no—
85C3×#121—21no—
86C3×#121—31no—
87C3×#121—61no—
88C3×#121C2×D311yescharacteristic
89C3×#121C2×D311yescharacteristic
90C3×#120—61no—
91C3×#120—61no—
92C2×C3×C22⋊C4—31no—
93C2×#217—61no—
94#939—21no—
95#937—21no—
96C2×#214—61no—
97C2×#214—62no—
98C2×#214—61no—
99C2×#214—61no—
100#930C2×D311yescharacteristic
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4C2×D311yescharacteristic
103C2×#204—61no—
104#894—21no—
105#883—21no—
106#882—21no—
107C3×C22⋊C8—31no—
108C3×#95—31no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic, complemented
112#830—31no—
113#830—31no—
114#830—61no—
115#830C2×D311yescharacteristic, complemented
116#816—61no—
117#810—61no—
118#810—62no—
119#810—61no—
120#810—61no—
121C23×C32—21no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3—42no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—81no—
130C22×C3×D3—81no—
131C22×C3×D3SD1612yescomplemented
132C32×D4—41no—
133C32×D4—41no—
134C32×D4—41no—
135C2×C32×C4—21no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142#634—22no—
143#634—22no—
144#634—41no—
145#634—41no—
146C3×#67—42no—
147C3×#67—41no—
148C3×#67—41no—
149C3×#67—81no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C3×D12—41no—
157C3×D12—42no—
158C3×C4×D3—42no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—41no—
161#534—31no—
162#448—91no—
163#448—91no—
164#393—91no—
165#327—31no—
166#327—91no—
167#323—91no—
168C24×C3—31no—
169C24×C3—61no—
170C23×D3—21no—
171C23×D3#6711yescharacteristic
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—31no—
176C2×C3×D4—41no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—122no—
182C2×C3×D4—122no—
183C2×C3×D4D1211yescharacteristic
184C2×C3×D4#6711yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4—31no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C2×#67—21no—
193C2×#67—21no—
194C22×Dic3—21no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—121no—
198C22×Dic3#6711yescharacteristic
199D3×D4—42no—
200D3×D4—42no—
201C2×D12—21no—
202C2×D12#6711yescharacteristic
203C2×C4×D3—21no—
204C2×Dic6—62no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—121no—
210C2×Dic6—122no—
211C2×Dic6—122no—
212C2×Dic6—124no—
213C2×C3×C8—61no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—31no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4D1211yescharacteristic
218C3×C4⋊C4#6711yescharacteristic
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221C3×C22⋊C4—41no—
222C3×C22⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—61no—
227#217—21no—
228#217—122no—
229#214—122no—
230#214—122no—
231#214—122no—
232#214—124no—
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—21no—
235(C2×D3)⋊C4—21no—
236(C2×D3)⋊C4—21no—
237(C2×D3)⋊C4—122no—
238C4⋊Dic3#6711yescharacteristic
239Dic3⋊C4—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244#204—122no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—41no—
248C22×C32—41no—
249C22×C32—41no—
250C22×C32#12011yescharacteristic
251C22×C32C2×SD1611yescharacteristic
252C22×C32AGL(1,ℤ/8)11yescharacteristic
253C2×C3×D3—22no—
254C2×C3×D3—41no—
255C2×C3×D3—41no—
256C2×C3×D3—42no—
257C2×C3×D3—41no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C2×C3×D3—81no—
261C2×C3×D3—84no—
262C32×C4—21no—
263C32×C4—21no—
264C32×C4—41no—
265C3⋊Dic3—42no—
266C3×Dic3—41no—
267C3×Dic3—41no—
268C3×Dic3—81no—
269C22×Q8—91no—
270C22×D4—61no—
271C2×SD16—181no—
272C2×SD16—181no—
273#123—61no—
274#123—61no—
275#121—31no—
276#121—61no—
277#121D3211yescharacteristic
278#120—61no—
279#120—61no—
280C2×C22⋊C4—31no—
281C2×C22⋊C4—181no—
282#103—181no—
283#103—181no—
284C22⋊C8—31no—
285C22⋊C8—91no—
286#95—31no—
287#95—181no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—32no—
292C23×C3—41no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—61no—
296C23×C3—121no—
297C23×C3—121no—
298C23×C3—122no—
299C23×C3—241no—
300C23×C3—241no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—21no—
304C22×D3—21no—
305C22×D3—21no—
306C22×D3—42no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—81no—
310C22×D3—81no—
311C22×D3#21412yescomplemented
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—42no—
315C3×D4—41no—
316C3×D4—41no—
317C3×D4—41no—
318C3×D4—41no—
319C3×D4—81no—
320C3×D4—81no—
321C3×D4—121no—
322C3×D4—122no—
323C3×D4—122no—
324C3×D4—121no—
325C3×D4—121no—
326C3×D4—241no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—42no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—122no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346#67—42no—
347#67—41no—
348#67—41no—
349#67—81no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—122no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365D12—41no—
366D12—42no—
367C4×D3—42no—
368Dic6—62no—
369Dic6—64no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—122no—
374Dic6—122no—
375Dic6—121no—
376Dic6—121no—
377Dic6—121no—
378Dic6—121no—
379Dic6—122no—
380C3×C8—121no—
381C3⋊C8—41no—
382C3⋊C8—122no—
383C3⋊C8—121no—
384C3⋊C8—121no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32—81no—
388C2×C32#45011yescharacteristic
389C2×C32#45511yescharacteristic
390C2×C32B(4,𝔽2)11yescharacteristic
391C3×D3—42no—
392C3×D3—81no—
393C24—31no—
394C24—61no—
395C2×Q8—181no—
396C2×Q8—181no—
397C2×Q8—362no—
398C2×D4—21no—
399C2×D4—31no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—122no—
405C2×D4—122no—
406C2×D4#62611yescharacteristic
407C22×C4—31no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—181no—
411C22×C4C2×D3211yescharacteristic
412SD16—362no—
413SD16—362no—
414C2×C8—61no—
415C2×C8—181no—
416C4⋊C4—31no—
417C4⋊C4—61no—
418C4⋊C4#62611yescharacteristic
419C22⋊C4—21no—
420C22⋊C4—61no—
421C22⋊C4—61no—
422C22⋊C4—61no—
423C22⋊C4—61no—
424C22⋊C4—61no—
425C22⋊C4—362no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—62no—
442C22×C3—81no—
443C22×C3—81no—
444C22×C3—81no—
445C22×C3—122no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3—241no—
452C22×C3—244no—
453C22×C3#88211yescharacteristic
454C22×C3#91111yescharacteristic
455C22×C3D3×SD1611yescharacteristic
456C22×C3#93211yescharacteristic
457C22×C3C2×#21411yescharacteristic
458C22×C3#95311yescharacteristic
459C2×D3—22no—
460C2×D3—41no—
461C2×D3—41no—
462C2×D3—42no—
463C2×D3—41no—
464C2×D3—41no—
465C2×D3—41no—
466C2×D3—81no—
467C2×D3—84no—
468C3×C4—22no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—81no—
477C3×C4—121no—
478C3×C4—121no—
479C3×C4—241no—
480Dic3—41no—
481Dic3—41no—
482Dic3—81no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486C32#160111yescharacteristic, complemented, Sylow
487C23—21no—
488C23—32no—
489C23—61no—
490C23—61no—
491C23—61no—
492C23—121no—
493C23—121no—
494C23—122no—
495C23—241no—
496C23—241no—
497C23D3×#6711yescharacteristic
498Q8—182no—
499Q8—182no—
500Q8—361no—
501Q8—361no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—121no—
506D4—122no—
507D4—122no—
508D4—121no—
509D4—121no—
510D4—241no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—122no—
516C2×C4—121no—
517C2×C4—121no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—182no—
521C2×C4—361no—
522C2×C4—361no—
523C2×C4C2×#62611yescharacteristic
524C2×C4D3×#6711yescharacteristic
525C8—121no—
526C8—361no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—41no—
535C2×C3—41no—
536C2×C3—81no—
537C2×C3—81no—
538C2×C3—122no—
539C2×C3—161no—
540C2×C3—241no—
541C2×C3#474111yescharacteristic
542C2×C3#477611yescharacteristic
543C2×C3#482511yescharacteristic
544C2×C3#521811yescharacteristic
545C2×C3#524211yescharacteristic
546C2×C3#524411yescharacteristic
547D3—42no—
548D3—81no—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—62no—
555C22—122no—
556C22—121no—
557C22—121no—
558C22—121no—
559C22—121no—
560C22—121no—
561C22—241no—
562C22—244no—
563C22D3×#21411yescharacteristic
564C22#6393211yescharacteristic
565C22#6397711yescharacteristic
566C4—21no—
567C4—21no—
568C4—41no—
569C4—121no—
570C4—121no—
571C4—241no—
572C4—362no—
573C3—21no—
574C3#6828611yescharacteristic, complemented
575C3#7184611yescharacteristic, complemented
576C2—21no—
577C2—21no—
578C2—81no—
579C2—122no—
580C2—241no—
581C2#1059145911yescharacteristic
582C2#1059153111yescharacteristic
583C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radicalC3×#5605C2
hypercenter#121D32
hypocenterC32#1601
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10592739C2semidirect
3. #10591322C2semidirect
4. #10591181C2semidirect
5. C3×#4537C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
10. C22×#634C22semidirect
23. #63657C22semidirect
25. C3×C3⋊#95C22semidirect
26. C3×#830C22semidirect
40. #4537D3semidirect
111. C3⋊#95C2×D3semidirect
115. #830C2×D3semidirect
131. C22×C3×D3SD16semidirect
311. C22×D3#214semidirect
486. C32#1601semidirect
574. C3#68286semidirect
575. C3#71846semidirect

Maximal subgroups

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

subgroupindex
C3×#56052
#105927392
#105913222
#105911812
C3×#45372
#105891492
#105891452
#718463
#682863