Finite Group Databasebeta

← #11778221

Subgroups — #11778221

Order 1152.

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

normal subgroups only

This group has 661 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
2C3×#5040C211yesmaximal, characteristic, complemented
3#10591304C211yesmaximal, characteristic, complemented
4#10591171C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71846—31nomaximal
9#70972—31nomaximal
10C2×C3×D3×D4—21no—
11C22×C3×Dic6C2211yescharacteristic, complemented
12C32×#121C2211yescharacteristic
13C3×#939—21no—
14C3×#937—21no—
15C2×C3×#214—21no—
16C3×#930C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C3×#894—21no—
19C3×#883—21no—
20C3×#882—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×#3715—21no—
23#63658C2211yescharacteristic, complemented
24#63657C2211yescharacteristic, complemented
25C3×#830C2211yescharacteristic, complemented
26C3×#810—21no—
27#63579—21no—
28#63565—21no—
29C3×#534—31no—
30#5605D311yescharacteristic
31C3×#448—31no—
32#5231—31no—
33#5227—31no—
34#5040—31no—
35#5040D311yescharacteristic, complemented
36#4947—31no—
37#4537—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4525—31no—
42#4470—31no—
43#4468—31no—
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C3×D3×D4—42no—
56C3×D3×D4—42no—
57C2×C3×D12—21no—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—42no—
63C32×C4⋊C4D411yescharacteristic
64C32×C22⋊C4—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—21no—
67C3×#214—42no—
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#3715—42no—
77#1601—91noSylow
78C22×C3×Q8—31no—
79C22×C3×D4—61no—
80C2×D3×D4—21no—
81C22×Dic6C2×D311yescharacteristic, complemented
82C2×C3×SD16—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—
94C2×#215—61no—
95#939—21no—
96#937—21no—
97C2×#214—21no—
98C2×#214—61no—
99#930C2×D311yescharacteristic
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4C2×D311yescharacteristic
102#894—21no—
103#883—21no—
104#882—21no—
105C3×#103—61no—
106C3×C22⋊C8—31no—
107#835—61no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#830—31no—
114#830—31no—
115#830—61no—
116#830C2×D311yescharacteristic, complemented
117#810—21no—
118#810—61no—
119C23×C32—21no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—42no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—81no—
128C22×C3×D3—81no—
129C22×C3×D3SD1612yescomplemented
130C32×D4—41no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4—21no—
134C2×C32×C4—41no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C3×#67—42no—
141C3×#67—41no—
142C3×#67—41no—
143C3×#67—81no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×D12—41no—
151C3×D12—42no—
152C3×C4×D3—42no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—41no—
159#534—31no—
160#448—31no—
161#448—91no—
162#393—91no—
163#327—91no—
164#327—91no—
165#323—91no—
166C24×C3—31no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3#6711yescharacteristic
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—122no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—31no—
177C2×C3×D4—41no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—122no—
183C2×C3×D4—122no—
184C2×C3×D4#6711yescharacteristic
185C2×C3×D4#6711yescharacteristic
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—21no—
193C2×#67—21no—
194C2×#67—21no—
195C22×Dic3—21no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—121no—
199C22×Dic3#6711yescharacteristic
200D3×D4—42no—
201D3×D4—42no—
202C2×D12—21no—
203C2×D12#6711yescharacteristic
204C2×C4×D3—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—42no—
208C3×SD16—122no—
209C2×C3×C8—61no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—31no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4#6711yescharacteristic
214C3×C4⋊C4#6711yescharacteristic
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—41no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4—61no—
223#217—21no—
224#217—122no—
225#215—122no—
226#214—42no—
227#214—122no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—21no—
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—122no—
233C4⋊Dic3#6711yescharacteristic
234Dic3⋊C4—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—121no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32—41no—
242C22×C32—41no—
243C22×C32—41no—
244C22×C32#12011yescharacteristic
245C22×C32C2×SD1611yescharacteristic
246C22×C32AGL(1,ℤ/8)11yescharacteristic
247C2×C3×D3—22no—
248C2×C3×D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3—42no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—81no—
255C2×C3×D3—84no—
256C32×C4—21no—
257C32×C4—21no—
258C32×C4—41no—
259C3⋊Dic3—81no—
260C3×Dic3—41no—
261C3×Dic3—41no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×D4—61no—
265C2×SD16—61no—
266C2×SD16—181no—
267#123—61no—
268#123—61no—
269#121—31no—
270#121—61no—
271#121D3211yescharacteristic
272#120—61no—
273#120—61no—
274C2×C22⋊C4—31no—
275C2×C22⋊C4—181no—
276#103—61no—
277#103—181no—
278C22⋊C8—31no—
279C22⋊C8—91no—
280#95—91no—
281#95—181no—
282C23×C3—21no—
283C23×C3—21no—
284C23×C3—21no—
285C23×C3—32no—
286C23×C3—41no—
287C23×C3—61no—
288C23×C3—61no—
289C23×C3—61no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—122no—
293C23×C3—241no—
294C23×C3—241no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C22×D3—21no—
298C22×D3—21no—
299C22×D3—21no—
300C22×D3—42no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—81no—
304C22×D3—81no—
305C22×D3#21412yescomplemented
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—121no—
309C3×Q8—121no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—81no—
317C3×D4—81no—
318C3×D4—81no—
319C3×D4—121no—
320C3×D4—122no—
321C3×D4—122no—
322C3×D4—121no—
323C3×D4—121no—
324C3×D4—241no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—81no—
336C2×C3×C4—122no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344#67—42no—
345#67—41no—
346#67—41no—
347#67—81no—
348C2×Dic3—22no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—122no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—241no—
362C2×Dic3—241no—
363D12—41no—
364D12—42no—
365C4×D3—42no—
366Dic6—22no—
367Dic6—22no—
368Dic6—41no—
369Dic6—41no—
370C3×C8—121no—
371C3⋊C8—41no—
372C3⋊C8—121no—
373C3⋊C8—121no—
374C3⋊C8—241no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—81no—
378C2×C32#45011yescharacteristic
379C2×C32#45511yescharacteristic
380C2×C32B(4,𝔽2)11yescharacteristic
381C3×D3—42no—
382C3×D3—81no—
383C24—31no—
384C24—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—122no—
388C2×D4—21no—
389C2×D4—31no—
390C2×D4—61no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—122no—
395C2×D4—122no—
396C2×D4#62511yescharacteristic
397C22×C4—31no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—181no—
401C22×C4C2×D3211yescharacteristic
402SD16—122no—
403SD16—362no—
404C2×C8—61no—
405C2×C8—181no—
406C4⋊C4—31no—
407C4⋊C4—61no—
408C4⋊C4#62511yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—61no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—362no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—62no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—122no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—241no—
442C22×C3—244no—
443C22×C3D3×SD1611yescharacteristic
444C22×C3#91411yescharacteristic
445C22×C3#93211yescharacteristic
446C22×C3C2×#21411yescharacteristic
447C22×C3#93711yescharacteristic
448C22×C3#95311yescharacteristic
449C2×D3—22no—
450C2×D3—41no—
451C2×D3—41no—
452C2×D3—42no—
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—81no—
457C2×D3—84no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—81no—
467C3×C4—121no—
468C3×C4—121no—
469C3×C4—122no—
470Dic3—41no—
471Dic3—41no—
472Dic3—42no—
473Dic3—241no—
474Dic3—241no—
475Dic3—242no—
476C32#160111yescharacteristic, complemented, Sylow
477C23—21no—
478C23—32no—
479C23—61no—
480C23—61no—
481C23—61no—
482C23—121no—
483C23—121no—
484C23—122no—
485C23—241no—
486C23—241no—
487C23D3×#6711yescharacteristic
488Q8—62no—
489Q8—62no—
490Q8—121no—
491Q8—121no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—121no—
496D4—122no—
497D4—122no—
498D4—121no—
499D4—121no—
500D4—241no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—62no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—122no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4—361no—
511C2×C4—361no—
512C2×C4—361no—
513C2×C4C2×#62511yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C8—121no—
516C8—361no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—81no—
527C2×C3—81no—
528C2×C3—122no—
529C2×C3—161no—
530C2×C3—241no—
531C2×C3#503211yescharacteristic
532C2×C3#516911yescharacteristic
533C2×C3#520211yescharacteristic
534C2×C3#521811yescharacteristic
535C2×C3#524211yescharacteristic
536C2×C3#524411yescharacteristic
537D3—42no—
538D3—81no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—62no—
545C22—122no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22—121no—
551C22—241no—
552C22—244no—
553C22D3×#21411yescharacteristic
554C22#6393411yescharacteristic
555C22#6397611yescharacteristic
556C4—21no—
557C4—21no—
558C4—41no—
559C4—122no—
560C4—121no—
561C4—121no—
562C4—721no—
563C3—21no—
564C3#7097211yescharacteristic, complemented
565C3#7184611yescharacteristic, complemented
566C2—21no—
567C2—21no—
568C2—81no—
569C2—122no—
570C2—241no—
571C2#1059145811yescharacteristic
572C2#1059153011yescharacteristic
573C2#1059166411yescharacteristic
subgroupG/H
centerC22#63976
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. C3×#5040C2semidirect
3. #10591304C2semidirect
4. #10591171C2semidirect
5. #10589403C2semidirect
6. #10589150C2semidirect
7. #10589145C2semidirect
11. C22×C3×Dic6C22semidirect
23. #63658C22semidirect
24. #63657C22semidirect
25. C3×#830C22semidirect
35. #5040D3semidirect
81. C22×Dic6C2×D3semidirect
116. #830C2×D3semidirect
129. C22×C3×D3SD16semidirect
305. C22×D3#214semidirect
476. C32#1601semidirect
564. C3#70972semidirect
565. C3#71846semidirect

Maximal subgroups

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

subgroupindex
C3×#56052
C3×#50402
#105913042
#105911712
#105894032
#105891502
#105891452
#718463
#709723