Finite Group Databasebeta

← #11790812

Subgroups — #11790812

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595029C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic, complemented
4C3×#5118C211yesmaximal, characteristic, complemented
5#10591222C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63568C211yesmaximal, characteristic, complemented
8#70513—31nomaximal
9#70357—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63978—22no—
18#63911C411yescharacteristic, complemented
19C4×#626—22no—
20#63866C411yescharacteristic, complemented
21#63864C411yescharacteristic, complemented
22#63860C411yescharacteristic, complemented
23#63652—22no—
24C3×#825—22no—
25C3×Dic3⋊C8—22no—
26#63579—22no—
27#63570—22no—
28#63568—22no—
29#5832—31no—
30#5477—31no—
31C3×#423—31no—
32C2×C3×#104—31no—
33C2×#837—31no—
34C2×#825—31no—
35C2×#825—31no—
36C2×#825—31no—
37C2×#825—31no—
38C2×#825—61no—
39C2×#825D311yescharacteristic, complemented
40#5118D311yescharacteristic, complemented
41#4932—31no—
42#4932—31no—
43C2×#805—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
52C2×C4×C3⋊D3—21no—
53C2×#634C2×C411yescharacteristic
54C2×C3×#67—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D412yes—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic
64C2×#626—22no—
65C32×M16—21no—
66C32×M16—21no—
67C2×C32×C8—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3D412yescomplemented
70C3×C4×Dic3—21no—
71C3×C4×Dic3C2×C411yescharacteristic
72C3×C4×Dic3C2×C411yescharacteristic
73C3×C4×Dic3D412yes—
74C3×C4×Dic3D412yescomplemented
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78Dic3⋊Dic3—22no—
79#3722—22no—
80(C2×D3)⋊Dic3—22no—
81#1963—91noSylow
82C2×C3×#41—31no—
83C2×#235—31no—
84C2×#235—31no—
85C2×#235—61no—
86C2×#235C2×D311yescharacteristic
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×C42—31no—
92C2×C3×C42—31no—
93#947—31no—
94#944—31no—
95#940—31no—
96#939—62no—
97#936—31no—
98#930—62no—
99C4×#67—62no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3C2×D311yescharacteristic
104C2×C4×Dic3C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106#875—31no—
107#875—31no—
108#874—31no—
109C4×D12—62no—
110#869—31no—
111C3×C4⋊C8—62no—
112C3×#104—62no—
113#837—62no—
114C3⋊#95—62no—
115C3⋊#95—62no—
116#825—22no—
117#825—62no—
118#825—62no—
119#825—62no—
120#825—64no—
121#825—62no—
122Dic3⋊C8—22no—
123#805—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—21no—
126C22×C3×D3—21no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—42no—
138C4⋊(C3⋊D3)—21no—
139C4⋊(C3⋊D3)—21no—
140C4×C3⋊D3—41no—
141C4×C3⋊D3—41no—
142#634—21no—
143#634—21no—
144C3×#67—41no—
145C3×#67—41no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—42no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3C22⋊C412yes—
151C2×C3×Dic3C22⋊C412yes—
152C3×D12—21no—
153C3×D12—21no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×Dic6—21no—
157C3×Dic6—21no—
158#626—44no—
159C32×C8—41no—
160C3×C3⋊C8—41no—
161#532—91no—
162#423—31no—
163C2×#104—31no—
164C2×#104—91no—
165C2×#104—91no—
166C2×#104—91no—
167#376—91no—
168C3×#41—61no—
169C3×#41—61no—
170C3×#41—61no—
171C3×#41—61no—
172C2×C3×Q8—31no—
173C2×C3×D4—31no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—32no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—21no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—62no—
185C2×#67—121no—
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C22×Dic3D1212yes—
191#235—21no—
192#235—21no—
193#235—21no—
194#235—21no—
195#235—62no—
196#235—62no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—61no—
205#235—121no—
206#235—121no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—61no—
210C2×D12—62no—
211C2×D12C4×D311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—121no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—61no—
219C2×Dic6C4×D311yescharacteristic
220C3×M16—22no—
221C3×M16—21no—
222C3×M16—21no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—41no—
226C3×M16—61no—
227C3×M16—61no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—41no—
231C2×C3×C8—61no—
232C3×C42—31no—
233C3×C42—31no—
234C3×C42—32no—
235C3×C42—32no—
236C3×C42—61no—
237#217—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—62no—
242Dic3⋊C4—62no—
243C4×Dic3—21no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—62no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—121no—
250C4×Dic3C4×D311yescharacteristic
251C4×Dic3C4×D311yescharacteristic
252C4×Dic3#6712yes—
253C4×Dic3#6712yescomplemented
254#208—21no—
255#208—21no—
256C2×C3⋊C8—21no—
257C22×C32—22no—
258C22×C32C2×C22⋊C411yescharacteristic
259C22×C32#12111yescharacteristic
260C22×C32#12111yescharacteristic
261C2×C3⋊D3—41no—
262C2×C3⋊D3—42no—
263C2×C3×D3—41no—
264C2×C3×D3—42no—
265C32×C4C4×D411yescharacteristic
266C32×C4C4×D411yescharacteristic
267C32×C4#12411yescharacteristic
268C32×C4#12711yescharacteristic
269C3⋊Dic3—42no—
270C3⋊Dic3—41no—
271C3×Dic3—22no—
272C3×Dic3—22no—
273C3×Dic3—42no—
274C3×Dic3—41no—
275C2×#41—31no—
276C2×#41—91no—
277C2×M16—31no—
278C2×M16D3211yescharacteristic
279C4⋊Q8—91no—
280#127—91no—
281#124—91no—
282#124—91no—
283#121—182no—
284C4×D4—182no—
285C2×C42—31no—
286C2×C42—31no—
287C2×C42—91no—
288C4⋊C8—62no—
289#104—62no—
290#104—182no—
291#104—182no—
292#104—182no—
293#95—182no—
294C23×C3—21no—
295C23×C3—61no—
296C23×C3C2×D1211yescharacteristic
297C23×C3D3×D411yescharacteristic
298C22×D3—21no—
299C22×D3—61no—
300C22×D3—61no—
301C22×D3—121no—
302C3×Q8—61no—
303C3×Q8—61no—
304C3×D4—61no—
305C3×D4—61no—
306C3×D4—121no—
307C3×D4—121no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—62no—
317C2×C3×C4—61no—
318C2×C3×C4—122no—
319C2×C3×C4—122no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4#23511yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4#23911yescharacteristic
331C2×C3×C4#23911yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334#67—41no—
335#67—41no—
336#67—124no—
337#67—122no—
338#67—122no—
339#67—121no—
340#67—121no—
341#67—121no—
342#67—121no—
343C2×Dic3—21no—
344C2×Dic3—22no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3—61no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—61no—
351C2×Dic3—122no—
352C2×Dic3—121no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355C2×Dic3—124no—
356C2×Dic3(C2×D3)⋊C412yes—
357C2×Dic3(C2×D3)⋊C412yes—
358D12—21no—
359D12—21no—
360D12—62no—
361D12—61no—
362D12—61no—
363D12—61no—
364D12—61no—
365D12—121no—
366D12—124no—
367C4×D3—41no—
368C4×D3—41no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—121no—
372C4×D3—121no—
373C4×D3—121no—
374C4×D3—121no—
375Dic6—21no—
376Dic6—21no—
377Dic6—62no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—61no—
382Dic6—121no—
383C3×C8—42no—
384C3×C8—41no—
385C3×C8—41no—
386C3×C8—121no—
387C3⋊C8—41no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32#39011yescharacteristic
391C2×C32#42112yes—
392C3⋊D3—81no—
393C3×D3—81no—
394#41—61no—
395#41—61no—
396#41—61no—
397#41—61no—
398#41—181no—
399#41—181no—
400#41—181no—
401#41—181no—
402C2×Q8—31no—
403C2×Q8—91no—
404C2×D4—31no—
405C2×D4—61no—
406C2×D4—91no—
407C2×D4—182no—
408C2×D4—181no—
409C22×C4—32no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4C2×D3211yescharacteristic
415M16—21no—
416M16—21no—
417M16—61no—
418M16—61no—
419C2×C8—21no—
420C2×C8—61no—
421C4⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C42—31no—
425C42—31no—
426C42—32no—
427C42—32no—
428C42—61no—
429C42—92no—
430C42—181no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—42no—
437C22×C3—122no—
438C22×C3—121no—
439C22×C3D3×C22⋊C411yescharacteristic
440C22×C3#88411yescharacteristic
441C22×C3#89511yescharacteristic
442C22×C3#89511yescharacteristic
443C22×C3C2×(C2×D3)⋊C411yescharacteristic
444C22×C3#93911yescharacteristic
445C2×D3—41no—
446C2×D3—42no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—122no—
452C2×D3—242no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—122no—
460C3×C4—121no—
461C3×C4#67⋊C411yescharacteristic
462C3×C4#88511yescharacteristic
463C3×C4#89311yescharacteristic
464C3×C4#89311yescharacteristic
465C3×C4C4×#6711yescharacteristic
466C3×C4#94011yescharacteristic
467C3×C4#94011yescharacteristic
468C3×C4#94711yescharacteristic
469Dic3—22no—
470Dic3—22no—
471Dic3—42no—
472Dic3—41no—
473Dic3—122no—
474Dic3—122no—
475Dic3—122no—
476Dic3—124no—
477Dic3—121no—
478Dic3—121no—
479C32#196311yescharacteristic, complemented, Sylow
480C23—61no—
481C23—181no—
482C23D3×D1211yescharacteristic
483Q8—61no—
484Q8—61no—
485Q8—181no—
486Q8—181no—
487D4—61no—
488D4—61no—
489D4—121no—
490D4—121no—
491D4—181no—
492D4—181no—
493D4—364no—
494D4—361no—
495D4—361no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—122no—
501C2×C4—122no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—182no—
505C2×C4—181no—
506C2×C4—362no—
507C2×C4—361no—
508C2×C4—361no—
509C2×C4#379611yescharacteristic
510C2×C4#379911yescharacteristic
511C2×C4C4×D3211yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C2×C4D3×#6711yescharacteristic
514C2×C4#381111yescharacteristic
515C8—41no—
516C8—121no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—22no—
522C2×C3—21no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—241no—
526C2×C3#482112yes—
527C2×C3#495711yescharacteristic
528C2×C3#498811yescharacteristic
529C2×C3#513912yes—
530D3—81no—
531D3—242no—
532D3—241no—
533D3—241no—
534C22—22no—
535C22—122no—
536C22—121no—
537C22—362no—
538C22—361no—
539C22#6388611yescharacteristic
540C22#6391011yescharacteristic
541C22D3×(C2×D3)⋊C411yescharacteristic
542C4—62no—
543C4—62no—
544C4—122no—
545C4—121no—
546C4—362no—
547C4—361no—
548C4#6388111yescharacteristic
549C4#6390411yescharacteristic
550C4#6390711yescharacteristic
551C4#6397911yescharacteristic
552C3—21no—
553C3#7035711yescharacteristic, complemented
554C3#7051311yescharacteristic, complemented
555C2—21no—
556C2—21no—
557C2—241no—
558C2—721no—
559C2#1059100512yes—
560C2#1059138411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595029C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1963
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63652C2semidirect
3. C2×C3×#825C2semidirect
4. C3×#5118C2semidirect
5. #10591222C2semidirect
6. C2×#63570C2semidirect
7. C2×#63568C2semidirect
18. #63911C4semidirect
20. #63866C4semidirect
21. #63864C4semidirect
22. #63860C4semidirect
39. C2×#825D3semidirect
40. #5118D3semidirect
69. C4×C3⋊Dic3D4semidirect
74. C3×C4×Dic3D4semidirect
253. C4×Dic3#67semidirect
479. C32#1963semidirect
553. C3#70357semidirect
554. C3#70513semidirect

Maximal subgroups

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

subgroupindex
#105950292
C2×#636522
C2×C3×#8252
C3×#51182
#105912222
C2×#635702
C2×#635682
#705133
#703573