Finite Group Databasebeta

← #11792366

Subgroups — #11792366

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591232C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#71869—31nomaximal
9#70412—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64160—21no—
14#64159—22no—
15#64158—21no—
16#64151—21no—
17#64141—21no—
18C2×#3748C2211yescharacteristic
19C3×#944—21no—
20C3×#936—21no—
21C3×#935—22no—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#924—22no—
25C2×C3×#208C2211yescharacteristic
26C2×#3719—21no—
27#63833—22no—
28#63833—22no—
29C2×#3717—21no—
30C3×#837—22no—
31#63581—22no—
32#63565—22no—
33C3×#536—31no—
34#5825D311yescharacteristic, complemented
35#5822—31no—
36#5822—31no—
37#5822—61no—
38C2×#942—31no—
39C2×#909—31no—
40C3×#421—31no—
41#5236D311yescharacteristic, complemented
42#5225—31no—
43#5006—31no—
44#5006—31no—
45#5004—31no—
46#4559—31no—
47#4533—31no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8D411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4D411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58#3828—21no—
59#3828—21no—
60#3828—21no—
61#3828—21no—
62C2×C4⋊(C3⋊D3)D411yescharacteristic
63C2×C4×C3⋊D3—21no—
64C2×#634D411yescharacteristic
65C22×C3×Dic3—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D412yes—
72#3756—22no—
73#3755—22no—
74#3754—22no—
75#3753—22no—
76#3748—21no—
77#3748—21no—
78C2×C3⋊(C3⋊C8)D412yes—
79C3×#217—24no—
80C3×#217—21no—
81C3×#217D412yes—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×Dic3⋊C4—24no—
85C3×C4×Dic3—21no—
86C3×C4×Dic3—21no—
87C3×#208—21no—
88C3×#208D412yes—
89C2×C3×C3⋊C8—21no—
90#3719—24no—
91#3717—24no—
92#2009—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41C2×D311yescharacteristic
95C2×C3×#41C2×D311yescharacteristic
96C22×C3×Q8—31no—
97C2×#235—31no—
98C2×#235—31no—
99C2×#235—61no—
100C22×Dic6C2×D311yescharacteristic
101C2×C3×M16—31no—
102C3×C4⋊Q8—61no—
103C3×#124—61no—
104C3×#123—62no—
105C3×C22⋊Q8—62no—
106C3×#117—31no—
107C3×#117—31no—
108#951—61no—
109#951—61no—
110#951—62no—
111#950—62no—
112#950—62no—
113#950—64no—
114#949—61no—
115#949—61no—
116#949—62no—
117#944—21no—
118C2×#216—61no—
119#942—62no—
120#942—62no—
121#942—61no—
122#942—61no—
123#942—62no—
124C2×#215—61no—
125#936—21no—
126#935—22no—
127#932—62no—
128#932—61no—
129#932—61no—
130#926C2×D311yescharacteristic
131#926C2×D311yescharacteristic
132#924—22no—
133C2×#208—31no—
134C2×#208—31no—
135C2×#208—61no—
136C2×#208C2×D311yescharacteristic
137#909—62no—
138#909—62no—
139C2×Dic12—61no—
140C2×#204—61no—
141C3×#104—62no—
142#837—22no—
143#835—62no—
144#810—62no—
145#806—62no—
146#806—62no—
147C23×C32—21no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—21no—
150C32×Q8—21no—
151C32×Q8—21no—
152C32×D4—21no—
153C32×D4—21no—
154C32×D4—41no—
155C32×D4—41no—
156C2×C32×C4—21no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4#4111yescharacteristic
165#638—41no—
166#638—41no—
167C2×C3⋊Dic3—21no—
168C4⋊(C3⋊D3)—21no—
169C4⋊(C3⋊D3)—21no—
170C4×C3⋊D3—41no—
171C4×C3⋊D3—41no—
172#634—21no—
173#634—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—41no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—41no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×Dic6—41no—
182C3×Dic6—41no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—22no—
185#575—91no—
186C2×#137—91no—
187#536—31no—
188#421—31no—
189#419—91no—
190#410—91no—
191#344—91no—
192C3×#41—22no—
193C3×#41—22no—
194C3×#41—21no—
195C3×#41—21no—
196C3×#41—21no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—41no—
203C3×#41—41no—
204C2×C3×Q8—21no—
205C2×C3×Q8—32no—
206C2×C3×Q8—61no—
207C2×C3×Q8—61no—
208C2×C3×Q8—61no—
209C2×C3×Q8—61no—
210C2×C3×Q8—61no—
211C2×C3×Q8D1211yescharacteristic
212C2×C3×Q8#6711yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—41no—
217C2×C3×D4D1211yescharacteristic
218C2×C3×D4#6711yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—41no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—121no—
229C22×Dic3—21no—
230#235—62no—
231#235—62no—
232#235—61no—
233#235—61no—
234#235—61no—
235#235—61no—
236#235—61no—
237#235—61no—
238#235—61no—
239#235—61no—
240#235—121no—
241#235—121no—
242C2×D12—31no—
243C2×D12—31no—
244C2×D12—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—121no—
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—31no—
254C2×Dic6—31no—
255C2×Dic6—61no—
256C2×Dic6#6712yes—
257C3×M16—32no—
258C3×M16—61no—
259C2×C3×C8—61no—
260C3×C4⋊C4—64no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C22⋊C4—32no—
264C3×C22⋊C4—64no—
265C3×C22⋊C4—61no—
266C3×C42—61no—
267C3×C42—61no—
268#217—24no—
269#217—21no—
270#217#6712yes—
271#216—64no—
272#216—64no—
273#216—62no—
274#216—62no—
275#215—64no—
276#215—64no—
277#215—62no—
278#215—62no—
279#214—64no—
280#214—62no—
281#214—62no—
282#213—64no—
283#213—62no—
284#213—62no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287Dic3⋊C4—24no—
288C4×Dic3—21no—
289C4×Dic3—21no—
290#208—21no—
291#208—62no—
292#208—62no—
293#208—61no—
294#208—61no—
295#208—61no—
296#208—61no—
297#208#6712yes—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302Dic12—64no—
303#204—64no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—42no—
307C22×C32#12011yescharacteristic
308C22×C32#12111yescharacteristic
309C22×C32#12711yescharacteristic
310C2×C3⋊D3—41no—
311C2×C3⋊D3—81no—
312C32×C4—41no—
313C32×C4#12011yescharacteristic
314C32×C4#12011yescharacteristic
315C32×C4#12111yescharacteristic
316C32×C4#12111yescharacteristic
317C3⋊Dic3—41no—
318C3×Dic3—42no—
319C3×Dic3—42no—
320C3×Dic3—81no—
321C2×#41—91no—
322C2×#41D3211yescharacteristic
323C22×Q8—31no—
324#137—182no—
325#137—182no—
326#137—181no—
327#137—181no—
328AGL(1,ℤ/8)—181no—
329AGL(1,ℤ/8)—181no—
330#135—182no—
331C2×Q16—181no—
332C2×SD16—181no—
333C2×M16—31no—
334C2×M16—91no—
335C4⋊Q8—61no—
336#124—61no—
337#123—62no—
338C22⋊Q8—62no—
339#117—31no—
340#117—31no—
341#104—62no—
342#103—182no—
343#99—182no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—41no—
348C23×C3D3×D411yescharacteristic
349C23×C3C2×#6711yescharacteristic
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—121no—
353C3×Q8—22no—
354C3×Q8—21no—
355C3×Q8—21no—
356C3×Q8—21no—
357C3×Q8—21no—
358C3×Q8—41no—
359C3×Q8—62no—
360C3×Q8—62no—
361C3×Q8—121no—
362C3×Q8—121no—
363C3×D4—22no—
364C3×D4—21no—
365C3×D4—21no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—41no—
369C3×D4—42no—
370C3×D4—42no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—41no—
374C3×D4—41no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—121no—
393C2×C3×C4—121no—
394C2×C3×C4—121no—
395C2×C3×C4C2×D1211yescharacteristic
396C2×C3×C4#23511yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4#23711yescharacteristic
404C2×C3×C4C2×#6711yescharacteristic
405C2×C3×C4C2×#6711yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407#67—122no—
408#67—122no—
409#67—121no—
410#67—121no—
411#67—121no—
412#67—121no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—41no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—121no—
421D12—62no—
422D12—61no—
423D12—61no—
424D12—61no—
425D12—61no—
426D12—121no—
427C4×D3—122no—
428C4×D3—122no—
429C4×D3—121no—
430C4×D3—121no—
431C4×D3—121no—
432C4×D3—121no—
433Dic6—22no—
434Dic6—22no—
435Dic6—41no—
436Dic6—41no—
437Dic6—62no—
438Dic6—61no—
439Dic6—61no—
440Dic6—61no—
441Dic6—61no—
442Dic6—121no—
443C3×C8—62no—
444C3⋊C8—22no—
445C3⋊C8—64no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—81no—
452C2×C32#39211yescharacteristic
453C3⋊D3—81no—
454#41—21no—
455#41—21no—
456#41—21no—
457#41—21no—
458#41—181no—
459#41—181no—
460#41—181no—
461#41—181no—
462C2×Q8—32no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—61no—
466C2×Q8—61no—
467C2×Q8—61no—
468C2×Q8—91no—
469C2×Q8#62611yescharacteristic
470C2×D4—21no—
471C2×D4—91no—
472C2×D4—181no—
473C2×D4#62611yescharacteristic
474C22×C4—21no—
475C22×C4—61no—
476C22×C4—181no—
477C22×C4C2×D3211yescharacteristic
478Q16—184no—
479Q16—182no—
480SD16—184no—
481SD16—182no—
482SD16—182no—
483D8—182no—
484M16—32no—
485M16—61no—
486M16—181no—
487M16—181no—
488C2×C8—61no—
489C2×C8—92no—
490C4⋊C4—64no—
491C4⋊C4—61no—
492C4⋊C4—61no—
493C22⋊C4—32no—
494C22⋊C4—64no—
495C22⋊C4—61no—
496C42—61no—
497C42—61no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—81no—
509C22×C3—82no—
510C22×C3#88211yescharacteristic
511C22×C3#88411yescharacteristic
512C22×C3#93811yescharacteristic
513C22×C3#94011yescharacteristic
514C22×C3#94011yescharacteristic
515C22×C3#95311yescharacteristic
516C2×D3—122no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—242no—
520C2×D3—241no—
521C2×D3—241no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—42no—
527C3×C4—41no—
528C3×C4—41no—
529C3×C4—122no—
530C3×C4—122no—
531C3×C4—241no—
532C3×C4#88211yescharacteristic
533C3×C4#88411yescharacteristic
534C3×C4#93011yescharacteristic
535C3×C4#93711yescharacteristic
536C3×C4#93711yescharacteristic
537C3×C4#93711yescharacteristic
538C3×C4#93911yescharacteristic
539C3×C4#93911yescharacteristic
540Dic3—42no—
541Dic3—42no—
542Dic3—81no—
543Dic3—122no—
544Dic3—121no—
545Dic3—121no—
546C32#200911yescharacteristic, complemented, Sylow
547C23—21no—
548C23—181no—
549C23D3×#6711yescharacteristic
550Q8—21no—
551Q8—21no—
552Q8—62no—
553Q8—62no—
554Q8—121no—
555Q8—121no—
556Q8—181no—
557Q8—181no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—181no—
563D4—181no—
564D4—361no—
565D4—361no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—181no—
575C2×C4—361no—
576C2×C4—361no—
577C2×C4#380411yescharacteristic
578C2×C4C2×#62611yescharacteristic
579C2×C4D3×#6711yescharacteristic
580C2×C4D3×#6711yescharacteristic
581C2×C4#381111yescharacteristic
582C2×C4#381111yescharacteristic
583C8—62no—
584C8—182no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—41no—
593C2×C3—41no—
594C2×C3—41no—
595C2×C3—82no—
596C2×C3—81no—
597C2×C3—81no—
598C2×C3#496011yescharacteristic
599C2×C3#522311yescharacteristic
600D3—242no—
601D3—241no—
602D3—241no—
603C22—41no—
604C22—42no—
605C22—41no—
606C22—361no—
607C22—721no—
608C22#6395811yescharacteristic
609C22#6397711yescharacteristic
610C22#6397911yescharacteristic
611C4—41no—
612C4—122no—
613C4—122no—
614C4—241no—
615C4—361no—
616C4#6397111yescharacteristic
617C4#6397811yescharacteristic
618C4#6398111yescharacteristic
619C4#6398311yescharacteristic
620C3—21no—
621C3#7041211yescharacteristic, complemented
622C3#7186911yescharacteristic, complemented
623C2—21no—
624C2—21no—
625C2—21no—
626C2—81no—
627C2—721no—
628C2#1059172411yescharacteristic
subgroupG/H
centerC2#10591724
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#392
prime radical#10596293C2
hypercenterC2×#41D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5825C2semidirect
3. C2×#63833C2semidirect
4. C3×#5236C2semidirect
5. #10591232C2semidirect
6. #10591099C2semidirect
7. #10589170C2semidirect
34. #5825D3semidirect
41. #5236D3semidirect
546. C32#2009semidirect
621. C3#70412semidirect
622. C3#71869semidirect

Maximal subgroups

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

subgroupindex
#105962932
C3×#58252
C2×#638332
C3×#52362
#105912322
#105910992
#105891702
#718693
#704123