Finite Group Databasebeta

← #11792369

Subgroups — #11792369

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic, complemented
2C3×#5816C211yesmaximal, characteristic, complemented
3#10594795C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591232C211yesmaximal, characteristic, complemented
6#10591111C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#71869—31nomaximal
9#70351—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×#3756—21no—
14#64151—22no—
15#64151—22no—
16C2×#3755—21no—
17C2×#3748C2211yescharacteristic
18C3×#947—21no—
19C3×#946—22no—
20C3×#944—21no—
21C3×#929—22no—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63833—21no—
26#63831—21no—
27#63830—21no—
28#63829—22no—
29#63825—21no—
30C3×#835—22no—
31#63581—22no—
32#63569—22no—
33C3×#536—31no—
34#5822—31no—
35#5816D311yescharacteristic, complemented
36C2×#942—31no—
37C2×#942—31no—
38C2×#942—61no—
39#5748—31no—
40C3×#419—31no—
41#5236—31no—
42#5225D311yescharacteristic, complemented
43#5006—31no—
44#5006—31no—
45#5005—31no—
46#4556—31no—
47#4533—31no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8D412yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57#3828—21no—
58#3828—21no—
59#3828—21no—
60#3828—21no—
61C2×C4⋊(C3⋊D3)D411yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×#634D411yescharacteristic
64C2×C3×#67—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235—21no—
68C3×#235—21no—
69C2×C3×D12D411yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72#3756—24no—
73#3755—24no—
74#3748—21no—
75#3748D412yes—
76C2×C3⋊(C3⋊C8)—21no—
77C3×#217—21no—
78C3×#217D412yes—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×Dic3⋊C4—24no—
83C3×C4×Dic3—21no—
84C3×C4×Dic3—21no—
85C3×#208—21no—
86C3×#208—21no—
87C2×C3×C3⋊C8D412yes—
88#3719—22no—
89#3717—22no—
90#3716—22no—
91#3714—22no—
92#2009—91noSylow
93C2×C3×#41—31no—
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C2×#235—31no—
98C2×#235—31no—
99C2×#235—61no—
100C2×#235C2×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#950—62no—
110#949—61no—
111#947—21no—
112#946—22no—
113#944—21no—
114C2×#216—61no—
115C2×#216—61no—
116C2×#216—62no—
117#942—61no—
118#942—62no—
119#942—62no—
120#942—64no—
121#942—64no—
122#942—62no—
123#942—62no—
124C2×#215—61no—
125C2×#215—61no—
126C2×#215—62no—
127#932—61no—
128#929—22no—
129#926C2×D311yescharacteristic
130#926C2×D311yescharacteristic
131C2×#208—31no—
132C2×#208—31no—
133C2×#208—61no—
134C2×#208C2×D311yescharacteristic
135#909—61no—
136#909—61no—
137#908—61no—
138#908—61no—
139#904—62no—
140C3×#103—62no—
141#837—62no—
142#835—22no—
143#806—62no—
144#806—62no—
145#805—62no—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—21no—
148C22×C3×D3—21no—
149C32×Q8—22no—
150C32×Q8—22no—
151C32×Q8—41no—
152C32×Q8—41no—
153C2×C32×C4—22no—
154C2×C32×C4—41no—
155C2×C32×C4—41no—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4#4111yescharacteristic
162#638—41no—
163#638—41no—
164C2×C3⋊Dic3—21no—
165C4⋊(C3⋊D3)—21no—
166C4⋊(C3⋊D3)—21no—
167C4×C3⋊D3—41no—
168C4×C3⋊D3—41no—
169#634—21no—
170#634—21no—
171C3×#67—41no—
172C3×#67—41no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—41no—
176C3×D12—21no—
177C3×D12—21no—
178C3×C4×D3—41no—
179C3×C4×D3—41no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3⋊(C3⋊C8)—22no—
183C3×C3⋊C8—22no—
184#575—91no—
185C2×#137—91no—
186#536—31no—
187#421—91no—
188#419—31no—
189#410—91no—
190#344—91no—
191C3×#41—61no—
192C3×#41—61no—
193C3×#41—61no—
194C3×#41—61no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—22no—
208C2×C3×Q8—31no—
209C2×C3×Q8—41no—
210C2×C3×Q8—41no—
211C2×C3×Q8—41no—
212C2×C3×Q8D1212yes—
213C2×C3×Q8#6712yes—
214C2×C3×D4—31no—
215C2×C3×D4—61no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—41no—
220C22×C3×C4—61no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67—21no—
224C2×#67—61no—
225C2×#67—61no—
226C2×#67—121no—
227#235—21no—
228#235—21no—
229#235—21no—
230#235—21no—
231#235—62no—
232#235—62no—
233#235—61no—
234#235—61no—
235#235—61no—
236#235—61no—
237#235—61no—
238#235—61no—
239#235—61no—
240#235—61no—
241#235—121no—
242#235—121no—
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—61no—
246C2×D12#6711yescharacteristic
247C2×C4×D3—21no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3—121no—
251C2×Dic6—31no—
252C2×Dic6—31no—
253C2×Dic6—61no—
254C2×Dic6#6711yescharacteristic
255C3×M16—61no—
256C3×M16—61no—
257C2×C3×C8—32no—
258C3×C4⋊C4—64no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C22⋊C4—32no—
262C3×C22⋊C4—64no—
263C3×C22⋊C4—61no—
264C3×C42—61no—
265C3×C42—61no—
266#217—21no—
267#217#6712yes—
268#216—62no—
269#216—68no—
270#216—64no—
271#216—64no—
272#215—62no—
273#215—68no—
274#215—64no—
275#215—64no—
276#214—62no—
277#213—62no—
278(C2×D3)⋊C4—24no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281Dic3⋊C4—24no—
282C4×Dic3—21no—
283C4×Dic3—21no—
284#208—21no—
285#208—21no—
286#208—32no—
287#208—32no—
288#208—62no—
289#208—62no—
290#208—61no—
291#208—61no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—61no—
295C2×C3⋊C8#6712yes—
296Dic12—62no—
297D24—62no—
298#204—62no—
299#204—62no—
300C22×C32—41no—
301C22×C32#12011yescharacteristic
302C22×C32#12111yescharacteristic
303C22×C32#12711yescharacteristic
304C2×C3⋊D3—41no—
305C2×C3⋊D3—81no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C32×C4—42no—
309C32×C4#12011yescharacteristic
310C32×C4#12011yescharacteristic
311C32×C4#12111yescharacteristic
312C32×C4#12111yescharacteristic
313C3⋊Dic3—41no—
314C3×Dic3—42no—
315C3×Dic3—41no—
316C3×Dic3—81no—
317C2×#41—31no—
318C2×#41—91no—
319C22×Q8D3211yescharacteristic
320#137—181no—
321#137—181no—
322#137—182no—
323#137—182no—
324AGL(1,ℤ/8)—181no—
325AGL(1,ℤ/8)—181no—
326#135—182no—
327C2×Q16—181no—
328C2×SD16—181no—
329C2×M16—31no—
330C2×M16—91no—
331C4⋊Q8—61no—
332#124—61no—
333#123—62no—
334C22⋊Q8—62no—
335#117—31no—
336#117—31no—
337#104—182no—
338#103—62no—
339#99—182no—
340C23×C3—21no—
341C23×C3—61no—
342C23×C3D3×D411yescharacteristic
343C23×C3C2×#6711yescharacteristic
344C22×D3—21no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—121no—
348C3×Q8—24no—
349C3×Q8—22no—
350C3×Q8—22no—
351C3×Q8—22no—
352C3×Q8—22no—
353C3×Q8—42no—
354C3×Q8—42no—
355C3×Q8—42no—
356C3×Q8—41no—
357C3×Q8—41no—
358C3×Q8—41no—
359C3×Q8—41no—
360C3×Q8—61no—
361C3×Q8—61no—
362C3×D4—61no—
363C3×D4—61no—
364C3×D4—121no—
365C3×D4—121no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4#23511yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4#23711yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398#67—41no—
399#67—41no—
400#67—122no—
401#67—122no—
402#67—121no—
403#67—121no—
404#67—121no—
405#67—121no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—41no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—121no—
412D12—21no—
413D12—21no—
414D12—62no—
415D12—61no—
416D12—61no—
417D12—61no—
418D12—61no—
419D12—121no—
420C4×D3—41no—
421C4×D3—41no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—121no—
427C4×D3—121no—
428Dic6—21no—
429Dic6—21no—
430Dic6—62no—
431Dic6—61no—
432Dic6—61no—
433Dic6—61no—
434Dic6—61no—
435Dic6—121no—
436C3×C8—62no—
437C3⋊C8—22no—
438C3⋊C8—64no—
439C3⋊C8—62no—
440C3⋊C8—62no—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32#39211yescharacteristic
445C3⋊D3—81no—
446C3×D3—81no—
447#41—61no—
448#41—61no—
449#41—61no—
450#41—61no—
451#41—181no—
452#41—181no—
453#41—181no—
454#41—181no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—31no—
461C2×Q8—91no—
462C2×Q8#62612yes—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4—91no—
466C2×D4—181no—
467C22×C4—21no—
468C22×C4—61no—
469C22×C4—181no—
470C22×C4C2×D3211yescharacteristic
471Q16—182no—
472Q16—184no—
473SD16—182no—
474SD16—182no—
475SD16—184no—
476D8—182no—
477M16—61no—
478M16—61no—
479M16—92no—
480M16—181no—
481C2×C8—32no—
482C2×C8—181no—
483C4⋊C4—64no—
484C4⋊C4—61no—
485C4⋊C4—61no—
486C22⋊C4—32no—
487C22⋊C4—64no—
488C22⋊C4—61no—
489C42—61no—
490C42—61no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—42no—
497C22×C3—122no—
498C22×C3—121no—
499C22×C3#88211yescharacteristic
500C22×C3#88411yescharacteristic
501C22×C3#93811yescharacteristic
502C22×C3#94011yescharacteristic
503C22×C3#94011yescharacteristic
504C22×C3#95311yescharacteristic
505C2×D3—42no—
506C2×D3—41no—
507C2×D3—122no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—242no—
511C2×D3—241no—
512C2×D3—241no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—44no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—122no—
521C3×C4—121no—
522C3×C4—241no—
523C3×C4#88211yescharacteristic
524C3×C4#88411yescharacteristic
525C3×C4#93011yescharacteristic
526C3×C4#93711yescharacteristic
527C3×C4#93711yescharacteristic
528C3×C4#93711yescharacteristic
529C3×C4#93911yescharacteristic
530C3×C4#93911yescharacteristic
531Dic3—42no—
532Dic3—41no—
533Dic3—81no—
534Dic3—122no—
535Dic3—121no—
536Dic3—121no—
537C32#200911yescharacteristic, complemented, Sylow
538C23—61no—
539C23—181no—
540C23D3×#6711yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—61no—
546Q8—61no—
547Q8—181no—
548Q8—181no—
549D4—61no—
550D4—61no—
551D4—121no—
552D4—121no—
553D4—181no—
554D4—181no—
555D4—361no—
556D4—361no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—62no—
561C2×C4—61no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—181no—
566C2×C4—361no—
567C2×C4—361no—
568C2×C4#380411yescharacteristic
569C2×C4C2×#62611yescharacteristic
570C2×C4D3×#6711yescharacteristic
571C2×C4D3×#6711yescharacteristic
572C2×C4#381111yescharacteristic
573C2×C4#381111yescharacteristic
574C8—62no—
575C8—182no—
576C2×C3—22no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—41no—
585C2×C3—41no—
586C2×C3—241no—
587C2×C3#496011yescharacteristic
588C2×C3#522311yescharacteristic
589D3—81no—
590D3—242no—
591D3—241no—
592D3—241no—
593C22—41no—
594C22—122no—
595C22—121no—
596C22—361no—
597C22—721no—
598C22#6395811yescharacteristic
599C22#6397711yescharacteristic
600C22#6397911yescharacteristic
601C4—42no—
602C4—122no—
603C4—121no—
604C4—241no—
605C4—361no—
606C4#6397111yescharacteristic
607C4#6397811yescharacteristic
608C4#6398111yescharacteristic
609C4#6398311yescharacteristic
610C3—21no—
611C3#7035111yescharacteristic, complemented
612C3#7186911yescharacteristic, complemented
613C2—21no—
614C2—21no—
615C2—21no—
616C2—241no—
617C2—721no—
618C2#1059172411yescharacteristic
subgroupG/H
centerC2#10591724
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC2×C32#392
prime radical#10594795C2
hypercenterC22×Q8D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64151C2semidirect
2. C3×#5816C2semidirect
4. C3×#5225C2semidirect
5. #10591232C2semidirect
6. #10591111C2semidirect
7. #10589169C2semidirect
35. #5816D3semidirect
42. #5225D3semidirect
537. C32#2009semidirect
611. C3#70351semidirect
612. C3#71869semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C3×#58162
#105947952
C3×#52252
#105912322
#105911112
#105891692
#718693
#703513