Finite Group Databasebeta

← #11867808

Subgroups — #11867808

Order 1152.

1091 conjugacy classes of subgroups.

The subgroup lattice has 651 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596304C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4C2×#63833C211yesmaximal, characteristic, complemented
5#10591187C212yesmaximal, complemented
6#10591178C212yesmaximal, complemented
7#10591177C212yesmaximal, complemented
8#10591131C211yesmaximal, characteristic, complemented
9#10591121C212yesmaximal, complemented
10#10591105C211yesmaximal, characteristic, complemented
11C2×#63566C211yesmaximal, characteristic, complemented
12#83808—31nomaximal
13#83400—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17#64155—21no—
18#64148—22no—
19#64147—21no—
20#64139C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133C2212yes—
23C3×#948—24no—
24C3×#944—21no—
25C3×#936—21no—
26C3×#935—22no—
27C3×#926C2211yescharacteristic
28C3×#924C2212yes—
29C3×#924C2212yes—
30C2×C3×#208C2212yes—
31C2×C3×#208C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33C22×C3×C3⋊C8C2212yes—
34C2×#3719C2212yes—
35#63833—24no—
36C2×#3717C2212yes—
37#63575C2212yes—
38#63573C2212yes—
39#63567C2211yescharacteristic
40#63567C2211yescharacteristic
41#63566C2212yes—
42#63566C2212yes—
43#63564C2211yescharacteristic
44#63564C2211yescharacteristic
45C2×C3×#131—31no—
46C3×#536—31no—
47#5833—31no—
48#5833—31no—
49#5833—61no—
50#5825D311yescharacteristic, complemented
51C2×#948D311yescharacteristic, complemented
52C2×#942—31no—
53C2×#909—31no—
54C2×#835—31no—
55#5137—32no—
56#5134—32no—
57#5121—31no—
58#5116—32no—
59#5114—32no—
60#5113—31no—
61C2×#816—31no—
62#5052—32no—
63#5051—32no—
64#5049—32no—
65#5048—32no—
66#5002—31no—
67#4995—31no—
68C32×#41—22no—
69C32×#41—22no—
70C2×C32×Q8D411yescharacteristic
71C2×C32×D4D412yes—
72C2×C32×D4D411yescharacteristic
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76C2×#638—22no—
77C22×C3⋊Dic3—21no—
78#3828—22no—
79#3828—22no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—21no—
82C2×#634C2311yescharacteristic
83C22×C3×Dic3—21no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6C2312yes—
88#3757—22no—
89#3752—22no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2312yes—
92#3750—22no—
93C3×#217—22no—
94C3×#217—22no—
95C3×#217—21no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4—22no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×#208—24no—
102C3×#208D414yescomplemented
103C2×C3×C3⋊C8—22no—
104C2×C3×C3⋊C8—24no—
105C2×C3×C3⋊C8C2311yescharacteristic
106C2×C3×C3⋊C8C2311yescharacteristic
107C2×C3×C3⋊C8C2312yes—
108#3719—24no—
109#3717—24no—
110#3063—91noSylow
111C2×C3×#41—21no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—31no—
115C2×#235—31no—
116C2×#235—31no—
117C2×#235—61no—
118C22×Dic6C2×D311yescharacteristic
119C3×#131—64no—
120C2×C3×M16—31no—
121C2×C3×M16—32no—
122C22×C3×C8—31no—
123C22×C3×C8—32no—
124C3×C4⋊Q8—61no—
125C3×#124—61no—
126C3×#123—62no—
127C3×C22⋊Q8—32no—
128C3×C22⋊Q8—32no—
129C3×#117—31no—
130#948—24no—
131#946—62no—
132#946—61no—
133#946—61no—
134#944—21no—
135C2×#216—32no—
136#942—64no—
137C2×#215—32no—
138#939—64no—
139#939—62no—
140#939—62no—
141#938—62no—
142#938—61no—
143#938—61no—
144#936—21no—
145#935—22no—
146#930—32no—
147#930—32no—
148#930—62no—
149#926C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—61no—
153#924—32no—
154#924—32no—
155#924—62no—
156#924C2×D312yes—
157#924C2×D312yes—
158C2×#208C2×D312yes—
159C2×#208C2×D311yescharacteristic
160C22×C3⋊C8C2×D311yescharacteristic
161C22×C3⋊C8C2×D312yes—
162#909—64no—
163C2×Dic12—32no—
164C2×#204—32no—
165#835—32no—
166#835—32no—
167#821—31no—
168#821—31no—
169#818—32no—
170#817—32no—
171#816—32no—
172#816—32no—
173#816—31no—
174#816—31no—
175#810—31no—
176#810—31no—
177#809—31no—
178#809—31no—
179#808—32no—
180#807—32no—
181C23×C32C2×D412yes—
182C23×C32C2×D411yescharacteristic
183C22×C3⋊D3—21no—
184C32×Q8—22no—
185C32×D4—24no—
186C32×D4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4C2×D412yes—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D412yes—
192C2×C32×C4#4112yes—
193C2×C32×C4C2411yescharacteristic
194#638—42no—
195#638—82no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—81no—
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)—21no—
201C4×C3⋊D3—42no—
202#634—21no—
203#634—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—42no—
208C3×Dic6—22no—
209C3×Dic6—22no—
210C3×Dic6—42no—
211C3×C3⋊C8—21no—
212C3×C3⋊C8—21no—
213C3×C3⋊C8C2×D414yes—
214C2×#137—91no—
215C2×#131—31no—
216#537—91no—
217#536—31no—
218#470—92no—
219#468—92no—
220#467—92no—
221#465—92no—
222#428—91no—
223#416—91no—
224C2×#103—91no—
225C3×#41—22no—
226C3×#41—22no—
227C3×#41—22no—
228C3×#41—22no—
229C3×#41—42no—
230C3×#41—42no—
231C2×C3×Q8—21no—
232C2×C3×Q8—32no—
233C2×C3×Q8—61no—
234C2×C3×Q8—62no—
235C2×C3×Q8—62no—
236C2×C3×Q8D1211yescharacteristic
237C2×C3×Q8#6711yescharacteristic
238C2×C3×D4—21no—
239C2×C3×D4—22no—
240C2×C3×D4D1211yescharacteristic
241C2×C3×D4D1212yes—
242C2×C3×D4#6712yes—
243C2×C3×D4#6711yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—61no—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C2×#67—62no—
252C2×#67—61no—
253C2×#67—61no—
254C2×#67—64no—
255C2×#67—62no—
256C2×#67—62no—
257C22×Dic3—21no—
258C22×Dic3—62no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261#235—62no—
262#235—62no—
263#235—62no—
264#235—62no—
265#235—122no—
266#235—122no—
267C2×D12—31no—
268C2×D12—31no—
269C2×D12—61no—
270C2×C4×D3—62no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×Dic6—22no—
274C2×Dic6—22no—
275C2×Dic6—21no—
276C2×Dic6—31no—
277C2×Dic6—31no—
278C2×Dic6—61no—
279C2×Dic6C22×D312yes—
280C3×M16—34no—
281C3×M16—64no—
282C2×C3×C8—32no—
283C2×C3×C8—31no—
284C2×C3×C8—31no—
285C2×C3×C8—64no—
286C2×C3×C8—62no—
287C3×C4⋊C4—31no—
288C3×C4⋊C4—31no—
289C3×C4⋊C4—62no—
290C3×C4⋊C4—62no—
291C3×C22⋊C4—61no—
292C3×C22⋊C4—62no—
293C3×C22⋊C4—62no—
294C3×C42—61no—
295#217—22no—
296#217—22no—
297#217—21no—
298#217—64no—
299#217—62no—
300#217—62no—
301#216—64no—
302#215—64no—
303(C2×D3)⋊C4—64no—
304(C2×D3)⋊C4—62no—
305(C2×D3)⋊C4—62no—
306C4⋊Dic3—32no—
307C4⋊Dic3—32no—
308C4⋊Dic3—62no—
309C4⋊Dic3—62no—
310C4⋊Dic3—61no—
311C4⋊Dic3—61no—
312C4⋊Dic3C22×D311yescharacteristic
313C4⋊Dic3C22×D311yescharacteristic
314Dic3⋊C4—22no—
315Dic3⋊C4—22no—
316Dic3⋊C4—64no—
317Dic3⋊C4—62no—
318Dic3⋊C4—62no—
319C4×Dic3—21no—
320#208—24no—
321#208#6714yescomplemented
322C2×C3⋊C8—22no—
323C2×C3⋊C8—24no—
324C2×C3⋊C8C22×D311yescharacteristic
325C2×C3⋊C8C22×D311yescharacteristic
326C2×C3⋊C8C22×D312yes—
327Dic12—64no—
328#204—64no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32#12112yes—
335C22×C32C22×D411yescharacteristic
336C2×C3⋊D3—41no—
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
339C32×C4—22no—
340C32×C4#12112yes—
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3⋊Dic3—41no—
344C3⋊Dic3—42no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3—41no—
348C2×#41—91no—
349C2×#41D3211yescharacteristic
350C22×Q8—31no—
351#137—184no—
352C2×Q16—92no—
353C2×SD16—92no—
354#131—64no—
355C2×M16—31no—
356C2×M16—32no—
357C22×C8—31no—
358C22×C8—32no—
359C4⋊Q8—61no—
360#124—61no—
361#123—62no—
362C22⋊Q8—32no—
363C22⋊Q8—32no—
364C22⋊Q8—92no—
365C22⋊Q8—181no—
366#121—92no—
367#121—181no—
368#121—182no—
369#117—31no—
370C2×C4⋊C4—91no—
371#107—92no—
372#106—92no—
373#103—91no—
374#103—91no—
375#103—92no—
376#103—92no—
377#102—91no—
378#102—91no—
379C23×C3—21no—
380C23×C3—22no—
381C23×C3C2×D1212yes—
382C23×C3C2×D1211yescharacteristic
383C23×C3C2×#6712yes—
384C23×C3C2×#6711yescharacteristic
385C22×D3—62no—
386C22×D3—61no—
387C22×D3—61no—
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8—42no—
391C3×Q8—62no—
392C3×Q8—62no—
393C3×Q8—122no—
394C3×D4—24no—
395C3×D4—24no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—42no—
399C3×D4—44no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—62no—
414C2×C3×C4—122no—
415C2×C3×C4C2×D1212yes—
416C2×C3×C4C2×D1211yescharacteristic
417C2×C3×C4#23512yes—
418C2×C3×C4D3×D412yes—
419C2×C3×C4#23712yes—
420C2×C3×C4C2×#6712yes—
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6712yes—
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—124no—
426#67—122no—
427#67—122no—
428#67—242no—
429#67—242no—
430#67—244no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—22no—
434C2×Dic3—42no—
435C2×Dic3—62no—
436C2×Dic3—64no—
437C2×Dic3—61no—
438C2×Dic3—62no—
439C2×Dic3—61no—
440C2×Dic3—62no—
441C2×Dic3—241no—
442C2×Dic3—241no—
443C2×Dic3—242no—
444D12—61no—
445D12—61no—
446D12—61no—
447D12—61no—
448D12—121no—
449D12—121no—
450C4×D3—124no—
451C4×D3—122no—
452C4×D3—122no—
453Dic6—22no—
454Dic6—22no—
455Dic6—42no—
456Dic6—61no—
457Dic6—61no—
458Dic6—61no—
459Dic6—61no—
460Dic6—121no—
461Dic6—121no—
462C3×C8—34no—
463C3×C8—61no—
464C3×C8—61no—
465C3⋊C8—21no—
466C3⋊C8—21no—
467C3⋊C8C2×#6714yes—
468C2×C32—22no—
469C2×C32—42no—
470C2×C32C2×#12111yescharacteristic
471C2×C32#57711yescharacteristic
472C2×C32#57811yescharacteristic
473C3⋊D3—81no—
474#41—22no—
475#41—22no—
476#41—182no—
477#41—182no—
478C2×Q8—32no—
479C2×Q8—61no—
480C2×Q8—62no—
481C2×Q8—62no—
482C2×Q8—91no—
483C2×Q8#62611yescharacteristic
484C2×D4—91no—
485C2×D4—181no—
486C2×D4—182no—
487C2×D4#62612yes—
488C2×D4#62611yescharacteristic
489C22×C4—61no—
490C22×C4—181no—
491C22×C4—181no—
492C22×C4C2×D3212yes—
493C22×C4C2×D3211yescharacteristic
494Q16—184no—
495SD16—184no—
496M16—34no—
497M16—64no—
498C2×C8—32no—
499C2×C8—31no—
500C2×C8—31no—
501C2×C8—64no—
502C2×C8—62no—
503C4⋊C4—31no—
504C4⋊C4—31no—
505C4⋊C4—62no—
506C4⋊C4—62no—
507C4⋊C4—92no—
508C4⋊C4—181no—
509C4⋊C4—182no—
510C22⋊C4—61no—
511C22⋊C4—62no—
512C22⋊C4—62no—
513C22⋊C4—182no—
514C22⋊C4—182no—
515C42—61no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—21no—
527C22×C3—22no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3#93012yes—
534C22×C3#93912yes—
535C22×C3C22×D1211yescharacteristic
536C22×C3C22×#6711yescharacteristic
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—121no—
541C2×D3—121no—
542C2×D3—121no—
543C2×D3—121no—
544C2×D3—121no—
545C2×D3—121no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—22no—
551C3×C4—42no—
552C3×C4—121no—
553C3×C4—121no—
554C3×C4—122no—
555C3×C4#93012yes—
556C3×C4#93912yes—
557C3×C4C2×#23511yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×#23711yescharacteristic
560C3×C4C22×#6711yescharacteristic
561Dic3—42no—
562Dic3—41no—
563Dic3—41no—
564Dic3—122no—
565Dic3—124no—
566Dic3—122no—
567Dic3—121no—
568Dic3—121no—
569Dic3—122no—
570C32#306311yescharacteristic, complemented, Sylow
571C23—181no—
572C23C2×#62612yes—
573C23C2×#62611yescharacteristic
574Q8—22no—
575Q8—62no—
576Q8—62no—
577Q8—122no—
578Q8—181no—
579Q8—181no—
580D4—24no—
581D4—22no—
582D4—181no—
583D4—181no—
584D4—362no—
585D4—722no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—61no—
589C2×C4—61no—
590C2×C4—62no—
591C2×C4—122no—
592C2×C4—182no—
593C2×C4—181no—
594C2×C4—362no—
595C2×C4—721no—
596C2×C4#380412yes—
597C2×C4C2×#62612yes—
598C2×C4C2×#62611yescharacteristic
599C2×C4D3×#6712yes—
600C2×C4C22×D3211yescharacteristic
601C8—34no—
602C8—61no—
603C8—61no—
604C2×C3—22no—
605C2×C3—22no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—42no—
610C2×C3—42no—
611C2×C3—42no—
612C2×C3—82no—
613C2×C3#575111yescharacteristic
614C2×C3#575311yescharacteristic
615C2×C3C2×#93011yescharacteristic
616C2×C3C2×#93911yescharacteristic
617C2×C3#583711yescharacteristic
618C2×C3#583811yescharacteristic
619D3—242no—
620D3—241no—
621D3—241no—
622C22—21no—
623C22—21no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—361no—
628C22—361no—
629C22—361no—
630C22#6397812yes—
631C22C22×#62611yescharacteristic
632C4—22no—
633C4—121no—
634C4—121no—
635C4—122no—
636C4—362no—
637C4—361no—
638C4#6397812yes—
639C4C2×#380411yescharacteristic
640C4C2×D3×#6711yescharacteristic
641C3—21no—
642C3#8340011yescharacteristic, complemented
643C3#8380811yescharacteristic, complemented
644C2—22no—
645C2—42no—
646C2—721no—
647C2#1059544811yescharacteristic
648C2#1059545011yescharacteristic
649C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radical#10596304C2
hypercenterC2×#41D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5825C2semidirect
3. C2×C3×#948C2semidirect
4. C2×#63833C2semidirect
5. #10591187C2semidirect
6. #10591178C2semidirect
7. #10591177C2semidirect
8. #10591131C2semidirect
9. #10591121C2semidirect
10. #10591105C2semidirect
11. C2×#63566C2semidirect
50. #5825D3semidirect
51. C2×#948D3semidirect
102. C3×#208D4semidirect
321. #208#67semidirect
570. C32#3063semidirect
642. C3#83400semidirect
643. C3#83808semidirect

Maximal subgroups

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

subgroupindex
#105963042
C3×#58252
C2×C3×#9482
C2×#638332
#105911872
#105911782
#105911772
#105911312
#105911212
#105911052
C2×#635662
#838083
#834003