Finite Group Databasebeta

← #11867806

Subgroups — #11867806

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596296C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic
3C2×C3×#948C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5#10591187C212yesmaximal, complemented
6#10591176C212yesmaximal, complemented
7#10591175C212yesmaximal, complemented
8#10591130C211yesmaximal, characteristic, complemented
9#10591121C212yesmaximal, complemented
10C2×#63567C211yesmaximal, characteristic, complemented
11#10591084C211yesmaximal, characteristic, complemented
12#83808—31nomaximal
13#83423—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17#64153—21no—
18#64145—21no—
19#64144—22no—
20#64135C2211yescharacteristic
21#64133C2212yes—
22#64133C2212yes—
23C3×#948—24no—
24C3×#946—21no—
25C3×#939—22no—
26C3×#938—21no—
27C3×#930C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C3×#924C2212yes—
30C2×C3×#208C2212yes—
31C2×C3×#208C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33C22×C3×C3⋊C8C2212yes—
34C2×#3719C2212yes—
35#63831—24no—
36C2×#3716C2212yes—
37#63575C2212yes—
38#63573C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63566C2211yescharacteristic
42#63566C2211yescharacteristic
43#63563C2211yescharacteristic
44#63563C2211yescharacteristic
45C2×C3×#131—31no—
46C3×#537—31no—
47#5833D311yescharacteristic
48#5825—31no—
49#5825—31no—
50#5825—61no—
51C2×#951—31no—
52C2×#948D311yescharacteristic, complemented
53C2×#909—31no—
54#5233—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#5042—32no—
65#5041—32no—
66C2×#810—31no—
67#4964—31no—
68C32×#41—22no—
69C32×#41—22no—
70C2×C32×Q8D411yescharacteristic
71C2×C32×D4D411yescharacteristic
72C2×C32×D4D412yes—
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—21no—
76C2×#634—22no—
77C2×#634—22no—
78C2×#634—21no—
79C2×#634C2312yes—
80C2×C3×#67—21no—
81C2×C3×#67—22no—
82C22×C3×Dic3—21no—
83C3×#235—22no—
84C3×#235—22no—
85C2×C3×D12C2311yescharacteristic
86C2×C3×C4×D3—21no—
87C2×C3×Dic6C2311yescharacteristic
88#3757—22no—
89#3757—22no—
90#3757—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—22no—
94#3750—22no—
95C4×C3⋊Dic3—21no—
96C3×#217—22no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—22no—
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#3716—24no—
110#3063—91noSylow
111C2×C3×#41—21no—
112C2×C3×#41—31no—
113C2×C3×#41C2×D311yescharacteristic
114C2×C3×#41C2×D311yescharacteristic
115C2×#235C2×D311yescharacteristic
116C22×Dic6—31no—
117C22×Dic6—31no—
118C22×Dic6—61no—
119C3×#131—64no—
120C2×C3×M16—31no—
121C2×C3×M16—32no—
122C22×C3×C8—31no—
123C22×C3×C8—32no—
124C3×C22⋊Q8—32no—
125C3×C22⋊Q8—61no—
126C3×#121—32no—
127C3×#121—61no—
128C3×#121—62no—
129C2×C3×C4⋊C4—31no—
130#951—64no—
131#948—24no—
132#946—21no—
133#944—62no—
134#944—61no—
135#944—61no—
136C2×#216—32no—
137#939—22no—
138#938—21no—
139#936—62no—
140#936—61no—
141#936—61no—
142#935—64no—
143#935—62no—
144#935—62no—
145C2×#214—32no—
146#930C2×D312yes—
147#926—31no—
148#926—31no—
149#926—61no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151#924—32no—
152#924—32no—
153#924—32no—
154#924—32no—
155#924—62no—
156#924—62no—
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—31no—
166#835—31no—
167#832—31no—
168#832—31no—
169#821—31no—
170#821—31no—
171#818—32no—
172#817—32no—
173#816—31no—
174#816—31no—
175#816—32no—
176#816—32no—
177#810—32no—
178#810—32no—
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
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—42no—
198#634—22no—
199#634—22no—
200#634—42no—
201C3×#67—42no—
202C3×#67—82no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—81no—
206C3×D12—21no—
207C3×D12—21no—
208C3×C4×D3—42no—
209C3×Dic6—21no—
210C3×Dic6—21no—
211C3×C3⋊C8—21no—
212C3×C3⋊C8—21no—
213C3×C3⋊C8C2×D414yes—
214C2×#137—91no—
215C2×#131—31no—
216#537—31no—
217#536—91no—
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—
231C3×#41—62no—
232C3×#41—62no—
233C2×C3×Q8—21no—
234C2×C3×Q8—31no—
235C2×C3×Q8D1211yescharacteristic
236C2×C3×Q8#6711yescharacteristic
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—31no—
240C2×C3×D4—61no—
241C2×C3×D4—62no—
242C2×C3×D4D1212yes—
243C2×C3×D4D1211yescharacteristic
244C2×C3×D4#6712yes—
245C2×C3×D4#6711yescharacteristic
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—61no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—21no—
255C2×#67—22no—
256C22×Dic3—21no—
257C22×Dic3—62no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260#235—22no—
261#235—22no—
262C2×D12C22×D311yescharacteristic
263C2×C4×D3—21no—
264C2×Dic6—32no—
265C2×Dic6—32no—
266C2×Dic6—62no—
267C2×Dic6—62no—
268C2×Dic6—62no—
269C2×Dic6—62no—
270C2×Dic6—62no—
271C2×Dic6—62no—
272C2×Dic6—61no—
273C2×Dic6—61no—
274C2×Dic6—122no—
275C2×Dic6—122no—
276C2×Dic6C22×D311yescharacteristic
277C3×M16—34no—
278C3×M16—64no—
279C2×C3×C8—32no—
280C2×C3×C8—31no—
281C2×C3×C8—31no—
282C2×C3×C8—64no—
283C2×C3×C8—62no—
284C3×C4⋊C4—32no—
285C3×C4⋊C4—62no—
286C3×C4⋊C4—61no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4—62no—
289#217—22no—
290#217—64no—
291#217—64no—
292#217—62no—
293#217—62no—
294#217—62no—
295#217—61no—
296#217—62no—
297#217—62no—
298#217—61no—
299#216—64no—
300#214—64no—
301(C2×D3)⋊C4—22no—
302C4⋊Dic3—21no—
303C4⋊Dic3—31no—
304C4⋊Dic3—31no—
305C4⋊Dic3—31no—
306C4⋊Dic3—31no—
307C4⋊Dic3—61no—
308C4⋊Dic3—61no—
309C4⋊Dic3C22×D312yes—
310Dic3⋊C4—22no—
311Dic3⋊C4—64no—
312Dic3⋊C4—64no—
313Dic3⋊C4—62no—
314Dic3⋊C4—62no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317C4×Dic3—62no—
318C4×Dic3—61no—
319C4×Dic3—61no—
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—42no—
344C3⋊Dic3—41no—
345C3⋊Dic3—41no—
346C3×Dic3—41no—
347C3×Dic3—42no—
348C2×#41—31no—
349C2×#41D3211yescharacteristic
350C22×Q8—91no—
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—181no—
360#124—181no—
361#123—182no—
362C22⋊Q8—32no—
363C22⋊Q8—61no—
364C22⋊Q8—92no—
365C22⋊Q8—92no—
366#121—32no—
367#121—61no—
368#121—62no—
369#117—91no—
370C2×C4⋊C4—31no—
371#107—92no—
372#106—92no—
373#103—92no—
374#103—92no—
375#103—91no—
376#103—91no—
377#102—91no—
378#102—91no—
379C23×C3—21no—
380C23×C3—22no—
381C23×C3—61no—
382C23×C3C2×D1212yes—
383C23×C3C2×D1211yescharacteristic
384C23×C3C2×#6712yes—
385C23×C3C2×#6711yescharacteristic
386C22×D3—21no—
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—42no—
390C3×Q8—61no—
391C3×Q8—61no—
392C3×D4—24no—
393C3×D4—24no—
394C3×D4—22no—
395C3×D4—22no—
396C3×D4—42no—
397C3×D4—44no—
398C3×D4—61no—
399C3×D4—61no—
400C3×D4—122no—
401C3×D4—242no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—122no—
416C2×C3×C4—241no—
417C2×C3×C4C2×D1212yes—
418C2×C3×C4C2×D1211yescharacteristic
419C2×C3×C4#23512yes—
420C2×C3×C4D3×D412yes—
421C2×C3×C4#23712yes—
422C2×C3×C4C2×#6712yes—
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6712yes—
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427#67—42no—
428#67—82no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—64no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—62no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—62no—
440C2×Dic3—81no—
441C2×Dic3—124no—
442C2×Dic3—122no—
443C2×Dic3—122no—
444D12—21no—
445D12—21no—
446C4×D3—42no—
447Dic6—21no—
448Dic6—21no—
449Dic6—62no—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—122no—
454Dic6—122no—
455Dic6—124no—
456Dic6—122no—
457Dic6—122no—
458C3×C8—34no—
459C3×C8—61no—
460C3×C8—61no—
461C3⋊C8—21no—
462C3⋊C8—21no—
463C3⋊C8C2×#6714yes—
464C2×C32—22no—
465C2×C32—42no—
466C2×C32C2×#12111yescharacteristic
467C2×C32#57711yescharacteristic
468C2×C32#57811yescharacteristic
469C3×D3—81no—
470#41—22no—
471#41—22no—
472#41—62no—
473#41—62no—
474C2×Q8—31no—
475C2×Q8—92no—
476C2×Q8—181no—
477C2×Q8—182no—
478C2×Q8—182no—
479C2×Q8#62611yescharacteristic
480C2×D4—31no—
481C2×D4—61no—
482C2×D4—62no—
483C2×D4#62612yes—
484C2×D4#62611yescharacteristic
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—181no—
488C22×C4C2×D3212yes—
489C22×C4C2×D3211yescharacteristic
490Q16—184no—
491SD16—184no—
492M16—34no—
493M16—64no—
494C2×C8—32no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—64no—
498C2×C8—62no—
499C4⋊C4—32no—
500C4⋊C4—61no—
501C4⋊C4—62no—
502C4⋊C4—91no—
503C4⋊C4—91no—
504C4⋊C4—182no—
505C4⋊C4—182no—
506C22⋊C4—62no—
507C22⋊C4—62no—
508C22⋊C4—181no—
509C22⋊C4—182no—
510C22⋊C4—182no—
511C42—181no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—22no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—121no—
530C22×C3—121no—
531C22×C3—121no—
532C22×C3#93012yes—
533C22×C3#93912yes—
534C22×C3C22×D1211yescharacteristic
535C22×C3C22×#6711yescharacteristic
536C2×D3—41no—
537C2×D3—41no—
538C2×D3—41no—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—22no—
544C3×C4—42no—
545C3×C4—122no—
546C3×C4—121no—
547C3×C4#93012yes—
548C3×C4#93912yes—
549C3×C4C2×#23511yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C2×#23711yescharacteristic
552C3×C4C22×#6711yescharacteristic
553Dic3—41no—
554Dic3—42no—
555Dic3—124no—
556Dic3—122no—
557Dic3—122no—
558Dic3—121no—
559Dic3—121no—
560Dic3—122no—
561Dic3—122no—
562Dic3—121no—
563Dic3—121no—
564C32#306311yescharacteristic, complemented, Sylow
565C23—61no—
566C23C2×#62612yes—
567C23C2×#62611yescharacteristic
568Q8—22no—
569Q8—61no—
570Q8—61no—
571Q8—182no—
572Q8—182no—
573Q8—362no—
574D4—24no—
575D4—22no—
576D4—61no—
577D4—61no—
578D4—122no—
579D4—242no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—62no—
583C2×C4—61no—
584C2×C4—122no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—182no—
588C2×C4—241no—
589C2×C4—362no—
590C2×C4#380412yes—
591C2×C4C2×#62612yes—
592C2×C4C2×#62611yescharacteristic
593C2×C4D3×#6712yes—
594C2×C4C22×D3211yescharacteristic
595C8—34no—
596C8—61no—
597C8—61no—
598C2×C3—22no—
599C2×C3—22no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—42no—
604C2×C3—42no—
605C2×C3—42no—
606C2×C3—82no—
607C2×C3—241no—
608C2×C3#575111yescharacteristic
609C2×C3#575311yescharacteristic
610C2×C3C2×#93011yescharacteristic
611C2×C3C2×#93911yescharacteristic
612C2×C3#583611yescharacteristic
613C2×C3#583811yescharacteristic
614D3—81no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—121no—
621C22—121no—
622C22—121no—
623C22#6397812yes—
624C22C22×#62611yescharacteristic
625C4—22no—
626C4—122no—
627C4—121no—
628C4—361no—
629C4—361no—
630C4—362no—
631C4#6397812yes—
632C4C2×#380411yescharacteristic
633C4C2×D3×#6711yescharacteristic
634C3—21no—
635C3#8342311yescharacteristic, complemented
636C3#8380811yescharacteristic, complemented
637C2—22no—
638C2—42no—
639C2—241no—
640C2#1059544711yescharacteristic
641C2#1059545011yescharacteristic
642C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5833C2
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
1. #10596296C2semidirect
3. C2×C3×#948C2semidirect
4. C2×#63831C2semidirect
5. #10591187C2semidirect
6. #10591176C2semidirect
7. #10591175C2semidirect
8. #10591130C2semidirect
9. #10591121C2semidirect
10. C2×#63567C2semidirect
11. #10591084C2semidirect
52. C2×#948D3semidirect
102. C3×#208D4semidirect
321. #208#67semidirect
564. C32#3063semidirect
635. C3#83423semidirect
636. C3#83808semidirect

Maximal subgroups

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

subgroupindex
#105962962
C3×#58332
C2×C3×#9482
C2×#638312
#105911872
#105911762
#105911752
#105911302
#105911212
C2×#635672
#105910842
#838083
#834233