Finite Group Databasebeta

← #11867810

Subgroups — #11867810

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
2C2×C3×#951C211yesmaximal, characteristic, complemented
3#10594866C211yesmaximal, characteristic, complemented
4C2×#63817C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591601C212yesmaximal, complemented
7#10591600C212yesmaximal, complemented
8#10591465C212yesmaximal, complemented
9#10591464C212yesmaximal, complemented
10#10591131C211yesmaximal, characteristic, complemented
11C2×#63566C211yesmaximal, characteristic, complemented
12#83986—31nomaximal
13#78841—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17#64155C2212yes—
18#64148—22no—
19#64147C2212yes—
20#64139—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133—21no—
23C3×#951—24no—
24C2×C3×#216C2212yes—
25C2×C3×#214C2212yes—
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63966—22no—
30#63871C2212yes—
31#63871C2212yes—
32#63866—21no—
33#63864—21no—
34C2×#3712C2212yes—
35#63817—24no—
36C2×#3710C2212yes—
37C3×#835C2211yescharacteristic
38C3×#835C2211yescharacteristic
39C3×#832C2211yescharacteristic
40C3×#832C2211yescharacteristic
41#63575C2212yes—
42#63573C2212yes—
43#63566C2212yes—
44#63566C2212yes—
45C2×C3×#137—31no—
46#5833—31no—
47#5833—31no—
48#5833—61no—
49C2×#951D311yescharacteristic, complemented
50#5816—31no—
51C2×#907—31no—
52C2×#901—31no—
53#5526—31no—
54C3×#416—31no—
55#5233D311yescharacteristic, complemented
56C2×#835—31no—
57#5189—32no—
58#5188—32no—
59#5174—32no—
60#5171—32no—
61#5121—31no—
62C2×#816—31no—
63#4995—31no—
64#4816—32no—
65#4813—32no—
66#4780—32no—
67#4778—32no—
68C32×#41—22no—
69C32×#41—22no—
70C2×C32×Q8C2311yescharacteristic
71C2×C32×D4—21no—
72C2×C32×D4C2311yescharacteristic
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—22no—
76C2×#638D412yes—
77C22×C3⋊Dic3—21no—
78#3828—22no—
79#3828—22no—
80C2×C4⋊(C3⋊D3)D411yescharacteristic
81C2×C4×C3⋊D3C2312yes—
82C2×#634D411yescharacteristic
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—21no—
94C3×#216—24no—
95C3×#214—24no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3—21no—
99C3×#208D414yescomplemented
100C2×C3×C3⋊C8—22no—
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106#3722—22no—
107#3722—22no—
108#3712—24no—
109#3710—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×#137—64no—
120C2×C3×Q16—32no—
121C2×C3×SD16—32no—
122C2×C3×M16—31no—
123C22×C3×C8—31no—
124C3×#117—31no—
125#951—24no—
126#947—61no—
127#946—32no—
128#946—32no—
129#946—32no—
130#946—32no—
131#946—62no—
132#944—61no—
133C2×#216C2×D312yes—
134#939—62no—
135#939—62no—
136#939—64no—
137#938—32no—
138#938—32no—
139#938—62no—
140C2×#214C2×D312yes—
141#930—61no—
142#930—61no—
143#930—62no—
144#929—62no—
145#926C2×D311yescharacteristic
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—61no—
149#924—61no—
150#924—61no—
151#924—62no—
152C2×#208C2×D311yescharacteristic
153C22×C3⋊C8C2×D311yescharacteristic
154#907—64no—
155#901—64no—
156C2×ΓL(1,𝔽25)—32no—
157C2×ΓL(1,𝔽25)—32no—
158C2×D3×C8—32no—
159C2×D3×C8—32no—
160#897—32no—
161#897—32no—
162#886—62no—
163#875—61no—
164#869—61no—
165C3×#103—31no—
166C3×#103—31no—
167C3×#102—31no—
168C3×#102—31no—
169#835—32no—
170#835—32no—
171#835C2×D311yescharacteristic
172#835C2×D311yescharacteristic
173#832C2×D311yescharacteristic
174#832C2×D311yescharacteristic
175#818—32no—
176#817—32no—
177#816—32no—
178#816—32no—
179#808—32no—
180#807—32no—
181C23×C32—21no—
182C23×C32C2×D411yescharacteristic
183C22×C3⋊D3C2×D412yes—
184C32×Q8—21no—
185C32×Q8—21no—
186C32×D4—21no—
187C32×D4—21no—
188C32×D4—42no—
189C2×C32×C4—21no—
190C2×C32×C4—42no—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D412yes—
193C2×C32×C4#4112yes—
194C2×C32×C4C2411yescharacteristic
195#638—24no—
196#638—82no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—81no—
199C2×C3⋊Dic3C2×D412yes—
200C4⋊(C3⋊D3)—22no—
201C4×C3⋊D3—22no—
202C4×C3⋊D3—22no—
203#634—22no—
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—31no—
215C2×#131—91no—
216#537—91no—
217#536—91no—
218#470—92no—
219#468—92no—
220#467—92no—
221#465—92no—
222#428—91no—
223#416—31no—
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×Q8C22×D311yescharacteristic
237C2×C3×Q8C22×D311yescharacteristic
238C2×C3×D4—22no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4C22×D311yescharacteristic
243C2×C3×D4C22×D311yescharacteristic
244C22×C3×C4—22no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—61no—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C2×#67—32no—
252C2×#67—32no—
253C2×#67—62no—
254C2×#67—62no—
255C2×#67—62no—
256C2×#67—64no—
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—32no—
271C2×C4×D3—32no—
272C2×C4×D3—62no—
273C2×Dic6—22no—
274C2×Dic6—22no—
275C2×Dic6—21no—
276C2×Dic6—31no—
277C2×Dic6—31no—
278C2×Dic6—61no—
279C2×Dic6C22×D312yes—
280C3×Q16—64no—
281C3×SD16—64no—
282C3×M16—34no—
283C2×C3×C8—32no—
284C2×C3×C8—31no—
285C2×C3×C8—31no—
286C2×C3×C8—62no—
287C3×C4⋊C4—31no—
288C3×C4⋊C4—31no—
289C3×C22⋊C4—61no—
290C3×C42—61no—
291#217—21no—
292#217—62no—
293#217—62no—
294#217—64no—
295#216—24no—
296#214—24no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303(C2×D3)⋊C4—64no—
304C4⋊Dic3—32no—
305C4⋊Dic3—32no—
306C4⋊Dic3—62no—
307C4⋊Dic3—62no—
308C4⋊Dic3—62no—
309C4⋊Dic3—62no—
310C4⋊Dic3—61no—
311C4⋊Dic3—61no—
312C4⋊Dic3C22×D311yescharacteristic
313C4⋊Dic3C22×D311yescharacteristic
314Dic3⋊C4—62no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317Dic3⋊C4—62no—
318Dic3⋊C4—64no—
319C4×Dic3—21no—
320#208#6714yescomplemented
321C2×C3⋊C8—22no—
322C2×C3⋊C8C22×D311yescharacteristic
323C2×C3⋊C8C22×D311yescharacteristic
324C2×C3⋊C8C22×D312yes—
325ΓL(1,𝔽25)—64no—
326ΓL(1,𝔽25)—64no—
327D3×C8—64no—
328D3×C8—64no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32#12112yes—
335C22×C32C22×D411yescharacteristic
336C2×C3⋊D3—22no—
337C2×C3⋊D3—22no—
338C2×C3⋊D3—22no—
339C32×C4—41no—
340C32×C4#12112yes—
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3⋊Dic3—22no—
344C3⋊Dic3—42no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3—41no—
348C2×#41—91no—
349C2×#41D3211yescharacteristic
350C22×Q8—31no—
351#137—64no—
352C2×Q16—32no—
353C2×SD16—32no—
354#131—184no—
355C2×M16—31no—
356C2×M16—92no—
357C22×C8—31no—
358C22×C8—92no—
359C4⋊Q8—181no—
360#124—181no—
361#123—182no—
362C22⋊Q8—92no—
363C22⋊Q8—92no—
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—31no—
374#103—31no—
375#103—92no—
376#103—92no—
377#102—31no—
378#102—31no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3D3×D411yescharacteristic
384C23×C3D3×D411yescharacteristic
385C22×D3—32no—
386C22×D3—32no—
387C22×D3—62no—
388C3×Q8—21no—
389C3×Q8—21no—
390C3×Q8—21no—
391C3×Q8—21no—
392C3×Q8—41no—
393C3×Q8—41no—
394C3×Q8—62no—
395C3×Q8—62no—
396C3×Q8—122no—
397C3×D4—21no—
398C3×D4—21no—
399C3×D4—21no—
400C3×D4—21no—
401C3×D4—41no—
402C3×D4—41no—
403C3×D4—44no—
404C3×D4—42no—
405C3×D4—42no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—44no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—122no—
420C2×C3×C4#23512yes—
421C2×C3×C4D3×D412yes—
422C2×C3×C4D3×D411yescharacteristic
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4#23712yes—
425C2×C3×C4C2×#6712yes—
426C2×C3×C4C23×D311yescharacteristic
427C2×C3×C4C23×D311yescharacteristic
428#67—64no—
429#67—64no—
430#67—124no—
431#67—242no—
432#67—242no—
433#67—244no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—22no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—42no—
440C2×Dic3—62no—
441C2×Dic3—64no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—241no—
445C2×Dic3—241no—
446C2×Dic3—242no—
447D12—62no—
448D12—62no—
449D12—122no—
450C4×D3—62no—
451C4×D3—62no—
452C4×D3—62no—
453C4×D3—62no—
454C4×D3—122no—
455C4×D3—122no—
456Dic6—22no—
457Dic6—22no—
458Dic6—42no—
459Dic6—62no—
460Dic6—62no—
461Dic6—122no—
462C3×C8—34no—
463C3×C8—61no—
464C3×C8—61no—
465C3⋊C8—21no—
466C3⋊C8—21no—
467C3⋊C8C2×#6714yes—
468C2×C32—22no—
469C2×C32—81no—
470C2×C32C2×#12111yescharacteristic
471C2×C32#57711yescharacteristic
472C2×C32#57811yescharacteristic
473C3⋊D3—42no—
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×Q8C2×D3211yescharacteristic
484C2×D4—21no—
485C2×D4—92no—
486C2×D4—91no—
487C2×D4—182no—
488C2×D4C2×D3211yescharacteristic
489C22×C4—21no—
490C22×C4—61no—
491C22×C4—92no—
492C22×C4—181no—
493C22×C4C2×D3211yescharacteristic
494Q16—64no—
495SD16—64no—
496M16—34no—
497M16—184no—
498C2×C8—32no—
499C2×C8—31no—
500C2×C8—31no—
501C2×C8—62no—
502C2×C8—184no—
503C4⋊C4—31no—
504C4⋊C4—31no—
505C4⋊C4—92no—
506C4⋊C4—182no—
507C4⋊C4—182no—
508C4⋊C4—182no—
509C4⋊C4—181no—
510C22⋊C4—61no—
511C22⋊C4—182no—
512C22⋊C4—182no—
513C22⋊C4—182no—
514C22⋊C4—182no—
515C42—61no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—22no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3#88412yes—
534C22×C3#93812yes—
535C22×C3C2×D3×D411yescharacteristic
536C22×C3C2×D3×D411yescharacteristic
537C2×D3—62no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—122no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—22no—
549C3×C4—42no—
550C3×C4—41no—
551C3×C4—41no—
552C3×C4—122no—
553C3×C4—121no—
554C3×C4—121no—
555C3×C4#88412yes—
556C3×C4#93812yes—
557C3×C4C2×#23511yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×#23711yescharacteristic
560C3×C4C22×#6711yescharacteristic
561Dic3—41no—
562Dic3—41no—
563Dic3—42no—
564Dic3—62no—
565Dic3—62no—
566Dic3—122no—
567Dic3—124no—
568Dic3—122no—
569Dic3—122no—
570C32#306311yescharacteristic, complemented, Sylow
571C23—21no—
572C23—92no—
573C23#381111yescharacteristic
574Q8—21no—
575Q8—21no—
576Q8—62no—
577Q8—62no—
578Q8—122no—
579Q8—182no—
580D4—21no—
581D4—21no—
582D4—42no—
583D4—184no—
584D4—182no—
585D4—722no—
586C2×C4—21no—
587C2×C4—42no—
588C2×C4—61no—
589C2×C4—61no—
590C2×C4—62no—
591C2×C4—92no—
592C2×C4—122no—
593C2×C4—182no—
594C2×C4—182no—
595C2×C4—182no—
596C2×C4—721no—
597C2×C4#380412yes—
598C2×C4D3×#6712yes—
599C2×C4#381111yescharacteristic
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—82no—
611C2×C3—81no—
612C2×C3—81no—
613C2×C3C2×#88411yescharacteristic
614C2×C3#577011yescharacteristic
615C2×C3#577111yescharacteristic
616C2×C3#577811yescharacteristic
617C2×C3#577911yescharacteristic
618C2×C3C2×#93811yescharacteristic
619D3—122no—
620D3—122no—
621D3—242no—
622C22—21no—
623C22—21no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—182no—
628C22—182no—
629C22—182no—
630C22#6395812yes—
631C22C2×#381111yescharacteristic
632C4—41no—
633C4—121no—
634C4—121no—
635C4—122no—
636C4—182no—
637C4—362no—
638C4#6395812yes—
639C4C2×#380411yescharacteristic
640C4C2×D3×#6711yescharacteristic
641C3—21no—
642C3#7884111yescharacteristic, complemented
643C3#8398611yescharacteristic, complemented
644C2—22no—
645C2—81no—
646C2—362no—
647C2#1059547211yescharacteristic
648C2#1059547311yescharacteristic
649C2C2×#6395811yescharacteristic
subgroupG/H
centerC22C2×#3811
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 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. #10594866C2semidirect
4. C2×#63817C2semidirect
5. C3×#5233C2semidirect
6. #10591601C2semidirect
7. #10591600C2semidirect
8. #10591465C2semidirect
9. #10591464C2semidirect
10. #10591131C2semidirect
11. C2×#63566C2semidirect
49. C2×#951D3semidirect
55. #5233D3semidirect
99. C3×#208D4semidirect
320. #208#67semidirect
570. C32#3063semidirect
642. C3#78841semidirect
643. C3#83986semidirect

Maximal subgroups

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

subgroupindex
#105963042
C2×C3×#9512
#105948662
C2×#638172
C3×#52332
#105916012
#105916002
#105914652
#105914642
#105911312
C2×#635662
#839863
#788413