Finite Group Databasebeta

← #11867816

Subgroups — #11867816

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3#10594866C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5C3×#5113C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7#10591139C211yesmaximal, characteristic, complemented
8#10590856C212yesmaximal, complemented
9#10590855C212yesmaximal, complemented
10#10590842C212yesmaximal, complemented
11#10590841C212yesmaximal, complemented
12#78841—31nomaximal
13#78800—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×C32×C8C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19#64110—24no—
20C2×#3743C2212yes—
21C2×C8×C3⋊D3C2212yes—
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24#63978—22no—
25#63966—22no—
26#63916C2212yes—
27#63909—21no—
28#63871C2212yes—
29#63871C2212yes—
30#63871C2212yes—
31#63866—21no—
32#63864—21no—
33#63857—21no—
34C2×#3718C2212yes—
35#63827—24no—
36C2×#3715C2212yes—
37C3×#821C2211yescharacteristic
38C3×#821C2211yescharacteristic
39C3×#816C2212yes—
40C3×#816C2212yes—
41C3×#816C2211yescharacteristic
42C3×#816C2211yescharacteristic
43#63576C2212yes—
44#63574C2212yes—
45#5833—31no—
46C2×#951—31no—
47#5816—31no—
48C2×#942—31no—
49C2×#901—31no—
50C2×#901—31no—
51C2×#901—61no—
52#5526—31no—
53#5510—31no—
54C3×#416—31no—
55C2×C3×#103—31no—
56#5113D311yescharacteristic, complemented
57C2×#816D311yescharacteristic, complemented
58#4995—31no—
59#4964—31no—
60#4816—32no—
61#4816—32no—
62#4813—32no—
63#4813—32no—
64#4812—32no—
65#4807—32no—
66#4780—32no—
67#4778—32no—
68C22×C32×C4C2311yescharacteristic
69C2×#638D412yes—
70#3828—22no—
71#3828—22no—
72C2×C4⋊(C3⋊D3)D411yescharacteristic
73C2×C4×C3⋊D3C2312yes—
74C2×#634D411yescharacteristic
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C3×#235—22no—
79C3×#235—22no—
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×Dic6—22no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6—21no—
85C2×C3×Dic6C2312yes—
86C2×C3×Dic6C2311yescharacteristic
87C2×#626—22no—
88C2×C32×C8—22no—
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91#3748D414yescomplemented
92C2×C3⋊(C3⋊C8)C2312yes—
93#3743—24no—
94C8×C3⋊D3—24no—
95C3×#217—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4×Dic3—21no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104#3722—22no—
105#3722—22no—
106#3722—22no—
107(C2×D3)⋊Dic3—22no—
108#3718—24no—
109#3715—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C22×C3×Q8—31no—
113C2×#235—31no—
114C2×#235—31no—
115C2×#235—61no—
116C2×#235C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C22×C3×C8—21no—
119C22×C3×C8C2×D311yescharacteristic
120C22×C3×C8C2×D311yescharacteristic
121C3×#117—31no—
122C2×C3×C4⋊C4—31no—
123#951—64no—
124#947—61no—
125#946—32no—
126#946—32no—
127#946—32no—
128#944—61no—
129C2×#216—32no—
130C2×#216—32no—
131#942—64no—
132C2×#215—32no—
133#939—62no—
134#938—32no—
135C2×#214—32no—
136#930—61no—
137#930—62no—
138#929—62no—
139#926C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D311yescharacteristic
141#924—61no—
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—61no—
145#901—64no—
146#901—64no—
147#901—68no—
148C2×ΓL(1,𝔽25)—32no—
149C2×ΓL(1,𝔽25)—32no—
150C2×ΓL(1,𝔽25)—62no—
151C2×D3×C8—32no—
152C2×D3×C8—32no—
153C2×D3×C8—62no—
154#897—32no—
155#897—32no—
156#897—32no—
157#897—61no—
158#895—32no—
159#895—61no—
160#886—62no—
161#875—61no—
162#869—61no—
163C3×#103—32no—
164C3×#103—32no—
165C3×#103—31no—
166C3×#103—31no—
167C3×#102—31no—
168C3×#102—31no—
169#821C2×D311yescharacteristic
170#821C2×D311yescharacteristic
171#816C2×D312yes—
172#816C2×D312yes—
173#816C2×D311yescharacteristic
174#816C2×D311yescharacteristic
175#808—32no—
176#808—32no—
177#807—32no—
178#807—32no—
179C23×C32C2×D411yescharacteristic
180C22×C3⋊D3C2×D412yes—
181C22×C3×D3—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D412yes—
184C2×C32×C4#4112yes—
185C2×C32×C4C2411yescharacteristic
186#638—24no—
187C2×C3⋊Dic3C2×D412yes—
188C4⋊(C3⋊D3)—22no—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191#634—22no—
192C3×#67—42no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—42no—
199C2×C3×Dic3—81no—
200C3×D12—21no—
201C3×D12—21no—
202C3×C4×D3—42no—
203C3×Dic6—22no—
204C3×Dic6—21no—
205C3×Dic6—22no—
206C3×Dic6—21no—
207C3×Dic6—42no—
208#626—82no—
209C32×C8—21no—
210C32×C8—21no—
211C3⋊(C3⋊C8)C2×D414yes—
212C2×#137—91no—
213C2×#131—91no—
214#537—91no—
215#536—91no—
216#470—92no—
217#468—92no—
218#467—92no—
219#465—92no—
220#428—91no—
221#416—31no—
222C2×#103—31no—
223C3×#41—62no—
224C3×#41—62no—
225C2×C3×Q8—32no—
226C2×C3×Q8—31no—
227C2×C3×Q8—61no—
228C2×C3×Q8—62no—
229C2×C3×Q8—62no—
230C2×C3×D4—31no—
231C2×C3×D4—61no—
232C22×C3×C4—21no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—21no—
239C2×#67—32no—
240C2×#67—32no—
241C2×#67—62no—
242C2×#67—62no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245#235—22no—
246#235—22no—
247#235—64no—
248#235—64no—
249#235—62no—
250#235—62no—
251#235—62no—
252#235—62no—
253C2×D12—31no—
254C2×D12—31no—
255C2×D12—61no—
256C2×D12—62no—
257C2×D12C22×D311yescharacteristic
258C2×C4×D3—21no—
259C2×C4×D3—32no—
260C2×C4×D3—32no—
261C2×C4×D3—62no—
262C2×Dic6—22no—
263C2×Dic6—22no—
264C2×Dic6—21no—
265C2×Dic6—31no—
266C2×Dic6—31no—
267C2×Dic6—61no—
268C2×Dic6C22×D312yes—
269C2×Dic6C22×D311yescharacteristic
270C2×C3×C8—24no—
271C2×C3×C8—22no—
272C2×C3×C8—22no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8C22×D311yescharacteristic
276C2×C3×C8C22×D311yescharacteristic
277C2×C3×C8C22×D311yescharacteristic
278C2×C3×C8C22×D311yescharacteristic
279C3×C4⋊C4—31no—
280C3×C4⋊C4—32no—
281C3×C4⋊C4—31no—
282C3×C4⋊C4—61no—
283C3×C22⋊C4—61no—
284C3×C42—61no—
285#217—21no—
286#217—62no—
287#216—64no—
288#216—64no—
289#215—64no—
290#214—64no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298C4⋊Dic3—21no—
299C4⋊Dic3—62no—
300C4⋊Dic3—62no—
301C4⋊Dic3—62no—
302C4⋊Dic3C22×D311yescharacteristic
303C4⋊Dic3C22×D312yes—
304C4⋊Dic3C22×D311yescharacteristic
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308C4×Dic3—21no—
309#208—34no—
310#208—34no—
311#208—64no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—62no—
315ΓL(1,𝔽25)—64no—
316ΓL(1,𝔽25)—64no—
317ΓL(1,𝔽25)—68no—
318D3×C8—64no—
319D3×C8—64no—
320D3×C8—68no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32#12112yes—
324C22×C32C22×D411yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C2×C3×D3—41no—
331C32×C4#12112yes—
332C32×C4C22×D411yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—22no—
335C3×Dic3—42no—
336C3×Dic3—41no—
337C3×Dic3—42no—
338C3×Dic3—41no—
339C3×Dic3—41no—
340C2×#41—31no—
341C2×#41—91no—
342C22×Q8—31no—
343#137—184no—
344C2×Q16—92no—
345C2×SD16—92no—
346#131—184no—
347C2×M16—91no—
348C2×M16—92no—
349C22×C8—92no—
350C22×C8D3211yescharacteristic
351C4⋊Q8—181no—
352#124—181no—
353#123—182no—
354C22⋊Q8—92no—
355C22⋊Q8—92no—
356C22⋊Q8—92no—
357C22⋊Q8—181no—
358#121—92no—
359#121—181no—
360#121—182no—
361#117—31no—
362C2×C4⋊C4—31no—
363#107—92no—
364#106—92no—
365#103—32no—
366#103—32no—
367#103—31no—
368#103—31no—
369#102—31no—
370#102—31no—
371C23×C3—21no—
372C23×C3—61no—
373C23×C3D3×D411yescharacteristic
374C23×C3D3×D411yescharacteristic
375C22×D3—21no—
376C22×D3—32no—
377C22×D3—32no—
378C22×D3—62no—
379C3×Q8—62no—
380C3×Q8—61no—
381C3×Q8—62no—
382C3×Q8—61no—
383C3×Q8—122no—
384C3×D4—61no—
385C3×D4—61no—
386C3×D4—122no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—62no—
396C2×C3×C4—122no—
397C2×C3×C4—122no—
398C2×C3×C4—241no—
399C2×C3×C4#23512yes—
400C2×C3×C4#23512yes—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D412yes—
404C2×C3×C4D3×D412yes—
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—42no—
408#67—68no—
409#67—64no—
410#67—64no—
411#67—242no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—21no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—42no—
420C2×Dic3—62no—
421C2×Dic3—81no—
422D12—21no—
423D12—21no—
424D12—64no—
425D12—62no—
426D12—62no—
427D12—242no—
428C4×D3—42no—
429C4×D3—64no—
430C4×D3—64no—
431C4×D3—62no—
432C4×D3—62no—
433C4×D3—62no—
434C4×D3—62no—
435Dic6—22no—
436Dic6—21no—
437Dic6—22no—
438Dic6—21no—
439Dic6—42no—
440Dic6—64no—
441Dic6—62no—
442Dic6—62no—
443C3×C8—22no—
444C3×C8—22no—
445C3×C8—21no—
446C3×C8—21no—
447C3×C8—21no—
448C3×C8—21no—
449C3⋊C8—34no—
450C3⋊C8—34no—
451C3⋊C8—64no—
452C2×C32—22no—
453C2×C32C2×#12111yescharacteristic
454C2×C32#57711yescharacteristic
455C2×C32#57811yescharacteristic
456C3⋊D3—42no—
457C3×D3—81no—
458#41—62no—
459#41—62no—
460#41—182no—
461#41—182no—
462C2×Q8—32no—
463C2×Q8—31no—
464C2×Q8—61no—
465C2×Q8—62no—
466C2×Q8—62no—
467C2×Q8—91no—
468C2×D4—31no—
469C2×D4—61no—
470C2×D4—92no—
471C2×D4—91no—
472C2×D4—182no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—92no—
477C22×C4C2×D3211yescharacteristic
478Q16—184no—
479SD16—184no—
480M16—94no—
481M16—184no—
482C2×C8—22no—
483C2×C8—92no—
484C2×C8—184no—
485C2×C8C2×D3211yescharacteristic
486C2×C8C2×D3211yescharacteristic
487C4⋊C4—31no—
488C4⋊C4—31no—
489C4⋊C4—32no—
490C4⋊C4—61no—
491C4⋊C4—182no—
492C4⋊C4—182no—
493C4⋊C4—182no—
494C22⋊C4—61no—
495C22⋊C4—182no—
496C22⋊C4—182no—
497C22⋊C4—182no—
498C22⋊C4—182no—
499C42—61no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—22no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3—121no—
511C22×C3#88412yes—
512C22×C3#88412yes—
513C22×C3C2×D3×D411yescharacteristic
514C22×C3C2×D3×D411yescharacteristic
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—41no—
518C2×D3—64no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—122no—
526C2×D3—122no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—22no—
530C3×C4—121no—
531C3×C4—122no—
532C3×C4—121no—
533C3×C4—121no—
534C3×C4—122no—
535C3×C4#88412yes—
536C3×C4#88412yes—
537C3×C4C2×#23511yescharacteristic
538C3×C4C2×#23511yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C2×D3×D411yescharacteristic
541Dic3—42no—
542Dic3—41no—
543Dic3—42no—
544Dic3—41no—
545Dic3—41no—
546Dic3—64no—
547Dic3—62no—
548Dic3—62no—
549C32#306311yescharacteristic, complemented, Sylow
550C23—61no—
551C23—92no—
552C23#380211yescharacteristic
553Q8—62no—
554Q8—61no—
555Q8—62no—
556Q8—61no—
557Q8—122no—
558Q8—182no—
559D4—61no—
560D4—61no—
561D4—122no—
562D4—184no—
563D4—182no—
564D4—722no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—92no—
571C2×C4—122no—
572C2×C4—122no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—241no—
576C2×C4#379812yes—
577C2×C4#380211yescharacteristic
578C2×C4#381112yes—
579C2×C4C22×D3211yescharacteristic
580C8—21no—
581C8—21no—
582C8—94no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—42no—
589C2×C3—241no—
590C2×C3C2×#88411yescharacteristic
591C2×C3C2×#88411yescharacteristic
592C2×C3#576211yescharacteristic
593C2×C3#576611yescharacteristic
594C2×C3#577011yescharacteristic
595C2×C3#577111yescharacteristic
596D3—81no—
597D3—124no—
598D3—122no—
599D3—122no—
600C22—21no—
601C22—21no—
602C22—121no—
603C22—121no—
604C22—121no—
605C22—182no—
606C22—182no—
607C22—182no—
608C22#6391212yes—
609C22C2×#380211yescharacteristic
610C4—122no—
611C4—121no—
612C4—121no—
613C4—121no—
614C4—122no—
615C4—182no—
616C4#6391212yes—
617C4C2×#379811yescharacteristic
618C4C2×#381111yescharacteristic
619C3—21no—
620C3#7880011yescharacteristic, complemented
621C3#7884111yescharacteristic, complemented
622C2—22no—
623C2—241no—
624C2—362no—
625C2#1059468611yescharacteristic
626C2#1059470311yescharacteristic
627C2C2×#6391211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenterC22×C8D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64110C2semidirect
3. #10594866C2semidirect
4. C2×#63827C2semidirect
5. C3×#5113C2semidirect
6. C2×C3×#816C2semidirect
7. #10591139C2semidirect
8. #10590856C2semidirect
9. #10590855C2semidirect
10. #10590842C2semidirect
11. #10590841C2semidirect
56. #5113D3semidirect
57. C2×#816D3semidirect
91. #3748D4semidirect
549. C32#3063semidirect
620. C3#78800semidirect
621. C3#78841semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
#105950432
#105948662
C2×#638272
C3×#51132
C2×C3×#8162
#105911392
#105908562
#105908552
#105908422
#105908412
#788413
#788003