Finite Group Databasebeta

← #11867807

Subgroups — #11867807

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×#64157C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic
3C3×#5825C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10591189C212yesmaximal, complemented
6#10591188C212yesmaximal, complemented
7#10591180C212yesmaximal, complemented
8#10591179C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10C2×#63565C211yesmaximal, characteristic, complemented
11#10591083C211yesmaximal, characteristic, complemented
12#83423—31nomaximal
13#83400—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17#64157—24no—
18C2×#3748C2212yes—
19C2×#3748C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2212yes—
22C3×#946—21no—
23C3×#944—21no—
24C3×#939—22no—
25C3×#938—21no—
26C3×#936—21no—
27C3×#935—22no—
28C3×#930C2212yes—
29C3×#926C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924C2212yes—
32C3×#924C2212yes—
33C3×#924C2212yes—
34C2×#3718C2212yes—
35#63827—24no—
36C2×#3715C2212yes—
37#63576C2212yes—
38#63574C2212yes—
39#63565C2211yescharacteristic
40#63565C2211yescharacteristic
41#63565C2212yes—
42#63565C2212yes—
43#63562C2211yescharacteristic
44#63562C2211yescharacteristic
45C3×#537—31no—
46C3×#536—31no—
47#5833D311yescharacteristic
48#5825D311yescharacteristic, complemented
49C2×#951—31no—
50C2×#948—31no—
51C2×#948—31no—
52C2×#948—61no—
53C2×#942—31no—
54#5233—31no—
55C2×#835—31no—
56#5052—32no—
57#5052—32no—
58#5051—32no—
59#5051—32no—
60#5049—32no—
61#5048—32no—
62#5042—32no—
63#5041—32no—
64#5002—31no—
65#4995—31no—
66C2×#810—31no—
67#4964—31no—
68C32×#41—22no—
69C32×#41—22no—
70C2×C32×Q8D411yescharacteristic
71C2×C32×D4D412yes—
72C2×C32×D4D411yescharacteristic
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—21no—
76C2×C3×#67—22no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C3×#235—22no—
80C3×#235—22no—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6C2312yes—
87C2×C3×Dic6C2311yescharacteristic
88#3748—24no—
89#3748D414yescomplemented
90C2×C3⋊(C3⋊C8)—22no—
91C2×C3⋊(C3⋊C8)—24no—
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—22no—
96C3×#217—22no—
97C3×#217—22no—
98C3×#217—21no—
99C3×(C2×D3)⋊C4—22no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2311yescharacteristic
102C3×C4⋊Dic3C2311yescharacteristic
103C3×C4⋊Dic3C2312yes—
104C3×Dic3⋊C4—22no—
105C3×Dic3⋊C4—22no—
106C3×Dic3⋊C4—22no—
107C3×C4×Dic3—21no—
108#3718—24no—
109#3715—24no—
110#3063—91noSylow
111C2×C3×#41—21no—
112C2×C3×#41—31no—
113C2×C3×#41C2×D311yescharacteristic
114C2×C3×#41C2×D311yescharacteristic
115C22×C3×Q8—31no—
116C2×#235C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C3×C4⋊Q8—61no—
119C3×#124—61no—
120C3×#123—62no—
121C3×C22⋊Q8—32no—
122C3×C22⋊Q8—32no—
123C3×C22⋊Q8—32no—
124C3×C22⋊Q8—61no—
125C3×#121—32no—
126C3×#121—61no—
127C3×#121—62no—
128C3×#117—31no—
129C2×C3×C4⋊C4—31no—
130#951—64no—
131#948—64no—
132#948—64no—
133#948—68no—
134#946—21no—
135#944—21no—
136C2×#216—32no—
137C2×#216—32no—
138#942—64no—
139C2×#215—32no—
140#939—22no—
141#938—21no—
142#936—21no—
143#935—22no—
144C2×#214—32no—
145#930C2×D312yes—
146#926C2×D311yescharacteristic
147C2×C4⋊Dic3C2×D311yescharacteristic
148#924C2×D312yes—
149#924C2×D312yes—
150#924C2×D312yes—
151C2×#208—31no—
152C2×#208—31no—
153C2×#208—32no—
154C2×#208—32no—
155C2×#208—61no—
156C2×#208—62no—
157C22×C3⋊C8—31no—
158C22×C3⋊C8—31no—
159C22×C3⋊C8—32no—
160C22×C3⋊C8—32no—
161C22×C3⋊C8—61no—
162C22×C3⋊C8—62no—
163#835—32no—
164#835—32no—
165#835—31no—
166#835—31no—
167#832—31no—
168#832—31no—
169#810—32no—
170#810—32no—
171#810—31no—
172#810—31no—
173#809—31no—
174#809—31no—
175#808—32no—
176#808—32no—
177#807—32no—
178#807—32no—
179C23×C32C2×D412yes—
180C23×C32C2×D411yescharacteristic
181C22×C3×D3—21no—
182C32×Q8—22no—
183C32×D4—24no—
184C32×D4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4C2×D412yes—
188C2×C32×C4C2×D412yes—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4#4112yes—
191C2×C32×C4C2411yescharacteristic
192C3×#67—42no—
193C3×#67—82no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—42no—
200C2×C3×Dic3—81no—
201C3×D12—21no—
202C3×D12—21no—
203C3×C4×D3—42no—
204C3×Dic6—22no—
205C3×Dic6—21no—
206C3×Dic6—22no—
207C3×Dic6—21no—
208C3×Dic6—42no—
209C3⋊(C3⋊C8)—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)C2×D414yes—
212C2×#137—91no—
213C2×#131—91no—
214#537—31no—
215#536—31no—
216#470—92no—
217#468—92no—
218#467—92no—
219#465—92no—
220#428—91no—
221#416—91no—
222C2×#103—91no—
223C3×#41—24no—
224C3×#41—24no—
225C3×#41—22no—
226C3×#41—22no—
227C3×#41—22no—
228C3×#41—22no—
229C3×#41—62no—
230C3×#41—62no—
231C2×C3×Q8—21no—
232C2×C3×Q8—32no—
233C2×C3×Q8—31no—
234C2×C3×Q8—61no—
235C2×C3×Q8—62no—
236C2×C3×Q8—62no—
237C2×C3×Q8#6711yescharacteristic
238C2×C3×Q8#6711yescharacteristic
239C2×C3×D4—22no—
240C2×C3×D4—21no—
241C2×C3×D4—31no—
242C2×C3×D4—61no—
243C2×C3×D4—62no—
244C2×C3×D4#6712yes—
245C2×C3×D4#6711yescharacteristic
246C2×C3×D4#6711yescharacteristic
247C2×C3×D4#6712yes—
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—61no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C2×#67—21no—
258C2×#67—22no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261#235—22no—
262#235—22no—
263C2×D12C22×D311yescharacteristic
264C2×C4×D3—21no—
265C2×Dic6—22no—
266C2×Dic6—22no—
267C2×Dic6—21no—
268C2×Dic6C22×D312yes—
269C2×Dic6C22×D311yescharacteristic
270C3×C4⋊C4—31no—
271C3×C4⋊C4—32no—
272C3×C4⋊C4—31no—
273C3×C4⋊C4—62no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—61no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—62no—
280C3×C22⋊C4—62no—
281C3×C22⋊C4—62no—
282C3×C42—61no—
283#217—22no—
284#217—22no—
285#217—22no—
286#217—21no—
287#216—64no—
288#216—64no—
289#215—64no—
290#214—64no—
291(C2×D3)⋊C4—22no—
292C4⋊Dic3—21no—
293C4⋊Dic3C22×D311yescharacteristic
294C4⋊Dic3C22×D312yes—
295C4⋊Dic3C22×D311yescharacteristic
296Dic3⋊C4—22no—
297Dic3⋊C4—22no—
298Dic3⋊C4—22no—
299C4×Dic3—21no—
300#208—34no—
301#208—34no—
302#208—64no—
303#208—64no—
304#208—64no—
305#208—68no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—31no—
309C2×C3⋊C8—31no—
310C2×C3⋊C8—31no—
311C2×C3⋊C8—31no—
312C2×C3⋊C8—61no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—64no—
316C2×C3⋊C8—64no—
317C2×C3⋊C8—68no—
318C2×C3⋊C8—64no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8—62no—
321C22×C32—22no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32#12112yes—
327C22×C32C22×D411yescharacteristic
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C2×C3×D3—41no—
331C32×C4—22no—
332C32×C4#12112yes—
333C32×C4C22×D411yescharacteristic
334C32×C4C2×#4111yescharacteristic
335C3×Dic3—42no—
336C3×Dic3—41no—
337C3×Dic3—41no—
338C3×Dic3—42no—
339C3×Dic3—41no—
340C2×#41—31no—
341C2×#41D3211yescharacteristic
342C22×Q8—31no—
343#137—184no—
344C2×Q16—92no—
345C2×SD16—92no—
346#131—184no—
347C2×M16—91no—
348C2×M16—92no—
349C22×C8—91no—
350C22×C8—92no—
351C4⋊Q8—61no—
352#124—61no—
353#123—62no—
354C22⋊Q8—32no—
355C22⋊Q8—32no—
356C22⋊Q8—32no—
357C22⋊Q8—61no—
358#121—32no—
359#121—61no—
360#121—62no—
361#117—31no—
362C2×C4⋊C4—31no—
363#107—92no—
364#106—92no—
365#103—92no—
366#103—92no—
367#103—91no—
368#103—91no—
369#102—91no—
370#102—91no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—61no—
374C23×C3C2×#6712yes—
375C23×C3C2×#6712yes—
376C23×C3C2×#6711yescharacteristic
377C23×C3C2×#6711yescharacteristic
378C22×D3—21no—
379C3×Q8—24no—
380C3×Q8—22no—
381C3×Q8—22no—
382C3×Q8—62no—
383C3×Q8—61no—
384C3×Q8—62no—
385C3×Q8—61no—
386C3×Q8—122no—
387C3×D4—28no—
388C3×D4—24no—
389C3×D4—24no—
390C3×D4—24no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—61no—
394C3×D4—61no—
395C3×D4—122no—
396C3×D4—242no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—62no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—122no—
414C2×C3×C4—122no—
415C2×C3×C4—241no—
416C2×C3×C4D3×D412yes—
417C2×C3×C4D3×D412yes—
418C2×C3×C4#23712yes—
419C2×C3×C4#23712yes—
420C2×C3×C4C2×#6712yes—
421C2×C3×C4C2×#6712yes—
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—42no—
427#67—82no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—21no—
432C2×Dic3—22no—
433C2×Dic3—42no—
434C2×Dic3—81no—
435D12—21no—
436D12—21no—
437C4×D3—42no—
438Dic6—22no—
439Dic6—21no—
440Dic6—22no—
441Dic6—21no—
442Dic6—42no—
443C3⋊C8—34no—
444C3⋊C8—34no—
445C3⋊C8—64no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8—61no—
449C3⋊C8—61no—
450C3⋊C8—61no—
451C3⋊C8—61no—
452C2×C32—22no—
453C2×C32—42no—
454C2×C32C2×#12111yescharacteristic
455C2×C32#57711yescharacteristic
456C2×C32#57811yescharacteristic
457C3×D3—81no—
458#41—22no—
459#41—22no—
460#41—62no—
461#41—62no—
462C2×Q8—32no—
463C2×Q8—31no—
464C2×Q8—61no—
465C2×Q8—62no—
466C2×Q8—62no—
467C2×Q8#62511yescharacteristic
468C2×D4—31no—
469C2×D4—61no—
470C2×D4—62no—
471C2×D4#62512yes—
472C2×D4#62511yescharacteristic
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4C2×D3212yes—
477C22×C4C2×D3211yescharacteristic
478Q16—184no—
479SD16—184no—
480M16—94no—
481M16—184no—
482C2×C8—92no—
483C2×C8—91no—
484C2×C8—91no—
485C2×C8—184no—
486C2×C8—182no—
487C4⋊C4—31no—
488C4⋊C4—31no—
489C4⋊C4—32no—
490C4⋊C4—61no—
491C4⋊C4—62no—
492C4⋊C4—62no—
493C4⋊C4—62no—
494C22⋊C4—61no—
495C22⋊C4—62no—
496C22⋊C4—62no—
497C22⋊C4—62no—
498C22⋊C4—62no—
499C42—61no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—24no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—22no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—121no—
518C22×C3—121no—
519C22×C3—121no—
520C22×C3#93912yes—
521C22×C3#93912yes—
522C22×C3C22×#6711yescharacteristic
523C22×C3C22×#6711yescharacteristic
524C2×D3—41no—
525C2×D3—41no—
526C2×D3—41no—
527C3×C4—24no—
528C3×C4—22no—
529C3×C4—22no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—22no—
533C3×C4—121no—
534C3×C4—122no—
535C3×C4—121no—
536C3×C4—122no—
537C3×C4—121no—
538C3×C4#93912yes—
539C3×C4#93912yes—
540C3×C4C2×D3×D411yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C2×#23711yescharacteristic
543C3×C4C2×#23711yescharacteristic
544Dic3—42no—
545Dic3—41no—
546Dic3—42no—
547Dic3—41no—
548Dic3—41no—
549C32#306311yescharacteristic, complemented, Sylow
550C23—61no—
551C23C2×#62512yes—
552C23C2×#62511yescharacteristic
553Q8—22no—
554Q8—62no—
555Q8—61no—
556Q8—62no—
557Q8—61no—
558Q8—122no—
559D4—24no—
560D4—22no—
561D4—61no—
562D4—61no—
563D4—122no—
564D4—242no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—61no—
571C2×C4—62no—
572C2×C4—122no—
573C2×C4—122no—
574C2×C4—241no—
575C2×C4#380512yes—
576C2×C4C2×#62512yes—
577C2×C4C2×#62511yescharacteristic
578C2×C4#381112yes—
579C2×C4C22×D3211yescharacteristic
580C8—94no—
581C8—181no—
582C8—181no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—42no—
589C2×C3—44no—
590C2×C3—42no—
591C2×C3—42no—
592C2×C3—241no—
593C2×C3C2×#93911yescharacteristic
594C2×C3C2×#93911yescharacteristic
595C2×C3#583611yescharacteristic
596C2×C3#583711yescharacteristic
597C2×C3#583811yescharacteristic
598C2×C3#583811yescharacteristic
599D3—81no—
600C22—21no—
601C22—21no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—121no—
606C22—121no—
607C22—121no—
608C22#6398012yes—
609C22C22×#62511yescharacteristic
610C4—22no—
611C4—121no—
612C4—122no—
613C4—121no—
614C4—121no—
615C4—122no—
616C4#6398012yes—
617C4C2×#380511yescharacteristic
618C4C2×#381111yescharacteristic
619C3—21no—
620C3#8340011yescharacteristic, complemented
621C3#8342311yescharacteristic, complemented
622C2—22no—
623C2—42no—
624C2—241no—
625C2#1059544511yescharacteristic
626C2#1059544611yescharacteristic
627C2C2×#6398011yescharacteristic
subgroupG/H
centerC22C22×#625
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. C2×#64157C2semidirect
3. C3×#5825C2semidirect
4. C2×#63827C2semidirect
5. #10591189C2semidirect
6. #10591188C2semidirect
7. #10591180C2semidirect
8. #10591179C2semidirect
9. #10591139C2semidirect
10. C2×#63565C2semidirect
11. #10591083C2semidirect
48. #5825D3semidirect
89. #3748D4semidirect
549. C32#3063semidirect
620. C3#83400semidirect
621. C3#83423semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#58332
C3×#58252
C2×#638272
#105911892
#105911882
#105911802
#105911792
#105911392
C2×#635652
#105910832
#834233
#834003