Finite Group Databasebeta

← #11867809

Subgroups — #11867809

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic
3#10594856C211yesmaximal, characteristic, complemented
4C2×#63814C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591598C212yesmaximal, complemented
7#10591596C212yesmaximal, complemented
8#10591462C212yesmaximal, complemented
9#10591460C212yesmaximal, complemented
10#10591139C211yesmaximal, characteristic, complemented
11C2×#63567C211yesmaximal, characteristic, complemented
12#83423—31nomaximal
13#78841—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17#64160—24no—
18C2×#3756C2212yes—
19C2×#3754C2212yes—
20C2×#3748C2211yescharacteristic
21C3×#946C2212yes—
22C3×#939—22no—
23C3×#938C2212yes—
24C3×#930—21no—
25C3×#926C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#924—21no—
28C22×C3×C3⋊C8C2211yescharacteristic
29#63962—22no—
30#63866—21no—
31#63860—21no—
32#63857C2212yes—
33#63857C2212yes—
34C2×#3711C2212yes—
35#63814—24no—
36C2×D3×C3⋊C8C2212yes—
37C3×#835C2211yescharacteristic
38C3×#835C2211yescharacteristic
39C3×#832C2211yescharacteristic
40C3×#832C2211yescharacteristic
41#63576C2212yes—
42#63574C2212yes—
43#63567C2212yes—
44#63567C2212yes—
45C3×#537—31no—
46#5833D311yescharacteristic
47#5825—31no—
48C2×#951—31no—
49C2×#951—31no—
50C2×#951—61no—
51C2×#948—31no—
52C2×#901—31no—
53#5526—31no—
54C3×#416—31no—
55#5233D311yescharacteristic, complemented
56C2×#816—31no—
57#5052—32no—
58#5051—32no—
59#5042—32no—
60#5041—32no—
61#4995—31no—
62C2×#810—31no—
63#4964—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
75C22×C3⋊Dic3—21no—
76C2×#634—22no—
77C2×#634—22no—
78C2×#634—21no—
79C2×#634C2312yes—
80C2×C3×#67—22no—
81C2×C3×#67D412yes—
82C22×C3×Dic3—21no—
83C3×#235—22no—
84C3×#235—22no—
85C2×C3×D12D411yescharacteristic
86C2×C3×C4×D3C2312yes—
87C2×C3×Dic6D411yescharacteristic
88#3756—24no—
89#3754—24no—
90#3748D414yescomplemented
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×#217—21no—
93C3×#217—22no—
94C3×(C2×D3)⋊C4—22no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C2×C3×C3⋊C8—22no—
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3711—24no—
109D3×C3⋊C8—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—
119C22×C3×C8—31no—
120C3×C22⋊Q8—32no—
121C3×C22⋊Q8—61no—
122C3×#121—32no—
123C3×#121—61no—
124C3×#121—62no—
125C3×#117—31no—
126C2×C3×C4⋊C4—31no—
127#951—64no—
128#951—64no—
129#951—68no—
130#948—64no—
131#946C2×D312yes—
132#944—61no—
133C2×#216—32no—
134C2×#216—32no—
135C2×#216—62no—
136#939—22no—
137#938C2×D312yes—
138#936—61no—
139#935—62no—
140C2×#214—32no—
141C2×#214—32no—
142C2×#214—62no—
143#930—21no—
144#926C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146#924—21no—
147#924—32no—
148#924—32no—
149C2×#208—31no—
150C2×#208—31no—
151C2×#208—32no—
152C2×#208—61no—
153C22×C3⋊C8—32no—
154C22×C3⋊C8C2×D311yescharacteristic
155#901—64no—
156C2×ΓL(1,𝔽25)—32no—
157C2×D3×C8—32no—
158#897—32no—
159#897—32no—
160#886—62no—
161#875—61no—
162#869—61no—
163C3×#103—31no—
164C3×#103—31no—
165C3×#102—31no—
166C3×#102—31no—
167#835C2×D311yescharacteristic
168#835C2×D311yescharacteristic
169#832C2×D311yescharacteristic
170#832C2×D311yescharacteristic
171#816—32no—
172#816—32no—
173#810—32no—
174#810—32no—
175#808—32no—
176#808—32no—
177#807—32no—
178#807—32no—
179C23×C32—21no—
180C23×C32C2×D411yescharacteristic
181C22×C3×D3C2×D412yes—
182C32×Q8—21no—
183C32×Q8—21no—
184C32×D4—21no—
185C32×D4—21no—
186C32×D4—42no—
187C2×C32×C4—21no—
188C2×C32×C4—42no—
189C2×C32×C4C2×D412yes—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4#4112yes—
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—42no—
195#634—22no—
196#634—22no—
197#634—42no—
198C3×#67—24no—
199C3×#67—82no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—81no—
204C2×C3×Dic3C2×D412yes—
205C3×D12—22no—
206C3×C4×D3—22no—
207C3×C4×D3—22no—
208C3×Dic6—22no—
209C3⋊(C3⋊C8)C2×D414yes—
210C3×C3⋊C8—21no—
211C3×C3⋊C8—21no—
212C2×#137—91no—
213C2×#131—91no—
214#537—31no—
215#536—91no—
216#470—92no—
217#468—92no—
218#467—92no—
219#465—92no—
220#428—91no—
221#416—31no—
222C2×#103—91no—
223C3×#41—24no—
224C3×#41—22no—
225C3×#41—22no—
226C3×#41—22no—
227C3×#41—22no—
228C3×#41—42no—
229C3×#41—62no—
230C3×#41—62no—
231C2×C3×Q8—21no—
232C2×C3×Q8—31no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—32no—
239C2×C3×D4—31no—
240C2×C3×D4—41no—
241C2×C3×D4—62no—
242C2×C3×D4C22×D311yescharacteristic
243C2×C3×D4C22×D311yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—32no—
248C22×C3×C4—41no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—22no—
253C2×#67#6712yes—
254C22×Dic3—21no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3—121no—
258#235—22no—
259#235—22no—
260C2×D12#6711yescharacteristic
261C2×C4×D3C22×D312yes—
262C2×Dic6—32no—
263C2×Dic6—32no—
264C2×Dic6—62no—
265C2×Dic6—64no—
266C2×Dic6—62no—
267C2×Dic6—62no—
268C2×Dic6—62no—
269C2×Dic6—62no—
270C2×Dic6—61no—
271C2×Dic6—61no—
272C2×Dic6—121no—
273C2×Dic6—122no—
274C2×Dic6#6711yescharacteristic
275C2×C3×C8—31no—
276C2×C3×C8—31no—
277C2×C3×C8—62no—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—32no—
280C3×C4⋊C4—31no—
281C3×C4⋊C4—62no—
282C3×C4⋊C4—61no—
283C3×C22⋊C4—62no—
284C3×C22⋊C4—62no—
285C3×C22⋊C4—61no—
286C3×C42—61no—
287#217—21no—
288#217—22no—
289#217—62no—
290#217—62no—
291#216—64no—
292#216—64no—
293#216—68no—
294#214—64no—
295#214—64no—
296#214—68no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—62no—
300C4⋊Dic3—21no—
301C4⋊Dic3—62no—
302C4⋊Dic3—62no—
303C4⋊Dic3C22×D311yescharacteristic
304C4⋊Dic3C22×D312yes—
305C4⋊Dic3C22×D311yescharacteristic
306Dic3⋊C4—22no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309C4×Dic3—21no—
310#208—34no—
311#208—34no—
312#208—64no—
313#208—64no—
314C2×C3⋊C8—22no—
315C2×C3⋊C8—32no—
316C2×C3⋊C8—32no—
317C2×C3⋊C8—62no—
318C2×C3⋊C8—64no—
319C2×C3⋊C8C22×D311yescharacteristic
320C2×C3⋊C8C22×D311yescharacteristic
321ΓL(1,𝔽25)—64no—
322D3×C8—64no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32#12112yes—
329C22×C32C22×D411yescharacteristic
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C32×C4—41no—
334C32×C4#12112yes—
335C32×C4C22×D411yescharacteristic
336C32×C4C2×#4111yescharacteristic
337C3⋊Dic3—42no—
338C3×Dic3—22no—
339C3×Dic3—41no—
340C3×Dic3—42no—
341C3×Dic3—41no—
342C2×#41—31no—
343C2×#41D3211yescharacteristic
344C22×Q8—91no—
345#137—184no—
346C2×Q16—92no—
347C2×SD16—92no—
348#131—184no—
349C2×M16—92no—
350C2×M16—91no—
351C22×C8—31no—
352C22×C8—92no—
353C4⋊Q8—181no—
354#124—181no—
355#123—182no—
356C22⋊Q8—32no—
357C22⋊Q8—61no—
358C22⋊Q8—92no—
359C22⋊Q8—92no—
360#121—32no—
361#121—61no—
362#121—62no—
363#117—31no—
364C2×C4⋊C4—31no—
365#107—92no—
366#106—92no—
367#103—31no—
368#103—31no—
369#103—92no—
370#103—92no—
371#102—31no—
372#102—31no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—32no—
377C23×C3—41no—
378C23×C3D3×D411yescharacteristic
379C23×C3C2×#6711yescharacteristic
380C22×D3C2×#6712yes—
381C3×Q8—22no—
382C3×Q8—21no—
383C3×Q8—21no—
384C3×Q8—21no—
385C3×Q8—21no—
386C3×Q8—41no—
387C3×Q8—62no—
388C3×D4—22no—
389C3×D4—21no—
390C3×D4—21no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—41no—
394C3×D4—44no—
395C3×D4—42no—
396C3×D4—42no—
397C3×D4—64no—
398C3×D4—62no—
399C3×D4—242no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—32no—
407C2×C3×C4—41no—
408C2×C3×C4—44no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—241no—
417C2×C3×C4#23512yes—
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4D3×D412yes—
420C2×C3×C4D3×D412yes—
421C2×C3×C4#23712yes—
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—24no—
426#67—82no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—22no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—81no—
433C2×Dic3—122no—
434C2×Dic3—124no—
435C2×Dic3—122no—
436C2×Dic3—122no—
437C2×Dic3C2×#6712yes—
438D12—22no—
439C4×D3—22no—
440C4×D3—22no—
441Dic6—22no—
442Dic6—64no—
443Dic6—62no—
444Dic6—62no—
445Dic6—62no—
446Dic6—62no—
447Dic6—122no—
448Dic6—124no—
449Dic6—122no—
450Dic6—122no—
451C3×C8—61no—
452C3×C8—61no—
453C3⋊C8—21no—
454C3⋊C8—21no—
455C3⋊C8—34no—
456C3⋊C8—34no—
457C3⋊C8—64no—
458C2×C32—22no—
459C2×C32—81no—
460C2×C32C2×#12111yescharacteristic
461C2×C32#57711yescharacteristic
462C2×C32#57811yescharacteristic
463C3×D3—42no—
464#41—22no—
465#41—22no—
466#41—62no—
467#41—62no—
468C2×Q8—31no—
469C2×Q8—92no—
470C2×Q8—181no—
471C2×Q8—182no—
472C2×Q8—182no—
473C2×Q8C2×D3211yescharacteristic
474C2×D4—21no—
475C2×D4—32no—
476C2×D4—31no—
477C2×D4—62no—
478C2×D4C2×D3211yescharacteristic
479C22×C4—21no—
480C22×C4—32no—
481C22×C4—61no—
482C22×C4—181no—
483C22×C4C2×D3211yescharacteristic
484Q16—184no—
485SD16—184no—
486M16—94no—
487M16—184no—
488C2×C8—31no—
489C2×C8—31no—
490C2×C8—62no—
491C2×C8—92no—
492C2×C8—184no—
493C4⋊C4—31no—
494C4⋊C4—31no—
495C4⋊C4—32no—
496C4⋊C4—62no—
497C4⋊C4—61no—
498C4⋊C4—182no—
499C4⋊C4—182no—
500C22⋊C4—62no—
501C22⋊C4—62no—
502C22⋊C4—61no—
503C22⋊C4—182no—
504C22⋊C4—182no—
505C42—61no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—22no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—42no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—81no—
525C22×C3—81no—
526C22×C3#88412yes—
527C22×C3#93912yes—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C22×#6711yescharacteristic
530C2×D3—22no—
531C2×D3—22no—
532C2×D3—22no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—22no—
536C3×C4—42no—
537C3×C4—41no—
538C3×C4—41no—
539C3×C4—62no—
540C3×C4—122no—
541C3×C4—121no—
542C3×C4—121no—
543C3×C4#88412yes—
544C3×C4#93912yes—
545C3×C4C2×#23511yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C2×#23711yescharacteristic
549Dic3—22no—
550Dic3—41no—
551Dic3—41no—
552Dic3—42no—
553Dic3—124no—
554Dic3—122no—
555Dic3—122no—
556C32#306311yescharacteristic, complemented, Sylow
557C23—21no—
558C23—32no—
559C23D3×#6711yescharacteristic
560Q8—21no—
561Q8—21no—
562Q8—62no—
563Q8—182no—
564Q8—182no—
565Q8—362no—
566D4—21no—
567D4—21no—
568D4—42no—
569D4—64no—
570D4—62no—
571D4—242no—
572C2×C4—21no—
573C2×C4—32no—
574C2×C4—42no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—62no—
580C2×C4—182no—
581C2×C4—241no—
582C2×C4—362no—
583C2×C4#380412yes—
584C2×C4D3×#6711yescharacteristic
585C2×C4#381112yes—
586C2×C4C22×D3211yescharacteristic
587C8—61no—
588C8—61no—
589C8—94no—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—42no—
596C2×C3—82no—
597C2×C3—81no—
598C2×C3—81no—
599C2×C3—122no—
600C2×C3C2×#88411yescharacteristic
601C2×C3#577011yescharacteristic
602C2×C3#577111yescharacteristic
603C2×C3C2×#93911yescharacteristic
604C2×C3#583611yescharacteristic
605C2×C3#583811yescharacteristic
606D3—42no—
607C22—21no—
608C22—21no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—62no—
613C22—62no—
614C22—62no—
615C22#6397112yes—
616C22C2×D3×#6711yescharacteristic
617C4—41no—
618C4—62no—
619C4—122no—
620C4—121no—
621C4—121no—
622C4—362no—
623C4#6397112yes—
624C4C2×#380411yescharacteristic
625C4C2×#381111yescharacteristic
626C3—21no—
627C3#7884111yescharacteristic, complemented
628C3#8342311yescharacteristic, complemented
629C2—22no—
630C2—81no—
631C2—122no—
632C2#1059546611yescharacteristic
633C2#1059546711yescharacteristic
634C2C2×#6397111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64160C2semidirect
3. #10594856C2semidirect
4. C2×#63814C2semidirect
5. C3×#5233C2semidirect
6. #10591598C2semidirect
7. #10591596C2semidirect
8. #10591462C2semidirect
9. #10591460C2semidirect
10. #10591139C2semidirect
11. C2×#63567C2semidirect
55. #5233D3semidirect
90. #3748D4semidirect
556. C32#3063semidirect
627. C3#78841semidirect
628. C3#83423semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×#58332
#105948562
C2×#638142
C3×#52332
#105915982
#105915962
#105914622
#105914602
#105911392
C2×#635672
#834233
#788413