Finite Group Databasebeta

← #11861228

Subgroups — #11861228

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596290C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic
3#10594776C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591676C214yesmaximal, complemented
6#10591675C214yesmaximal, complemented
7C2×#63577C211yesmaximal, characteristic, complemented
8#10591111C211yesmaximal, characteristic, complemented
9#10591055C211yesmaximal, characteristic, complemented
10#83910—31nomaximal
11#78990—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14#64157—22no—
15#64157C2214yescomplemented
16C2×#3748—22no—
17C2×#3748C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#950C412yescomplemented
20C3×#950C412yescomplemented
21C3×#950C2212yes—
22C3×#950C2212yes—
23C2×C3×#216C411yescharacteristic, complemented
24C2×C3×#215C411yescharacteristic, complemented
25C2×C3×#214C411yescharacteristic, complemented
26C2×C3×#213C411yescharacteristic, complemented
27C3×#926C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30#63815C2214yescomplemented
31#63814—22no—
32D3×#208—22no—
33C3×#837C2214yescomplemented
34#63577C2212yescomplemented
35#63577C2212yescomplemented
36#63569C2214yescomplemented
37#63554C2212yescomplemented
38Dic3×C3⋊C8C2212yescomplemented
39C2×C3×#135—31no—
40C2×#950D311yescharacteristic
41#5819—31no—
42#5819—31no—
43#5819—31no—
44#5819—61no—
45#5745—31no—
46C3×#421—31no—
47#5236—31no—
48#5236D311yescharacteristic, complemented
49#5197—34no—
50#5196—34no—
51C2×#822—31no—
52C2×#819—31no—
53#5101—31no—
54#5005—31no—
55#4997—31no—
56#4824—34no—
57#4823—34no—
58C32×#41—21no—
59C32×#41—21no—
60C32×#41C2×C412yes—
61C32×#41C2312yes—
62C2×C32×Q8C2×C411yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2×C411yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235C2×C412yes—
71C3×#235C2312yes—
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6C2×C411yescharacteristic
75#3748—21no—
76#3748—24no—
77#3748D412yes—
78#3748D412yes—
79#3748C2312yes—
80C2×C3⋊(C3⋊C8)—21no—
81C2×C3⋊(C3⋊C8)—24no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#217—21no—
84C3×#216C2×C412yes—
85C3×#216C2×C412yes—
86C3×#215C2×C412yes—
87C3×#215C2×C412yes—
88C3×#214C2×C412yes—
89C3×#214C2×C412yes—
90C3×#213C2×C412yes—
91C3×#213C2×C412yes—
92C3×C4⋊Dic3—21no—
93C3×C4×Dic3C2312yes—
94C3×#208—21no—
95C3×#208C2312yes—
96C2×C3×C3⋊C8—21no—
97C2×C3×C3⋊C8C2×C411yescharacteristic
98C2×C3×C3⋊C8C2×C411yescharacteristic
99C2×C3×C3⋊C8C2×C411yescharacteristic
100C2×C3×C3⋊C8C2×C411yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103#3711—24no—
104D3×C3⋊C8—24no—
105#2957—91noSylow
106C2×C3×#41—21no—
107C2×C3×#41—31no—
108C2×C3×#41C2×D311yescharacteristic
109C2×C3×#41C2×D311yescharacteristic
110C2×#235C2×D311yescharacteristic
111C3×#135—32no—
112C3×#135—32no—
113C3×#135—32no—
114C3×#135—32no—
115C2×C3×Q16—31no—
116C2×C3×SD16—31no—
117C2×C3×SD16—31no—
118C2×C3×D8—31no—
119C2×C3×M16—31no—
120C22×C3×C8—31no—
121C3×#117—31no—
122#950Dic312yescomplemented
123#950Dic312yescomplemented
124#950C2×D312yes—
125#950C2×D312yes—
126#948—34no—
127#948—34no—
128#948—34no—
129#948—64no—
130#948—62no—
131#948—62no—
132#948—62no—
133#948—64no—
134C2×#216Dic311yescharacteristic, complemented
135C2×#215Dic311yescharacteristic, complemented
136C2×#214Dic311yescharacteristic, complemented
137C2×#213Dic311yescharacteristic, complemented
138#926C2×D311yescharacteristic
139C2×#208—31no—
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—61no—
144C2×#208—61no—
145C2×#208—62no—
146C2×#208—62no—
147C2×#208—62no—
148C2×#208—64no—
149C2×#208C2×D311yescharacteristic
150C22×C3⋊C8C2×D311yescharacteristic
151#907—34no—
152D3×M16—62no—
153#901—62no—
154C3×#104—34no—
155#837—34no—
156#837C2×D314yescomplemented
157#822—32no—
158#822—32no—
159#819—32no—
160#819—32no—
161#815—32no—
162C8×Dic3—32no—
163#805—34no—
164#803—32no—
165C4×C3⋊C8—32no—
166C23×C32—21no—
167C23×C32#4111yescharacteristic
168C22×C3×D3—21no—
169C32×Q8—21no—
170C32×Q8C22×C412yes—
171C32×D4—22no—
172C32×D4—22no—
173C32×D4—21no—
174C32×D4C22×C412yes—
175C2×C32×C4—21no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4C22×C411yescharacteristic
179C2×C32×C4C22×C411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4#4111yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C3×#67—22no—
185C3×#67—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C3×D12—21no—
189C3×D12C22×C412yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×Dic6—21no—
193C3×Dic6C22×C412yes—
194C3⋊(C3⋊C8)—22no—
195C3⋊(C3⋊C8)C2×D414yes—
196C3×C3⋊C8—22no—
197C3×C3⋊C8C22×C411yescharacteristic
198C3×C3⋊C8C22×C411yescharacteristic
199C3×C3⋊C8C22×C411yescharacteristic
200C3×C3⋊C8C22×C411yescharacteristic
201C2×#135—31no—
202#568—91no—
203#568—91no—
204#444—94no—
205#443—94no—
206C2×#108—91no—
207#421—31no—
208#421—91no—
209#405—91no—
210C3×#41—22no—
211C3×#41—22no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—32no—
219C3×#41—32no—
220C3×#41—61no—
221C3×#41—61no—
222C3×#41C4×D312yes—
223C3×#41C2×Dic312yes—
224C3×#41C22×D312yes—
225C3×#41C22×D312yes—
226C2×C3×Q8—21no—
227C2×C3×Q8—31no—
228C2×C3×Q8C4×D311yescharacteristic
229C2×C3×Q8C2×Dic311yescharacteristic
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—31no—
235C2×C3×D4—61no—
236C2×C3×D4C4×D311yescharacteristic
237C2×C3×D4C2×Dic311yescharacteristic
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—61no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—21no—
246#235—21no—
247#235—21no—
248#235C2×Dic312yes—
249#235C22×D312yes—
250C2×D12C2×Dic311yescharacteristic
251C2×C4×D3—21no—
252C2×Dic6C2×Dic311yescharacteristic
253C3×Q16—32no—
254C3×Q16—32no—
255C3×SD16—32no—
256C3×SD16—32no—
257C3×SD16—32no—
258C3×SD16—32no—
259C3×D8—32no—
260C3×D8—32no—
261C3×M16—32no—
262C3×M16—61no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—61no—
270C3×C4⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C42—32no—
273#217—21no—
274#216C2×Dic312yes—
275#216C2×Dic312yes—
276#215C2×Dic312yes—
277#215C2×Dic312yes—
278#214C2×Dic312yes—
279#214C2×Dic312yes—
280#213C2×Dic312yes—
281#213C2×Dic312yes—
282C4⋊Dic3—21no—
283C4×Dic3C22×D312yes—
284#208—21no—
285#208—32no—
286#208—32no—
287#208—32no—
288#208—32no—
289#208—32no—
290#208—32no—
291#208—62no—
292#208—62no—
293#208—62no—
294#208—64no—
295#208—64no—
296#208—64no—
297#208—62no—
298#208—68no—
299#208—61no—
300#208—61no—
301#208C22×D312yes—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—32no—
305C2×C3⋊C8—62no—
306C2×C3⋊C8—64no—
307C2×C3⋊C8—64no—
308C2×C3⋊C8—64no—
309C2×C3⋊C8—68no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8—61no—
312C2×C3⋊C8—61no—
313C2×C3⋊C8C2×Dic311yescharacteristic
314C2×C3⋊C8C2×Dic311yescharacteristic
315C2×C3⋊C8C2×Dic311yescharacteristic
316C2×C3⋊C8C2×Dic311yescharacteristic
317C2×C3⋊C8C22×D311yescharacteristic
318C2×C3⋊C8C22×D311yescharacteristic
319ΓL(1,𝔽25)—64no—
320D3×C8—64no—
321C22×C32—22no—
322C22×C32—41no—
323C22×C32—81no—
324C22×C32C4×D411yescharacteristic
325C22×C32C4×D411yescharacteristic
326C22×C32C2×#4111yescharacteristic
327C2×C3×D3—22no—
328C2×C3×D3—81no—
329C32×C4—22no—
330C32×C4C4×D411yescharacteristic
331C32×C4C4×D411yescharacteristic
332C32×C4C23×C411yescharacteristic
333C32×C4C22×D411yescharacteristic
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—31no—
337C2×#41D3211yescharacteristic
338#135—32no—
339#135—32no—
340#135—32no—
341#135—32no—
342C2×Q16—31no—
343C2×SD16—31no—
344C2×SD16—31no—
345C2×D8—31no—
346#131—94no—
347#131—94no—
348#131—182no—
349#131—182no—
350C2×M16—31no—
351C2×M16—91no—
352C2×M16—91no—
353C2×M16—182no—
354C2×M16—182no—
355C22×C8—31no—
356#117—31no—
357#108—92no—
358#108—92no—
359#104—34no—
360#104—94no—
361#97—92no—
362C4×C8—92no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—61no—
368C23×C3#23711yescharacteristic
369C23×C3#23711yescharacteristic
370C22×D3—21no—
371C3×Q8—22no—
372C3×Q8—21no—
373C3×Q8—21no—
374C3×Q8—22no—
375C3×Q8—32no—
376C3×Q8—61no—
377C3×Q8C2×C4×D312yes—
378C3×Q8C22×Dic312yes—
379C3×D4—24no—
380C3×D4—24no—
381C3×D4—22no—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—21no—
387C3×D4—21no—
388C3×D4—22no—
389C3×D4—32no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—61no—
393C3×D4C2×C4×D312yes—
394C3×D4C22×Dic312yes—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—24no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—61no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4C2×C4×D311yescharacteristic
415C2×C3×C4C2×C4×D311yescharacteristic
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4#23711yescharacteristic
421C2×C3×C4#23711yescharacteristic
422C2×C3×C4C22×Dic311yescharacteristic
423C2×C3×C4C22×Dic311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—22no—
427#67—22no—
428C2×Dic3—21no—
429C2×Dic3—22no—
430D12—21no—
431D12C22×Dic312yes—
432C4×D3—22no—
433C4×D3—22no—
434Dic6—21no—
435Dic6C22×Dic312yes—
436C3×C8—31no—
437C3×C8—31no—
438C3×C8—31no—
439C3×C8—31no—
440C3×C8—62no—
441C3⋊C8—22no—
442C3⋊C8—34no—
443C3⋊C8—34no—
444C3⋊C8—64no—
445C3⋊C8—64no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8C22×Dic311yescharacteristic
449C3⋊C8C22×Dic311yescharacteristic
450C3⋊C8C22×Dic311yescharacteristic
451C3⋊C8C22×Dic311yescharacteristic
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32—42no—
456C2×C32C2×C4×D411yescharacteristic
457C3×D3—42no—
458#41—21no—
459#41—21no—
460#41—32no—
461#41—32no—
462#41—61no—
463#41—61no—
464#41D3×Dic312yes—
465#41C2×D3212yes—
466C2×Q8—31no—
467C2×Q8D3×Dic311yescharacteristic
468C2×D4—21no—
469C2×D4—31no—
470C2×D4—61no—
471C2×D4D3×Dic311yescharacteristic
472C22×C4—21no—
473C22×C4—61no—
474C22×C4C2×D3211yescharacteristic
475Q16—32no—
476Q16—32no—
477SD16—32no—
478SD16—32no—
479SD16—32no—
480SD16—32no—
481D8—32no—
482D8—32no—
483M16—32no—
484M16—61no—
485M16—92no—
486M16—92no—
487M16—92no—
488M16—184no—
489M16—184no—
490M16—181no—
491C2×C8—31no—
492C2×C8—31no—
493C2×C8—31no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—61no—
498C2×C8—92no—
499C2×C8—184no—
500C2×C8—184no—
501C2×C8—181no—
502C4⋊C4—61no—
503C22⋊C4—61no—
504C42—32no—
505C22×C3—24no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—62no—
514C22×C3—81no—
515C22×C3—81no—
516C22×C3—81no—
517C22×C3—82no—
518C22×C3—241no—
519C22×C3#67⋊C411yescharacteristic
520C22×C3#67⋊C411yescharacteristic
521C22×C3D4×Dic311yescharacteristic
522C22×C3D4×Dic311yescharacteristic
523C22×C3C2×#23711yescharacteristic
524C22×C3C2×#23711yescharacteristic
525C2×D3—22no—
526C2×D3—81no—
527C3×C4—24no—
528C3×C4—22no—
529C3×C4—22no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—62no—
535C3×C4—122no—
536C3×C4#67⋊C411yescharacteristic
537C3×C4#67⋊C411yescharacteristic
538C3×C4D4×Dic311yescharacteristic
539C3×C4D4×Dic311yescharacteristic
540C3×C4C22×C4×D311yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543C3×C4C23×Dic311yescharacteristic
544Dic3—22no—
545Dic3—42no—
546C32#295711yescharacteristic, complemented, Sylow
547C23—21no—
548C23—61no—
549C23#380511yescharacteristic
550Q8—21no—
551Q8—32no—
552Q8—61no—
553Q8C2×D3×Dic312yes—
554D4—22no—
555D4—22no—
556D4—21no—
557D4—32no—
558D4—62no—
559D4—62no—
560D4—61no—
561D4C2×D3×Dic312yes—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4C2×D3×Dic311yescharacteristic
570C2×C4C2×D3×Dic311yescharacteristic
571C2×C4#380511yescharacteristic
572C2×C4#381111yescharacteristic
573C2×C4#381111yescharacteristic
574C2×C4C22×D3211yescharacteristic
575C8—31no—
576C8—31no—
577C8—31no—
578C8—31no—
579C8—62no—
580C8—94no—
581C8—182no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—41no—
590C2×C3—41no—
591C2×C3—41no—
592C2×C3—44no—
593C2×C3—42no—
594C2×C3—42no—
595C2×C3—122no—
596C2×C3C2×#67⋊C411yescharacteristic
597C2×C3C2×D4×Dic311yescharacteristic
598D3—42no—
599C22—22no—
600C22—41no—
601C22—62no—
602C22—81no—
603C22—241no—
604C22#67⋊Dic311yescharacteristic
605C22#67⋊Dic311yescharacteristic
606C22C2×#380511yescharacteristic
607C4—22no—
608C4—62no—
609C4—122no—
610C4#67⋊Dic311yescharacteristic
611C4#67⋊Dic311yescharacteristic
612C4C22×D3×Dic311yescharacteristic
613C4C2×#381111yescharacteristic
614C3—21no—
615C3#7899011yescharacteristic, complemented
616C3#8391011yescharacteristic, complemented
617C2—21no—
618C2—21no—
619C2—21no—
620C2—42no—
621C2—122no—
622C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC4C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596290C2semidirect
3. #10594776C2semidirect
4. C3×#5236C2semidirect
5. #10591676C2semidirect
6. #10591675C2semidirect
7. C2×#63577C2semidirect
8. #10591111C2semidirect
9. #10591055C2semidirect
15. #64157C22semidirect
19. C3×#950C4semidirect
20. C3×#950C4semidirect
23. C2×C3×#216C4semidirect
24. C2×C3×#215C4semidirect
25. C2×C3×#214C4semidirect
26. C2×C3×#213C4semidirect
30. #63815C22semidirect
33. C3×#837C22semidirect
34. #63577C22semidirect
35. #63577C22semidirect
36. #63569C22semidirect
37. #63554C22semidirect
38. Dic3×C3⋊C8C22semidirect
48. #5236D3semidirect
122. #950Dic3semidirect
123. #950Dic3semidirect
134. C2×#216Dic3semidirect
135. C2×#215Dic3semidirect
136. C2×#214Dic3semidirect
137. C2×#213Dic3semidirect
156. #837C2×D3semidirect
546. C32#2957semidirect
615. C3#78990semidirect
616. C3#83910semidirect

Maximal subgroups

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

subgroupindex
#105962902
C2×C3×#9502
#105947762
C3×#52362
#105916762
#105916752
C2×#635772
#105911112
#105910552
#839103
#789903