Finite Group Databasebeta

← #11861111

Subgroups — #11861111

Order 1152.

989 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
1C3×#5822C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5#10591674C214yesmaximal, complemented
6#10591673C214yesmaximal, complemented
7#10591141C211yesmaximal, characteristic, complemented
8#10591110C211yesmaximal, characteristic, complemented
9#10591059C211yesmaximal, characteristic, complemented
10#83999—31nomaximal
11#83792—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#951C412yescomplemented
17C3×#950C2214yes—
18C3×#949C412yescomplemented
19C3×#948—21no—
20C3×#948—21no—
21C3×#948C2212yescomplemented
22C3×#948C2212yescomplemented
23C3×#942C412yescomplemented
24C3×#932C412yescomplemented
25C2×C3×#208—21no—
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8—21no—
29C22×C3×C3⋊C8C2211yescharacteristic
30C2×#3711—21no—
31#63814—21no—
32#63814—21no—
33#63814C2212yescomplemented
34#63814C2212yescomplemented
35C2×D3×C3⋊C8—21no—
36#63664C2214yescomplemented
37#63577C2214yescomplemented
38#63568C2214yescomplemented
39#63555C2212yescomplemented
40#63553C2212yescomplemented
41C3×#575—31no—
42C2×C3×#131—31no—
43#5822D311yescharacteristic
44C2×#948—31no—
45C2×#948D311yescharacteristic, complemented
46C2×#901—31no—
47#5236—31no—
48#5236—31no—
49#5236—31no—
50#5236—61no—
51#5197—34no—
52#5196—34no—
53#5145—34no—
54#5144—34no—
55#5139—31no—
56#5125—31no—
57#5124—31no—
58#5122—31no—
59#5101—31no—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41C2×C412yes—
63C32×#41C2312yes—
64C2×C32×Q8C2×C411yescharacteristic
65C2×C32×D4—21no—
66C2×C32×D4C2×C411yescharacteristic
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235C2×C412yes—
73C3×#235C2312yes—
74C2×C3×D12C2×C411yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6C2×C411yescharacteristic
77#3757—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4×C3⋊Dic3C2312yes—
80#3748—21no—
81#3748C2312yes—
82C2×C3⋊(C3⋊C8)—21no—
83C3×#216C2×C414yes—
84C3×#215C2×C414yes—
85C3×#214C2×C414yes—
86C3×#213C2×C414yes—
87C3×#208—21no—
88C3×#208—22no—
89C3×#208—22no—
90C3×#208C2×C412yes—
91C3×#208C2×C412yes—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C2×C3×C3⋊C8—22no—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8D411yescharacteristic
97C2×C3×C3⋊C8D411yescharacteristic
98C2×C3×C3⋊C8D411yescharacteristic
99C2×C3×C3⋊C8D411yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103#3711—22no—
104#3711—22no—
105D3×C3⋊C8—22no—
106D3×C3⋊C8—22no—
107#2955—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41—31no—
110C2×C3×#41C2×D311yescharacteristic
111C2×C3×#41C2×D311yescharacteristic
112C2×#235C2×D311yescharacteristic
113C3×#137—32no—
114C3×#137—32no—
115C3×AGL(1,ℤ/8)—32no—
116C3×AGL(1,ℤ/8)—32no—
117C3×#135—34no—
118C3×#131—32no—
119C3×#131—32no—
120C3×#131—61no—
121C3×#131—61no—
122C2×C3×M16—31no—
123C2×C3×M16—31no—
124C2×C3×M16—61no—
125C22×C3×C8—31no—
126C22×C3×C8—61no—
127#951Dic312yescomplemented
128#950C2×D314yes—
129#949Dic312yescomplemented
130#948—21no—
131#948—21no—
132#948—32no—
133#948—32no—
134#948—61no—
135#948—61no—
136#948C2×D312yescomplemented
137#948C2×D312yescomplemented
138#942Dic312yescomplemented
139#932Dic312yescomplemented
140#926—31no—
141#926—31no—
142#926—61no—
143C2×#208—21no—
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C2×#208—61no—
148C2×#208C2×D311yescharacteristic
149C2×#208C2×D311yescharacteristic
150C22×C3⋊C8—21no—
151C22×C3⋊C8—61no—
152C22×C3⋊C8C2×D311yescharacteristic
153#901—32no—
154#901—32no—
155#901—61no—
156#901—61no—
157C2×ΓL(1,𝔽25)—61no—
158C2×D3×C8—61no—
159#837—34no—
160#837—34no—
161#837—34no—
162#837—64no—
163#825—34no—
164#822—34no—
165#819—34no—
166#815—32no—
167#815—32no—
168C8×Dic3—32no—
169C8×Dic3—32no—
170C23×C32—21no—
171C23×C32#4111yescharacteristic
172C22×C3×D3—21no—
173C32×Q8—21no—
174C32×Q8C22×C412yes—
175C32×D4—22no—
176C32×D4—22no—
177C32×D4—21no—
178C32×D4C22×C412yes—
179C2×C32×C4—21no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C22×C411yescharacteristic
183C2×C32×C4C22×C411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4#4111yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—22no—
189C3×#67—22no—
190C3×#67—22no—
191C2×C3×Dic3—21no—
192C3×D12—21no—
193C3×D12C22×C412yes—
194C3×C4×D3—22no—
195C3×C4×D3—22no—
196C3×Dic6—21no—
197C3×Dic6C22×C412yes—
198C3⋊(C3⋊C8)—22no—
199C3×C3⋊C8—22no—
200C3×C3⋊C8C22×C414yes—
201C3×C3⋊C8C2×D411yescharacteristic
202C3×C3⋊C8C2×D411yescharacteristic
203C3×C3⋊C8C2×D411yescharacteristic
204C3×C3⋊C8C2×D411yescharacteristic
205#575—31no—
206C2×#131—31no—
207C2×#131—91no—
208#444—94no—
209#443—94no—
210#430—91no—
211#421—91no—
212#421—91no—
213#405—91no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—21no—
217C3×#41—21no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—32no—
221C3×#41—32no—
222C3×#41—41no—
223C3×#41—41no—
224C3×#41—61no—
225C3×#41—61no—
226C3×#41C4×D312yes—
227C3×#41C2×Dic312yes—
228C3×#41C22×D312yes—
229C3×#41C22×D312yes—
230C2×C3×Q8—21no—
231C2×C3×Q8—31no—
232C2×C3×Q8C4×D311yescharacteristic
233C2×C3×Q8C2×Dic311yescharacteristic
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—31no—
238C2×C3×D4—41no—
239C2×C3×D4—61no—
240C2×C3×D4C4×D311yescharacteristic
241C2×C3×D4C2×Dic311yescharacteristic
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—41no—
246C22×C3×C4—61no—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—21no—
250#235—21no—
251#235—21no—
252#235C2×Dic312yes—
253#235C22×D312yes—
254C2×D12C2×Dic311yescharacteristic
255C2×C4×D3—21no—
256C2×Dic6C2×Dic311yescharacteristic
257C3×Q16—34no—
258C3×SD16—34no—
259C3×SD16—34no—
260C3×D8—34no—
261C3×M16—32no—
262C3×M16—32no—
263C3×M16—32no—
264C3×M16—62no—
265C3×M16—62no—
266C3×M16—61no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—31no—
270C2×C3×C8—31no—
271C2×C3×C8—31no—
272C2×C3×C8—32no—
273C2×C3×C8—31no—
274C2×C3×C8—62no—
275C2×C3×C8—62no—
276C2×C3×C8—61no—
277#217—61no—
278#217—61no—
279#217—121no—
280#216C2×Dic314yes—
281#215C2×Dic314yes—
282#214C2×Dic314yes—
283#213C2×Dic314yes—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—121no—
287C4×Dic3—32no—
288C4×Dic3—32no—
289C4×Dic3—62no—
290#208—21no—
291#208—22no—
292#208—22no—
293#208—32no—
294#208—32no—
295#208—62no—
296#208—61no—
297#208—61no—
298#208—62no—
299#208—62no—
300#208—121no—
301#208C2×Dic312yes—
302#208C2×Dic312yes—
303#208C22×D312yes—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—22no—
306C2×C3⋊C8—22no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8—121no—
312C2×C3⋊C8#6711yescharacteristic
313C2×C3⋊C8#6711yescharacteristic
314C2×C3⋊C8#6711yescharacteristic
315C2×C3⋊C8#6711yescharacteristic
316C2×C3⋊C8C22×D312yes—
317C2×C3⋊C8C22×D311yescharacteristic
318C2×C3⋊C8C22×D311yescharacteristic
319ΓL(1,𝔽25)—62no—
320ΓL(1,𝔽25)—62no—
321D3×C8—62no—
322D3×C8—62no—
323C22×C32—22no—
324C22×C32—41no—
325C22×C32—42no—
326C22×C32C4×D411yescharacteristic
327C22×C32C4×D411yescharacteristic
328C22×C32C2×#4111yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—42no—
331C32×C4—22no—
332C32×C4C4×D411yescharacteristic
333C32×C4C4×D411yescharacteristic
334C32×C4C23×C411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3⋊Dic3—42no—
337C3×Dic3—22no—
338C2×#41—31no—
339C2×#41D3211yescharacteristic
340#137—32no—
341#137—32no—
342AGL(1,ℤ/8)—32no—
343AGL(1,ℤ/8)—32no—
344#135—34no—
345#131—32no—
346#131—32no—
347#131—61no—
348#131—61no—
349#131—92no—
350#131—92no—
351#131—181no—
352#131—181no—
353C2×M16—31no—
354C2×M16—31no—
355C2×M16—61no—
356C2×M16—91no—
357C2×M16—181no—
358C22×C8—31no—
359C22×C8—61no—
360C22×C8—181no—
361#117—91no—
362#108—94no—
363#104—94no—
364#104—94no—
365#97—92no—
366C4×C8—92no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—41no—
371C23×C3—61no—
372C23×C3#23511yescharacteristic
373C23×C3#23711yescharacteristic
374C22×D3—21no—
375C3×Q8—21no—
376C3×Q8—21no—
377C3×Q8—22no—
378C3×Q8—32no—
379C3×Q8—41no—
380C3×Q8—61no—
381C3×Q8C2×C4×D312yes—
382C3×Q8C22×Dic312yes—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—21no—
388C3×D4—21no—
389C3×D4—22no—
390C3×D4—32no—
391C3×D4—41no—
392C3×D4—42no—
393C3×D4—42no—
394C3×D4—62no—
395C3×D4—62no—
396C3×D4—61no—
397C3×D4C2×C4×D312yes—
398C3×D4C22×Dic312yes—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—41no—
414C2×C3×C4—61no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4C2×C4×D311yescharacteristic
418C2×C3×C4C2×C4×D311yescharacteristic
419C2×C3×C4#23511yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4#23711yescharacteristic
423C2×C3×C4C22×Dic311yescharacteristic
424C2×C3×C4C22×Dic311yescharacteristic
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—22no—
430#67—22no—
431C2×Dic3—21no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435D12—21no—
436D12C22×Dic312yes—
437C4×D3—22no—
438C4×D3—22no—
439Dic6—21no—
440Dic6C22×Dic312yes—
441C3×C8—34no—
442C3×C8—31no—
443C3×C8—31no—
444C3×C8—31no—
445C3×C8—31no—
446C3×C8—62no—
447C3⋊C8—22no—
448C3⋊C8—62no—
449C3⋊C8—62no—
450C3⋊C8—122no—
451C3⋊C8C22×Dic314yes—
452C3⋊C8C2×#6711yescharacteristic
453C3⋊C8C2×#6711yescharacteristic
454C3⋊C8C2×#6711yescharacteristic
455C3⋊C8C2×#6711yescharacteristic
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—42no—
460C2×C32C2×C4×D411yescharacteristic
461C3×D3—42no—
462#41—21no—
463#41—21no—
464#41—32no—
465#41—32no—
466#41—61no—
467#41—61no—
468#41D3×Dic312yes—
469#41C2×D3212yes—
470C2×Q8—31no—
471C2×Q8D3×Dic311yescharacteristic
472C2×D4—21no—
473C2×D4—31no—
474C2×D4—61no—
475C2×D4D3×Dic311yescharacteristic
476C22×C4—21no—
477C22×C4—61no—
478C22×C4C2×D3211yescharacteristic
479Q16—34no—
480SD16—34no—
481SD16—34no—
482D8—34no—
483M16—32no—
484M16—32no—
485M16—32no—
486M16—62no—
487M16—62no—
488M16—61no—
489M16—92no—
490M16—182no—
491M16—182no—
492M16—181no—
493C2×C8—31no—
494C2×C8—32no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8—62no—
501C2×C8—62no—
502C2×C8—61no—
503C2×C8—182no—
504C2×C8—182no—
505C2×C8—181no—
506C4⋊C4—181no—
507C22⋊C4—181no—
508C42—92no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—42no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—62no—
520C22×C3—81no—
521C22×C3—82no—
522C22×C3—122no—
523C22×C3C4×#6711yescharacteristic
524C22×C3C4×#6711yescharacteristic
525C22×C3D4×Dic311yescharacteristic
526C22×C3D4×Dic311yescharacteristic
527C22×C3C2×#23511yescharacteristic
528C22×C3C2×#23711yescharacteristic
529C2×D3—22no—
530C2×D3—42no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—42no—
538C3×C4—62no—
539C3×C4C4×#6711yescharacteristic
540C3×C4C4×#6711yescharacteristic
541C3×C4D4×Dic311yescharacteristic
542C3×C4D4×Dic311yescharacteristic
543C3×C4C22×C4×D311yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C23×Dic311yescharacteristic
546C3×C4C22×#6711yescharacteristic
547Dic3—22no—
548Dic3—122no—
549Dic3—122no—
550Dic3—242no—
551C32#295511yescharacteristic, complemented, Sylow
552C23—21no—
553C23—61no—
554C23#380411yescharacteristic
555Q8—21no—
556Q8—32no—
557Q8—61no—
558Q8C2×D3×Dic312yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4—32no—
563D4—62no—
564D4—62no—
565D4—61no—
566D4C2×D3×Dic312yes—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—61no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—182no—
574C2×C4C2×D3×Dic311yescharacteristic
575C2×C4C2×D3×Dic311yescharacteristic
576C2×C4#380411yescharacteristic
577C2×C4D3×#6711yescharacteristic
578C2×C4D3×#6711yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—34no—
581C8—31no—
582C8—31no—
583C8—31no—
584C8—31no—
585C8—62no—
586C8—182no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—41no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—42no—
598C2×C3—42no—
599C2×C3—82no—
600C2×C3—122no—
601C2×C3C2×C4×#6711yescharacteristic
602C2×C3C2×D4×Dic311yescharacteristic
603D3—42no—
604C22—22no—
605C22—41no—
606C22—42no—
607C22—62no—
608C22—122no—
609C22Dic3×#6711yescharacteristic
610C22Dic3×#6711yescharacteristic
611C22C2×#380411yescharacteristic
612C4—22no—
613C4—62no—
614C4—362no—
615C4Dic3×#6711yescharacteristic
616C4Dic3×#6711yescharacteristic
617C4C22×D3×Dic311yescharacteristic
618C4C2×D3×#6711yescharacteristic
619C3—21no—
620C3#8379211yescharacteristic, complemented
621C3#8399911yescharacteristic, complemented
622C2—21no—
623C2—21no—
624C2—21no—
625C2—42no—
626C2—122no—
627C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radicalC3×#5822C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2955
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
2. C2×C3×#948C2semidirect
3. C2×#63814C2semidirect
4. #10592935C2semidirect
5. #10591674C2semidirect
6. #10591673C2semidirect
7. #10591141C2semidirect
8. #10591110C2semidirect
9. #10591059C2semidirect
16. C3×#951C4semidirect
18. C3×#949C4semidirect
21. C3×#948C22semidirect
22. C3×#948C22semidirect
23. C3×#942C4semidirect
24. C3×#932C4semidirect
33. #63814C22semidirect
34. #63814C22semidirect
36. #63664C22semidirect
37. #63577C22semidirect
38. #63568C22semidirect
39. #63555C22semidirect
40. #63553C22semidirect
45. C2×#948D3semidirect
127. #951Dic3semidirect
129. #949Dic3semidirect
136. #948C2×D3semidirect
137. #948C2×D3semidirect
138. #942Dic3semidirect
139. #932Dic3semidirect
551. C32#2955semidirect
620. C3#83792semidirect
621. C3#83999semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
C2×C3×#9482
C2×#638142
#105929352
#105916742
#105916732
#105911412
#105911102
#105910592
#839993
#837923