Finite Group Databasebeta

← #11861116

Subgroups — #11861116

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
1#10594795C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592704C211yesmaximal, characteristic, complemented
5C3×#5005C211yesmaximal, characteristic, complemented
6C3×#4997C211yesmaximal, characteristic, complemented
7#10591141C211yesmaximal, characteristic, complemented
8#10590342C214yesmaximal, complemented
9#10590341C214yesmaximal, complemented
10#78989—31nomaximal
11#78579—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19#63833C412yescomplemented
20#63831C412yescomplemented
21#63830C412yescomplemented
22#63829C2214yes—
23#63825C412yescomplemented
24C2×#3712—21no—
25C2×#3711—21no—
26#63817—21no—
27#63817—21no—
28#63817C2212yescomplemented
29#63817C2212yescomplemented
30C2×#3710—21no—
31#63814—21no—
32#63814—21no—
33#63814C2212yescomplemented
34#63814C2212yescomplemented
35C2×D3×C3⋊C8—21no—
36#63632C2214yescomplemented
37C3×#805C2214yescomplemented
38C3×#803C2212yescomplemented
39C3×C4×C3⋊C8C2212yescomplemented
40#63577C2214yescomplemented
41#5822—31no—
42C2×#948—31no—
43#5748—31no—
44C2×#907—31no—
45C2×#901—31no—
46C2×#901—31no—
47C3×#421—31no—
48C3×#405—31no—
49#5125—31no—
50#5124—31no—
51#5005—31no—
52#5005—31no—
53#5005—61no—
54#5005D311yescharacteristic, complemented
55#4997D311yescharacteristic, complemented
56#4824—34no—
57#4823—34no—
58#4717—34no—
59#4700—34no—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62#3828—21no—
63#3828—21no—
64#3828C2×C412yes—
65#3828C2312yes—
66C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2×C411yescharacteristic
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
77C32×C4⋊C4—21no—
78C32×C22⋊C4—21no—
79C32×C42C2312yes—
80#3748—21no—
81#3748C2312yes—
82C2×C3⋊(C3⋊C8)—21no—
83C3×#208—21no—
84C3×#208C2×C412yes—
85C3×#208C2×C412yes—
86C3×#208C2312yes—
87C2×C3×C3⋊C8—21no—
88C2×C3×C3⋊C8D411yescharacteristic
89C2×C3×C3⋊C8D411yescharacteristic
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8D411yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3719C2×C414yes—
96#3717C2×C414yes—
97#3716C2×C414yes—
98#3714C2×C414yes—
99#3712—22no—
100#3712—22no—
101#3711—22no—
102#3711—22no—
103#3710—22no—
104#3710—22no—
105D3×C3⋊C8—22no—
106D3×C3⋊C8—22no—
107#2955—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C22×C3×C8—31no—
116C3×#117—21no—
117C3×#117C2×D311yescharacteristic
118C3×#117C2×D311yescharacteristic
119#951—32no—
120#950—34no—
121#949—32no—
122#948—32no—
123#948—32no—
124#948—61no—
125#948—61no—
126#942—32no—
127#932—32no—
128C2×#208—31no—
129C2×#208—31no—
130C2×#208—61no—
131C2×#208—61no—
132C2×#208C2×D311yescharacteristic
133C2×#208C2×D311yescharacteristic
134C22×C3⋊C8—61no—
135C22×C3⋊C8C2×D311yescharacteristic
136#909—32no—
137#909—32no—
138#908—32no—
139#908—32no—
140#907—32no—
141#907—32no—
142#907—61no—
143#907—61no—
144#904—34no—
145#901—32no—
146#901—32no—
147#901—32no—
148#901—32no—
149#901—61no—
150#901—61no—
151#901—61no—
152#901—61no—
153C2×ΓL(1,𝔽25)—61no—
154C2×ΓL(1,𝔽25)—61no—
155C2×ΓL(1,𝔽25)—61no—
156C2×D3×C8—61no—
157C2×D3×C8—61no—
158C2×D3×C8—61no—
159C3×#104—34no—
160C3×#97—32no—
161C3×C4×C8—32no—
162#822—34no—
163#819—34no—
164#805—34no—
165#805—34no—
166#805—64no—
167#805C2×D314yescomplemented
168#803C2×D312yescomplemented
169C4×C3⋊C8C2×D312yescomplemented
170C23×C32#4111yescharacteristic
171C22×C3⋊D3—21no—
172C22×C3×D3—21no—
173C2×C32×C4—22no—
174C2×C32×C4C22×C411yescharacteristic
175C2×C32×C4C22×C411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4#4111yescharacteristic
179C2×C32×C4C2411yescharacteristic
180#638—22no—
181#638—22no—
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)C22×C412yes—
185C4×C3⋊D3—22no—
186C4×C3⋊D3—22no—
187#634—21no—
188#634C22×C412yes—
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—91no—
206C2×#131—91no—
207C2×#131—91no—
208#444—94no—
209#443—94no—
210#430—91no—
211#421—31no—
212#421—91no—
213#405—31no—
214C3×#41—32no—
215C3×#41—32no—
216C3×#41—61no—
217C3×#41—61no—
218C2×C3×Q8—31no—
219C2×C3×D4—31no—
220C2×C3×D4—61no—
221C22×C3×C4—21no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—21no—
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—121no—
229#235—21no—
230#235—21no—
231#235—32no—
232#235—32no—
233#235—32no—
234#235—32no—
235#235—62no—
236#235—62no—
237#235—61no—
238#235—61no—
239#235—61no—
240#235—61no—
241#235—121no—
242#235—121no—
243#235C4×D312yes—
244#235C22×D312yes—
245C2×D12—31no—
246C2×D12—31no—
247C2×D12—61no—
248C2×D12C4×D311yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—121no—
253C2×Dic6—31no—
254C2×Dic6—31no—
255C2×Dic6—61no—
256C2×Dic6C4×D311yescharacteristic
257C3×M16—32no—
258C3×M16—32no—
259C3×M16—32no—
260C3×M16—61no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C2×C3×C8—32no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—61no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—41no—
272C3×C22⋊C4—21no—
273C3×C22⋊C4—21no—
274C3×C22⋊C4—41no—
275C3×C42—22no—
276C3×C42C22×D312yes—
277C3×C42C22×D312yes—
278#216—34no—
279#215—34no—
280#214—34no—
281#213—34no—
282#208—21no—
283#208—32no—
284#208—32no—
285#208—62no—
286#208—61no—
287#208—61no—
288#208—62no—
289#208—62no—
290#208—121no—
291#208C4×D312yes—
292#208C4×D312yes—
293#208C22×D312yes—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—62no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8—121no—
300C2×C3⋊C8D1211yescharacteristic
301C2×C3⋊C8D1211yescharacteristic
302C2×C3⋊C8D1211yescharacteristic
303C2×C3⋊C8D1211yescharacteristic
304C2×C3⋊C8C22×D312yes—
305C2×C3⋊C8C22×D311yescharacteristic
306C2×C3⋊C8C22×D311yescharacteristic
307Dic12—34no—
308D24—34no—
309#204—34no—
310#204—34no—
311ΓL(1,𝔽25)—62no—
312ΓL(1,𝔽25)—62no—
313ΓL(1,𝔽25)—62no—
314ΓL(1,𝔽25)—62no—
315ΓL(1,𝔽25)—62no—
316ΓL(1,𝔽25)—62no—
317D3×C8—62no—
318D3×C8—62no—
319D3×C8—62no—
320D3×C8—62no—
321D3×C8—62no—
322D3×C8—62no—
323C22×C32—41no—
324C22×C32C4×D411yescharacteristic
325C22×C32C4×D411yescharacteristic
326C22×C32C2×#4111yescharacteristic
327C2×C3⋊D3—22no—
328C2×C3⋊D3—42no—
329C2×C3×D3—22no—
330C2×C3×D3—42no—
331C32×C4—42no—
332C32×C4C4×D411yescharacteristic
333C32×C4C4×D411yescharacteristic
334C32×C4C23×C411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3⋊Dic3—22no—
337C3×Dic3—22no—
338C2×#41—31no—
339C2×#41—91no—
340#137—92no—
341#137—92no—
342AGL(1,ℤ/8)—92no—
343AGL(1,ℤ/8)—92no—
344#135—94no—
345#131—92no—
346#131—92no—
347#131—92no—
348#131—92no—
349#131—181no—
350#131—181no—
351#131—181no—
352#131—181no—
353C2×M16—31no—
354C2×M16—31no—
355C2×M16—91no—
356C2×M16—181no—
357C2×M16—181no—
358C22×C8—31no—
359C22×C8—181no—
360C22×C8—181no—
361#117D3211yescharacteristic
362#108—94no—
363#104—34no—
364#104—94no—
365#97—32no—
366C4×C8—32no—
367C23×C3—21no—
368C23×C3—61no—
369C23×C3#23511yescharacteristic
370C23×C3#23711yescharacteristic
371C22×D3—21no—
372C22×D3—61no—
373C22×D3—61no—
374C22×D3—121no—
375C3×Q8—32no—
376C3×Q8—61no—
377C3×D4—32no—
378C3×D4—62no—
379C3×D4—62no—
380C3×D4—61no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—42no—
390C2×C3×C4—61no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4C2×C4×D311yescharacteristic
394C2×C3×C4C2×C4×D311yescharacteristic
395C2×C3×C4C2×C4×D311yescharacteristic
396C2×C3×C4C2×C4×D311yescharacteristic
397C2×C3×C4C2×D1211yescharacteristic
398C2×C3×C4C2×D1211yescharacteristic
399C2×C3×C4#23511yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4#23711yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—22no—
406#67—22no—
407#67—62no—
408#67—62no—
409#67—62no—
410#67—62no—
411#67—122no—
412#67—122no—
413C2×Dic3—21no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—121no—
417D12—21no—
418D12—32no—
419D12—32no—
420D12—62no—
421D12—61no—
422D12—61no—
423D12—121no—
424D12C2×C4×D312yes—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—122no—
432C4×D3—122no—
433Dic6—21no—
434Dic6—32no—
435Dic6—32no—
436Dic6—62no—
437Dic6—61no—
438Dic6—61no—
439Dic6—121no—
440Dic6C2×C4×D312yes—
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⋊C8C2×C4×D314yes—
452C3⋊C8C2×D1211yescharacteristic
453C3⋊C8C2×D1211yescharacteristic
454C3⋊C8C2×D1211yescharacteristic
455C3⋊C8C2×D1211yescharacteristic
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32C2×C4×D411yescharacteristic
460C3⋊D3—42no—
461C3×D3—42no—
462#41—32no—
463#41—32no—
464#41—61no—
465#41—61no—
466#41—92no—
467#41—92no—
468#41—181no—
469#41—181no—
470C2×Q8—31no—
471C2×Q8—91no—
472C2×D4—31no—
473C2×D4—61no—
474C2×D4—91no—
475C2×D4—181no—
476C22×C4—61no—
477C22×C4—181no—
478C22×C4C2×D3211yescharacteristic
479Q16—94no—
480SD16—94no—
481SD16—94no—
482D8—94no—
483M16—32no—
484M16—32no—
485M16—32no—
486M16—61no—
487M16—92no—
488M16—182no—
489M16—182no—
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—61no—
501C2×C8—182no—
502C2×C8—182no—
503C2×C8—182no—
504C2×C8—182no—
505C2×C8—181no—
506C4⋊C4—21no—
507C22⋊C4—21no—
508C42C2×D3212yes—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—62no—
515C22×C3—81no—
516C22×C3—122no—
517C22×C3C4×D1211yescharacteristic
518C22×C3C4×D1211yescharacteristic
519C22×C3#67⋊C411yescharacteristic
520C22×C3#67⋊C411yescharacteristic
521C22×C3C2×#23511yescharacteristic
522C22×C3C2×#23711yescharacteristic
523C2×D3—22no—
524C2×D3—42no—
525C2×D3—62no—
526C2×D3—62no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—242no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—42no—
536C3×C4—42no—
537C3×C4—62no—
538C3×C4—82no—
539C3×C4C4×D1211yescharacteristic
540C3×C4C4×D1211yescharacteristic
541C3×C4#67⋊C411yescharacteristic
542C3×C4#67⋊C411yescharacteristic
543C3×C4C22×C4×D311yescharacteristic
544C3×C4C22×C4×D311yescharacteristic
545C3×C4C22×D1211yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547Dic3—22no—
548Dic3—62no—
549Dic3—62no—
550Dic3—122no—
551C32#295511yescharacteristic, complemented, Sylow
552C23—61no—
553C23—181no—
554C23#380411yescharacteristic
555Q8—32no—
556Q8—61no—
557Q8—92no—
558Q8—181no—
559D4—32no—
560D4—62no—
561D4—62no—
562D4—61no—
563D4—92no—
564D4—182no—
565D4—182no—
566D4—181no—
567C2×C4—22no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—181no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4C4×D3211yescharacteristic
575C2×C4C4×D3211yescharacteristic
576C2×C4D3×D1211yescharacteristic
577C2×C4D3×D1211yescharacteristic
578C2×C4#380411yescharacteristic
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—122no—
598C2×C3C2×C4×D1211yescharacteristic
599C2×C3C2×#67⋊C411yescharacteristic
600D3—42no—
601D3—122no—
602D3—122no—
603D3—242no—
604C22—41no—
605C22—62no—
606C22—122no—
607C22—182no—
608C22—362no—
609C22#6388011yescharacteristic
610C22#6388011yescharacteristic
611C22C2×#380411yescharacteristic
612C4—42no—
613C4—62no—
614C4—182no—
615C4#6388011yescharacteristic
616C4#6388011yescharacteristic
617C4C2×C4×D3211yescharacteristic
618C4C2×D3×D1211yescharacteristic
619C3—21no—
620C3#7857911yescharacteristic, complemented
621C3#7898911yescharacteristic, complemented
622C2—21no—
623C2—21no—
624C2—21no—
625C2—122no—
626C2—362no—
627C2C2×#6388011yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC2×C32C2×C4×D4
prime radical#10594795C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C2×#63814C2semidirect
4. #10592704C2semidirect
5. C3×#5005C2semidirect
6. C3×#4997C2semidirect
7. #10591141C2semidirect
8. #10590342C2semidirect
9. #10590341C2semidirect
19. #63833C4semidirect
20. #63831C4semidirect
21. #63830C4semidirect
23. #63825C4semidirect
28. #63817C22semidirect
29. #63817C22semidirect
33. #63814C22semidirect
34. #63814C22semidirect
36. #63632C22semidirect
37. C3×#805C22semidirect
38. C3×#803C22semidirect
39. C3×C4×C3⋊C8C22semidirect
40. #63577C22semidirect
54. #5005D3semidirect
55. #4997D3semidirect
167. #805C2×D3semidirect
168. #803C2×D3semidirect
169. C4×C3⋊C8C2×D3semidirect
551. C32#2955semidirect
620. C3#78579semidirect
621. C3#78989semidirect

Maximal subgroups

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

subgroupindex
#105947952
C2×#638172
C2×#638142
#105927042
C3×#50052
C3×#49972
#105911412
#105903422
#105903412
#789893
#785793