Finite Group Databasebeta

← #11860229

Subgroups — #11860229

Order 1152.

1139 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4C2×C3×#803C211yesmaximal, characteristic, complemented
5#10591122C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590383C212yesmaximal, complemented
9#10590362C212yesmaximal, complemented
10#10590360C212yesmaximal, complemented
11#10590346C212yesmaximal, complemented
12#82506—31nomaximal
13#78494—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C4×#638—22no—
18#64135C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2212yes—
20#64081—21no—
21C42×C3⋊D3—21no—
22C4×#634C2212yes—
23C3×C4×#67—22no—
24C3×#926C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×C4×D12C2212yes—
28C3×#872—21no—
29C3×C42×D3—21no—
30C3×C4×Dic6C2212yes—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36C3×#803C2212yes—
37C3×#803C2212yes—
38#63575C2212yes—
39#63573C2212yes—
40#63567C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#63563C2212yes—
44C3×C4×#41—31no—
45C2×#950—31no—
46C2×#904—31no—
47C4×#235—31no—
48C4×#235—31no—
49C4×#235—61no—
50C4×#235D311yescharacteristic, complemented
51C2×C3×#97—31no—
52#5233—31no—
53#5113—31no—
54#5113—31no—
55#5106—31no—
56#5030—32no—
57#5026—32no—
58#5018—32no—
59#5014—32no—
60#5002—31no—
61#4998—31no—
62C2×#803D311yescharacteristic, complemented
63#4716—32no—
64#4711—32no—
65#4710—32no—
66#4710—32no—
67C22×C32×C4D412yes—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70#3828—22no—
71#3828C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×#634C2311yescharacteristic
76C2×C3×#67—21no—
77C3×#235—22no—
78C3×#235C2×C414yescomplemented
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—22no—
82C2×C3×Dic6C2311yescharacteristic
83C32×C42D411yescharacteristic
84C32×C42D411yescharacteristic
85C32×C42C2312yes—
86#3757—21no—
87#3752—22no—
88C4⋊(C3⋊Dic3)C2312yes—
89#3750—22no—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3—21no—
92C3×#217—21no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3—22no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2×C414yescomplemented
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107#2943—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C22×C3×C8—31no—
114C22×C3×C8—31no—
115C3×C4×Q8—32no—
116C3×C4×D4—32no—
117C3×C4×D4—62no—
118C3×#117—31no—
119C3×#117—61no—
120C2×C3×C42—21no—
121C2×C3×C42—61no—
122C2×C3×C42C2×D311yescharacteristic
123C2×C3×C42C2×D311yescharacteristic
124#950—38no—
125C2×#216—31no—
126C2×#215—31no—
127C2×#214—31no—
128C2×#213—31no—
129C4×#67—22no—
130C4×#67—64no—
131C4×#67—62no—
132C4×#67—62no—
133#926—31no—
134#926—31no—
135#926—61no—
136#926C2×D311yescharacteristic
137C22×C3⋊C8C2×D311yescharacteristic
138C22×C3⋊C8C2×D311yescharacteristic
139C2×Dic12—31no—
140#904—38no—
141C2×D24—31no—
142C2×#204—31no—
143C2×#204—31no—
144C4×D12—32no—
145C4×D12—32no—
146C4×D12—62no—
147C4×D12C2×D312yes—
148#872—21no—
149#872—62no—
150#872—61no—
151#872—61no—
152C42×D3—21no—
153C42×D3—62no—
154C42×D3—61no—
155C42×D3—61no—
156C4×Dic6—32no—
157C4×Dic6—32no—
158C4×Dic6—62no—
159C4×Dic6C2×D312yes—
160C3×#97—32no—
161C3×#97—32no—
162#835—32no—
163#832—32no—
164#821—32no—
165#821—32no—
166#818—32no—
167#817—32no—
168#816—32no—
169#816—32no—
170#810—32no—
171#809—32no—
172#808—32no—
173#807—32no—
174#803C2×D312yes—
175#803C2×D312yes—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3×D3—21no—
179C2×C32×C4—42no—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4#4112yes—
185C2×C32×C4C2411yescharacteristic
186#638—24no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—22no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)C22×C412yes—
191C4×C3⋊D3—24no—
192C4×C3⋊D3—44no—
193#634—21no—
194#634C22×C412yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C3×D12—21no—
199C3×D12C22×C412yes—
200C3×C4×D3—24no—
201C3×C4×D3—44no—
202C3×Dic6—21no—
203C3×Dic6C22×C412yes—
204C3×C3⋊C8—22no—
205C3×C3⋊C8C22×C412yes—
206C3×C3⋊C8C22×C412yes—
207C2×#135—91no—
208C4×#41—31no—
209C4×#41—91no—
210#442—92no—
211#441—92no—
212#440—92no—
213#440—92no—
214#427—91no—
215#416—91no—
216#416—91no—
217C2×#97—31no—
218C3×#41—34no—
219C3×#41—62no—
220C2×C3×Q8—31no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—61no—
226C22×C3×C4—62no—
227C22×C3×C4D1212yes—
228C22×C3×C4#6712yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—21no—
232C2×#67—62no—
233C2×#67—61no—
234C2×#67—61no—
235#235—22no—
236#235—34no—
237#235—34no—
238#235—64no—
239#235—64no—
240#235—62no—
241#235—62no—
242#235C4×D314yescomplemented
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—61no—
246C2×D12C22×D311yescharacteristic
247C2×C4×D3—21no—
248C2×C4×D3—22no—
249C2×C4×D3—62no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—64no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×Dic6—31no—
256C2×Dic6—31no—
257C2×Dic6—61no—
258C2×Dic6C22×D311yescharacteristic
259C2×C3×C8—34no—
260C2×C3×C8—31no—
261C2×C3×C8—31no—
262C2×C3×C8—32no—
263C2×C3×C8—62no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—62no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—62no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—22no—
271C3×C42—61no—
272C3×C42—62no—
273C3×C42D1211yescharacteristic
274C3×C42D1211yescharacteristic
275C3×C42#6711yescharacteristic
276C3×C42#6711yescharacteristic
277C3×C42C22×D312yes—
278C3×C42C22×D312yes—
279#217—21no—
280#217—62no—
281#217—61no—
282#217—61no—
283#216—34no—
284#215—34no—
285#214—34no—
286#213—34no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—62no—
291C4⋊Dic3—32no—
292C4⋊Dic3—32no—
293C4⋊Dic3—62no—
294C4⋊Dic3C22×D312yes—
295Dic3⋊C4—22no—
296Dic3⋊C4—64no—
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299C4×Dic3—22no—
300C4×Dic3—21no—
301C4×Dic3—64no—
302C4×Dic3—62no—
303C4×Dic3—62no—
304C4×Dic3—61no—
305C4×Dic3—62no—
306C4×Dic3—61no—
307C2×C3⋊C8—22no—
308C2×C3⋊C8C4×D314yescomplemented
309C2×C3⋊C8C22×D312yes—
310C2×C3⋊C8C22×D311yescharacteristic
311C2×C3⋊C8C22×D311yescharacteristic
312Dic12—34no—
313D24—34no—
314#204—34no—
315#204—34no—
316C22×C32—22no—
317C22×C32C4×D412yes—
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—22no—
320C2×C3⋊D3—42no—
321C2×C3×D3—22no—
322C2×C3×D3—42no—
323C32×C4—22no—
324C32×C4—22no—
325C32×C4C4×D412yes—
326C32×C4C23×C411yescharacteristic
327C32×C4C2×#4111yescharacteristic
328C3⋊Dic3—22no—
329C3⋊Dic3—42no—
330C3×Dic3—22no—
331C3×Dic3—42no—
332C2×#41—31no—
333C2×#41—91no—
334#135—98no—
335C2×Q16—91no—
336C2×SD16—91no—
337C2×SD16—91no—
338C2×D8—91no—
339C22×C8—31no—
340C22×C8—31no—
341C4×Q8—32no—
342C4×Q8—92no—
343C4×D4—32no—
344C4×D4—62no—
345C4×D4—92no—
346C4×D4—182no—
347#117—31no—
348#117—61no—
349#117—91no—
350#117—181no—
351C2×C42—61no—
352C2×C42—181no—
353C2×C42D3211yescharacteristic
354#107—92no—
355#106—92no—
356#103—92no—
357#103—92no—
358#102—92no—
359#102—92no—
360#97—32no—
361#97—32no—
362C23×C3—21no—
363C23×C3—61no—
364C23×C3C2×D1211yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C22×D3—21no—
367C22×D3—62no—
368C22×D3—61no—
369C22×D3—61no—
370C3×Q8—32no—
371C3×Q8—61no—
372C3×D4—32no—
373C3×D4—64no—
374C3×D4—61no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—44no—
384C2×C3×C4—61no—
385C2×C3×C4—64no—
386C2×C3×C4—62no—
387C2×C3×C4—124no—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4C2×C4×D312yes—
390C2×C3×C4C2×D1212yes—
391C2×C3×C4C2×D1212yes—
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4#23512yes—
394C2×C3×C4#23512yes—
395C2×C3×C4C2×#6712yes—
396C2×C3×C4C2×#6712yes—
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400#67—24no—
401#67—68no—
402#67—64no—
403#67—64no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—62no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—64no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412D12—21no—
413D12—32no—
414D12—32no—
415D12—62no—
416D12—62no—
417D12—61no—
418D12—61no—
419D12C2×C4×D312yes—
420C4×D3—24no—
421C4×D3—44no—
422C4×D3—68no—
423C4×D3—64no—
424C4×D3—64no—
425C4×D3—128no—
426C4×D3—124no—
427C4×D3—124no—
428Dic6—21no—
429Dic6—32no—
430Dic6—32no—
431Dic6—62no—
432Dic6—62no—
433Dic6—61no—
434Dic6—61no—
435Dic6C2×C4×D312yes—
436C3×C8—32no—
437C3×C8—32no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8C2×C4×D312yes—
441C3⋊C8C2×C4×D312yes—
442C2×C32—22no—
443C2×C32C2×C4×D411yescharacteristic
444C2×C32#57512yes—
445C3⋊D3—42no—
446C3×D3—42no—
447#41—34no—
448#41—62no—
449#41—94no—
450#41—182no—
451C2×Q8—31no—
452C2×Q8—91no—
453C2×D4—31no—
454C2×D4—61no—
455C2×D4—91no—
456C2×D4—181no—
457C22×C4—61no—
458C22×C4—62no—
459C22×C4—181no—
460C22×C4—182no—
461C22×C4#62612yes—
462C22×C4C2×D3211yescharacteristic
463Q16—94no—
464SD16—94no—
465SD16—94no—
466D8—94no—
467C2×C8—31no—
468C2×C8—31no—
469C2×C8—34no—
470C2×C8—32no—
471C2×C8—62no—
472C4⋊C4—32no—
473C4⋊C4—62no—
474C4⋊C4—92no—
475C4⋊C4—182no—
476C22⋊C4—61no—
477C22⋊C4—62no—
478C22⋊C4—181no—
479C22⋊C4—182no—
480C42—62no—
481C42—61no—
482C42—182no—
483C42—181no—
484C42#62611yescharacteristic
485C42#62611yescharacteristic
486C42C2×D3212yes—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—42no—
492C22×C3—62no—
493C22×C3—122no—
494C22×C3C4×D1212yes—
495C22×C3C4×#6712yes—
496C22×C3C22×D1211yescharacteristic
497C22×C3C22×#6711yescharacteristic
498C2×D3—22no—
499C2×D3—42no—
500C2×D3—64no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—124no—
504C2×D3—122no—
505C2×D3—122no—
506C3×C4—24no—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—22no—
514C3×C4—42no—
515C3×C4—62no—
516C3×C4—122no—
517C3×C4C4×D1212yes—
518C3×C4C4×#6712yes—
519C3×C4C22×C4×D311yescharacteristic
520C3×C4C22×C4×D311yescharacteristic
521C3×C4C2×#23511yescharacteristic
522C3×C4C2×#23511yescharacteristic
523Dic3—22no—
524Dic3—42no—
525Dic3—64no—
526Dic3—62no—
527Dic3—62no—
528Dic3—124no—
529Dic3—122no—
530Dic3—122no—
531C32#294311yescharacteristic, complemented, Sylow
532C23—61no—
533C23—181no—
534C23C2×#62611yescharacteristic
535Q8—32no—
536Q8—61no—
537Q8—92no—
538Q8—181no—
539D4—32no—
540D4—64no—
541D4—61no—
542D4—92no—
543D4—184no—
544D4—181no—
545C2×C4—42no—
546C2×C4—61no—
547C2×C4—64no—
548C2×C4—62no—
549C2×C4—124no—
550C2×C4—181no—
551C2×C4—184no—
552C2×C4—182no—
553C2×C4—364no—
554C2×C4#379812yes—
555C2×C4C4×D3212yes—
556C2×C4C2×#62612yes—
557C2×C4C2×#62612yes—
558C2×C4C2×#62611yescharacteristic
559C2×C4C22×D3211yescharacteristic
560C8—32no—
561C8—32no—
562C8—62no—
563C2×C3—22no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—22no—
567C2×C3—42no—
568C2×C3—122no—
569C2×C3C2×C4×D1211yescharacteristic
570C2×C3#574812yes—
571C2×C3C2×C4×#6711yescharacteristic
572C2×C3#582212yes—
573D3—42no—
574D3—124no—
575D3—122no—
576D3—122no—
577C22—22no—
578C22—62no—
579C22—122no—
580C22—182no—
581C22—362no—
582C22C4×#62612yes—
583C22C22×#62611yescharacteristic
584C4—22no—
585C4—22no—
586C4—62no—
587C4—122no—
588C4—182no—
589C4—362no—
590C4C4×#62612yes—
591C4C2×#379811yescharacteristic
592C4C2×C4×D3211yescharacteristic
593C3—21no—
594C3#7849411yescharacteristic, complemented
595C3#8250611yescharacteristic, complemented
596C2—22no—
597C2—122no—
598C2—362no—
599C2#1059479512yes—
600C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×#3828C2semidirect
2. C3×C4×#235C2semidirect
4. C2×C3×#803C2semidirect
5. #10591122C2semidirect
6. #10591105C2semidirect
7. #10591084C2semidirect
8. #10590383C2semidirect
9. #10590362C2semidirect
10. #10590360C2semidirect
11. #10590346C2semidirect
33. #63829C4semidirect
50. C4×#235D3semidirect
62. C2×#803D3semidirect
71. #3828C2×C4semidirect
78. C3×#235C2×C4semidirect
99. C2×C3×C3⋊C8C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
242. #235C4×D3semidirect
308. C2×C3⋊C8C4×D3semidirect
531. C32#2943semidirect
594. C3#78494semidirect
595. C3#82506semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×C4×#2352
C2×#638292
C2×C3×#8032
#105911222
#105911052
#105910842
#105903832
#105903622
#105903602
#105903462
#825063
#784943