Finite Group Databasebeta

← #11860424

Subgroups — #11860424

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2#10594954C211yesmaximal, characteristic
3C2×#63833C211yesmaximal, characteristic
4#10592665C211yesmaximal, characteristic
5C3×#4964C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590481C212yesmaximal, complemented
9#10590480C212yesmaximal, complemented
10#10590458C212yesmaximal, complemented
11#10590457C212yesmaximal, complemented
12C4×#942—31nomaximal
13#79200—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×Dic3⋊C4—21no—
20C2×C3×C4×Dic3—21no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C3×#887—21no—
24C3×#887—21no—
25C3×#887C2212yes—
26C3×#887C2212yes—
27#63952—21no—
28#63952—21no—
29#63894C2211yescharacteristic
30#63894C2211yescharacteristic
31C4×#624—21no—
32#63874—21no—
33#63844C2211yescharacteristic
34#63844C2211yescharacteristic
35C2×#3719C2212yes—
36#63833C418yescomplemented
37C2×#3717C2212yes—
38#63637C2212yes—
39#63636C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42#63565C2212yes—
43#63565C2212yes—
44#63554C2212yes—
45Dic3×C3⋊C8C2212yes—
46C2×C3×C4×Q8—31no—
47C2×#942—31no—
48C2×#909—31no—
49#5522—31no—
50C2×#887D311yescharacteristic, complemented
51C4×#235—31no—
52C3×#428—31no—
53#5225—31no—
54Dic3×M16—31no—
55#5030—32no—
56C4×#216—32no—
57#5026—32no—
58C4×#215—32no—
59#5004—31no—
60#4966—31no—
61#4966—31no—
62#4966—61no—
63#4964D311yescharacteristic, complemented
64C4×#208—31no—
65#4889—32no—
66#4873—32no—
67#4853—32no—
68#4852—32no—
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72#3828—22no—
73#3828C2×C414yes—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3—21no—
76C2×#634C2311yescharacteristic
77C22×C3×Dic3—21no—
78C22×C3×Dic3D411yescharacteristic
79C22×C3×Dic3D411yescharacteristic
80C2×C3×Dic6—21no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6C2×C414yescomplemented
83C2×C3×Dic6C2312yes—
84C2×#624—21no—
85C2×#624—21no—
86C32×C4⋊C4—21no—
87C32×C4⋊C4C2312yes—
88#3748—22no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C3×#208C2×C414yescomplemented
103C2×C3×C3⋊C8C2312yes—
104#3724—21no—
105#3724—21no—
106#3722—21no—
107#3722—21no—
108Dic32—21no—
109Dic32—21no—
110#3719C2×C418yescomplemented
111#3717C2×C418yescomplemented
112C4×#137—91noSylow
113C22×C3×Q8—31no—
114C2×#235—31no—
115C2×#235—31no—
116C2×#235—61no—
117C22×Dic6C2×D311yescharacteristic
118C2×C3×M16—31no—
119C3×C4×Q8—32no—
120C3×C4×Q8—32no—
121C3×C4×Q8—61no—
122C3×C4×Q8—61no—
123C3×#117—31no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—61no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C2×D311yescharacteristic
128C2×C3×C42—31no—
129C2×C3×C42—61no—
130C2×#216—32no—
131#942—38no—
132C2×#215—32no—
133C4×#67—61no—
134C4×#67—61no—
135#926C2×D311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3C2×D311yescharacteristic
139C2×#208—31no—
140C2×#208—31no—
141C2×#208—61no—
142C2×#208C2×D311yescharacteristic
143#909—38no—
144C2×Dic12—32no—
145C2×#204—32no—
146#893—31no—
147#893—31no—
148#887—21no—
149#887—21no—
150#887—31no—
151#887—31no—
152#887C2×D312yes—
153#887C2×D312yes—
154#67⋊C4—61no—
155#67⋊C4—61no—
156C4×D12—31no—
157C4×D12—31no—
158#872—61no—
159#872—61no—
160C42×D3—61no—
161C42×D3—61no—
162C4×Dic6—31no—
163C4×Dic6—31no—
164C3×#107—32no—
165C3×#106—32no—
166#835—32no—
167#835—32no—
168#815—32no—
169C8×Dic3—32no—
170#810—32no—
171#810—32no—
172#810—32no—
173#810—32no—
174#810—62no—
175#809—32no—
176#809—32no—
177#809—62no—
178#808C2×D312yes—
179#807C2×D312yes—
180#803—32no—
181C4×C3⋊C8—32no—
182C23×C32C2×D411yescharacteristic
183C22×C3⋊D3—21no—
184C2×C32×C4—22no—
185C2×C32×C4—42no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190#638—24no—
191C2×C3⋊Dic3—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)C22×C412yes—
194C4×C3⋊D3—24no—
195#634—21no—
196#634C22×C412yes—
197C2×C3×Dic3—24no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—41no—
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C2×C3×Dic3C2×D411yescharacteristic
207C3×Dic6—24no—
208C3×Dic6—22no—
209C3×Dic6C22×C414yes—
210#624—42no—
211#624—42no—
212C3⋊(C3⋊C8)—22no—
213C3×C3⋊C8C22×C414yes—
214C2×#137—91no—
215C4×#41—91no—
216C2×C4×Q8—31no—
217#441—92no—
218#440—92no—
219C4×Q16—92no—
220C4×SD16—92no—
221#428—31no—
222#419—91no—
223#417—91no—
224C4×M16—91no—
225C2×C3×Q8—34no—
226C2×C3×Q8—32no—
227C2×C3×Q8—61no—
228C2×C3×Q8—62no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—41no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—61no—
239C2×#67—61no—
240C2×#67—121no—
241C22×Dic3—21no—
242C22×Dic3#6711yescharacteristic
243C22×Dic3#6711yescharacteristic
244#235—34no—
245#235—34no—
246#235—64no—
247#235—62no—
248#235—62no—
249#235—122no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—61no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×C4×D3—121no—
260C2×Dic6—22no—
261C2×Dic6—21no—
262C2×Dic6—31no—
263C2×Dic6—31no—
264C2×Dic6—61no—
265C2×Dic6C4×D314yescomplemented
266C2×Dic6C22×D312yes—
267C3×M16—34no—
268C2×C3×C8—32no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—31no—
273C3×C4⋊C4—31no—
274C3×C4⋊C4—41no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—62no—
277C3×C4⋊C4C22×D312yes—
278C3×C4⋊C4C22×D312yes—
279C3×C22⋊C4—61no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—62no—
285C3×C42—62no—
286C3×C42—61no—
287#217—21no—
288#216—38no—
289#215—38no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294C4⋊Dic3C22×D311yescharacteristic
295C4⋊Dic3C22×D311yescharacteristic
296Dic3⋊C4—22no—
297Dic3⋊C4—22no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302C4×Dic3—21no—
303C4×Dic3—22no—
304C4×Dic3—22no—
305C4×Dic3—61no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3#6711yescharacteristic
310C4×Dic3#6711yescharacteristic
311C4×Dic3C22×D311yescharacteristic
312C4×Dic3C22×D311yescharacteristic
313#208—62no—
314#208—62no—
315#208—122no—
316#208C4×D314yescomplemented
317C2×C3⋊C8—32no—
318C2×C3⋊C8—32no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8C22×D312yes—
321Dic12—38no—
322#204—38no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32C4×D412yes—
326C22×C32C22×D411yescharacteristic
327C2×C3⋊D3—22no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C32×C4—42no—
331C32×C4C4×D412yes—
332C32×C4C23×C411yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—22no—
335C3×Dic3—24no—
336C3×Dic3—21no—
337C3×Dic3—21no—
338C3×Dic3—21no—
339C3×Dic3—41no—
340C3×Dic3—41no—
341C3×Dic3#13712yescomplemented
342C2×#41—91no—
343C22×Q8—31no—
344#137—98no—
345C2×Q16—92no—
346C2×SD16—92no—
347C2×M16—31no—
348C2×M16—91no—
349C4×Q8—32no—
350C4×Q8—32no—
351C4×Q8—61no—
352C4×Q8—61no—
353C4×Q8—91no—
354C4×Q8—91no—
355C4×D4—91no—
356C4×D4—91no—
357C4×D4—181no—
358C4×D4—181no—
359#117—31no—
360#117—181no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4D3211yescharacteristic
363C2×C42—31no—
364C2×C42—61no—
365C2×C42—181no—
366#107—32no—
367#106—32no—
368#103—92no—
369#103—92no—
370#103—92no—
371#102—92no—
372#97—92no—
373C4×C8—92no—
374C23×C3—21no—
375C23×C3D3×D411yescharacteristic
376C23×C3C2×#6711yescharacteristic
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—121no—
380C3×Q8—34no—
381C3×Q8—64no—
382C3×Q8—62no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—62no—
397C2×C3×C4—64no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—82no—
402C2×C3×C4—121no—
403C2×C3×C4C2×C4×D312yes—
404C2×C3×C4C2×C4×D312yes—
405C2×C3×C4#23512yes—
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4#23912yes—
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—64no—
412#67—64no—
413#67—124no—
414C2×Dic3—24no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—41no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—121no—
423C2×Dic3C2×#6711yescharacteristic
424C2×Dic3C2×#6711yescharacteristic
425C2×Dic3C2×#6711yescharacteristic
426C2×Dic3C2×#6711yescharacteristic
427D12—32no—
428D12—32no—
429D12—62no—
430D12—61no—
431D12—61no—
432D12—121no—
433C4×D3—64no—
434C4×D3—64no—
435C4×D3—124no—
436C4×D3—122no—
437C4×D3—122no—
438C4×D3—122no—
439C4×D3—122no—
440Dic6—24no—
441Dic6—22no—
442Dic6—32no—
443Dic6—32no—
444Dic6—62no—
445Dic6—61no—
446Dic6—61no—
447Dic6—121no—
448Dic6C2×C4×D314yes—
449C3×C8—34no—
450C3⋊C8—62no—
451C3⋊C8—62no—
452C3⋊C8—122no—
453C3⋊C8C2×C4×D314yes—
454C2×C32—22no—
455C2×C32C2×C4×D411yescharacteristic
456C2×C32C2×#13711yescharacteristic
457C2×C32#57511yescharacteristic
458C3⋊D3—42no—
459#41—94no—
460#41—182no—
461C2×Q8—32no—
462C2×Q8—34no—
463C2×Q8—62no—
464C2×Q8—61no—
465C2×Q8—91no—
466C2×D4—91no—
467C2×D4—181no—
468C22×C4—21no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—61no—
472C22×C4—181no—
473C22×C4—181no—
474C22×C4—181no—
475C22×C4C2×D3211yescharacteristic
476Q16—98no—
477SD16—98no—
478M16—34no—
479M16—182no—
480C2×C8—32no—
481C2×C8—92no—
482C4⋊C4—21no—
483C4⋊C4—31no—
484C4⋊C4—31no—
485C4⋊C4—62no—
486C4⋊C4—62no—
487C4⋊C4—181no—
488C4⋊C4—181no—
489C4⋊C4C2×D3212yes—
490C22⋊C4—61no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C42—31no—
494C42—31no—
495C42—31no—
496C42—31no—
497C42—62no—
498C42—62no—
499C42—61no—
500C42—181no—
501C42—181no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3#89312yes—
511C22×C3C4×#6712yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C22×#6711yescharacteristic
514C2×D3—62no—
515C2×D3—62no—
516C2×D3—122no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—241no—
522C2×D3—241no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—22no—
526C3×C4—32no—
527C3×C4—42no—
528C3×C4—42no—
529C3×C4—64no—
530C3×C4—61no—
531C3×C4—61no—
532C3×C4—61no—
533C3×C4—82no—
534C3×C4—121no—
535C3×C4—121no—
536C3×C4#89312yes—
537C3×C4C4×#6712yes—
538C3×C4C22×C4×D311yescharacteristic
539C3×C4C22×C4×D311yescharacteristic
540C3×C4C2×#23511yescharacteristic
541C3×C4C2×#23911yescharacteristic
542Dic3—24no—
543Dic3—21no—
544Dic3—21no—
545Dic3—21no—
546Dic3—41no—
547Dic3—41no—
548Dic3—62no—
549Dic3—62no—
550Dic3—122no—
551Dic3#94212yescomplemented
552C32C4×#13711yescharacteristic, complemented, Sylow
553C23—181no—
554C23D3×#6711yescharacteristic
555Q8—34no—
556Q8—62no—
557Q8—64no—
558Q8—92no—
559Q8—181no—
560D4—92no—
561D4—184no—
562D4—181no—
563C2×C4—22no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—31no—
568C2×C4—42no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—64no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—121no—
575C2×C4—181no—
576C2×C4—184no—
577C2×C4—362no—
578C2×C4—362no—
579C2×C4#379912yes—
580C2×C4C4×D3212yes—
581C2×C4D3×#6711yescharacteristic
582C2×C4C22×D3211yescharacteristic
583C8—34no—
584C8—182no—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—42no—
591C2×C3C2×#89311yescharacteristic
592C2×C3#577311yescharacteristic
593C2×C3D3×#13711yescharacteristic
594C2×C3C2×C4×#6711yescharacteristic
595C2×C3C2×#94211yescharacteristic
596C2×C3#582211yescharacteristic
597D3—122no—
598D3—122no—
599D3—242no—
600C22—21no—
601C22—21no—
602C22—182no—
603C22—361no—
604C22—361no—
605C22#6390412yes—
606C22C2×D3×#6711yescharacteristic
607C4—32no—
608C4—42no—
609C4—61no—
610C4—61no—
611C4—64no—
612C4—61no—
613C4—121no—
614C4—121no—
615C4—182no—
616C4#6390412yes—
617C4C2×#379911yescharacteristic
618C4C2×C4×D3211yescharacteristic
619C3—21no—
620C3#7920011yescharacteristic, complemented
621C3C4×#94211yescharacteristic, complemented
622C2—22no—
623C2—362no—
624C2C2×#6390411yescharacteristic
625C2#1059509511yescharacteristic
626C2D3×#94211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#887C2semidirect
5. C3×#4964C2semidirect
6. #10591099C2semidirect
7. Dic3×#208C2semidirect
8. #10590481C2semidirect
9. #10590480C2semidirect
10. #10590458C2semidirect
11. #10590457C2semidirect
36. #63833C4semidirect
50. C2×#887D3semidirect
63. #4964D3semidirect
82. C2×C3×Dic6C2×C4semidirect
102. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3717C2×C4semidirect
265. C2×Dic6C4×D3semidirect
316. #208C4×D3semidirect
341. C3×Dic3#137semidirect
551. Dic3#942semidirect
552. C32C4×#137semidirect
620. C3#79200semidirect
621. C3C4×#942semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
#105949542
C2×#638332
#105926652
C3×#49642
#105910992
Dic3×#2082
#105904812
#105904802
#105904582
#105904572
C4×#9423
#792003