Finite Group Databasebeta

← #11895551

Subgroups — #11895551

Order 1152.

728 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5569C211yesmaximal, characteristic, complemented
2#10593850C211yesmaximal, characteristic
3#10592727C211yesmaximal, characteristic
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591625C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic
7#10591537C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic
9#10590560C211yesmaximal, characteristic, complemented
10#10590537C211yesmaximal, characteristic
11#10590492C211yesmaximal, characteristic, complemented
12#10590464C211yesmaximal, characteristic
13#10590293C211yesmaximal, characteristic
14#10590286C211yesmaximal, characteristic, complemented
15C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
16#83689—31nomaximal
17#79700—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21#64084C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#890—21no—
26C3×#890C2211yescharacteristic
27C3×#888—21no—
28C3×#888C2211yescharacteristic
29C3×#870—21no—
30C3×#870C2211yescharacteristic
31C3×C4×Dic6—21no—
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63894C2211yescharacteristic
35#63888—21no—
36#63868—21no—
37#63866C2211yescharacteristic
38#63864C2211yescharacteristic
39#63848—21no—
40#63844C2211yescharacteristic
41#63836—21no—
42#63637C2211yescharacteristic
43#63636C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×C4×C3⋊C8C2211yescharacteristic
49#63576C2211yescharacteristic
50#63574C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#557—31no—
62#5584—31no—
63#5569D311yescharacteristic, complemented
64#5568—31no—
65C3×C4×Q16—31no—
66#5185—31no—
67#5182—31no—
68#5093—31no—
69#5087—31no—
70#5068—31no—
71#5068—31no—
72#5063—31no—
73#5063—31no—
74#5031—31no—
75C4×#216—31no—
76C4×#216D311yescharacteristic, complemented
77#5028—31no—
78#5028—31no—
79#5028—31no—
80#5028—61no—
81C4×#215—31no—
82Q8×C3⋊C8—31no—
83#5022—31no—
84#4890—31no—
85#4877—31no—
86#4800—31no—
87#4792—31no—
88#4790—31no—
89#4788—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6D411yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#624—21no—
99C32×C4⋊C4—21no—
100C32×C4⋊C4C2311yescharacteristic
101C32×C42—21no—
102C32×C42C2311yescharacteristic
103#3756—22no—
104#3755—22no—
105#3752—21no—
106#3752—21no—
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×#216—22no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4D411yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138#3364—91noSylow
139C2×C3×Q16—31no—
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—61no—
142C3×#125—31no—
143C3×#125—31no—
144C3×#125—61no—
145C3×#125—61no—
146C3×C4×Q8—21no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—61no—
152C3×C4×Q8C2×D311yescharacteristic
153C3×C4×Q8C2×D311yescharacteristic
154#947—31no—
155#946—61no—
156Q8×Dic3C2×D311yescharacteristic
157Q8×Dic3C2×D311yescharacteristic
158#944—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#216—61no—
162C2×#216C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—61no—
166#898—61no—
167#898—61no—
168#898—61no—
169#896—61no—
170#893—31no—
171#892—61no—
172#890—21no—
173#890C2×D311yescharacteristic
174#888—21no—
175#888C2×D311yescharacteristic
176#887—31no—
177#876—61no—
178#875—31no—
179#875—31no—
180#875—31no—
181#875—61no—
182C4×D12—31no—
183#872—61no—
184#870—21no—
185#870C2×D311yescharacteristic
186#869—31no—
187C4×Dic6—21no—
188C4×Dic6—31no—
189C4×Dic6C2×D311yescharacteristic
190C4×Dic6C2×D311yescharacteristic
191C3×#107—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×C4×C8—31no—
195#835—31no—
196#835—31no—
197#835C2×D311yescharacteristic
198#821—31no—
199#821—31no—
200#816—31no—
201#816—31no—
202Dic3⋊C8—31no—
203Dic3⋊C8—31no—
204C8×Dic3—31no—
205C8×Dic3—31no—
206#810—31no—
207#810—31no—
208#810—31no—
209#810—31no—
210#810—31no—
211#810—31no—
212#810—61no—
213#810C2×D311yescharacteristic
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—61no—
219#808—31no—
220#808—31no—
221#807—31no—
222#807—31no—
223#807C2×D311yescharacteristic
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—61no—
229C4×C3⋊C8—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8C2×D311yescharacteristic
232C22×C3⋊D3—21no—
233C32×Q8—21no—
234C32×Q8#4112yes—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)—21no—
243#634—21no—
244#634—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—42no—
257#624—42no—
258C3⋊(C3⋊C8)—21no—
259C3⋊(C3⋊C8)—21no—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262#557—31no—
263#556—91no—
264#488—91no—
265#488—91no—
266#487—91no—
267#479—91no—
268#479—91no—
269#474—91no—
270#464—91no—
271#464—91no—
272#462—91no—
273C8×Q8—91no—
274C4×Q16—31no—
275C4×Q16—91no—
276C4×SD16—91no—
277C2×C3×Q8—21no—
278C2×C3×Q8—31no—
279C2×C3×Q8—31no—
280C2×C3×Q8—61no—
281C2×C3×Q8C22×D311yescharacteristic
282C2×C3×Q8C22×D311yescharacteristic
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—61no—
286C2×C4×D3—61no—
287C2×C4×D3—61no—
288C2×Dic6—21no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C2×Dic6#6711yescharacteristic
293C2×Dic6C22×D311yescharacteristic
294C3×Q16—62no—
295C2×C3×C8—31no—
296C2×C3×C8—31no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—31no—
301C3×C4⋊C4—31no—
302C3×C4⋊C4—31no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—41no—
307C3×C4⋊C4—61no—
308C3×C4⋊C4—61no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C42—21no—
318C3×C42—21no—
319C3×C42—21no—
320C3×C42—31no—
321C3×C42—31no—
322C3×C42—41no—
323C3×C42—61no—
324C3×C42—61no—
325C3×C42—61no—
326C3×C42C22×D311yescharacteristic
327C3×C42C22×D311yescharacteristic
328#216—22no—
329#216—62no—
330#216—62no—
331#216—122no—
332#215—62no—
333#215—62no—
334#215—122no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—121no—
346(C2×D3)⋊C4—121no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3#6711yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4#6711yescharacteristic
366Dic3⋊C4#6711yescharacteristic
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3C22×D311yescharacteristic
373C4×Dic3C22×D311yescharacteristic
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382C22×C32C22×D411yescharacteristic
383C2×C3⋊D3—41no—
384C2×C3⋊D3—41no—
385C2×C3⋊D3—41no—
386C32×C4—22no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4—41no—
390C32×C4C2×#4111yescharacteristic
391C32×C42−1+411yescharacteristic
392C3⋊Dic3—41no—
393C3×Dic3—21no—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13512yes—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—91no—
404C4⋊Q8—31no—
405C4⋊Q8—61no—
406C4⋊Q8—91no—
407#126—181no—
408#126—181no—
409#125—31no—
410#125—31no—
411#125—61no—
412#125—61no—
413#124—91no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—61no—
421C4×Q8—91no—
422C4×Q8D3211yescharacteristic
423C4×D4—91no—
424#117—181no—
425#107—31no—
426#107—91no—
427#106—91no—
428C4⋊C8—91no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—31no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—91no—
439#102—91no—
440#102—91no—
441C4×C8—31no—
442C4×C8—91no—
443C4×C8—91no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—121no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—22no—
450C3×Q8—41no—
451C3×Q8—62no—
452C3×Q8—61no—
453C3×Q8—61no—
454C3×Q8—122no—
455C3×Q8#23512yes—
456C3×Q8#23912yes—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4C2×#6711yescharacteristic
477C2×C3×C4C2×#6711yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—121no—
487C2×Dic3C2×#6711yescharacteristic
488C2×Dic3C2×#6711yescharacteristic
489C2×Dic3C2×#6711yescharacteristic
490C2×Dic3C2×#6711yescharacteristic
491D12—61no—
492D12—61no—
493D12—61no—
494D12—61no—
495D12—121no—
496D12—121no—
497C4×D3—122no—
498C4×D3—122no—
499Dic6—22no—
500Dic6—21no—
501Dic6—21no—
502Dic6—42no—
503Dic6—61no—
504Dic6—61no—
505Dic6—61no—
506Dic6—61no—
507Dic6—121no—
508Dic6—121no—
509C3×C8—61no—
510C3×C8—61no—
511C3⋊C8—21no—
512C3⋊C8—21no—
513C3⋊C8—61no—
514C3⋊C8—61no—
515C3⋊C8—61no—
516C3⋊C8—61no—
517C3⋊C8—121no—
518C3⋊C8—121no—
519C2×C32#54811yescharacteristic
520C2×C32C2×#13511yescharacteristic
521C2×C32#57811yescharacteristic
522C3⋊D3—81no—
523C2×Q8—31no—
524C2×Q8—31no—
525C2×Q8—61no—
526C2×Q8—91no—
527C2×Q8C2×D3211yescharacteristic
528C2×D4—91no—
529C22×C4—181no—
530Q16—62no—
531Q16—182no—
532SD16—182no—
533C2×C8—31no—
534C2×C8—31no—
535C2×C8—91no—
536C2×C8—91no—
537C4⋊C4—21no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4C2×D3211yescharacteristic
556C22⋊C4—181no—
557C22⋊C4—181no—
558C22⋊C4—181no—
559C22⋊C4—181no—
560C22⋊C4—181no—
561C42—21no—
562C42—31no—
563C42—31no—
564C42—61no—
565C42—61no—
566C42—61no—
567C42—181no—
568C42C2×D3211yescharacteristic
569C22×C3—21no—
570C22×C3C2×D3×D411yescharacteristic
571C22×C3C22×#6711yescharacteristic
572C2×D3—121no—
573C2×D3—121no—
574C2×D3—121no—
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—241no—
579C2×D3—241no—
580C2×D3—241no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—22no—
584C3×C4—22no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—32no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—42no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—81no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4C2×#23511yescharacteristic
604C3×C4C2×#23911yescharacteristic
605C3×C4#100711yescharacteristic
606C3×C4#101011yescharacteristic
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—41no—
614Dic3—121no—
615Dic3—121no—
616Dic3—241no—
617Dic3#95012yes—
618C32#336411yescharacteristic, complemented, Sylow
619C23—181no—
620Q8—21no—
621Q8—62no—
622Q8—61no—
623Q8—61no—
624Q8—122no—
625Q8—181no—
626Q8—181no—
627Q8#379912yes—
628D4—181no—
629D4—181no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—31no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—181no—
641C2×C4—362no—
642C2×C4D3×#6711yescharacteristic
643C2×C4D3×#6711yescharacteristic
644C2×C4C22×D3211yescharacteristic
645C8—61no—
646C8—61no—
647C8—181no—
648C8—181no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3#555211yescharacteristic
653C2×C3#576611yescharacteristic
654C2×C3D3×#13511yescharacteristic
655C2×C3#581711yescharacteristic
656C2×C3C2×#95011yescharacteristic
657C2×C3#583811yescharacteristic
658D3—241no—
659D3—241no—
660D3—481no—
661C22—361no—
662C22—361no—
663C22—361no—
664C22C2×D3×#6711yescharacteristic
665C4—22no—
666C4—21no—
667C4—21no—
668C4—32no—
669C4—41no—
670C4—61no—
671C4—61no—
672C4—61no—
673C4—121no—
674C4—121no—
675C4—121no—
676C4—121no—
677C4—361no—
678C4#6429711yescharacteristic
679C4C2×#379911yescharacteristic
680C3—21no—
681C3#7970011yescharacteristic, complemented
682C3#8368911yescharacteristic, complemented
683C2—721no—
684C2#1059490211yescharacteristic
685C2#1059532711yescharacteristic
686C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4×Q8D32
hypocenterC32#3364
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5569C2semidirect
4. C3×C4×#216C2semidirect
5. #10591625C2semidirect
7. #10591537C2semidirect
9. #10590560C2semidirect
11. #10590492C2semidirect
14. #10590286C2semidirect
15. C3⋊C8×Dic6C2semidirect
63. #5569D3semidirect
76. C4×#216D3semidirect
618. C32#3364semidirect
681. C3#79700semidirect
682. C3#83689semidirect

Maximal subgroups

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

subgroupindex
C3×#55692
#105938502
#105927272
C3×C4×#2162
#105916252
#105916072
#105915372
#105915362
#105905602
#105905372
#105904922
#105904642
#105902932
#105902862
C3⋊C8×Dic62
#836893
#797003