Finite Group Databasebeta

← #11896050

Subgroups — #11896050

Order 1152.

724 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×#5568C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592719C211yesmaximal, characteristic, complemented
4C3×#5030C211yesmaximal, characteristic, complemented
5#10591624C211yesmaximal, characteristic
6#10591623C211yesmaximal, characteristic, complemented
7#10591578C211yesmaximal, characteristic
8#10591574C211yesmaximal, characteristic, complemented
9#10590558C211yesmaximal, characteristic
10#10590556C211yesmaximal, characteristic, complemented
11#10590477C211yesmaximal, characteristic, complemented
12#10590475C211yesmaximal, characteristic
13#10590276C211yesmaximal, characteristic
14#10590267C211yesmaximal, characteristic
15#10590251C211yesmaximal, characteristic, complemented
16#83677—31nomaximal
17#79815—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19#64078C2211yescharacteristic
20C3×#947C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#898—21no—
24C3×#896—21no—
25C3×#893C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#876—21no—
28C3×#875C2211yescharacteristic
29C3×#872—21no—
30C3×C4×Dic6C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63918—21no—
33#63918C2211yescharacteristic
34#63918C2211yescharacteristic
35Dic3×Dic6—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63840—21no—
39#63840—21no—
40C2×#3718C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42#63662C2211yescharacteristic
43#63662C2211yescharacteristic
44#63635C2211yescharacteristic
45#63635C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#803C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#556—31no—
62#5568D311yescharacteristic
63Q8×Dic6—31no—
64Q8×Dic6—31no—
65C3×#441—31no—
66#5185—31no—
67#5182—31no—
68#5090—31no—
69#5079—31no—
70#5055—31no—
71#5055—31no—
72#5054—31no—
73#5054—31no—
74#5030—31no—
75#5030D311yescharacteristic, complemented
76#5028—31no—
77#5024—31no—
78#5020—31no—
79#5020—31no—
80#5020—31no—
81#5020—61no—
82C4×#214—31no—
83#5008—31no—
84#4870—31no—
85#4854—31no—
86#4794—31no—
87#4792—31no—
88#4789—31no—
89#4788—31no—
90#4714—31no—
91#4701—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6D411yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627—21no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C42—21no—
104C32×C42C2311yescharacteristic
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×#216—22no—
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3D411yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
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×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3718—22no—
137#3715—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C3×C4⋊Q8—31no—
141C3×#126—61no—
142C3×#126—61no—
143C3×#124—31no—
144C3×#124—31no—
145C3×C22⋊Q8—61no—
146C3×C4×Q8—21no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×Q8C2×D311yescharacteristic
152C3×C4×D4—31no—
153C3×#117—61no—
154#947C2×D311yescharacteristic
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—61no—
158#944C2×D311yescharacteristic
159C2×#216—31no—
160C2×#216—31no—
161C2×#216C2×D311yescharacteristic
162C2×#215—31no—
163C2×#214—31no—
164#898—21no—
165#896—21no—
166#893C2×D311yescharacteristic
167#888—31no—
168#888—31no—
169#888—61no—
170#888—61no—
171#888—61no—
172#888—61no—
173#888—61no—
174#887C2×D311yescharacteristic
175#876—21no—
176#875C2×D311yescharacteristic
177#872—21no—
178#869—31no—
179#869—31no—
180#869—31no—
181#869—31no—
182#869—61no—
183#869—61no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×#106—31no—
190C3×#103—31no—
191C3×#103—31no—
192C3×#97—31no—
193#835—31no—
194#835—31no—
195#835—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—61no—
201#835—61no—
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#832—31no—
206#821—31no—
207#821—31no—
208#816—31no—
209#816—31no—
210#815—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213C8×Dic3—31no—
214#810—31no—
215#810C2×D311yescharacteristic
216#809—31no—
217#808—31no—
218#808—31no—
219#808—31no—
220#808—31no—
221#808—61no—
222#808—61no—
223#808C2×D311yescharacteristic
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—61no—
229#803—31no—
230#803C2×D311yescharacteristic
231C4×C3⋊C8—31no—
232C22×C3×D3—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242#634—81no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×D12—21no—
251C3×D12—21no—
252C3×C4×D3—42no—
253C3×Dic6—21no—
254C3×Dic6—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6#4112yes—
258#627—81no—
259#627—81no—
260C3⋊(C3⋊C8)—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—91no—
265#556—31no—
266#489—91no—
267#489—91no—
268#487—91no—
269#476—91no—
270#475—91no—
271#475—91no—
272#464—91no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—31no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—21no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×D4—31no—
286C22×C3×C4—61no—
287C2×D12C22×D311yescharacteristic
288C2×C4×D3—21no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—121no—
296C2×Dic6#6711yescharacteristic
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C3×Q16—62no—
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—41no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C22⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C42—21no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—41no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331#216—22no—
332#216—62no—
333#216—62no—
334#215—62no—
335#214—62no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—121no—
354C4⋊Dic3#6711yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4#6711yescharacteristic
365Dic3⋊C4#6711yescharacteristic
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—61no—
369C4×Dic3—61no—
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—21no—
387C32×C4—21no—
388C32×C4—41no—
389C32×C4—41no—
390C32×C4C2×#4111yescharacteristic
391C32×C42−1+411yescharacteristic
392C3⋊Dic3—41no—
393C3⋊Dic3—41no—
394C3×Dic3—22no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13712yes—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—91no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411#126—61no—
412#126—61no—
413#124—31no—
414#124—31no—
415C22⋊Q8—61no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—181no—
422C4×Q8D3211yescharacteristic
423C4×D4—31no—
424#117—61no—
425#106—31no—
426#106—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—
441#97—31no—
442#97—91no—
443C4×C8—91no—
444C23×C3—61no—
445C22×D3—21no—
446C3×Q8—22no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—32no—
452C3×Q8—41no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×D4—61no—
458C3×D4—61no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—122no—
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4D3×D411yescharacteristic
478C2×C3×C4C2×#6711yescharacteristic
479C2×C3×C4C2×#6711yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481C2×C3×C4C23×D311yescharacteristic
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3C2×#6711yescharacteristic
492C2×Dic3C2×#6711yescharacteristic
493C2×Dic3C2×#6711yescharacteristic
494C2×Dic3C2×#6711yescharacteristic
495D12—21no—
496D12—21no—
497C4×D3—42no—
498Dic6—21no—
499Dic6—22no—
500Dic6—21no—
501Dic6—21no—
502Dic6—241no—
503Dic6—241no—
504Dic6—241no—
505Dic6—241no—
506Dic6—241no—
507Dic6—241no—
508Dic6—242no—
509Dic6#23512yes—
510C3×C8—61no—
511C3×C8—61no—
512C3⋊C8—21no—
513C3⋊C8—21no—
514C3⋊C8—61no—
515C3⋊C8—61no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—121no—
519C3⋊C8—121no—
520C2×C32#54811yescharacteristic
521C2×C32C2×#13711yescharacteristic
522C2×C32#57711yescharacteristic
523C3×D3—81no—
524C2×Q8—31no—
525C2×Q8—31no—
526C2×Q8—31no—
527C2×Q8—181no—
528C2×Q8—181no—
529C2×Q8—181no—
530C2×Q8C2×D3211yescharacteristic
531C2×D4—31no—
532C22×C4—61no—
533Q16—62no—
534Q16—182no—
535SD16—182no—
536C2×C8—31no—
537C2×C8—31no—
538C2×C8—91no—
539C2×C8—91no—
540C4⋊C4—21no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4C2×D3211yescharacteristic
557C22⋊C4—61no—
558C22⋊C4—61no—
559C22⋊C4—61no—
560C22⋊C4—61no—
561C22⋊C4—61no—
562C42—21no—
563C42—31no—
564C42—31no—
565C42—61no—
566C42—61no—
567C42—181no—
568C42—181no—
569C42C2×D3211yescharacteristic
570C22×C3—21no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C22×#6711yescharacteristic
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C3×C4—22no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—32no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—61no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—62no—
597C3×C4—81no—
598C3×C4—121no—
599C3×C4—121no—
600C3×C4C2×#23511yescharacteristic
601C3×C4D3×#4111yescharacteristic
602C3×C4#101011yescharacteristic
603C3×C4#101011yescharacteristic
604Dic3—22no—
605Dic3—21no—
606Dic3—21no—
607Dic3—21no—
608Dic3—41no—
609Dic3—41no—
610Dic3—121no—
611Dic3—121no—
612Dic3—121no—
613Dic3—121no—
614Dic3—241no—
615Dic3—241no—
616Dic3#95112yes—
617C32#336911yescharacteristic, complemented, Sylow
618C23—61no—
619Q8—21no—
620Q8—21no—
621Q8—32no—
622Q8—62no—
623Q8—61no—
624Q8—61no—
625Q8—61no—
626Q8—721no—
627Q8—721no—
628Q8—721no—
629D4—61no—
630D4—61no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—122no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C4D3×#6711yescharacteristic
644C2×C4D3×#6711yescharacteristic
645C2×C4C22×D3211yescharacteristic
646C8—61no—
647C8—61no—
648C8—181no—
649C8—181no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—241no—
654C2×C3#555211yescharacteristic
655C2×C3D3×#13711yescharacteristic
656C2×C3#577811yescharacteristic
657C2×C3C2×#95111yescharacteristic
658C2×C3#583111yescharacteristic
659C2×C3#583711yescharacteristic
660D3—81no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22C2×D3×#6711yescharacteristic
665C4—21no—
666C4—21no—
667C4—32no—
668C4—41no—
669C4—41no—
670C4—62no—
671C4—61no—
672C4—61no—
673C4—61no—
674C4—121no—
675C4—121no—
676C4—361no—
677C4—361no—
678C4#6429811yescharacteristic
679C4D3×#23511yescharacteristic
680C3—21no—
681C3#7981511yescharacteristic, complemented
682C3#8367711yescharacteristic, complemented
683C2—241no—
684C2#1059489911yescharacteristic
685C2#1059531911yescharacteristic
686C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4×Q8D32
hypocenterC32#3369
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
2. Dic62C2semidirect
3. #10592719C2semidirect
4. C3×#5030C2semidirect
6. #10591623C2semidirect
8. #10591574C2semidirect
10. #10590556C2semidirect
11. #10590477C2semidirect
15. #10590251C2semidirect
75. #5030D3semidirect
617. C32#3369semidirect
681. C3#79815semidirect
682. C3#83677semidirect

Maximal subgroups

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

subgroupindex
C3×#55682
Dic622
#105927192
C3×#50302
#105916242
#105916232
#105915782
#105915742
#105905582
#105905562
#105904772
#105904752
#105902762
#105902672
#105902512
#836773
#798153