Finite Group Databasebeta

← #11897637

Subgroups — #11897637

Order 1152.

734 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2#10593938C211yesmaximal, characteristic
3#10592786C211yesmaximal, characteristic
4C3×#5081C211yesmaximal, characteristic, complemented
5#10590557C211yesmaximal, characteristic, complemented
6#10590543C211yesmaximal, characteristic, complemented
7#10590466C211yesmaximal, characteristic
8#10590464C211yesmaximal, characteristic
9#10590458C211yesmaximal, characteristic
10#10590457C211yesmaximal, characteristic
11#10590421C211yesmaximal, characteristic, complemented
12#10590411C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic
14#10590286C211yesmaximal, characteristic, complemented
15#10590251C211yesmaximal, characteristic, complemented
16#83706—31nomaximal
17#81965—31nomaximal
18C32×C4⋊Q8C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C3×#944—21no—
21C3×#944—21no—
22C3×#888—21no—
23C3×#888C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887—21no—
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#870C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31#63918C2211yescharacteristic
32#63895—21no—
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35#63888—21no—
36#63883—21no—
37#63869C2211yescharacteristic
38#63865—21no—
39C2×#3717C2211yescharacteristic
40#63636C2211yescharacteristic
41#63636C2211yescharacteristic
42#63634C2211yescharacteristic
43#63634C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#808C2211yescharacteristic
46C3×#808C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×#803C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×Q82—31no—
62#5722D311yescharacteristic, complemented
63#5690—31no—
64#5579—31no—
65C3×#501—31no—
66#5087—31no—
67#5087—31no—
68#5087—31no—
69#5087—61no—
70#5084—31no—
71#5081—31no—
72#5081D311yescharacteristic, complemented
73#5078—31no—
74#5063—31no—
75#5026—31no—
76#5026—31no—
77C4×#215—31no—
78#5024—31no—
79#5022—31no—
80#5022—31no—
81#5021—31no—
82#4890—31no—
83#4889—31no—
84#4875—31no—
85#4874—31no—
86#4870—31no—
87#4857—31no—
88#4856—31no—
89#4852—31no—
90#4710—31no—
91#4701—31no—
92C2×C32×Q8—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#624—21no—
101C2×#624—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C42C2311yescharacteristic
106#3752—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×C4⋊Dic3D411yescharacteristic
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4D411yescharacteristic
122C3×Dic3⋊C4D411yescharacteristic
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135#3717Q814yescomplemented
136#3385—91noSylow
137C3×C4⋊Q8—21no—
138C3×C4⋊Q8—31no—
139C3×C4⋊Q8—31no—
140C3×C4⋊Q8—61no—
141C3×C4⋊Q8—61no—
142C3×C4⋊Q8—61no—
143C3×C4⋊Q8C2×D311yescharacteristic
144C3×C4⋊Q8C2×D311yescharacteristic
145C3×#125—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—61no—
151#946—61no—
152#944—21no—
153#944—21no—
154C2×#215—31no—
155C2×#204—31no—
156#897—61no—
157#896—61no—
158#896—61no—
159#896—61no—
160#896—61no—
161#893—31no—
162#893—31no—
163D3×C4⋊C4—61no—
164D3×C4⋊C4—61no—
165#890—31no—
166#888—21no—
167#888—31no—
168#888C2×D311yescharacteristic
169#888C2×D311yescharacteristic
170#887—21no—
171#887C2×D311yescharacteristic
172#887C2×D311yescharacteristic
173C4×D12—31no—
174C4×D12—31no—
175C4×D12—31no—
176C4×D12—31no—
177C4×D12—61no—
178#870—31no—
179#870C2×D311yescharacteristic
180#869—31no—
181C4×Dic6C2×D311yescharacteristic
182C4×Dic6C2×D311yescharacteristic
183C3×#107—31no—
184C3×#107—31no—
185C3×#106—31no—
186C3×#106—31no—
187C3×#97—31no—
188#835—31no—
189#835—31no—
190#835—31no—
191#821—31no—
192#818—31no—
193#816—31no—
194#815—31no—
195Dic3⋊C8—31no—
196Dic3⋊C8—31no—
197C8×Dic3—31no—
198#810—31no—
199#810—31no—
200#809—31no—
201#809—31no—
202#809—31no—
203#809—31no—
204#809—31no—
205#809—61no—
206#809—61no—
207#808—31no—
208#808—31no—
209#808C2×D311yescharacteristic
210#808C2×D311yescharacteristic
211#807—31no—
212#807—31no—
213#807—31no—
214#807—31no—
215#807—31no—
216#807—31no—
217#807—31no—
218#807—61no—
219#807—61no—
220#807C2×D311yescharacteristic
221#807C2×D311yescharacteristic
222C4⋊(C3⋊C8)—31no—
223C4⋊(C3⋊C8)—31no—
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—61no—
227#803—31no—
228#803C2×D311yescharacteristic
229C4×C3⋊C8—31no—
230C22×C3⋊D3—21no—
231C32×Q8—81no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C4⋊(C3⋊D3)—21no—
239C4⋊(C3⋊D3)C2×Q812yes—
240C4×C3⋊D3—81no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C3×Dic6—21no—
250C3×Dic6—22no—
251C3×Dic6—81no—
252C3×Dic6—81no—
253C3×Dic6C2×Q812yes—
254#627—81no—
255#624—42no—
256#624—81no—
257C3⋊(C3⋊C8)—21no—
258C3⋊(C3⋊C8)—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8C2×Q812yes—
261Q82—31no—
262#554—91no—
263#501—31no—
264#501—91no—
265#500—91no—
266#479—91no—
267#479—91no—
268#477—91no—
269#476—91no—
270#474—91no—
271#474—91no—
272#446—91no—
273#440—91no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—21no—
277C2×C3×Q8—21no—
278C2×C3×Q8—31no—
279C2×C3×Q8—31no—
280C2×C3×Q8—41no—
281C2×C3×Q8—61no—
282C2×C3×Q8—61no—
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—61no—
286C2×C4×D3—61no—
287C2×C4×D3—61no—
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—121no—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6#6711yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×C3×C8—31no—
300C2×C3×C8—31no—
301C3×C4⋊C4—21no—
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—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—41no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C42—21no—
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—61no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331#215—34no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—121no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3#6711yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4#6711yescharacteristic
360Dic3⋊C4#6711yescharacteristic
361C4×Dic3—21no—
362C4×Dic3—21no—
363C4×Dic3—21no—
364C4×Dic3C22×D311yescharacteristic
365C4×Dic3C22×D311yescharacteristic
366C2×C3⋊C8—31no—
367C2×C3⋊C8—31no—
368C2×C3⋊C8—31no—
369C2×C3⋊C8—31no—
370C2×C3⋊C8—61no—
371C2×C3⋊C8—61no—
372C2×C3⋊C8C22×D311yescharacteristic
373C2×C3⋊C8C22×D311yescharacteristic
374#204—34no—
375C22×C32C22×D411yescharacteristic
376C2×C3⋊D3—22no—
377C2×C3⋊D3—41no—
378C2×C3⋊D3—41no—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4C22×Q811yescharacteristic
384C32×C42−1+411yescharacteristic
385C3⋊Dic3—41no—
386C3×Dic3—22no—
387C3×Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3#13712yes—
394C2×SD16—91no—
395C4⋊Q8—31no—
396C4⋊Q8—31no—
397C4⋊Q8—61no—
398C4⋊Q8—61no—
399C4⋊Q8—61no—
400C4⋊Q8—91no—
401C4⋊Q8D3211yescharacteristic
402#125—31no—
403#125—91no—
404C22⋊Q8—181no—
405C22⋊Q8—181no—
406C22⋊Q8—181no—
407C4×Q8—31no—
408C4×Q8—31no—
409C4×Q8—31no—
410C4×Q8—31no—
411C4×Q8—61no—
412C4×D4—91no—
413C4×D4—91no—
414C4×D4—91no—
415C2×C4⋊C4—181no—
416#107—31no—
417#107—31no—
418#107—91no—
419#107—91no—
420#107—91no—
421#107—91no—
422#106—31no—
423#106—31no—
424#106—91no—
425C4⋊C8—91no—
426C4⋊C8—91no—
427C4⋊C8—91no—
428#103—91no—
429#103—91no—
430#103—91no—
431#102—91no—
432#102—91no—
433#102—91no—
434#97—31no—
435#97—91no—
436C4×C8—91no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—121no—
440C3×Q8—32no—
441C3×Q8—62no—
442C3×Q8—61no—
443C3×Q8—81no—
444C3×Q8—81no—
445C3×Q8—82no—
446C3×Q8—241no—
447C3×Q8—241no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4D3×D411yescharacteristic
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4C2×#6711yescharacteristic
468C2×C3×C4C2×#6711yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—121no—
478C2×Dic3C2×#6711yescharacteristic
479C2×Dic3C2×#6711yescharacteristic
480C2×Dic3C2×#6711yescharacteristic
481C2×Dic3C2×#6711yescharacteristic
482D12—32no—
483D12—32no—
484D12—62no—
485D12—61no—
486D12—61no—
487D12—121no—
488C4×D3—122no—
489C4×D3—122no—
490C4×D3—241no—
491C4×D3—241no—
492C4×D3—241no—
493C4×D3—241no—
494C4×D3—242no—
495Dic6—21no—
496Dic6—22no—
497Dic6—81no—
498Dic6—81no—
499Dic6—241no—
500Dic6—241no—
501Dic6D3×Q812yes—
502C3×C8—32no—
503C3×C8—61no—
504C3⋊C8—21no—
505C3⋊C8—61no—
506C3⋊C8—61no—
507C3⋊C8—61no—
508C3⋊C8—61no—
509C3⋊C8—121no—
510C3⋊C8—121no—
511C3⋊C8D3×Q812yes—
512C2×C32D4×Q811yescharacteristic
513C2×C32C2×#13711yescharacteristic
514C2×C32#57611yescharacteristic
515C3⋊D3—42no—
516C2×Q8—21no—
517C2×Q8—31no—
518C2×Q8—31no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—181no—
522C2×D4—91no—
523C22×C4—181no—
524C22×C4—181no—
525C22×C4—181no—
526SD16—94no—
527C2×C8—31no—
528C2×C8—31no—
529C2×C8—91no—
530C2×C8—91no—
531C4⋊C4—21no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—91no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4C2×D3211yescharacteristic
550C4⋊C4C2×D3211yescharacteristic
551C22⋊C4—181no—
552C22⋊C4—181no—
553C22⋊C4—181no—
554C42—31no—
555C42—31no—
556C42—61no—
557C42—61no—
558C42—61no—
559C42C2×D3211yescharacteristic
560C22×C3—21no—
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C22×#6711yescharacteristic
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—122no—
566C2×D3—121no—
567C2×D3—121no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—241no—
571C2×D3—241no—
572C3×C4—22no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—32no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—62no—
586C3×C4—61no—
587C3×C4—61no—
588C3×C4—61no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4C2×D3×Q811yescharacteristic
595C3×C4C2×D3×Q811yescharacteristic
596C3×C4#100711yescharacteristic
597C3×C4#100711yescharacteristic
598Dic3—21no—
599Dic3—22no—
600Dic3—21no—
601Dic3—21no—
602Dic3—41no—
603Dic3—41no—
604Dic3—41no—
605Dic3—121no—
606Dic3—121no—
607Dic3—241no—
608Dic3#94212yes—
609C32#338511yescharacteristic, complemented, Sylow
610C23—181no—
611Q8—32no—
612Q8—62no—
613Q8—61no—
614Q8—81no—
615Q8—241no—
616Q8—241no—
617Q8—721no—
618D4—92no—
619D4—181no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—181no—
631C2×C4—362no—
632C2×C4—721no—
633C2×C4—721no—
634C2×C4D3×#6711yescharacteristic
635C2×C4D3×#6711yescharacteristic
636C2×C4C22×D3211yescharacteristic
637C8—32no—
638C8—61no—
639C8—181no—
640C8—181no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3#572711yescharacteristic
645C2×C3#577411yescharacteristic
646C2×C3D3×#13711yescharacteristic
647C2×C3C2×#94211yescharacteristic
648C2×C3Q8×#6711yescharacteristic
649C2×C3#583511yescharacteristic
650D3—122no—
651D3—122no—
652D3—242no—
653C22—182no—
654C22—361no—
655C22—361no—
656C22C2×D3×#6711yescharacteristic
657C4—21no—
658C4—21no—
659C4—32no—
660C4—41no—
661C4—41no—
662C4—61no—
663C4—61no—
664C4—62no—
665C4—61no—
666C4—121no—
667C4—121no—
668C4—121no—
669C4—361no—
670C4#6431611yescharacteristic
671C4D32×Q811yescharacteristic
672C3—21no—
673C3#8196511yescharacteristic, complemented
674C3#8370611yescharacteristic, complemented
675C2—362no—
676C2#1059509711yescharacteristic
677C2D3×#94211yescharacteristic
678C2#1059540311yescharacteristic
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#3385
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×#5722C2semidirect
4. C3×#5081C2semidirect
5. #10590557C2semidirect
6. #10590543C2semidirect
11. #10590421C2semidirect
12. #10590411C2semidirect
14. #10590286C2semidirect
15. #10590251C2semidirect
62. #5722D3semidirect
72. #5081D3semidirect
135. #3717Q8semidirect
609. C32#3385semidirect
673. C3#81965semidirect
674. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
#105939382
#105927862
C3×#50812
#105905572
#105905432
#105904662
#105904642
#105904582
#105904572
#105904212
#105904112
#105903622
#105902862
#105902512
#837063
#819653