Finite Group Databasebeta

← #11897645

Subgroups — #11897645

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 675 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593929C211yesmaximal, characteristic
3#10592721C211yesmaximal, characteristic, complemented
4C3×#5026C211yesmaximal, characteristic
5#10591566C211yesmaximal, characteristic
6Dic3×#215C211yesmaximal, characteristic
7#10591546C211yesmaximal, characteristic, complemented
8#10591545C211yesmaximal, characteristic, complemented
9#10590465C211yesmaximal, characteristic
10#10590463C211yesmaximal, characteristic
11#10590420C211yesmaximal, characteristic, complemented
12#10590411C211yesmaximal, characteristic, complemented
13#10590305C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic
15#10590251C211yesmaximal, characteristic, complemented
16#83706—31nomaximal
17#79759—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19#64079C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#215C2211yescharacteristic
23C3×#888—21no—
24C3×#888—21no—
25C3×#888C2211yescharacteristic
26C3×#888C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×#869—21no—
29C3×#869C2211yescharacteristic
30C3×C4×Dic6—21no—
31C3×C4×Dic6C2211yescharacteristic
32#63918C2211yescharacteristic
33#63899—21no—
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63887—21no—
37D3×Dic3⋊C4—21no—
38#63869C2211yescharacteristic
39#63851—21no—
40#63662C2211yescharacteristic
41#63662C2211yescharacteristic
42#63635C2211yescharacteristic
43#63634C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×#803C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×Q82—31no—
62#5579—31no—
63Q8×Dic6D311yescharacteristic, complemented
64#5539—31no—
65C3×#440—31no—
66#5164—31no—
67Dic3×SD16—31no—
68#5087—31no—
69#5087—31no—
70#5084—31no—
71#5081—31no—
72#5081—31no—
73#5078—31no—
74#5026—31no—
75#5026D311yescharacteristic
76C4×#215—31no—
77#5024—31no—
78#5022—31no—
79#5022—31no—
80#5022—31no—
81#5022—61no—
82#5021—31no—
83#5007—31no—
84#4876—31no—
85#4874—31no—
86#4799—31no—
87#4793—31no—
88#4761—31no—
89#4759—31no—
90#4702—31no—
91#4701—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6D411yescharacteristic
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C42—21no—
105C32×C42C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#215Q814yescomplemented
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4D411yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
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(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3385—91noSylow
137C2×C3×SD16—31no—
138C3×C4⋊Q8—31no—
139C3×C4⋊Q8—31no—
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—61no—
142C3×C4⋊Q8—61no—
143C3×C4⋊Q8—61no—
144C3×C4×Q8—21no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—61no—
149C3×C4×Q8C2×D311yescharacteristic
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×D4—31no—
152#946—61no—
153Q8×Dic3C2×D311yescharacteristic
154Q8×Dic3C2×D311yescharacteristic
155C2×#215C2×D311yescharacteristic
156D4×Dic3—31no—
157D4×Dic3—31no—
158#924—61no—
159C2×Dic3⋊C4—61no—
160#896—61no—
161#896—61no—
162D3×C4⋊C4—61no—
163#890—31no—
164#888—21no—
165#888—21no—
166#888—31no—
167#888C2×D311yescharacteristic
168#888C2×D311yescharacteristic
169#878—61no—
170#878—61no—
171C4×D12—31no—
172C4×D12—31no—
173C4×D12C2×D311yescharacteristic
174#870—31no—
175#870—31no—
176#870—31no—
177#870—61no—
178#869—21no—
179#869—31no—
180#869C2×D311yescharacteristic
181C4×Dic6—21no—
182C4×Dic6C2×D311yescharacteristic
183C3×#107—31no—
184C3×#103—31no—
185C3×#102—31no—
186C3×#97—31no—
187#835—31no—
188#835—31no—
189#835—31no—
190#835—31no—
191#835—61no—
192#835—61no—
193#835C2×D311yescharacteristic
194#832—31no—
195#832—31no—
196#818—31no—
197#818—31no—
198#817—31no—
199#817—31no—
200#815—31no—
201Dic3⋊C8—31no—
202Dic3⋊C8—31no—
203C8×Dic3—31no—
204#809—31no—
205#809—31no—
206#809C2×D311yescharacteristic
207#808—31no—
208#808—31no—
209#808—31no—
210#808—31no—
211#808—61no—
212#807—31no—
213#807—31no—
214#807—31no—
215#807—31no—
216#807—31no—
217#807—31no—
218#807—31no—
219#807—31no—
220#807—61no—
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—21no—
232C32×Q8C2×Q812yes—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3C2×D411yescharacteristic
244C2×C3×Dic3C2×D411yescharacteristic
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C3×D12—21no—
248C3×D12C2×Q812yes—
249C3×C4×D3—81no—
250C3×Dic6—22no—
251C3×Dic6—81no—
252C3×Dic6—81no—
253C3×Dic6—81no—
254#627—81no—
255D3×Dic3—42no—
256D3×Dic3—81no—
257C3⋊(C3⋊C8)—21no—
258C3⋊(C3⋊C8)—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8C2×Q812yes—
261Q82—31no—
262#554—91no—
263#501—91no—
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—31no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—21no—
277C2×C3×Q8—31no—
278C2×C3×Q8—61no—
279C2×C3×Q8—61no—
280C2×C3×Q8—61no—
281C2×C3×Q8C22×D311yescharacteristic
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C2×D12C22×D311yescharacteristic
288C2×C4×D3—21no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6#6711yescharacteristic
297C3×SD16—34no—
298C2×C3×C8—31no—
299C2×C3×C8—31no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
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⋊C4—61no—
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C22⋊C4—61no—
318C3×C42—21no—
319C3×C42—21no—
320C3×C42—21no—
321C3×C42—31no—
322C3×C42—31no—
323C3×C42—41no—
324C3×C42—61no—
325C3×C42—61no—
326C3×C42C22×D311yescharacteristic
327C3×C42C22×D311yescharacteristic
328#217—61no—
329#217—61no—
330#215Dic614yescomplemented
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3#6711yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—121no—
360Dic3⋊C4—121no—
361Dic3⋊C4#6711yescharacteristic
362Dic3⋊C4#6711yescharacteristic
363C4×Dic3—21no—
364C4×Dic3—21no—
365C4×Dic3C22×D311yescharacteristic
366C4×Dic3C22×D311yescharacteristic
367C2×C3⋊C8—31no—
368C2×C3⋊C8—31no—
369C2×C3⋊C8—31no—
370C2×C3⋊C8—31no—
371C2×C3⋊C8—61no—
372C2×C3⋊C8—61no—
373C2×C3⋊C8C22×D311yescharacteristic
374C2×C3⋊C8C22×D311yescharacteristic
375C22×C32C22×D411yescharacteristic
376C2×C3×D3—22no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C32×C4—22no—
380C32×C4—21no—
381C32×C4—21no—
382C32×C4—41no—
383C32×C4C22×Q811yescharacteristic
384C32×C42−1+411yescharacteristic
385C3⋊Dic3—41no—
386C3⋊Dic3—41no—
387C3×Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3#13712yes—
394C2×SD16—31no—
395C4⋊Q8—31no—
396C4⋊Q8—31no—
397C4⋊Q8—31no—
398C4⋊Q8—61no—
399C4⋊Q8—61no—
400C4⋊Q8—61no—
401C4⋊Q8—91no—
402#125—91no—
403#125—91no—
404C22⋊Q8—181no—
405C22⋊Q8—181no—
406C22⋊Q8—181no—
407C4×Q8—31no—
408C4×Q8—31no—
409C4×Q8—31no—
410C4×Q8—61no—
411C4×Q8D3211yescharacteristic
412C4×D4—31no—
413C4×D4—91no—
414C4×D4—91no—
415C2×C4⋊C4—181no—
416#107—31no—
417#107—91no—
418#107—91no—
419#107—91no—
420#107—91no—
421#107—91no—
422#106—91no—
423#106—91no—
424#106—91no—
425C4⋊C8—91no—
426C4⋊C8—91no—
427C4⋊C8—91no—
428#103—31no—
429#103—91no—
430#103—91no—
431#102—31no—
432#102—91no—
433#102—91no—
434#97—31no—
435#97—91no—
436C4×C8—91no—
437C23×C3—61no—
438C22×D3—21no—
439C3×Q8—21no—
440C3×Q8—21no—
441C3×Q8—22no—
442C3×Q8—41no—
443C3×Q8—62no—
444C3×Q8—241no—
445C3×Q8—241no—
446C3×Q8—241no—
447C3×Q8C2×Dic612yes—
448C3×Q8D3×Q812yes—
449C3×D4—32no—
450C3×D4—61no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—241no—
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4D3×D411yescharacteristic
470C2×C3×C4C2×#6711yescharacteristic
471C2×C3×C4C2×#6711yescharacteristic
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—122no—
484C2×Dic3—241no—
485C2×Dic3C2×#6711yescharacteristic
486C2×Dic3C2×#6711yescharacteristic
487C2×Dic3C2×#6711yescharacteristic
488C2×Dic3C2×#6711yescharacteristic
489D12—21no—
490D12C2×Dic612yes—
491C4×D3—81no—
492C4×D3—122no—
493C4×D3—241no—
494Dic6—22no—
495Dic6—81no—
496Dic6—81no—
497Dic6—81no—
498Dic6—241no—
499Dic6—241no—
500C3×C8—32no—
501C3×C8—61no—
502C3⋊C8—21no—
503C3⋊C8—61no—
504C3⋊C8—61no—
505C3⋊C8—61no—
506C3⋊C8—61no—
507C3⋊C8—121no—
508C3⋊C8—121no—
509C3⋊C8C2×Dic612yes—
510C2×C32D4×Q811yescharacteristic
511C2×C32C2×#13711yescharacteristic
512C2×C32#57611yescharacteristic
513C3×D3—42no—
514C2×Q8—31no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—181no—
519C2×Q8C2×D3211yescharacteristic
520C2×D4—31no—
521C22×C4—61no—
522C22×C4—181no—
523C22×C4—181no—
524SD16—34no—
525C2×C8—31no—
526C2×C8—31no—
527C2×C8—91no—
528C2×C8—91no—
529C4⋊C4—21no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4C2×D3211yescharacteristic
549C22⋊C4—61no—
550C22⋊C4—181no—
551C22⋊C4—181no—
552C42—21no—
553C42—31no—
554C42—31no—
555C42—61no—
556C42—61no—
557C42C2×D3211yescharacteristic
558C22×C3—21no—
559C22×C3—62no—
560C22×C3—121no—
561C22×C3—121no—
562C22×C3C2×D3×D411yescharacteristic
563C22×C3C22×#6711yescharacteristic
564C2×D3—22no—
565C2×D3—41no—
566C2×D3—41no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—22no—
570C3×C4—21no—
571C3×C4—22no—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—32no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—42no—
579C3×C4—41no—
580C3×C4—41no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—61no—
584C3×C4—81no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4C22×Dic611yescharacteristic
589C3×C4C2×D3×Q811yescharacteristic
590C3×C4#100711yescharacteristic
591C3×C4#101011yescharacteristic
592Dic3—21no—
593Dic3—21no—
594Dic3—21no—
595Dic3—41no—
596Dic3—41no—
597Dic3—41no—
598Dic3—121no—
599Dic3—121no—
600Dic3—121no—
601Dic3—121no—
602Dic3—241no—
603Dic3—241no—
604Dic3#94212yes—
605C32#338511yescharacteristic, complemented, Sylow
606C23—61no—
607Q8—21no—
608Q8—62no—
609Q8—241no—
610Q8—241no—
611Q8—241no—
612Q8—721no—
613Q8D3×Dic612yes—
614D4—32no—
615D4—61no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—31no—
619C2×C4—31no—
620C2×C4—31no—
621C2×C4—31no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—241no—
628C2×C4—362no—
629C2×C4—721no—
630C2×C4D3×#6711yescharacteristic
631C2×C4D3×#6711yescharacteristic
632C2×C4C22×D3211yescharacteristic
633C8—32no—
634C8—61no—
635C8—181no—
636C8—181no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—122no—
641C2×C3D4×Dic611yescharacteristic
642C2×C3#577411yescharacteristic
643C2×C3D3×#13711yescharacteristic
644C2×C3C2×#94211yescharacteristic
645C2×C3Q8×#6711yescharacteristic
646C2×C3#583511yescharacteristic
647D3—42no—
648C22—62no—
649C22—121no—
650C22—121no—
651C22C2×D3×#6711yescharacteristic
652C4—22no—
653C4—21no—
654C4—21no—
655C4—32no—
656C4—41no—
657C4—61no—
658C4—61no—
659C4—61no—
660C4—121no—
661C4—121no—
662C4—121no—
663C4—361no—
664C4—361no—
665C4C2×D3×Dic611yescharacteristic
666C4#6429711yescharacteristic
667C3—21no—
668C3#7975911yescharacteristic, complemented
669C3#8370611yescharacteristic, complemented
670C2—122no—
671C2Dic6×#6711yescharacteristic
672C2D3×#94211yescharacteristic
673C2#1059545411yescharacteristic
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#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×Q8×Dic6C2semidirect
3. #10592721C2semidirect
7. #10591546C2semidirect
8. #10591545C2semidirect
11. #10590420C2semidirect
12. #10590411C2semidirect
13. #10590305C2semidirect
15. #10590251C2semidirect
63. Q8×Dic6D3semidirect
112. C3×#215Q8semidirect
330. #215Dic6semidirect
605. C32#3385semidirect
668. C3#79759semidirect
669. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105939292
#105927212
C3×#50262
#105915662
Dic3×#2152
#105915462
#105915452
#105904652
#105904632
#105904202
#105904112
#105903052
#105902692
#105902512
#837063
#797593