Finite Group Databasebeta

← #11897648

Subgroups — #11897648

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593929C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592401C211yesmaximal, characteristic, complemented
4C3×#4710C211yesmaximal, characteristic
5C3×#4701C211yesmaximal, characteristic, complemented
6#10590894C211yesmaximal, characteristic, complemented
7#10590891C211yesmaximal, characteristic, complemented
8#10590815C211yesmaximal, characteristic, complemented
9#10590804C211yesmaximal, characteristic, complemented
10#10590766C211yesmaximal, characteristic
11#10590762C211yesmaximal, characteristic
12#10590757C211yesmaximal, characteristic
13Dic3×#204C211yesmaximal, characteristic
14#10590302C211yesmaximal, characteristic, complemented
15#10590272C211yesmaximal, characteristic
16#79976—31nomaximal
17#79759—31nomaximal
18#64079C2211yescharacteristic
19#64078C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63918—21no—
25#63918C2211yescharacteristic
26#63918C2211yescharacteristic
27#63918C2211yescharacteristic
28#63899—21no—
29Dic3×D12C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31#63887—21no—
32D3×Dic3⋊C4—21no—
33#63869C2211yescharacteristic
34#63851—21no—
35Dic3×Dic6—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63840—21no—
39#63840—21no—
40C32×#97C2211yescharacteristic
41#63645C2211yescharacteristic
42#63645C2211yescharacteristic
43#63644C2211yescharacteristic
44#63644C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#815C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5579—31no—
62Q8×Dic6—31no—
63Q8×Dic6—31no—
64#5539—31no—
65C3×#446—31no—
66C3×#440—31no—
67#5164—31no—
68Dic3×SD16—31no—
69#5022—31no—
70#5007—31no—
71#4876—31no—
72#4874—31no—
73#4850—31no—
74#4846—31no—
75#4846—31no—
76#4842—31no—
77#4829—31no—
78#4829—31no—
79#4799—31no—
80#4793—31no—
81#4761—31no—
82#4759—31no—
83#4710—31no—
84#4710D311yescharacteristic
85#4702—31no—
86#4702—31no—
87#4702—31no—
88#4702—61no—
89#4701D311yescharacteristic, complemented
90C4×#204—31no—
91#4682—31no—
92C2×#634—21no—
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6D411yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627—21no—
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4D411yescharacteristic
118C3×Dic3⋊C4D411yescharacteristic
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×#204Q814yescomplemented
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3385—91noSylow
137C2×C3×SD16—31no—
138C3×C4×Q8—31no—
139C3×C4×Q8—31no—
140C3×C4×D4—31no—
141#946—61no—
142Q8×Dic3—31no—
143Q8×Dic3—31no—
144Q8×Dic3—61no—
145D4×Dic3—31no—
146D4×Dic3—31no—
147#924—61no—
148C2×Dic3⋊C4—61no—
149C2×#204C2×D311yescharacteristic
150#896—61no—
151#896—61no—
152D3×C4⋊C4—61no—
153#890—31no—
154#888—31no—
155#888—31no—
156#888—31no—
157#888—61no—
158#888—61no—
159#888—61no—
160#888—61no—
161#888—61no—
162#878—61no—
163#878—61no—
164C4×D12—31no—
165C4×D12—31no—
166C4×D12C2×D311yescharacteristic
167#870—31no—
168#870—31no—
169#870—31no—
170#870—61no—
171#869—31no—
172#869—31no—
173#869—31no—
174#869—31no—
175#869—31no—
176#869—61no—
177#869—61no—
178C4×Dic6—31no—
179C4×Dic6—31no—
180C4×Dic6—61no—
181C4×Dic6C2×D311yescharacteristic
182C4×Dic6C2×D311yescharacteristic
183C3×#107—31no—
184C3×C4⋊C8—31no—
185C3×C4⋊C8—31no—
186C3×C4⋊C8—31no—
187C3×#103—31no—
188C3×#102—31no—
189C3×#97—21no—
190C3×#97—31no—
191C3×#97C2×D311yescharacteristic
192C3×#97C2×D311yescharacteristic
193C3×C4×C8—31no—
194#835—31no—
195#835—31no—
196#832—31no—
197#832—31no—
198#821—31no—
199#821—31no—
200#821C2×D311yescharacteristic
201#818—31no—
202#818—31no—
203#818—31no—
204#818—31no—
205#818—31no—
206#818—31no—
207#818—31no—
208#818—61no—
209#818—61no—
210#818C2×D311yescharacteristic
211#817—31no—
212#817—31no—
213#817—31no—
214#817—31no—
215#817—31no—
216#817—61no—
217#817—61no—
218#816—31no—
219#816—31no—
220#816C2×D311yescharacteristic
221#815C2×D311yescharacteristic
222Dic3⋊C8C2×D311yescharacteristic
223Dic3⋊C8C2×D311yescharacteristic
224C8×Dic3C2×D311yescharacteristic
225#808—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)C2×D311yescharacteristic
230C22×C3×D3—21no—
231C2×C32×C4C2×D411yescharacteristic
232C2×C32×C4C2×D411yescharacteristic
233C2×C32×C4C2411yescharacteristic
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238#634—81no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3C2×D411yescharacteristic
243C2×C3×Dic3C2×D411yescharacteristic
244C2×C3×Dic3C2×D411yescharacteristic
245C2×C3×Dic3C2×D411yescharacteristic
246C3×D12—21no—
247C3×D12C2×Q812yes—
248C3×C4×D3—81no—
249C3×Dic6—21no—
250C3×Dic6—22no—
251C3×Dic6C2×Q812yes—
252#627—81no—
253#627—81no—
254#627—81no—
255D3×Dic3—42no—
256D3×Dic3—81no—
257C32×C8—21no—
258C32×C8C2×Q812yes—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
261Q82—91no—
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—31no—
273#440—31no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—31no—
277C2×C3×Q8—31no—
278C2×C3×D4—31no—
279C22×C3×C4—61no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C2×D12C22×D311yescharacteristic
283C2×C4×D3—21no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×Dic6—61no—
287C2×Dic6—61no—
288C2×Dic6—61no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—121no—
295C2×Dic6D1211yescharacteristic
296C2×Dic6C22×D311yescharacteristic
297C3×SD16—34no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C2×C3×C8C22×D311yescharacteristic
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C22⋊C4—61no—
313C3×C42—21no—
314C3×C42—31no—
315C3×C42—31no—
316C3×C42—61no—
317C3×C42C22×D311yescharacteristic
318C3×C42C22×D311yescharacteristic
319#217—61no—
320#217—61no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324C4⋊Dic3—31no—
325C4⋊Dic3—31no—
326C4⋊Dic3—31no—
327C4⋊Dic3—31no—
328C4⋊Dic3—31no—
329C4⋊Dic3—31no—
330C4⋊Dic3—31no—
331C4⋊Dic3—31no—
332C4⋊Dic3—61no—
333C4⋊Dic3—61no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—121no—
345C4⋊Dic3D1211yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
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—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—121no—
362Dic3⋊C4—121no—
363Dic3⋊C4D1211yescharacteristic
364Dic3⋊C4D1211yescharacteristic
365C4×Dic3—21no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3C22×D311yescharacteristic
371C4×Dic3C22×D311yescharacteristic
372C2×C3⋊C8C22×D311yescharacteristic
373C2×C3⋊C8C22×D311yescharacteristic
374#204Dic614yescomplemented
375C22×C32C22×D411yescharacteristic
376C2×C3×D3—22no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4C22×Q811yescharacteristic
382C32×C42−1+411yescharacteristic
383C3⋊Dic3—41no—
384C3⋊Dic3—41no—
385C3⋊Dic3—41no—
386C3⋊Dic3—41no—
387C3×Dic3—22no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—21no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3#13712yes—
394C2×SD16—31no—
395C4⋊Q8—91no—
396C4⋊Q8—91no—
397C4⋊Q8—91no—
398C4⋊Q8—91no—
399C4⋊Q8—181no—
400C4⋊Q8—181no—
401C4⋊Q8—181no—
402#125—91no—
403#125—91no—
404C22⋊Q8—181no—
405C22⋊Q8—181no—
406C22⋊Q8—181no—
407C4×Q8—31no—
408C4×Q8—31no—
409C4×Q8—91no—
410C4×Q8—91no—
411C4×Q8—181no—
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—31no—
426C4⋊C8—31no—
427C4⋊C8—31no—
428#103—31no—
429#103—91no—
430#103—91no—
431#102—31no—
432#102—91no—
433#102—91no—
434#97—31no—
435#97D3211yescharacteristic
436C4×C8—31no—
437C23×C3—61no—
438C22×D3—21no—
439C3×Q8—32no—
440C3×Q8—62no—
441C3×Q8—61no—
442C3×D4—32no—
443C3×D4—61no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—241no—
455C2×C3×C4C2×D1211yescharacteristic
456C2×C3×C4C2×D1211yescharacteristic
457C2×C3×C4D3×D411yescharacteristic
458C2×C3×C4D3×D411yescharacteristic
459C2×C3×C4C23×D311yescharacteristic
460C2×C3×C4C23×D311yescharacteristic
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—121no—
473C2×Dic3—121no—
474C2×Dic3—121no—
475C2×Dic3—121no—
476C2×Dic3—122no—
477C2×Dic3—241no—
478C2×Dic3C2×D1211yescharacteristic
479C2×Dic3C2×D1211yescharacteristic
480C2×Dic3C2×D1211yescharacteristic
481C2×Dic3C2×D1211yescharacteristic
482D12—21no—
483D12C2×Dic612yes—
484C4×D3—81no—
485C4×D3—122no—
486C4×D3—241no—
487Dic6—21no—
488Dic6—22no—
489Dic6—241no—
490Dic6—241no—
491Dic6—241no—
492Dic6—241no—
493Dic6—241no—
494Dic6—241no—
495Dic6—241no—
496Dic6—241no—
497Dic6—242no—
498Dic6C2×Dic612yes—
499C3×C8—22no—
500C3×C8—21no—
501C3×C8—21no—
502C3×C8—22no—
503C3×C8—61no—
504C3×C8—61no—
505C3×C8C2×Dic612yes—
506C3×C8D3×Q812yes—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C2×C32D4×Q811yescharacteristic
510C2×C32C2×#13711yescharacteristic
511C2×C32#57611yescharacteristic
512C3×D3—42no—
513C2×Q8—31no—
514C2×Q8—31no—
515C2×Q8—181no—
516C2×Q8—181no—
517C2×Q8—181no—
518C2×Q8—181no—
519C2×D4—31no—
520C22×C4—61no—
521C22×C4—181no—
522C22×C4—181no—
523SD16—34no—
524C2×C8—31no—
525C2×C8—31no—
526C2×C8C2×D3211yescharacteristic
527C2×C8C2×D3211yescharacteristic
528C4⋊C4—31no—
529C4⋊C4—31no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—61no—
534C4⋊C4—91no—
535C4⋊C4—91no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—181no—
539C4⋊C4—181no—
540C4⋊C4—181no—
541C4⋊C4—181no—
542C4⋊C4—181no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C22⋊C4—61no—
549C22⋊C4—181no—
550C22⋊C4—181no—
551C42—31no—
552C42—31no—
553C42—61no—
554C42—181no—
555C42—181no—
556C42C2×D3211yescharacteristic
557C22×C3—21no—
558C22×C3—62no—
559C22×C3—121no—
560C22×C3—121no—
561C22×C3C22×D1211yescharacteristic
562C22×C3C2×D3×D411yescharacteristic
563C2×D3—22no—
564C2×D3—41no—
565C2×D3—41no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—32no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—61no—
576C3×C4—61no—
577C3×C4—61no—
578C3×C4—62no—
579C3×C4—121no—
580C3×C4—121no—
581C3×C4C22×Dic611yescharacteristic
582C3×C4C2×D3×Q811yescharacteristic
583C3×C4#101011yescharacteristic
584C3×C4#101011yescharacteristic
585Dic3—21no—
586Dic3—21no—
587Dic3—21no—
588Dic3—22no—
589Dic3—41no—
590Dic3—41no—
591Dic3—121no—
592Dic3—121no—
593Dic3—121no—
594Dic3—121no—
595Dic3—121no—
596Dic3—121no—
597Dic3—121no—
598Dic3—121no—
599Dic3—241no—
600Dic3—241no—
601Dic3—241no—
602Dic3—241no—
603Dic3#90912yes—
604C32#338511yescharacteristic, complemented, Sylow
605C23—61no—
606Q8—32no—
607Q8—62no—
608Q8—61no—
609Q8—721no—
610Q8—721no—
611Q8—721no—
612Q8—721no—
613D4—32no—
614D4—61no—
615C2×C4—31no—
616C2×C4—31no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—181no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—241no—
627C2×C4—362no—
628C2×C4—721no—
629C2×C4D3×D1211yescharacteristic
630C2×C4D3×D1211yescharacteristic
631C2×C4C22×D3211yescharacteristic
632C8—21no—
633C8—61no—
634C8—61no—
635C8D3×Dic612yes—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—122no—
640C2×C3D4×Dic611yescharacteristic
641C2×C3Q8×D1211yescharacteristic
642C2×C3C2×#90911yescharacteristic
643C2×C3#575211yescharacteristic
644C2×C3#577411yescharacteristic
645C2×C3D3×#13711yescharacteristic
646D3—42no—
647C22—62no—
648C22—121no—
649C22—121no—
650C22C2×D3×D1211yescharacteristic
651C4—21no—
652C4—21no—
653C4—32no—
654C4—62no—
655C4—61no—
656C4—61no—
657C4—61no—
658C4—121no—
659C4—121no—
660C4—361no—
661C4—361no—
662C4—361no—
663C4—361no—
664C4C2×D3×Dic611yescharacteristic
665C4#6429811yescharacteristic
666C3—21no—
667C3#7975911yescharacteristic, complemented
668C3#7997611yescharacteristic, complemented
669C2—122no—
670C2Dic6×D1211yescharacteristic
671C2D3×#90911yescharacteristic
672C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenter#97D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
3. #10592401C2semidirect
5. C3×#4701C2semidirect
6. #10590894C2semidirect
7. #10590891C2semidirect
8. #10590815C2semidirect
9. #10590804C2semidirect
14. #10590302C2semidirect
89. #4701D3semidirect
124. C3×#204Q8semidirect
374. #204Dic6semidirect
604. C32#3385semidirect
667. C3#79759semidirect
668. C3#79976semidirect

Maximal subgroups

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

subgroupindex
#105939292
Dic622
#105924012
C3×#47102
C3×#47012
#105908942
#105908912
#105908152
#105908042
#105907662
#105907622
#105907572
Dic3×#2042
#105903022
#105902722
#799763
#797593