Finite Group Databasebeta

← #11897642

Subgroups — #11897642

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
1#10593929C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592528C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic
5C3×#4828C211yesmaximal, characteristic, complemented
6#10590894C211yesmaximal, characteristic, complemented
7#10590891C211yesmaximal, characteristic, complemented
8#10590814C211yesmaximal, characteristic, complemented
9#10590805C211yesmaximal, characteristic, complemented
10#10590762C211yesmaximal, characteristic
11#10590757C211yesmaximal, characteristic
12#10590747C211yesmaximal, characteristic
13#10590744C211yesmaximal, characteristic
14#10590360C211yesmaximal, characteristic
15#10590305C211yesmaximal, characteristic, complemented
16#80960—31nomaximal
17#79976—31nomaximal
18#64079C2211yescharacteristic
19C4×#634C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63919—21no—
24#63918C2211yescharacteristic
25#63918C2211yescharacteristic
26#63918C2211yescharacteristic
27#63899—21no—
28Dic3×D12C2211yescharacteristic
29Dic3×D12C2211yescharacteristic
30#63887—21no—
31D3×Dic3⋊C4—21no—
32#63869C2211yescharacteristic
33#63851—21no—
34#63844C2211yescharacteristic
35#63844C2211yescharacteristic
36#63843—21no—
37#63839—21no—
38#63839—21no—
39C2×#3716C2211yescharacteristic
40C32×C4⋊C8C2211yescharacteristic
41#63645C2211yescharacteristic
42#63644C2211yescharacteristic
43#63643C2211yescharacteristic
44#63643C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#818C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#815C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63575C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63573C2211yescharacteristic
59#63567C2211yescharacteristic
60#63563C2211yescharacteristic
61#5722—31no—
62#5579—31no—
63Q8×Dic6—31no—
64#5539—31no—
65C3×#474—31no—
66C3×#446—31no—
67#5081—31no—
68#5018—31no—
69#4877—31no—
70#4876—31no—
71#4875—31no—
72#4874—31no—
73#4850—31no—
74#4846—31no—
75#4846D311yescharacteristic
76#4842—31no—
77#4829—31no—
78#4829—31no—
79#4829—31no—
80#4829—61no—
81#4828D311yescharacteristic, complemented
82#4761—31no—
83#4759—31no—
84#4758—31no—
85#4757—31no—
86#4710—31no—
87#4710—31no—
88#4702—31no—
89#4702—31no—
90C4×#204—31no—
91#4682—31no—
92C2×#634C2311yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6D411yescharacteristic
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)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4D411yescharacteristic
119C3×Dic3⋊C4D411yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125#3724—21no—
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135#3716Q814yescomplemented
136#3385—91noSylow
137C3×C4⋊Q8—31no—
138C3×C4×Q8—31no—
139C3×C4×D4—31no—
140#946—61no—
141Q8×Dic3—61no—
142#944—61no—
143#944—61no—
144D4×Dic3—31no—
145D4×Dic3—31no—
146C2×#214—31no—
147#924—61no—
148C2×Dic3⋊C4—61no—
149C2×#204—31no—
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#887—31no—
162#887—31no—
163#887—61no—
164#878—61no—
165#878—61no—
166C4×D12—31no—
167C4×D12—31no—
168C4×D12C2×D311yescharacteristic
169#870—31no—
170#870—31no—
171#870—31no—
172#870—61no—
173#869—31no—
174#869—31no—
175#869—31no—
176#869C2×D311yescharacteristic
177C4×Dic6—31no—
178C4×Dic6—31no—
179C4×Dic6—31no—
180C4×Dic6—31no—
181C4×Dic6—61no—
182C4×Dic6C2×D311yescharacteristic
183C3×#107—31no—
184C3×#107—31no—
185C3×C4⋊C8—21no—
186C3×C4⋊C8—31no—
187C3×C4⋊C8—31no—
188C3×C4⋊C8C2×D311yescharacteristic
189C3×C4⋊C8C2×D311yescharacteristic
190C3×#102—31no—
191C3×#102—31no—
192C3×#97—31no—
193C3×#97—31no—
194C3×C4×C8—31no—
195#832—31no—
196#821—31no—
197#821C2×D311yescharacteristic
198#821C2×D311yescharacteristic
199#818—31no—
200#818—31no—
201#818—31no—
202#818—31no—
203#818—31no—
204#818—61no—
205#818C2×D311yescharacteristic
206#818C2×D311yescharacteristic
207#817—31no—
208#817—31no—
209#817—31no—
210#817—31no—
211#817—61no—
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—61no—
218#816—61no—
219#815C2×D311yescharacteristic
220Dic3⋊C8C2×D311yescharacteristic
221Dic3⋊C8C2×D311yescharacteristic
222C8×Dic3C2×D311yescharacteristic
223#810—31no—
224#808—31no—
225#808—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#803C2×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—21no—
239#634C2×Q812yes—
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—
252#627—81no—
253#627—81no—
254#627—81no—
255D3×Dic3—42no—
256D3×Dic3—81no—
257C32×C8—21no—
258C32×C8—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8C2×Q812yes—
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—31no—
271#474—91no—
272#446—31no—
273#440—91no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—31no—
277C2×C3×Q8—61no—
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—21no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6D1211yescharacteristic
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—31no—
300C2×C3×C8—31no—
301C2×C3×C8C22×D311yescharacteristic
302C2×C3×C8C22×D311yescharacteristic
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
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—61no—
312C3×C22⋊C4—61no—
313C3×C42—21no—
314C3×C42—31no—
315C3×C42—31no—
316C3×C42C22×D311yescharacteristic
317C3×C42C22×D311yescharacteristic
318#217—61no—
319#217—61no—
320#214—34no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324C4⋊Dic3—21no—
325C4⋊Dic3—31no—
326C4⋊Dic3—31no—
327C4⋊Dic3—31no—
328C4⋊Dic3—31no—
329C4⋊Dic3—31no—
330C4⋊Dic3—31no—
331C4⋊Dic3—61no—
332C4⋊Dic3—61no—
333C4⋊Dic3—61no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3D1211yescharacteristic
339C4⋊Dic3C22×D311yescharacteristic
340C4⋊Dic3C22×D311yescharacteristic
341C4⋊Dic3C22×D311yescharacteristic
342Dic3⋊C4—61no—
343Dic3⋊C4—61no—
344Dic3⋊C4—61no—
345Dic3⋊C4—61no—
346Dic3⋊C4—61no—
347Dic3⋊C4—61no—
348Dic3⋊C4—61no—
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—121no—
359Dic3⋊C4—121no—
360Dic3⋊C4—121no—
361Dic3⋊C4D1211yescharacteristic
362Dic3⋊C4D1211yescharacteristic
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—121no—
370C4×Dic3C22×D311yescharacteristic
371C4×Dic3C22×D311yescharacteristic
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×C4C22×Q811yescharacteristic
382C32×C42−1+411yescharacteristic
383C3⋊Dic3—22no—
384C3⋊Dic3—41no—
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—91no—
395C4⋊Q8—31no—
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—91no—
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—31no—
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⋊C8D3211yescharacteristic
428#103—91no—
429#103—91no—
430#103—91no—
431#102—31no—
432#102—31no—
433#102—91no—
434#97—31no—
435#97—31no—
436C4×C8—31no—
437C23×C3—61no—
438C22×D3—21no—
439C3×Q8—62no—
440C3×Q8—241no—
441C3×D4—32no—
442C3×D4—61no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—31no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—241no—
454C2×C3×C4C2×D1211yescharacteristic
455C2×C3×C4C2×D1211yescharacteristic
456C2×C3×C4D3×D411yescharacteristic
457C2×C3×C4D3×D411yescharacteristic
458C2×C3×C4C23×D311yescharacteristic
459C2×C3×C4C23×D311yescharacteristic
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—61no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—121no—
472C2×Dic3—121no—
473C2×Dic3—121no—
474C2×Dic3—121no—
475C2×Dic3—122no—
476C2×Dic3—241no—
477C2×Dic3C2×D1211yescharacteristic
478C2×Dic3C2×D1211yescharacteristic
479C2×Dic3C2×D1211yescharacteristic
480C2×Dic3C2×D1211yescharacteristic
481D12—21no—
482D12D3×Q812yes—
483C4×D3—81no—
484C4×D3—122no—
485C4×D3—241no—
486Dic6—22no—
487Dic6—32no—
488Dic6—32no—
489Dic6—62no—
490Dic6—61no—
491Dic6—61no—
492Dic6—81no—
493Dic6—121no—
494Dic6—241no—
495Dic6—241no—
496Dic6—241no—
497Dic6—241no—
498Dic6—241no—
499Dic6—241no—
500C3×C8—21no—
501C3×C8—21no—
502C3×C8—21no—
503C3×C8—21no—
504C3×C8—32no—
505C3×C8—41no—
506C3×C8—41no—
507C3×C8—61no—
508C3⋊C8—21no—
509C3⋊C8D3×Q812yes—
510C2×C32D4×Q811yescharacteristic
511C2×C32C2×#13711yescharacteristic
512C2×C32#57611yescharacteristic
513C3×D3—42no—
514C2×Q8—31no—
515C2×Q8—61no—
516C2×Q8—91no—
517C2×Q8—181no—
518C2×Q8—181no—
519C2×Q8—181no—
520C2×D4—31no—
521C22×C4—61no—
522C22×C4—181no—
523C22×C4—181no—
524SD16—94no—
525C2×C8—31no—
526C2×C8—31no—
527C2×C8C2×D3211yescharacteristic
528C2×C8C2×D3211yescharacteristic
529C4⋊C4—31no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—61no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—91no—
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—
548C4⋊C4—181no—
549C22⋊C4—61no—
550C22⋊C4—181no—
551C22⋊C4—181no—
552C42—31no—
553C42—31no—
554C42—181no—
555C42—181no—
556C42—181no—
557C42C2×D3211yescharacteristic
558C22×C3—21no—
559C22×C3—62no—
560C22×C3—121no—
561C22×C3—121no—
562C22×C3C22×D1211yescharacteristic
563C22×C3C2×D3×D411yescharacteristic
564C2×D3—22no—
565C2×D3—41no—
566C2×D3—41no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—32no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—61no—
577C3×C4—61no—
578C3×C4—61no—
579C3×C4—121no—
580C3×C4—121no—
581C3×C4—121no—
582C3×C4C2×D3×Q811yescharacteristic
583C3×C4C2×D3×Q811yescharacteristic
584C3×C4#101011yescharacteristic
585C3×C4#101011yescharacteristic
586Dic3—21no—
587Dic3—21no—
588Dic3—21no—
589Dic3—41no—
590Dic3—41no—
591Dic3—41no—
592Dic3—62no—
593Dic3—62no—
594Dic3—122no—
595Dic3—121no—
596Dic3—121no—
597Dic3—121no—
598Dic3—121no—
599Dic3—121no—
600Dic3—121no—
601Dic3—241no—
602Dic3—241no—
603Dic3—241no—
604Dic3#90912yes—
605C32#338511yescharacteristic, complemented, Sylow
606C23—61no—
607Q8—62no—
608Q8—92no—
609Q8—181no—
610Q8—241no—
611Q8—721no—
612Q8—721no—
613Q8—721no—
614D4—32no—
615D4—61no—
616C2×C4—31no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—31no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—241no—
628C2×C4—362no—
629C2×C4—721no—
630C2×C4D3×D1211yescharacteristic
631C2×C4D3×D1211yescharacteristic
632C2×C4C22×D3211yescharacteristic
633C8—21no—
634C8—21no—
635C8—32no—
636C8—61no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—122no—
641C2×C3Q8×D1211yescharacteristic
642C2×C3#563211yescharacteristic
643C2×C3C2×#90911yescharacteristic
644C2×C3#575211yescharacteristic
645C2×C3#575711yescharacteristic
646C2×C3D3×#13711yescharacteristic
647D3—42no—
648C22—62no—
649C22—121no—
650C22—121no—
651C22C2×D3×D1211yescharacteristic
652C4—21no—
653C4—21no—
654C4—32no—
655C4—61no—
656C4—61no—
657C4—61no—
658C4—121no—
659C4—121no—
660C4—121no—
661C4—182no—
662C4—361no—
663C4—361no—
664C4—361no—
665C4#6430911yescharacteristic
666C4D32×Q811yescharacteristic
667C3—21no—
668C3#7997611yescharacteristic, complemented
669C3#8096011yescharacteristic, complemented
670C2—122no—
671C2#1059438311yescharacteristic
672C2#1059467811yescharacteristic
673C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. #10592528C2semidirect
5. C3×#4828C2semidirect
6. #10590894C2semidirect
7. #10590891C2semidirect
8. #10590814C2semidirect
9. #10590805C2semidirect
15. #10590305C2semidirect
81. #4828D3semidirect
135. #3716Q8semidirect
605. C32#3385semidirect
668. C3#79976semidirect
669. C3#80960semidirect

Maximal subgroups

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

subgroupindex
#105939292
#105938562
#105925282
C3×#48462
C3×#48282
#105908942
#105908912
#105908142
#105908052
#105907622
#105907572
#105907472
#105907442
#105903602
#105903052
#809603
#799763