Finite Group Databasebeta

← #11897657

Subgroups — #11897657

Order 1152.

740 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#627C211yesmaximal, characteristic, complemented
2#10595272C211yesmaximal, characteristic
3#10592863C211yesmaximal, characteristic
4C3×#5164C211yesmaximal, characteristic
5C3×Dic3×SD16C211yesmaximal, characteristic
6#10591615C211yesmaximal, characteristic, complemented
7#10591547C211yesmaximal, characteristic, complemented
8#10591546C211yesmaximal, characteristic, complemented
9#10591494C211yesmaximal, characteristic
10#10591410C211yesmaximal, characteristic
11#10591408C211yesmaximal, characteristic
12#10590903C211yesmaximal, characteristic, complemented
13#10590892C211yesmaximal, characteristic, complemented
14#10590891C211yesmaximal, characteristic, complemented
15#10590784C211yesmaximal, characteristic, complemented
16#79759—31nomaximal
17#79634—31nomaximal
18C2×C32×SD16C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25#63982—21no—
26C2×Dic3⋊Dic3—21no—
27#63964—21no—
28#63964—21no—
29#63919—21no—
30#63919C2211yescharacteristic
31#63918—21no—
32#63918—21no—
33#63918C2211yescharacteristic
34#63918C2211yescharacteristic
35#63918C2211yescharacteristic
36C4×#627—21no—
37C4×#627C2211yescharacteristic
38#63872C2211yescharacteristic
39#63869C2211yescharacteristic
40#63662C2211yescharacteristic
41#63659C2211yescharacteristic
42#63645C2211yescharacteristic
43#63642C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63575C2211yescharacteristic
56#63574C2211yescharacteristic
57#63573C2211yescharacteristic
58#63572C2211yescharacteristic
59Dic3⋊(C3⋊C8)C2211yescharacteristic
60Dic3⋊(C3⋊C8)C2211yescharacteristic
61Q8×Dic6—31no—
62Q8×Dic6—31no—
63#5543—31no—
64#5539—31no—
65C3×#440—31no—
66C3×C4×SD16—31no—
67#5164—31no—
68#5164—31no—
69#5164—61no—
70#5164D311yescharacteristic
71Dic3×SD16D311yescharacteristic
72#5022—31no—
73#5021—31no—
74#5008—31no—
75#5007—31no—
76#4876—31no—
77#4874—31no—
78#4856—31no—
79#4856—31no—
80#4799—31no—
81#4796—31no—
82#4796—31no—
83#4793—31no—
84#4761—31no—
85#4759—31no—
86#4759—31no—
87#4759—31no—
88#4702—31no—
89#4701—31no—
90#4682—31no—
91#4679—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×#627—21no—
98C2×#627—21no—
99C2×#627—21no—
100C2×#627—21no—
101C2×#627D411yescharacteristic
102C32×SD16Q814yescomplemented
103C2×C32×C8C2311yescharacteristic
104#3757—21no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724—21no—
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135Dic3⋊Dic3D411yescharacteristic
136#3385—91noSylow
137C2×C3×SD16—21no—
138C2×C3×SD16C2×D311yescharacteristic
139C2×C3×SD16C2×D311yescharacteristic
140C3×C4×Q8—31no—
141C3×C4×Q8—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144Q8×Dic3—31no—
145Q8×Dic3—31no—
146Q8×Dic3—61no—
147Q8×Dic3C2×D311yescharacteristic
148Q8×Dic3C2×D311yescharacteristic
149D4×Dic3—31no—
150D4×Dic3—31no—
151D4×Dic3—61no—
152D4×Dic3C2×D311yescharacteristic
153D4×Dic3C2×D311yescharacteristic
154C2×C4⋊Dic3—61no—
155#924—61no—
156#924—61no—
157C2×Dic3⋊C4—61no—
158#890—31no—
159#890—31no—
160#890—31no—
161#888—31no—
162#888—31no—
163#888—31no—
164#888—31no—
165#888—31no—
166#888—61no—
167#888—61no—
168#888—61no—
169#888—61no—
170#878—61no—
171#878—61no—
172#878—61no—
173#878—61no—
174#870—31no—
175#869—31no—
176#869—31no—
177#869—31no—
178#869—61no—
179#869—61no—
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—61no—
183C4×Dic6—61no—
184C3×#107—31no—
185C3×#106—31no—
186C3×#103—31no—
187C3×#103—31no—
188C3×#102—31no—
189C3×#102—31no—
190C3×#97—31no—
191C3×C4×C8—31no—
192#835—31no—
193#835—31no—
194#835—61no—
195#835C2×D311yescharacteristic
196#835C2×D311yescharacteristic
197#832—31no—
198#832—31no—
199#832—61no—
200#832C2×D311yescharacteristic
201#832C2×D311yescharacteristic
202#818—31no—
203#818—31no—
204#818—31no—
205#818—31no—
206#818—31no—
207#818—61no—
208#818C2×D311yescharacteristic
209#817—31no—
210#817C2×D311yescharacteristic
211#815—31no—
212#815—31no—
213#815—61no—
214#815C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219C8×Dic3C2×D311yescharacteristic
220#808—31no—
221#808—31no—
222#808—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C23×C32—21no—
231C32×Q8—21no—
232C32×Q8C2×Q812yes—
233C32×D4—21no—
234C32×D4C2×Q812yes—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—81no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—42no—
247C2×C3×Dic3—81no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252#627—22no—
253#627—81no—
254#627—81no—
255#627—81no—
256#627—81no—
257C32×C8C2×Q812yes—
258C3⋊(C3⋊C8)—21no—
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—91no—
273#440—31no—
274#440—91no—
275C4×SD16—31no—
276C2×C3×Q8—21no—
277C2×C3×Q8C22×D311yescharacteristic
278C2×C3×Q8C22×D311yescharacteristic
279C2×C3×D4—21no—
280C2×C3×D4C22×D311yescharacteristic
281C2×C3×D4C22×D311yescharacteristic
282C22×C3×C4—61no—
283C22×C3×C4—61no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C22×Dic3—121no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C3×SD16—24no—
300C3×SD16Dic614yescomplemented
301C3×SD16Dic614yescomplemented
302C2×C3×C8—21no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C22⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C42—31no—
316C3×C42—31no—
317C3×C42—61no—
318C3×C42—61no—
319#217—21no—
320#217—21no—
321#217—61no—
322#217—61no—
323#217—121no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
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—121no—
343C4⋊Dic3C22×D311yescharacteristic
344C4⋊Dic3C22×D311yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347Dic3⋊C4—31no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
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—
361C4×Dic3—21no—
362C4×Dic3—21no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—121no—
369C4×Dic3C22×D311yescharacteristic
370C4×Dic3C22×D311yescharacteristic
371C2×C3⋊C8—31no—
372C2×C3⋊C8—31no—
373C2×C3⋊C8—61no—
374C2×C3⋊C8C22×D311yescharacteristic
375C2×C3⋊C8C22×D311yescharacteristic
376C22×C32—22no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32C22×D411yescharacteristic
380C32×C4—22no—
381C32×C4C22×Q811yescharacteristic
382C32×C42−1+411yescharacteristic
383C3⋊Dic3—21no—
384C3⋊Dic3—21no—
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—41no—
394C3×Dic3#13712yes—
395C2×SD16D3211yescharacteristic
396C4⋊Q8—91no—
397C4⋊Q8—91no—
398C4⋊Q8—91no—
399C4⋊Q8—91no—
400C4⋊Q8—181no—
401C4⋊Q8—181no—
402C4⋊Q8—181no—
403#125—91no—
404#125—91no—
405C22⋊Q8—181no—
406C22⋊Q8—181no—
407C22⋊Q8—181no—
408C4×Q8—31no—
409C4×Q8—31no—
410C4×Q8—91no—
411C4×Q8—91no—
412C4×Q8—181no—
413C4×D4—31no—
414C4×D4—31no—
415C4×D4—91no—
416C2×C4⋊C4—181no—
417#107—31no—
418#107—91no—
419#107—91no—
420#107—91no—
421#107—91no—
422#107—91no—
423#106—31no—
424#106—91no—
425#106—91no—
426C4⋊C8—91no—
427C4⋊C8—91no—
428C4⋊C8—91no—
429#103—31no—
430#103—31no—
431#103—91no—
432#102—31no—
433#102—31no—
434#102—91no—
435#97—31no—
436#97—91no—
437C4×C8—31no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—41no—
441C3×Q8—21no—
442C3×Q8—21no—
443C3×Q8—22no—
444C3×Q8—41no—
445C3×Q8C2×Dic612yes—
446C3×Q8C2×Dic612yes—
447C3×D4—21no—
448C3×D4—21no—
449C3×D4—22no—
450C3×D4—41no—
451C3×D4C2×Dic612yes—
452C3×D4C2×Dic612yes—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—41no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—122no—
466C2×C3×C4—241no—
467C2×C3×C4C23×D311yescharacteristic
468C2×C3×C4C23×D311yescharacteristic
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—42no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—81no—
485C2×Dic3—121no—
486C2×Dic3—121no—
487C2×Dic3—241no—
488C2×Dic3—241no—
489C2×Dic3—242no—
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493C2×Dic3D3×D411yescharacteristic
494Dic6—62no—
495Dic6—62no—
496Dic6—241no—
497Dic6—241no—
498Dic6—241no—
499Dic6—241no—
500Dic6—241no—
501Dic6—241no—
502Dic6—241no—
503Dic6—241no—
504C3×C8—22no—
505C3×C8—61no—
506C3×C8—61no—
507C3×C8C2×Dic612yes—
508C3×C8C2×Dic612yes—
509C3⋊C8—21no—
510C3⋊C8—21no—
511C3⋊C8—61no—
512C3⋊C8—61no—
513C3⋊C8—121no—
514C2×C32—42no—
515C2×C32D4×Q811yescharacteristic
516C2×C32C2×#13711yescharacteristic
517C2×C32#57611yescharacteristic
518C2×Q8—91no—
519C2×Q8—181no—
520C2×Q8—181no—
521C2×Q8—181no—
522C2×Q8—181no—
523C2×Q8C2×D3211yescharacteristic
524C2×D4C2×D3211yescharacteristic
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—181no—
528SD16#62714yescomplemented
529C2×C8—31no—
530C2×C8—31no—
531C2×C8—91no—
532C2×C8C2×D3211yescharacteristic
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—91no—
540C4⋊C4—91no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—91no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C22⋊C4—61no—
554C22⋊C4—61no—
555C22⋊C4—181no—
556C42—31no—
557C42—31no—
558C42—61no—
559C42—61no—
560C42—91no—
561C42—181no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—21no—
565C22×C3—42no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C3×C4—22no—
575C3×C4—22no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—32no—
579C3×C4—42no—
580C3×C4—61no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—121no—
584C3×C4—121no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4C22×Dic611yescharacteristic
588C3×C4C22×Dic611yescharacteristic
589C3×C4#101011yescharacteristic
590C3×C4#101011yescharacteristic
591Dic3—21no—
592Dic3—21no—
593Dic3—21no—
594Dic3—41no—
595Dic3—41no—
596Dic3—41no—
597Dic3—41no—
598Dic3—61no—
599Dic3—61no—
600Dic3—61no—
601Dic3—61no—
602Dic3—121no—
603Dic3—121no—
604Dic3—121no—
605Dic3—121no—
606Dic3—121no—
607Dic3—121no—
608Dic3—241no—
609Dic3—241no—
610Dic3#91512yes—
611C32#338511yescharacteristic, complemented, Sylow
612C23—21no—
613Q8—21no—
614Q8—182no—
615Q8—721no—
616Q8—721no—
617Q8—721no—
618Q8—721no—
619Q8C2×#62712yes—
620D4—21no—
621D4C2×#62712yes—
622C2×C4—21no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—91no—
632C2×C4—91no—
633C2×C4—122no—
634C2×C4—181no—
635C2×C4—181no—
636C2×C4—241no—
637C2×C4—721no—
638C2×C4C22×D3211yescharacteristic
639C8—61no—
640C8—61no—
641C8—181no—
642C8C2×#62712yes—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—82no—
649C2×C3D4×Dic611yescharacteristic
650C2×C3D4×Dic611yescharacteristic
651C2×C3C2×#91511yescharacteristic
652C2×C3#576911yescharacteristic
653C2×C3#577411yescharacteristic
654C2×C3D3×#13711yescharacteristic
655C22—22no—
656C22—41no—
657C22—41no—
658C22D32×D411yescharacteristic
659C4—22no—
660C4—32no—
661C4—61no—
662C4—61no—
663C4—61no—
664C4—121no—
665C4—121no—
666C4—121no—
667C4—121no—
668C4—181no—
669C4—181no—
670C4—361no—
671C4—361no—
672C4#6430911yescharacteristic
673C4C22×#62711yescharacteristic
674C3—21no—
675C3#7963411yescharacteristic, complemented
676C3#7975911yescharacteristic, complemented
677C2—42no—
678C2D3×#91511yescharacteristic
679C2#1059475511yescharacteristic
680C2D4×#62711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC2×SD16D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×#627C2semidirect
6. #10591615C2semidirect
7. #10591547C2semidirect
8. #10591546C2semidirect
12. #10590903C2semidirect
13. #10590892C2semidirect
14. #10590891C2semidirect
15. #10590784C2semidirect
102. C32×SD16Q8semidirect
300. C3×SD16Dic6semidirect
301. C3×SD16Dic6semidirect
528. SD16#627semidirect
611. C32#3385semidirect
675. C3#79634semidirect
676. C3#79759semidirect

Maximal subgroups

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

subgroupindex
Q8×#6272
#105952722
#105928632
C3×#51642
C3×Dic3×SD162
#105916152
#105915472
#105915462
#105914942
#105914102
#105914082
#105909032
#105908922
#105908912
#105907842
#797593
#796343