Finite Group Databasebeta

← #11897639

Subgroups — #11897639

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
1C3×#5722C211yesmaximal, characteristic, complemented
2#10593929C211yesmaximal, characteristic
3#10592780C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic
5#10590557C211yesmaximal, characteristic, complemented
6#10590544C211yesmaximal, characteristic, complemented
7#10590465C211yesmaximal, characteristic
8#10590463C211yesmaximal, characteristic
9#10590454C211yesmaximal, characteristic
10#10590453C211yesmaximal, characteristic
11#10590420C211yesmaximal, characteristic, complemented
12#10590411C211yesmaximal, characteristic, complemented
13#10590358C211yesmaximal, characteristic
14#10590302C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#83706—31nomaximal
17#80960—31nomaximal
18C32×C4⋊Q8C2211yescharacteristic
19#64079C2211yescharacteristic
20C3×#944—21no—
21C3×#944—21no—
22C3×#888—21no—
23C3×#888C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887—21no—
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31#63918C2211yescharacteristic
32#63899—21no—
33Dic3×D12C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63887—21no—
36D3×Dic3⋊C4—21no—
37#63869C2211yescharacteristic
38#63851—21no—
39C2×#3715C2211yescharacteristic
40#63635C2211yescharacteristic
41#63635C2211yescharacteristic
42#63634C2211yescharacteristic
43#63634C2211yescharacteristic
44#63630C2211yescharacteristic
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×Q82—31no—
62#5722D311yescharacteristic, complemented
63#5579—31no—
64#5539—31no—
65C3×#474—31no—
66#5087—31no—
67#5087D311yescharacteristic
68#5084—31no—
69#5081—31no—
70#5081—31no—
71#5081—31no—
72#5081—61no—
73#5078—31no—
74#5026—31no—
75#5026—31no—
76C4×#215—31no—
77#5024—31no—
78#5022—31no—
79#5022—31no—
80#5021—31no—
81#5018—31no—
82#4877—31no—
83#4876—31no—
84#4875—31no—
85#4874—31no—
86#4829—31no—
87#4828—31no—
88#4761—31no—
89#4759—31no—
90#4758—31no—
91#4757—31no—
92C2×C32×Q8—21no—
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
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×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
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(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135#3715Q814yescomplemented
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×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—61no—
150C3×C4×D4—31no—
151#946—61no—
152#944—21no—
153#944—21no—
154C2×#215—31no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157C2×#214—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—31no—
166#888C2×D311yescharacteristic
167#888C2×D311yescharacteristic
168#887—21no—
169#887C2×D311yescharacteristic
170#887C2×D311yescharacteristic
171#878—61no—
172#878—61no—
173C4×D12—31no—
174C4×D12—31no—
175C4×D12C2×D311yescharacteristic
176#870—31no—
177#870—31no—
178#870—31no—
179#870—61no—
180#869—31no—
181C4×Dic6C2×D311yescharacteristic
182C4×Dic6C2×D311yescharacteristic
183C3×#107—31no—
184C3×#107—31no—
185C3×C4⋊C8—31no—
186C3×#102—31no—
187C3×#102—31no—
188#835—31no—
189#835—31no—
190#835—31no—
191#832—31no—
192#818—31no—
193#817—31no—
194#816—31no—
195#816—31no—
196#815—31no—
197Dic3⋊C8—31no—
198Dic3⋊C8—31no—
199C8×Dic3—31no—
200#810—31no—
201#809—31no—
202#809C2×D311yescharacteristic
203#809C2×D311yescharacteristic
204#808—31no—
205#808—31no—
206#808—31no—
207#808—31no—
208#808—31no—
209#808—61no—
210#808—61no—
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)C2×D311yescharacteristic
225#803—31no—
226#803—31no—
227#803—31no—
228#803—61no—
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—
238C2×C3⋊Dic3—21no—
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×Dic6—81no—
252C3×Dic6—81no—
253C3×Dic6C2×Q812yes—
254#627—81no—
255D3×Dic3—42no—
256D3×Dic3—81no—
257C3⋊(C3⋊C8)—21no—
258C3⋊(C3⋊C8)C2×Q812yes—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
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—31no—
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×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—61no—
294C2×Dic6—61no—
295C2×Dic6#6711yescharacteristic
296C2×Dic6C22×D311yescharacteristic
297C2×C3×C8—31no—
298C2×C3×C8—31no—
299C3×C4⋊C4—21no—
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—41no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C22⋊C4—61no—
319C3×C42—21no—
320C3×C42—31no—
321C3×C42—31no—
322C3×C42—61no—
323C3×C42—61no—
324C3×C42—61no—
325C3×C42C22×D311yescharacteristic
326C3×C42C22×D311yescharacteristic
327#217—61no—
328#217—61no—
329#215—34no—
330#214—34no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3#6711yescharacteristic
343C4⋊Dic3C22×D311yescharacteristic
344C4⋊Dic3C22×D311yescharacteristic
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
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#6711yescharacteristic
361Dic3⋊C4#6711yescharacteristic
362C4×Dic3—21no—
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—21no—
380C32×C4—21no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4C22×Q811yescharacteristic
384C32×C42−1+411yescharacteristic
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—91no—
395C4⋊Q8—31no—
396C4⋊Q8—31no—
397C4⋊Q8—61no—
398C4⋊Q8—61no—
399C4⋊Q8—61no—
400C4⋊Q8—91no—
401C4⋊Q8D3211yescharacteristic
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—31no—
411C4×Q8—61no—
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—91no—
427C4⋊C8—91no—
428#103—91no—
429#103—91no—
430#103—91no—
431#102—31no—
432#102—31no—
433#102—91no—
434#97—91no—
435#97—91no—
436C4×C8—91no—
437C23×C3—61no—
438C22×D3—21no—
439C3×Q8—32no—
440C3×Q8—62no—
441C3×Q8—61no—
442C3×Q8—81no—
443C3×Q8—81no—
444C3×Q8—82no—
445C3×Q8—241no—
446C3×Q8—241no—
447C3×D4—32no—
448C3×D4—61no—
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—21no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—241no—
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4D3×D411yescharacteristic
468C2×C3×C4C2×#6711yescharacteristic
469C2×C3×C4C2×#6711yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—121no—
480C2×Dic3—121no—
481C2×Dic3—122no—
482C2×Dic3—241no—
483C2×Dic3C2×#6711yescharacteristic
484C2×Dic3C2×#6711yescharacteristic
485C2×Dic3C2×#6711yescharacteristic
486C2×Dic3C2×#6711yescharacteristic
487D12—21no—
488D12D3×Q812yes—
489C4×D3—81no—
490C4×D3—122no—
491C4×D3—241no—
492Dic6—21no—
493Dic6—22no—
494Dic6—81no—
495Dic6—81no—
496Dic6—241no—
497Dic6—241no—
498Dic6D3×Q812yes—
499C3×C8—61no—
500C3×C8—61no—
501C3⋊C8—21no—
502C3⋊C8—21no—
503C3⋊C8—32no—
504C3⋊C8—32no—
505C3⋊C8—62no—
506C3⋊C8—62no—
507C3⋊C8—61no—
508C3⋊C8—61no—
509C2×C32D4×Q811yescharacteristic
510C2×C32C2×#13711yescharacteristic
511C2×C32#57611yescharacteristic
512C3×D3—42no—
513C2×Q8—21no—
514C2×Q8—31no—
515C2×Q8—31no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—181no—
519C2×D4—31no—
520C22×C4—61no—
521C22×C4—181no—
522C22×C4—181no—
523SD16—94no—
524C2×C8—31no—
525C2×C8—31no—
526C2×C8—91no—
527C2×C8—91no—
528C4⋊C4—21no—
529C4⋊C4—31no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—61no—
535C4⋊C4—61no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—91no—
540C4⋊C4—91no—
541C4⋊C4—181no—
542C4⋊C4—181no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4C2×D3211yescharacteristic
547C4⋊C4C2×D3211yescharacteristic
548C22⋊C4—61no—
549C22⋊C4—181no—
550C22⋊C4—181no—
551C42—31no—
552C42—31no—
553C42—61no—
554C42—61no—
555C42—61no—
556C42C2×D3211yescharacteristic
557C22×C3—21no—
558C22×C3—62no—
559C22×C3—121no—
560C22×C3—121no—
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C22×#6711yescharacteristic
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—41no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—62no—
580C3×C4—61no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—81no—
584C3×C4—81no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4C2×D3×Q811yescharacteristic
588C3×C4C2×D3×Q811yescharacteristic
589C3×C4#100711yescharacteristic
590C3×C4#101011yescharacteristic
591Dic3—21no—
592Dic3—22no—
593Dic3—21no—
594Dic3—21no—
595Dic3—41no—
596Dic3—41no—
597Dic3—121no—
598Dic3—121no—
599Dic3—121no—
600Dic3—121no—
601Dic3—241no—
602Dic3—241no—
603Dic3#94212yes—
604C32#338511yescharacteristic, complemented, Sylow
605C23—61no—
606Q8—32no—
607Q8—62no—
608Q8—61no—
609Q8—81no—
610Q8—241no—
611Q8—241no—
612Q8—721no—
613D4—32no—
614D4—61no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—31no—
620C2×C4—31no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—241no—
627C2×C4—362no—
628C2×C4—721no—
629C2×C4D3×#6711yescharacteristic
630C2×C4D3×#6711yescharacteristic
631C2×C4C22×D3211yescharacteristic
632C8—61no—
633C8—61no—
634C8—92no—
635C8—181no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—122no—
640C2×C3#563211yescharacteristic
641C2×C3#575711yescharacteristic
642C2×C3D3×#13711yescharacteristic
643C2×C3C2×#94211yescharacteristic
644C2×C3Q8×#6711yescharacteristic
645C2×C3#583511yescharacteristic
646D3—42no—
647C22—62no—
648C22—121no—
649C22—121no—
650C22C2×D3×#6711yescharacteristic
651C4—21no—
652C4—21no—
653C4—32no—
654C4—41no—
655C4—41no—
656C4—61no—
657C4—61no—
658C4—62no—
659C4—61no—
660C4—121no—
661C4—121no—
662C4—361no—
663C4—361no—
664C4#6431511yescharacteristic
665C4D32×Q811yescharacteristic
666C3—21no—
667C3#8096011yescharacteristic, complemented
668C3#8370611yescharacteristic, complemented
669C2—122no—
670C2#1059509611yescharacteristic
671C2D3×#94211yescharacteristic
672C2#1059540011yescharacteristic
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×#5722C2semidirect
3. #10592780C2semidirect
5. #10590557C2semidirect
6. #10590544C2semidirect
11. #10590420C2semidirect
12. #10590411C2semidirect
14. #10590302C2semidirect
15. #10590252C2semidirect
62. #5722D3semidirect
135. #3715Q8semidirect
604. C32#3385semidirect
667. C3#80960semidirect
668. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
#105939292
#105927802
C3×#50872
#105905572
#105905442
#105904652
#105904632
#105904542
#105904532
#105904202
#105904112
#105903582
#105903022
#105902522
#837063
#809603