Finite Group Databasebeta

← #11897640

Subgroups — #11897640

Order 1152.

734 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593938C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592545C211yesmaximal, characteristic
4C3×#4829C211yesmaximal, characteristic, complemented
5C3×#4828C211yesmaximal, characteristic, complemented
6#10590892C211yesmaximal, characteristic, complemented
7#10590891C211yesmaximal, characteristic, complemented
8#10590811C211yesmaximal, characteristic, complemented
9#10590804C211yesmaximal, characteristic, complemented
10#10590795C211yesmaximal, characteristic
11#10590792C211yesmaximal, characteristic
12#10590764C211yesmaximal, characteristic
13#10590759C211yesmaximal, characteristic
14#10590362C211yesmaximal, characteristic
15#10590306C211yesmaximal, characteristic, complemented
16#81223—31nomaximal
17#79976—31nomaximal
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19#64078C2211yescharacteristic
20C3×#870C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63918—21no—
24#63918C2211yescharacteristic
25#63918C2211yescharacteristic
26#63918C2211yescharacteristic
27#63895—21no—
28#63894C2211yescharacteristic
29#63894C2211yescharacteristic
30#63888—21no—
31#63883—21no—
32#63869C2211yescharacteristic
33#63865—21no—
34Dic3×Dic6—21no—
35Dic3×Dic6C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37#63840—21no—
38#63840—21no—
39C2×#3717C2211yescharacteristic
40C32×C4⋊C8C2211yescharacteristic
41#63648C2211yescharacteristic
42#63648C2211yescharacteristic
43#63645C2211yescharacteristic
44#63645C2211yescharacteristic
45C3×#818C2211yescharacteristic
46C3×#817C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#815C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63575C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63573C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#5690—31no—
62#5579—31no—
63Q8×Dic6—31no—
64Q8×Dic6—31no—
65C3×#479—31no—
66C3×#446—31no—
67#5064—31no—
68#5026—31no—
69#4890—31no—
70#4874—31no—
71#4870—31no—
72#4856—31no—
73#4850—31no—
74#4846—31no—
75#4846—31no—
76#4846—31no—
77#4846—61no—
78#4842—31no—
79#4829—31no—
80#4829D311yescharacteristic, complemented
81#4828D311yescharacteristic, complemented
82#4817—31no—
83#4796—31no—
84#4793—31no—
85#4788—31no—
86#4710—31no—
87#4710—31no—
88#4702—31no—
89#4702—31no—
90C4×#204—31no—
91#4682—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—21no—
95C2×C3×Dic6D411yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627—21no—
99C2×#627—21no—
100C2×#624—21no—
101C2×#624—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C3×C4⋊Dic3D411yescharacteristic
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
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
124#3724—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133Dic32—21no—
134Dic32—21no—
135#3717Q814yescomplemented
136#3385—91noSylow
137C3×#125—31no—
138C3×C4×Q8—31no—
139C3×C4×Q8—31no—
140#946—61no—
141Q8×Dic3—31no—
142Q8×Dic3—31no—
143Q8×Dic3—61no—
144C2×#215—31no—
145C2×#204—31no—
146#897—61no—
147#896—61no—
148#896—61no—
149#896—61no—
150#896—61no—
151#893—31no—
152#893—31no—
153D3×C4⋊C4—61no—
154D3×C4⋊C4—61no—
155#890—31no—
156#888—31no—
157#888—31no—
158#888—31no—
159#888—61no—
160#888—61no—
161#888—61no—
162#888—61no—
163#888—61no—
164C4×D12—31no—
165C4×D12—31no—
166C4×D12—31no—
167C4×D12—31no—
168C4×D12—61no—
169#870—31no—
170#870C2×D311yescharacteristic
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×#106—31no—
185C3×C4⋊C8—21no—
186C3×C4⋊C8—31no—
187C3×C4⋊C8—31no—
188C3×C4⋊C8C2×D311yescharacteristic
189C3×C4⋊C8C2×D311yescharacteristic
190C3×#103—31no—
191C3×#103—31no—
192C3×#97—31no—
193C3×#97—31no—
194C3×C4×C8—31no—
195#835—31no—
196#821—31no—
197#821—31no—
198#821—31no—
199#821—31no—
200#821—31no—
201#821—61no—
202#821—61no—
203#818—31no—
204#818—31no—
205#818—31no—
206#818—31no—
207#818—31no—
208#818—31no—
209#818—31no—
210#818—61no—
211#818—61no—
212#818C2×D311yescharacteristic
213#817—31no—
214#817—31no—
215#817C2×D311yescharacteristic
216#816—31no—
217#816C2×D311yescharacteristic
218#816C2×D311yescharacteristic
219#815C2×D311yescharacteristic
220Dic3⋊C8C2×D311yescharacteristic
221Dic3⋊C8C2×D311yescharacteristic
222C8×Dic3C2×D311yescharacteristic
223#809—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—
237C4⋊(C3⋊D3)—21no—
238C4⋊(C3⋊D3)C2×Q812yes—
239C4×C3⋊D3—81no—
240#634—81no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C3×Dic6—21no—
250C3×Dic6—22no—
251C3×Dic6C2×Q812yes—
252#627—81no—
253#627—81no—
254#627—81no—
255#624—42no—
256#624—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—31no—
267#479—91no—
268#477—91no—
269#476—91no—
270#474—91no—
271#474—91no—
272#446—31no—
273#440—91no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—31no—
277C2×C3×Q8—31no—
278C2×D12—31no—
279C2×D12—31no—
280C2×D12—61no—
281C2×C4×D3—61no—
282C2×C4×D3—61no—
283C2×C4×D3—61no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×C4×D3—61no—
287C2×C4×D3—121no—
288C2×Dic6—61no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—121no—
297C2×Dic6D1211yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—31no—
302C2×C3×C8—31no—
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
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—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C42—21no—
317C3×C42—31no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42C22×D311yescharacteristic
321C3×C42C22×D311yescharacteristic
322#215—34no—
323(C2×D3)⋊C4—61no—
324(C2×D3)⋊C4—61no—
325(C2×D3)⋊C4—61no—
326(C2×D3)⋊C4—61no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—121no—
330C4⋊Dic3—31no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
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—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—121no—
348C4⋊Dic3D1211yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
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#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—41no—
384C3⋊Dic3—41no—
385C3⋊Dic3—41no—
386C3×Dic3—22no—
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—91no—
396C4⋊Q8—91no—
397C4⋊Q8—91no—
398C4⋊Q8—91no—
399C4⋊Q8—181no—
400C4⋊Q8—181no—
401C4⋊Q8—181no—
402#125—31no—
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—91no—
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—31no—
423#106—91no—
424#106—91no—
425C4⋊C8—31no—
426C4⋊C8—31no—
427C4⋊C8D3211yescharacteristic
428#103—31no—
429#103—31no—
430#103—91no—
431#102—91no—
432#102—91no—
433#102—91no—
434#97—31no—
435#97—31no—
436C4×C8—31no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—121no—
440C3×Q8—32no—
441C3×Q8—62no—
442C3×Q8—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—61no—
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—21no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—121no—
471C2×Dic3—121no—
472C2×Dic3—121no—
473C2×Dic3C2×D1211yescharacteristic
474C2×Dic3C2×D1211yescharacteristic
475C2×Dic3C2×D1211yescharacteristic
476C2×Dic3C2×D1211yescharacteristic
477D12—32no—
478D12—32no—
479D12—62no—
480D12—61no—
481D12—61no—
482D12—121no—
483C4×D3—122no—
484C4×D3—122no—
485C4×D3—241no—
486C4×D3—241no—
487C4×D3—241no—
488C4×D3—241no—
489C4×D3—242no—
490Dic6—21no—
491Dic6—22no—
492Dic6—241no—
493Dic6—241no—
494Dic6—241no—
495Dic6—241no—
496Dic6—241no—
497Dic6—241no—
498Dic6—241no—
499Dic6—241no—
500Dic6—242no—
501Dic6D3×Q812yes—
502C3×C8—21no—
503C3×C8—21no—
504C3×C8—21no—
505C3×C8—21no—
506C3×C8—32no—
507C3×C8—41no—
508C3×C8—41no—
509C3×C8—61no—
510C3⋊C8—21no—
511C3⋊C8D3×Q812yes—
512C2×C32D4×Q811yescharacteristic
513C2×C32C2×#13711yescharacteristic
514C2×C32#57611yescharacteristic
515C3⋊D3—42no—
516C2×Q8—31no—
517C2×Q8—31no—
518C2×Q8—181no—
519C2×Q8—181no—
520C2×Q8—181no—
521C2×Q8—181no—
522C2×D4—91no—
523C22×C4—181no—
524C22×C4—181no—
525C22×C4—181no—
526SD16—94no—
527C2×C8—31no—
528C2×C8—31no—
529C2×C8C2×D3211yescharacteristic
530C2×C8C2×D3211yescharacteristic
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—91no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C22⋊C4—181no—
552C22⋊C4—181no—
553C22⋊C4—181no—
554C42—31no—
555C42—31no—
556C42—61no—
557C42—181no—
558C42—181no—
559C42C2×D3211yescharacteristic
560C22×C3—21no—
561C22×C3C22×D1211yescharacteristic
562C22×C3C2×D3×D411yescharacteristic
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—122no—
566C2×D3—121no—
567C2×D3—121no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—241no—
571C2×D3—241no—
572C3×C4—22no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—32no—
580C3×C4—41no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—61no—
584C3×C4—62no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4C2×D3×Q811yescharacteristic
589C3×C4C2×D3×Q811yescharacteristic
590C3×C4#101011yescharacteristic
591C3×C4#101011yescharacteristic
592Dic3—22no—
593Dic3—21no—
594Dic3—21no—
595Dic3—21no—
596Dic3—41no—
597Dic3—41no—
598Dic3—41no—
599Dic3—121no—
600Dic3—121no—
601Dic3—121no—
602Dic3—121no—
603Dic3—121no—
604Dic3—121no—
605Dic3—241no—
606Dic3—241no—
607Dic3—241no—
608Dic3#90912yes—
609C32#338511yescharacteristic, complemented, Sylow
610C23—181no—
611Q8—32no—
612Q8—62no—
613Q8—61no—
614Q8—721no—
615Q8—721no—
616Q8—721no—
617Q8—721no—
618D4—92no—
619D4—181no—
620C2×C4—31no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—181no—
629C2×C4—181no—
630C2×C4—181no—
631C2×C4—362no—
632C2×C4—721no—
633C2×C4—721no—
634C2×C4D3×D1211yescharacteristic
635C2×C4D3×D1211yescharacteristic
636C2×C4C22×D3211yescharacteristic
637C8—21no—
638C8—21no—
639C8—32no—
640C8—61no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3Q8×D1211yescharacteristic
645C2×C3#563211yescharacteristic
646C2×C3C2×#90911yescharacteristic
647C2×C3#575211yescharacteristic
648C2×C3#576911yescharacteristic
649C2×C3D3×#13711yescharacteristic
650D3—122no—
651D3—122no—
652D3—242no—
653C22—182no—
654C22—361no—
655C22—361no—
656C22C2×D3×D1211yescharacteristic
657C4—21no—
658C4—21no—
659C4—32no—
660C4—62no—
661C4—61no—
662C4—61no—
663C4—61no—
664C4—121no—
665C4—121no—
666C4—121no—
667C4—361no—
668C4—361no—
669C4—361no—
670C4#6430911yescharacteristic
671C4D32×Q811yescharacteristic
672C3—21no—
673C3#7997611yescharacteristic, complemented
674C3#8122311yescharacteristic, complemented
675C2—362no—
676C2#1059438311yescharacteristic
677C2#1059468011yescharacteristic
678C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
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. Dic62C2semidirect
4. C3×#4829C2semidirect
5. C3×#4828C2semidirect
6. #10590892C2semidirect
7. #10590891C2semidirect
8. #10590811C2semidirect
9. #10590804C2semidirect
15. #10590306C2semidirect
80. #4829D3semidirect
81. #4828D3semidirect
135. #3717Q8semidirect
609. C32#3385semidirect
673. C3#79976semidirect
674. C3#81223semidirect

Maximal subgroups

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

subgroupindex
#105939382
Dic622
#105925452
C3×#48292
C3×#48282
#105908922
#105908912
#105908112
#105908042
#105907952
#105907922
#105907642
#105907592
#105903622
#105903062
#812233
#799763