Finite Group Databasebeta

← #11897643

Subgroups — #11897643

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
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593938C211yesmaximal, characteristic
3#10592725C211yesmaximal, characteristic
4C3×#5022C211yesmaximal, characteristic, complemented
5#10591547C211yesmaximal, characteristic, complemented
6#10591546C211yesmaximal, characteristic, complemented
7#10591540C211yesmaximal, characteristic
8#10591536C211yesmaximal, characteristic
9#10590466C211yesmaximal, characteristic
10#10590464C211yesmaximal, characteristic
11#10590421C211yesmaximal, characteristic, complemented
12#10590411C211yesmaximal, characteristic, complemented
13#10590315C211yesmaximal, characteristic, complemented
14#10590313C211yesmaximal, characteristic
15#10590252C211yesmaximal, characteristic, complemented
16#83706—31nomaximal
17#81223—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19C2×#3755C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×#888—21no—
24C3×#888—21no—
25C3×#888C2211yescharacteristic
26C3×#888C2211yescharacteristic
27C3×#870C2211yescharacteristic
28C3×#869—21no—
29C3×#869C2211yescharacteristic
30C3×C4×Dic6—21no—
31C3×C4×Dic6C2211yescharacteristic
32#63918C2211yescharacteristic
33#63895—21no—
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36#63888—21no—
37#63883—21no—
38#63869C2211yescharacteristic
39#63865—21no—
40#63662C2211yescharacteristic
41#63636C2211yescharacteristic
42#63634C2211yescharacteristic
43#63630C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#808C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63574C2211yescharacteristic
54#63574C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×Q82—31no—
62#5690—31no—
63#5579—31no—
64Q8×Dic6D311yescharacteristic, complemented
65C3×#479—31no—
66#5087—31no—
67#5087—31no—
68#5084—31no—
69#5081—31no—
70#5081—31no—
71#5078—31no—
72#5064—31no—
73#5026—31no—
74#5026—31no—
75#5026—31no—
76#5026—61no—
77C4×#215—31no—
78#5024—31no—
79#5022—31no—
80#5022D311yescharacteristic, complemented
81#5021—31no—
82#4890—31no—
83#4874—31no—
84#4870—31no—
85#4856—31no—
86#4846—31no—
87#4828—31no—
88#4817—31no—
89#4796—31no—
90#4793—31no—
91#4788—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6D411yescharacteristic
99C2×#627—21no—
100C2×#624—21no—
101C2×#624—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C42—21no—
105C32×C42C2311yescharacteristic
106#3755Q814yescomplemented
107#3752—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4D411yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136#3385—91noSylow
137C3×C4⋊Q8—31no—
138C3×C4⋊Q8—31no—
139C3×C4⋊Q8—31no—
140C3×C4⋊Q8—61no—
141C3×C4⋊Q8—61no—
142C3×C4⋊Q8—61no—
143C3×#125—31no—
144C3×C4×Q8—21no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—61no—
149C3×C4×Q8C2×D311yescharacteristic
150C3×C4×Q8C2×D311yescharacteristic
151#946—61no—
152Q8×Dic3C2×D311yescharacteristic
153Q8×Dic3C2×D311yescharacteristic
154C2×#215—31no—
155C2×#215—31no—
156C2×#215—61no—
157#897—61no—
158#896—61no—
159#896—61no—
160#896—61no—
161#896—61no—
162#893—31no—
163#893—31no—
164D3×C4⋊C4—61no—
165D3×C4⋊C4—61no—
166#890—31no—
167#888—21no—
168#888—21no—
169#888—31no—
170#888C2×D311yescharacteristic
171#888C2×D311yescharacteristic
172C4×D12—31no—
173C4×D12—31no—
174C4×D12—31no—
175C4×D12—31no—
176C4×D12—61no—
177#870—31no—
178#870C2×D311yescharacteristic
179#869—21no—
180#869—31no—
181#869C2×D311yescharacteristic
182C4×Dic6—21no—
183C4×Dic6C2×D311yescharacteristic
184C3×#107—31no—
185C3×#106—31no—
186C3×C4⋊C8—31no—
187C3×#103—31no—
188C3×#103—31no—
189#835—31no—
190#835—31no—
191#835—61no—
192#835C2×D311yescharacteristic
193#835C2×D311yescharacteristic
194#821—31no—
195#821—31no—
196#818—31no—
197#818—31no—
198#815—31no—
199Dic3⋊C8—31no—
200Dic3⋊C8—31no—
201C8×Dic3—31no—
202#809—31no—
203#809—31no—
204#809—31no—
205#809—31no—
206#809—61no—
207#808—31no—
208#808—31no—
209#808—31no—
210#808—31no—
211#808C2×D311yescharacteristic
212#807—31no—
213#807—31no—
214#807—31no—
215#807—31no—
216#807—31no—
217#807—31no—
218#807—31no—
219#807—31no—
220#807—61no—
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—21no—
232C32×Q8C2×Q812yes—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C4⋊(C3⋊D3)—21no—
240C4⋊(C3⋊D3)C2×Q812yes—
241C4×C3⋊D3—81no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×Dic6—22no—
251C3×Dic6—81no—
252C3×Dic6—81no—
253C3×Dic6—81no—
254#627—81no—
255#624—42no—
256#624—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—31no—
267#479—91no—
268#477—91no—
269#476—91no—
270#474—91no—
271#474—91no—
272#446—91no—
273#440—91no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—21no—
277C2×C3×Q8—31no—
278C2×C3×Q8—61no—
279C2×C3×Q8—61no—
280C2×C3×Q8—61no—
281C2×C3×Q8C22×D311yescharacteristic
282C2×C3×Q8C22×D311yescharacteristic
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—61no—
286C2×C4×D3—61no—
287C2×C4×D3—61no—
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—121no—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6#6711yescharacteristic
299C2×C3×C8—31no—
300C2×C3×C8—31no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—31no—
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—41no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C42—21no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—41no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331#215—34no—
332#215—34no—
333#215—64no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—121no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3#6711yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4#6711yescharacteristic
363Dic3⋊C4#6711yescharacteristic
364C4×Dic3—21no—
365C4×Dic3—21no—
366C4×Dic3C22×D311yescharacteristic
367C4×Dic3C22×D311yescharacteristic
368C2×C3⋊C8—31no—
369C2×C3⋊C8—31no—
370C2×C3⋊C8—31no—
371C2×C3⋊C8—31no—
372C2×C3⋊C8—61no—
373C2×C3⋊C8—61no—
374C2×C3⋊C8C22×D311yescharacteristic
375C2×C3⋊C8C22×D311yescharacteristic
376C22×C32C22×D411yescharacteristic
377C2×C3⋊D3—22no—
378C2×C3⋊D3—41no—
379C2×C3⋊D3—41no—
380C32×C4—22no—
381C32×C4—21no—
382C32×C4—21no—
383C32×C4—41no—
384C32×C4C22×Q811yescharacteristic
385C32×C42−1+411yescharacteristic
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×SD16—91no—
396C4⋊Q8—31no—
397C4⋊Q8—31no—
398C4⋊Q8—31no—
399C4⋊Q8—61no—
400C4⋊Q8—61no—
401C4⋊Q8—61no—
402C4⋊Q8—91no—
403#125—31no—
404#125—91no—
405C22⋊Q8—181no—
406C22⋊Q8—181no—
407C22⋊Q8—181no—
408C4×Q8—31no—
409C4×Q8—31no—
410C4×Q8—31no—
411C4×Q8—61no—
412C4×Q8D3211yescharacteristic
413C4×D4—91no—
414C4×D4—91no—
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—31no—
427C4⋊C8—91no—
428C4⋊C8—91no—
429#103—31no—
430#103—31no—
431#103—91no—
432#102—91no—
433#102—91no—
434#102—91no—
435#97—91no—
436#97—91no—
437C4×C8—91no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—121no—
441C3×Q8—21no—
442C3×Q8—21no—
443C3×Q8—22no—
444C3×Q8—41no—
445C3×Q8—62no—
446C3×Q8—241no—
447C3×Q8—241no—
448C3×Q8—241no—
449C3×Q8D3×Q812yes—
450C3×Q8D3×Q812yes—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4D3×D411yescharacteristic
470C2×C3×C4C2×#6711yescharacteristic
471C2×C3×C4C2×#6711yescharacteristic
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—121no—
481C2×Dic3C2×#6711yescharacteristic
482C2×Dic3C2×#6711yescharacteristic
483C2×Dic3C2×#6711yescharacteristic
484C2×Dic3C2×#6711yescharacteristic
485D12—32no—
486D12—32no—
487D12—62no—
488D12—61no—
489D12—61no—
490D12—121no—
491C4×D3—122no—
492C4×D3—122no—
493C4×D3—241no—
494C4×D3—241no—
495C4×D3—241no—
496C4×D3—241no—
497C4×D3—242no—
498Dic6—22no—
499Dic6—81no—
500Dic6—81no—
501Dic6—81no—
502Dic6—241no—
503Dic6—241no—
504C3×C8—61no—
505C3×C8—61no—
506C3⋊C8—21no—
507C3⋊C8—21no—
508C3⋊C8—32no—
509C3⋊C8—32no—
510C3⋊C8—62no—
511C3⋊C8—61no—
512C3⋊C8—61no—
513C3⋊C8—121no—
514C2×C32D4×Q811yescharacteristic
515C2×C32C2×#13711yescharacteristic
516C2×C32#57611yescharacteristic
517C3⋊D3—42no—
518C2×Q8—31no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—61no—
522C2×Q8—181no—
523C2×Q8C2×D3211yescharacteristic
524C2×D4—91no—
525C22×C4—181no—
526C22×C4—181no—
527C22×C4—181no—
528SD16—94no—
529C2×C8—31no—
530C2×C8—31no—
531C2×C8—91no—
532C2×C8—91no—
533C4⋊C4—21no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—91no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4C2×D3211yescharacteristic
553C22⋊C4—181no—
554C22⋊C4—181no—
555C22⋊C4—181no—
556C42—21no—
557C42—31no—
558C42—31no—
559C42—61no—
560C42—61no—
561C42C2×D3211yescharacteristic
562C22×C3—21no—
563C22×C3C2×D3×D411yescharacteristic
564C22×C3C22×#6711yescharacteristic
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—122no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—121no—
571C2×D3—121no—
572C2×D3—241no—
573C2×D3—241no—
574C3×C4—22no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—22no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—32no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—42no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—61no—
589C3×C4—61no—
590C3×C4—61no—
591C3×C4—81no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4C2×D3×Q811yescharacteristic
597C3×C4C2×D3×Q811yescharacteristic
598C3×C4#100711yescharacteristic
599C3×C4#101011yescharacteristic
600Dic3—21no—
601Dic3—21no—
602Dic3—21no—
603Dic3—41no—
604Dic3—41no—
605Dic3—41no—
606Dic3—41no—
607Dic3—121no—
608Dic3—121no—
609Dic3—241no—
610Dic3#94212yes—
611C32#338511yescharacteristic, complemented, Sylow
612C23—181no—
613Q8—21no—
614Q8—62no—
615Q8—241no—
616Q8—241no—
617Q8—241no—
618Q8—721no—
619Q8#379712yes—
620D4—92no—
621D4—181no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—181no—
633C2×C4—362no—
634C2×C4—721no—
635C2×C4—721no—
636C2×C4D3×#6711yescharacteristic
637C2×C4D3×#6711yescharacteristic
638C2×C4C22×D3211yescharacteristic
639C8—61no—
640C8—61no—
641C8—92no—
642C8—181no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3#563211yescharacteristic
647C2×C3#576911yescharacteristic
648C2×C3D3×#13711yescharacteristic
649C2×C3C2×#94211yescharacteristic
650C2×C3Q8×#6711yescharacteristic
651C2×C3#583511yescharacteristic
652D3—122no—
653D3—122no—
654D3—242no—
655C22—182no—
656C22—361no—
657C22—361no—
658C22C2×D3×#6711yescharacteristic
659C4—21no—
660C4—22no—
661C4—21no—
662C4—32no—
663C4—41no—
664C4—61no—
665C4—61no—
666C4—61no—
667C4—121no—
668C4—121no—
669C4—121no—
670C4—121no—
671C4—361no—
672C4#6429711yescharacteristic
673C4C2×#379711yescharacteristic
674C3—21no—
675C3#8122311yescharacteristic, complemented
676C3#8370611yescharacteristic, complemented
677C2—362no—
678C2#1059480311yescharacteristic
679C2D3×#94211yescharacteristic
680C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
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×Q8×Dic6C2semidirect
4. C3×#5022C2semidirect
5. #10591547C2semidirect
6. #10591546C2semidirect
11. #10590421C2semidirect
12. #10590411C2semidirect
13. #10590315C2semidirect
15. #10590252C2semidirect
64. Q8×Dic6D3semidirect
80. #5022D3semidirect
106. #3755Q8semidirect
611. C32#3385semidirect
675. C3#81223semidirect
676. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105939382
#105927252
C3×#50222
#105915472
#105915462
#105915402
#105915362
#105904662
#105904642
#105904212
#105904112
#105903152
#105903132
#105902522
#837063
#812233