Finite Group Databasebeta

← #11897585

Subgroups — #11897585

Order 1152.

802 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#627C211yesmaximal, characteristic, complemented
2#10594485C211yesmaximal, characteristic, complemented
3#10592460C211yesmaximal, characteristic, complemented
4C3×#4785C211yesmaximal, characteristic
5C3×#4766C211yesmaximal, characteristic, complemented
6#10591435C211yesmaximal, characteristic
7#10591430C211yesmaximal, characteristic
8#10591409C211yesmaximal, characteristic, complemented
9#10590894C211yesmaximal, characteristic, complemented
10#10590789C211yesmaximal, characteristic, complemented
11#10590778C211yesmaximal, characteristic, complemented
12#10590757C211yesmaximal, characteristic, complemented
13#10590558C211yesmaximal, characteristic, complemented
14#10590419C211yesmaximal, characteristic, complemented
15#10590416C211yesmaximal, characteristic, complemented
16#81158—31nomaximal
17#79855—31nomaximal
18C22×#627—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#890C2211yescharacteristic
26#63982—21no—
27#63964—21no—
28#63964—21no—
29#63919C2211yescharacteristic
30#63918C2211yescharacteristic
31#63918C2211yescharacteristic
32C4×#627C2211yescharacteristic
33#63899—21no—
34#63898C2211yescharacteristic
35#63896—21no—
36Dic3×D12C2211yescharacteristic
37D3×Dic3⋊C4—21no—
38#63869C2211yescharacteristic
39#63857—21no—
40C32×#102C2211yescharacteristic
41#63659C2211yescharacteristic
42#63644C2211yescharacteristic
43#63641C2211yescharacteristic
44#63635C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#818C2211yescharacteristic
48C3×#815C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60#63553C2211yescharacteristic
61#5690—31no—
62#5539—31no—
63D4×Dic6—31no—
64D4×Dic6—31no—
65C3×#478—31no—
66C3×#442—31no—
67#5152—31no—
68Dic3×D8—31no—
69#5064—31no—
70#5014—31no—
71#5009—31no—
72#5008—31no—
73#4890—31no—
74#4876—31no—
75#4870—31no—
76#4856—31no—
77#4855—31no—
78#4855—31no—
79#4842—31no—
80#4828—31no—
81#4785D311yescharacteristic
82#4766D311yescharacteristic, complemented
83#4763—31no—
84#4761—31no—
85#4761—31no—
86#4761—31no—
87#4761—61no—
88#4759—31no—
89#4756—31no—
90#4702—31no—
91#4701—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×#627—21no—
100C2×#627—21no—
101C2×#627—21no—
102C2×#627—44no—
103C2×#627D411yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108#3757—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#213Q814yescomplemented
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724—21no—
129#3724D411yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137#3384—91noSylow
138C22×Dic6—61no—
139C22×Dic6—61no—
140C2×C3×D8—31no—
141C3×#125—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144C3×C4×D4—31no—
145D4×Dic3—31no—
146D4×Dic3—31no—
147D4×Dic3—31no—
148D4×Dic3—31no—
149D4×Dic3—61no—
150D4×Dic3C2×D311yescharacteristic
151D4×Dic3C2×D311yescharacteristic
152C2×#213C2×D311yescharacteristic
153#924—61no—
154#924—61no—
155#924—61no—
156C2×Dic3⋊C4—61no—
157#897—61no—
158#896—61no—
159#896—61no—
160#893—31no—
161#893C2×D311yescharacteristic
162D3×C4⋊C4—61no—
163#890—31no—
164#890C2×D311yescharacteristic
165#888—31no—
166#888—31no—
167#888—31no—
168#888—31no—
169#888—31no—
170#888—31no—
171#888—61no—
172#878—61no—
173#878—61no—
174#878—61no—
175#878—61no—
176#878—61no—
177#878—61no—
178C4×D12—31no—
179#870—31no—
180#869—31no—
181#869—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C3×#107—31no—
185C3×#106—31no—
186C3×#106—31no—
187C3×C4⋊C8—31no—
188C3×#102—21no—
189C3×#102—31no—
190C3×#102—31no—
191C3×#102C2×D311yescharacteristic
192C3×#102C2×D311yescharacteristic
193C3×#97—31no—
194#832—31no—
195#832—31no—
196#832—31no—
197#832—31no—
198#832—61no—
199#832C2×D311yescharacteristic
200#821—31no—
201#821C2×D311yescharacteristic
202#818—31no—
203#818C2×D311yescharacteristic
204#817—31no—
205#817—31no—
206#817—31no—
207#817—31no—
208#817—61no—
209#815—31no—
210#815C2×D311yescharacteristic
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—61no—
215Dic3⋊C8C2×D311yescharacteristic
216C8×Dic3—31no—
217C8×Dic3—31no—
218#809—31no—
219#808—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808—61no—
224#808C2×D311yescharacteristic
225#808C2×D311yescharacteristic
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230#803—31no—
231C23×C32—21no—
232C22×C3×D3—21no—
233C32×D4—21no—
234C32×D4C2×Q812yes—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—42no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—81no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—42no—
247C2×C3×Dic3—42no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12C2×Q812yescomplemented
254C3×C4×D3—81no—
255#627—22no—
256#627—42no—
257#627—42no—
258#627—42no—
259D3×Dic3—42no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8C2×Q812yescomplemented
265#554—91no—
266D4×Q8—91no—
267#501—91no—
268#501—91no—
269#498—91no—
270#478—31no—
271#478—91no—
272#476—91no—
273#476—91no—
274#476—91no—
275#474—91no—
276#446—91no—
277#442—31no—
278#442—91no—
279C4×D8—91no—
280C2×C3×D4—21no—
281C2×C3×D4—31no—
282C2×C3×D4C22×D311yescharacteristic
283C2×C3×D4C22×D311yescharacteristic
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×C3×C4—61no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—121no—
294C2×D12C22×D311yescharacteristic
295C2×C4×D3—21no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×Dic6—124no—
310C2×Dic6—124no—
311C3×D8—34no—
312C2×C3×C8—21no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—31no—
330#217—21no—
331#217—21no—
332#217—61no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—121no—
337#213Dic614yescomplemented
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341C4⋊Dic3—21no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—121no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381C22×C32—22no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32C22×D411yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C32×C4—41no—
389C32×C4C22×Q811yescharacteristic
390C32×C42−1+411yescharacteristic
391C3⋊Dic3—21no—
392C3⋊Dic3—41no—
393C3⋊Dic3—41no—
394C3⋊Dic3AGL(1,ℤ/8)12yes—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C22×Q8—181no—
403C2×D8—31no—
404C4⋊Q8—91no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408#125—31no—
409#125—91no—
410C22⋊Q8—181no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C22⋊Q8—181no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C4×Q8—91no—
417C4×D4—31no—
418C4×D4—31no—
419C4×D4—31no—
420C4×D4—91no—
421C4×D4—91no—
422C4×D4—91no—
423C2×C4⋊C4—181no—
424#107—31no—
425#107—91no—
426#107—91no—
427#106—31no—
428#106—31no—
429#106—91no—
430#106—91no—
431#106—91no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#102—31no—
437#102—31no—
438#102—91no—
439#102—91no—
440#102—91no—
441#102D3211yescharacteristic
442#97—31no—
443#97—91no—
444C4×C8—91no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—41no—
448C23×C3—61no—
449C22×D3—21no—
450C3×D4—21no—
451C3×D4—21no—
452C3×D4—22no—
453C3×D4—32no—
454C3×D4—41no—
455C3×D4—61no—
456C3×D4C2×Dic612yes—
457C3×D4D3×Q812yes—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—41no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—122no—
470C2×C3×C4—122no—
471C2×C3×C4—241no—
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—42no—
482C2×Dic3—42no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3—122no—
492C2×Dic3—122no—
493C2×Dic3—122no—
494C2×Dic3—242no—
495C2×Dic3—241no—
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500D12—21no—
501D12C2×Dic612yescomplemented
502C4×D3—81no—
503C4×D3—122no—
504C4×D3—241no—
505Dic6—62no—
506Dic6—62no—
507Dic6—122no—
508Dic6—122no—
509Dic6—122no—
510Dic6—122no—
511Dic6—122no—
512Dic6—122no—
513Dic6—241no—
514Dic6—241no—
515Dic6—242no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—32no—
519C3×C8—41no—
520C3×C8—61no—
521C3⋊C8—21no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C3⋊C8C2×Dic612yescomplemented
526C2×C32—42no—
527C2×C32D4×Q811yescharacteristic
528C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
529C2×C32#57711yescharacteristic
530C3×D3—42no—
531C2×Q8—91no—
532C2×Q8—181no—
533C2×Q8—181no—
534C2×Q8—181no—
535C2×Q8—181no—
536C2×Q8—364no—
537C2×D4—31no—
538C2×D4C2×D3211yescharacteristic
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—181no—
543C22×C4—181no—
544C22×C4—181no—
545D8—34no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—91no—
549C2×C8C2×D3211yescharacteristic
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4C2×D3211yescharacteristic
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C42—31no—
574C42—31no—
575C42—91no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—42no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—62no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C2×D3×D411yescharacteristic
591C2×D3—22no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—81no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4C22×Dic611yescharacteristic
607C3×C4C2×D3×Q811yescharacteristic
608C3×C4#101011yescharacteristic
609C3×C4#101011yescharacteristic
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613Dic3—21no—
614Dic3—32no—
615Dic3—32no—
616Dic3—41no—
617Dic3—41no—
618Dic3—41no—
619Dic3—62no—
620Dic3—61no—
621Dic3—61no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628Dic3—241no—
629C32#338411yescharacteristic, complemented, Sylow
630C23—21no—
631C23—61no—
632Q8—182no—
633Q8—362no—
634Q8—362no—
635Q8—362no—
636Q8—721no—
637D4—21no—
638D4—32no—
639D4—61no—
640D4D3×Dic612yes—
641C2×C4—21no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—122no—
652C2×C4—122no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—241no—
656C2×C4—362no—
657C2×C4—362no—
658C2×C4—721no—
659C2×C4C22×D3211yescharacteristic
660C8—21no—
661C8—32no—
662C8—61no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—42no—
668C2×C3—42no—
669C2×C3—82no—
670C2×C3—122no—
671C2×C3D4×Dic611yescharacteristic
672C2×C3#563211yescharacteristic
673C2×C3#577011yescharacteristic
674C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
675C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
676C2×C3#577511yescharacteristic
677D3—42no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—62no—
682C22—121no—
683C22—121no—
684C22D32×D411yescharacteristic
685C4—41no—
686C4—61no—
687C4—61no—
688C4—61no—
689C4—61no—
690C4—92no—
691C4—121no—
692C4—121no—
693C4—121no—
694C4—181no—
695C4—361no—
696C4—361no—
697C4C2×D3×Dic611yescharacteristic
698C4#6430911yescharacteristic
699C3—21no—
700C3#7985511yescharacteristic, complemented
701C3#8115811yescharacteristic, complemented
702C2—42no—
703C2—122no—
704C2#1059407111yescharacteristic
705C2#1059473611yescharacteristic
706C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenter#102D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#627C2semidirect
2. #10594485C2semidirect
3. #10592460C2semidirect
5. C3×#4766C2semidirect
8. #10591409C2semidirect
9. #10590894C2semidirect
10. #10590789C2semidirect
11. #10590778C2semidirect
12. #10590757C2semidirect
13. #10590558C2semidirect
14. #10590419C2semidirect
15. #10590416C2semidirect
82. #4766D3semidirect
116. C3×#213Q8semidirect
253. C3×D12C2×Q8semidirect
264. C3×C3⋊C8C2×Q8semidirect
337. #213Dic6semidirect
501. D12C2×Dic6semidirect
525. C3⋊C8C2×Dic6semidirect
629. C32#3384semidirect
700. C3#79855semidirect
701. C3#81158semidirect

Maximal subgroups

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

subgroupindex
D4×#6272
#105944852
#105924602
C3×#47852
C3×#47662
#105914352
#105914302
#105914092
#105908942
#105907892
#105907782
#105907572
#105905582
#105904192
#105904162
#811583
#798553