Finite Group Databasebeta

← #11870455

Subgroups — #11870455

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×D12C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592545C211yesmaximal, characteristic, complemented
4C3×#4843C211yesmaximal, characteristic, complemented
5C3×#4833C211yesmaximal, characteristic, complemented
6#10590944C212yesmaximal, complemented
7Dic3×D24C212yesmaximal, complemented
8#10590745C212yesmaximal, complemented
9#10590680C212yesmaximal, complemented
10#10590355C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#80312—31nomaximal
13#79297—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3795—21no—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C2×C3×D24C2212yes—
20C3×#874C2211yescharacteristic, complemented
21C3×C4×D12C2211yescharacteristic
22C3×C42×D3C2211yescharacteristic
23D3×(C2×D3)⋊C4—21no—
24#63908—21no—
25#63908C2212yes—
26C4×#626—21no—
27#63894C2211yescharacteristic
28Dic3×D12—21no—
29Dic3×D12C2211yescharacteristic
30Dic3×D12C2212yescomplemented
31D3×C4⋊Dic3C2211yescharacteristic
32#63880—21no—
33#63860—21no—
34C2×#3714C2212yes—
35C32×C4⋊C8C2211yescharacteristic, complemented
36#63648C2212yes—
37#63645C2212yescomplemented
38C3×#821C2212yescomplemented
39C3×(C2×D3)⋊C8C2212yes—
40C3×C8×Dic3C2212yescomplemented
41C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
42#63575C2212yescomplemented
43#63563C2212yes—
44#63563C2212yescomplemented
45#5716—31no—
46C4×D3×D4—31no—
47#5477—31no—
48C2×C4×D12—31no—
49C3×#459—31no—
50C3×#431—31no—
51#5156—32no—
52Dic3×D8—32no—
53#5072—31no—
54#5007—31no—
55#4846—31no—
56#4846—31no—
57#4846—31no—
58#4846—61no—
59#4843—31no—
60#4843D311yescharacteristic, complemented
61#4833D311yescharacteristic, complemented
62#4774—32no—
63#4756—32no—
64#4736—32no—
65#4732—32no—
66C4×D24—32no—
67C4×D24—32no—
68C22×D32—21no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×#634—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×#626—21no—
81C2×#625—22no—
82C2×#624—21no—
83C2×D3×Dic3—21no—
84C2×D3×Dic3—22no—
85C2×D3×Dic3—21no—
86D3×D12—22no—
87D3×D12—22no—
88C4×D32—44no—
89#3795—44no—
90C2×C32×C8C2312yes—
91C32×C42C2311yescharacteristic
92#3752—21no—
93C4⋊(C3⋊Dic3)—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95C4⋊(C3⋊Dic3)C2311yescharacteristic
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×D24—24no—
103Dic3⋊Dic3—21no—
104#3722—21no—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—21no—
108#3714—24no—
109#3100—91noSylow
110C2×#237—61no—
111C2×D3×D4—31no—
112C2×#235—61no—
113C22×D12—31no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C2×C3×D8—32no—
117C3×#127—31no—
118C3×C4×D4—31no—
119C2×C3×C42—31no—
120#938—32no—
121#938—61no—
122#936—61no—
123D4×Dic3—31no—
124D4×Dic3—32no—
125D4×Dic3—61no—
126C2×#213—32no—
127#930—32no—
128#930—61no—
129C4×#67—61no—
130C2×(C2×D3)⋊C4—61no—
131C2×C4⋊Dic3—31no—
132C2×D24—32no—
133C2×D24C2×D312yes—
134#893—31no—
135D3×C4⋊C4—31no—
136#67⋊C4—61no—
137D3×C22⋊C4—61no—
138#875—61no—
139#874C2×D311yescharacteristic, complemented
140C4×D12—31no—
141C4×D12—32no—
142C4×D12—31no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—61no—
146C4×D12—61no—
147C4×D12—61no—
148C4×D12—61no—
149C4×D12C2×D311yescharacteristic
150C42×D3C2×D311yescharacteristic
151#869—31no—
152#869—31no—
153#869—61no—
154C3×C4⋊C8—21no—
155C3×C4⋊C8—31no—
156C3×C4⋊C8C2×D311yescharacteristic, complemented
157C3×C4⋊C8C2×D311yescharacteristic, complemented
158C3×#102—32no—
159C3×C22⋊C8—32no—
160C3×C4×C8—32no—
161#832—32no—
162#832—32no—
163#821—32no—
164#821—32no—
165#821—32no—
166#821—32no—
167#821—62no—
168#821C2×D312yescomplemented
169(C2×D3)⋊C8C2×D312yes—
170#818—32no—
171#818—32no—
172#818—32no—
173#818—62no—
174C8×Dic3C2×D312yescomplemented
175#807—32no—
176C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
177C22×C3⋊D3—21no—
178C22×C3×D3—21no—
179C22×C3×D3—22no—
180C22×C3×D3C2×D411yescharacteristic
181C2×D32—24no—
182C2×D32—42no—
183C2×D32—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—21no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)#4112yescomplemented
191C4×C3⋊D3—42no—
192#634—42no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—21no—
198C3×D12—22no—
199C3×D12—22no—
200C3×D12—42no—
201C3×D12—42no—
202C3×D12#4112yescomplemented
203C3×C4×D3—21no—
204C3×C4×D3—21no—
205C3×C4×D3—41no—
206C3×C4×D3—42no—
207C3×C4×D3D814yescomplemented
208#626—24no—
209#625—44no—
210#624—42no—
211D3×Dic3—42no—
212D3×Dic3—44no—
213D3×Dic3—42no—
214C32×C8—22no—
215C3×C3⋊C8—22no—
216#532—91no—
217C2×C4×D4—91no—
218#480—92no—
219#474—91no—
220#474—91no—
221#459—31no—
222#459—91no—
223#447—92no—
224C4×D8—92no—
225C4×D8—92no—
226#431—31no—
227C23×D3—61no—
228C23×D3—61no—
229C2×C3×D4—31no—
230C2×C3×D4—32no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—61no—
237C2×#67—62no—
238C2×#67—62no—
239C2×#67—61no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—62no—
243#237—124no—
244D3×D4—62no—
245D3×D4—62no—
246#235—124no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—31no—
250C2×D12—31no—
251C2×D12—61no—
252C2×D12—62no—
253C2×D12—61no—
254C2×D12—62no—
255C2×D12C22×D312yes—
256C2×D12C22×D311yescharacteristic
257C2×C4×D3—21no—
258C2×C4×D3—61no—
259C2×C4×D3—61no—
260C2×C4×D3—62no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—121no—
266C2×C4×D3—124no—
267C2×C4×D3—124no—
268C2×C4×D3D1211yescharacteristic
269C2×C4×D3D1211yescharacteristic
270C2×C4×D3C22×D311yescharacteristic
271C2×Dic6—61no—
272C2×Dic6—61no—
273C2×Dic6—121no—
274C3×D8—64no—
275C2×C3×C8—22no—
276C2×C3×C8—32no—
277C2×C3×C8C22×D312yes—
278C2×C3×C8C22×D312yes—
279C3×C4⋊C4—31no—
280C3×C22⋊C4—61no—
281C3×C42—21no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42C22×D311yescharacteristic
286C3×C42C22×D311yescharacteristic
287#217—61no—
288#217—62no—
289#217—62no—
290#213—64no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—61no—
299(C2×D3)⋊C4—121no—
300C4⋊Dic3—32no—
301C4⋊Dic3—32no—
302C4⋊Dic3—31no—
303C4⋊Dic3—31no—
304C4⋊Dic3—61no—
305C4⋊Dic3—62no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3—61no—
309C4⋊Dic3—121no—
310C4⋊Dic3C22×D311yescharacteristic
311Dic3⋊C4—61no—
312C4×Dic3D1211yescharacteristic
313C4×Dic3D1211yescharacteristic
314C4×Dic3C22×D311yescharacteristic
315C2×C3⋊C8C22×D312yes—
316D24—24no—
317D24—64no—
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—22no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3×D3—21no—
323C2×C3×D3—21no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—42no—
328C2×C3×D3—42no—
329C2×C3×D3—42no—
330C2×C3×D3C2×D812yes—
331D32—48no—
332C32×C4—21no—
333C32×C4C2×D812yes—
334C32×C4C2×#4111yescharacteristic
335C32×C4C2×#4111yescharacteristic
336C3⋊Dic3—41no—
337C3⋊Dic3—42no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—41no—
341C3×Dic3C2×D812yes—
342C2×#41—181no—
343C22×D4—91no—
344C23×C4—181no—
345C2×D8—32no—
346C2×D8—92no—
347C4⋊Q8—91no—
348#127—31no—
349#124—181no—
350#121—92no—
351#121—181no—
352C4×D4—31no—
353C4×D4—91no—
354C4×D4—91no—
355C4×D4—92no—
356C4×D4—91no—
357C4×D4—181no—
358C4×D4—181no—
359C4×D4—181no—
360C2×C4⋊C4—91no—
361C2×C22⋊C4—181no—
362C2×C42—31no—
363#107—92no—
364#107—92no—
365C4⋊C8—31no—
366C4⋊C8D3211yescharacteristic, complemented
367#102—32no—
368#102—92no—
369#102—92no—
370#102—92no—
371C22⋊C8—32no—
372C4×C8—32no—
373C23×C3—31no—
374C23×C3—61no—
375C23×C3—62no—
376C22×D3—21no—
377C22×D3—22no—
378C22×D3—64no—
379C22×D3—64no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—121no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3C2×D1211yescharacteristic
388C3×D4—32no—
389C3×D4—61no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—122no—
393C3×D4—122no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—31no—
398C2×C3×C4—34no—
399C2×C3×C4—31no—
400C2×C3×C4—31no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—121no—
405C2×C3×C4—122no—
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4C2×D1211yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412#67—64no—
413#67—124no—
414#67—124no—
415C2×Dic3—21no—
416C2×Dic3—61no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—61no—
420C2×Dic3—122no—
421C2×Dic3—121no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3—124no—
425C2×Dic3C2×D1211yescharacteristic
426C2×Dic3C2×D1211yescharacteristic
427C2×Dic3C2×D1211yescharacteristic
428D12—22no—
429D12—21no—
430D12—22no—
431D12—32no—
432D12—32no—
433D12—42no—
434D12—42no—
435D12—62no—
436D12—64no—
437D12—61no—
438D12—61no—
439D12—121no—
440D12#23712yescomplemented
441C4×D3—21no—
442C4×D3—21no—
443C4×D3—41no—
444C4×D3—42no—
445C4×D3—122no—
446C4×D3—122no—
447C4×D3—124no—
448C4×D3—122no—
449C4×D3—122no—
450C4×D3—122no—
451C4×D3—122no—
452C4×D3—242no—
453C4×D3D2414yescomplemented
454Dic6—122no—
455Dic6—122no—
456Dic6—242no—
457C3×C8—22no—
458C3×C8—22no—
459C3×C8—42no—
460C3×C8—62no—
461C3⋊C8—22no—
462C2×C32#52511yescharacteristic
463C2×C32C22×D811yescharacteristic
464C2×C32#57511yescharacteristic
465C3⋊D3—42no—
466C3×D3—22no—
467C3×D3—42no—
468C3×D3—82no—
469C24—181no—
470#41—364no—
471C2×Q8—181no—
472C2×D4—31no—
473C2×D4—32no—
474C2×D4—61no—
475C2×D4—61no—
476C2×D4—91no—
477C2×D4—181no—
478C2×D4—182no—
479C2×D4—182no—
480C2×D4—182no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—61no—
485C22×C4—181no—
486C22×C4—181no—
487C22×C4—182no—
488C22×C4—181no—
489C22×C4—181no—
490C22×C4—364no—
491D8—64no—
492D8—184no—
493C2×C8—32no—
494C2×C8C2×D3212yes—
495C4⋊C4—31no—
496C4⋊C4—91no—
497C4⋊C4—92no—
498C4⋊C4—181no—
499C4⋊C4—181no—
500C22⋊C4—61no—
501C22⋊C4—181no—
502C22⋊C4—181no—
503C22⋊C4—182no—
504C22⋊C4—182no—
505C22⋊C4—181no—
506C42—31no—
507C42—31no—
508C42—31no—
509C42C2×D3211yescharacteristic
510C22×C3—21no—
511C22×C3—32no—
512C22×C3—61no—
513C22×C3—61no—
514C22×C3—62no—
515C22×C3—121no—
516C22×C3—121no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3C22×D1211yescharacteristic
521C22×C3C2×D3×D411yescharacteristic
522C2×D3—21no—
523C2×D3—21no—
524C2×D3—22no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—42no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—122no—
533C2×D3—128no—
534C2×D3—128no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—241no—
540C2×D3—241no—
541C2×D3C2×D2412yes—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—22no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—32no—
548C3×C4—41no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—121no—
552C3×C4C2×D2412yes—
553C3×C4D3×D812yes—
554C3×C4C2×#23711yescharacteristic
555C3×C4D3×#4111yescharacteristic
556C3×C4D3×#4111yescharacteristic
557C3×C4D3×#4111yescharacteristic
558Dic3—21no—
559Dic3—21no—
560Dic3—41no—
561Dic3—122no—
562Dic3—121no—
563Dic3—122no—
564Dic3—121no—
565Dic3—242no—
566Dic3—241no—
567Dic3C2×D2412yes—
568C32#310011yescharacteristic, complemented, Sylow
569C23—31no—
570C23—61no—
571C23—62no—
572C23—184no—
573C23—181no—
574C23—362no—
575C23—362no—
576Q8—362no—
577D4—32no—
578D4—62no—
579D4—61no—
580D4—62no—
581D4—92no—
582D4—122no—
583D4—122no—
584D4—184no—
585D4—181no—
586D4—364no—
587C2×C4—31no—
588C2×C4—34no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—121no—
595C2×C4—122no—
596C2×C4—181no—
597C2×C4—182no—
598C2×C4—362no—
599C2×C4—362no—
600C2×C4—364no—
601C2×C4—362no—
602C2×C4—362no—
603C2×C4D3×D1211yescharacteristic
604C2×C4D3×D1211yescharacteristic
605C2×C4C22×D3211yescharacteristic
606C8—22no—
607C8—62no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—62no—
612C2×C3—122no—
613C2×C3—242no—
614C2×C3#552411yescharacteristic
615C2×C3#560611yescharacteristic
616C2×C3C22×D2411yescharacteristic
617C2×C3#574811yescharacteristic
618C2×C3C2×D3×D811yescharacteristic
619C2×C3#577311yescharacteristic
620D3—22no—
621D3—42no—
622D3—82no—
623D3—122no—
624D3—122no—
625D3—242no—
626C22—32no—
627C22—61no—
628C22—61no—
629C22—62no—
630C22—121no—
631C22—121no—
632C22—122no—
633C22—122no—
634C22—122no—
635C22—182no—
636C22—368no—
637C22—361no—
638C22—361no—
639C22C2×D3×D1211yescharacteristic
640C4—21no—
641C4—32no—
642C4—61no—
643C4—61no—
644C4—121no—
645C4—361no—
646C4—362no—
647C4D3×D2412yes—
648C4D3×#23711yescharacteristic
649C4#6431911yescharacteristic
650C3—21no—
651C3#7929711yescharacteristic, complemented
652C3#8031211yescharacteristic, complemented
653C2—62no—
654C2—122no—
655C2—242no—
656C2—362no—
657C2#1059462611yescharacteristic
658C2C2×D3×D2411yescharacteristic
659C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3100
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
1. C4×D3×D12C2semidirect
2. #10593897C2semidirect
3. #10592545C2semidirect
4. C3×#4843C2semidirect
5. C3×#4833C2semidirect
6. #10590944C2semidirect
7. Dic3×D24C2semidirect
8. #10590745C2semidirect
9. #10590680C2semidirect
10. #10590355C2semidirect
11. #10590272C2semidirect
18. #64078C22semidirect
20. C3×#874C22semidirect
30. Dic3×D12C22semidirect
35. C32×C4⋊C8C22semidirect
37. #63645C22semidirect
38. C3×#821C22semidirect
40. C3×C8×Dic3C22semidirect
41. C3×C4⋊(C3⋊C8)C22semidirect
42. #63575C22semidirect
44. #63563C22semidirect
60. #4843D3semidirect
61. #4833D3semidirect
139. #874C2×D3semidirect
156. C3×C4⋊C8C2×D3semidirect
157. C3×C4⋊C8C2×D3semidirect
168. #821C2×D3semidirect
174. C8×Dic3C2×D3semidirect
176. C4⋊(C3⋊C8)C2×D3semidirect
190. C4⋊(C3⋊D3)#41semidirect
202. C3×D12#41semidirect
207. C3×C4×D3D8semidirect
366. C4⋊C8D32semidirect
440. D12#237semidirect
453. C4×D3D24semidirect
568. C32#3100semidirect
651. C3#79297semidirect
652. C3#80312semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
#105938972
#105925452
C3×#48432
C3×#48332
#105909442
Dic3×D242
#105907452
#105906802
#105903552
#105902722
#803123
#792973