Finite Group Databasebeta

← #11870454

Subgroups — #11870454

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3802C211yesmaximal, characteristic, complemented
2#10593907C211yesmaximal, characteristic, complemented
3#10592532C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4843C211yesmaximal, characteristic, complemented
6#10590945C212yesmaximal, complemented
7#10590777C212yesmaximal, complemented
8#10590740C212yesmaximal, complemented
9#10590650C212yesmaximal, complemented
10#10590347C211yesmaximal, characteristic, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#80948—31nomaximal
13#80312—31nomaximal
14C2×#3802C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3796—21no—
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×D24C2212yes—
19C3×#874C2211yescharacteristic, complemented
20C3×C4×D12C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×#869C2211yescharacteristic, complemented
23#63921—21no—
24#63916—21no—
25#63916C2212yes—
26#63902—21no—
27C4×#625—21no—
28#63900C2211yescharacteristic
29#63898—21no—
30#63898C2211yescharacteristic
31#63898C2211yescharacteristic
32#63898C2212yescomplemented
33#63863—21no—
34C2×#3713C2212yes—
35C32×C4⋊C8C2211yescharacteristic, complemented
36#63647C2212yes—
37C8×C3⋊Dic3C2212yescomplemented
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
39C3×#821C2212yes—
40C3×#821C2212yescomplemented
41C3×#818C2212yescomplemented
42#63576C2212yescomplemented
43#63562C2212yes—
44#63562C2212yescomplemented
45#5725—31no—
46#5716—31no—
47C4×D3×D4—31no—
48C4×D3×D4—31no—
49C3×#474—31no—
50C3×#459—31no—
51#5156—32no—
52Dic3×D8—32no—
53#5087—31no—
54#5072—31no—
55#5015—31no—
56#5007—31no—
57#4882—32no—
58#4872—32no—
59#4846D311yescharacteristic, complemented
60#4843D311yescharacteristic, complemented
61#4833—31no—
62#4833—31no—
63#4833—61no—
64#4774—32no—
65#4773—32no—
66#4756—32no—
67#4756—32no—
68C22×D32—21no—
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×Dic6—21no—
80C2×#626—22no—
81C2×#625—21no—
82C2×#624—21no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86#3802—22no—
87#3802—22no—
88C4×D32—44no—
89#3796—44no—
90C2×C32×C8C2312yes—
91C32×C42C2311yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4⋊Dic3C2311yescharacteristic
102C3×D24—24no—
103#3724—21no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—21no—
107(C2×D3)⋊Dic3—21no—
108#3713—24no—
109#3100—91noSylow
110C2×#239—61no—
111C2×#237—61no—
112C2×D3×D4—31no—
113C2×D3×D4—31no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C2×C3×D8—32no—
117C3×C4⋊Q8—31no—
118C3×#127—31no—
119C3×C4×D4—31no—
120C3×C4×D4—31no—
121#947—61no—
122#938—32no—
123#938—61no—
124#936—61no—
125D4×Dic3—31no—
126D4×Dic3—32no—
127D4×Dic3—31no—
128D4×Dic3—61no—
129C2×#213—32no—
130C2×#213—32no—
131C4×#67—61no—
132C4×#67—61no—
133C2×D24C2×D312yes—
134#895—32no—
135#895—61no—
136#893—31no—
137#893—32no—
138#893—31no—
139#893—61no—
140D3×C4⋊C4—31no—
141D3×C4⋊C4—31no—
142#67⋊C4—61no—
143#67⋊C4—61no—
144D3×C22⋊C4—61no—
145D3×C22⋊C4—61no—
146#874C2×D311yescharacteristic, complemented
147C4×D12C2×D311yescharacteristic
148C4×D12C2×D311yescharacteristic
149C42×D3—31no—
150C42×D3—31no—
151C42×D3—61no—
152#869C2×D311yescharacteristic, complemented
153C3×#107—32no—
154C3×C4⋊C8—21no—
155C3×C4⋊C8C2×D311yescharacteristic, complemented
156C3×C4⋊C8C2×D311yescharacteristic, complemented
157C3×#102—32no—
158C3×#102—32no—
159#832—32no—
160#832—32no—
161#821C2×D312yes—
162#821C2×D312yescomplemented
163(C2×D3)⋊C8—32no—
164(C2×D3)⋊C8—32no—
165(C2×D3)⋊C8—62no—
166#818C2×D312yescomplemented
167C8×Dic3—32no—
168C8×Dic3—32no—
169C8×Dic3—62no—
170#809—32no—
171#809—32no—
172#807—32no—
173#807—32no—
174C4⋊(C3⋊C8)—31no—
175C4⋊(C3⋊C8)—31no—
176C4⋊(C3⋊C8)—61no—
177C22×C3⋊D3C2×D411yescharacteristic
178C22×C3×D3—21no—
179C22×C3×D3—21no—
180C22×C3×D3—22no—
181C2×D32—24no—
182C2×D32—42no—
183C2×D32—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4×C3⋊D3—21no—
191C4×C3⋊D3—21no—
192C4×C3⋊D3—41no—
193C4×C3⋊D3D814yescomplemented
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C3×D12—21no—
198C3×D12—21no—
199C3×D12—22no—
200C3×D12—22no—
201C3×D12—42no—
202C3×D12—42no—
203C3×D12#4112yescomplemented
204C3×D12#4112yescomplemented
205C3×C4×D3—42no—
206C3×C4×D3—42no—
207C3×Dic6—42no—
208#626—44no—
209#625—24no—
210#624—42no—
211D3×Dic3—44no—
212D3×Dic3—42no—
213D3×Dic3—42no—
214C32×C8—22no—
215C3⋊(C3⋊C8)—22no—
216#532—91no—
217C2×C4×D4—91no—
218#480—92no—
219#474—31no—
220#474—91no—
221#459—31no—
222#459—91no—
223#447—92no—
224C4×D8—92no—
225C4×D8—92no—
226#431—91no—
227C23×D3—61no—
228C23×D3—61no—
229C2×C3×Q8—61no—
230C2×C3×D4—31no—
231C2×C3×D4—31no—
232C2×C3×D4—32no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C2×#67—62no—
238C2×#67—61no—
239C2×#67—61no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—62no—
243#239—124no—
244#237—124no—
245D3×D4—62no—
246D3×D4—62no—
247D3×D4—62no—
248D3×D4—62no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—62no—
252C2×D12C22×D312yes—
253C2×D12C22×D311yescharacteristic
254C2×D12C22×D311yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C2×C4×D3—31no—
261C2×C4×D3—31no—
262C2×C4×D3—31no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×C4×D3—62no—
271C2×C4×D3—124no—
272C2×C4×D3—124no—
273C2×Dic6—21no—
274C3×D8—64no—
275C2×C3×C8—22no—
276C2×C3×C8C22×D312yes—
277C2×C3×C8C22×D312yes—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—32no—
280C3×C4⋊C4—31no—
281C3×C4⋊C4—61no—
282C3×C22⋊C4—61no—
283C3×C22⋊C4—61no—
284C3×C42—21no—
285C3×C42C22×D311yescharacteristic
286C3×C42C22×D311yescharacteristic
287#217—61no—
288#217—61no—
289#217—62no—
290#217—62no—
291#213—64no—
292#213—64no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—21no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299C4⋊Dic3—21no—
300C4⋊Dic3C22×D311yescharacteristic
301C4⋊Dic3C22×D312yes—
302C4⋊Dic3C22×D311yescharacteristic
303Dic3⋊C4—61no—
304Dic3⋊C4—61no—
305C4×Dic3—31no—
306C4×Dic3—31no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C2×C3⋊C8—32no—
315C2×C3⋊C8—32no—
316C2×C3⋊C8—62no—
317D24—24no—
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—21no—
320C2×C3⋊D3—21no—
321C2×C3⋊D3C2×D812yes—
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—42no—
329C2×C3×D3—42no—
330C2×C3×D3—42no—
331D32—48no—
332C32×C4—21no—
333C32×C4C2×D812yes—
334C32×C4C2×#4111yescharacteristic
335C32×C4C2×#4111yescharacteristic
336C3⋊Dic3—21no—
337C3⋊Dic3—21no—
338C3⋊Dic3C2×D812yes—
339C3×Dic3—41no—
340C3×Dic3—41no—
341C3×Dic3—42no—
342C2×#41—181no—
343C22×D4—91no—
344C23×C4—181no—
345C2×D8—32no—
346C2×D8—92no—
347C4⋊Q8—31no—
348#127—31no—
349#124—181no—
350#121—92no—
351#121—181no—
352C4×D4—31no—
353C4×D4—31no—
354C4×D4—91no—
355C4×D4—91no—
356C4×D4—92no—
357C4×D4—181no—
358C4×D4—181no—
359C4×D4—181no—
360C2×C4⋊C4—91no—
361C2×C22⋊C4—181no—
362C2×C42—91no—
363#107—32no—
364#107—92no—
365C4⋊C8—91no—
366C4⋊C8D3211yescharacteristic, complemented
367#102—32no—
368#102—32no—
369#102—92no—
370#102—92no—
371C22⋊C8—92no—
372C4×C8—92no—
373C23×C3—61no—
374C23×C3—61no—
375C23×C3—62no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—22no—
379C22×D3—31no—
380C22×D3—31no—
381C22×D3—61no—
382C22×D3—64no—
383C22×D3—64no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3—122no—
388C3×Q8—122no—
389C3×D4—32no—
390C3×D4—32no—
391C3×D4—61no—
392C3×D4—61no—
393C3×D4—62no—
394C3×D4—62no—
395C3×D4—122no—
396C3×D4—122no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—62no—
403C2×C3×C4—122no—
404C2×C3×C4—122no—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—64no—
412#67—64no—
413#67—124no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—22no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—31no—
420C2×Dic3—31no—
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—124no—
429D12—22no—
430D12—21no—
431D12—21no—
432D12—22no—
433D12—42no—
434D12—42no—
435D12—124no—
436D12#23712yescomplemented
437D12#23912yescomplemented
438C4×D3—34no—
439C4×D3—34no—
440C4×D3—42no—
441C4×D3—42no—
442C4×D3—64no—
443C4×D3—61no—
444C4×D3—61no—
445C4×D3—61no—
446C4×D3—61no—
447C4×D3—121no—
448C4×D3—121no—
449C4×D3—122no—
450C4×D3—122no—
451C4×D3—124no—
452C4×D3—122no—
453C4×D3—122no—
454C4×D3—121no—
455C4×D3—121no—
456C4×D3—122no—
457Dic6—42no—
458C3×C8—22no—
459C3×C8—22no—
460C3×C8—42no—
461C3⋊C8—62no—
462C3⋊C8—62no—
463C3⋊C8—122no—
464C2×C32#52511yescharacteristic
465C2×C32C22×D811yescharacteristic
466C2×C32#57511yescharacteristic
467C3⋊D3—22no—
468C3×D3—42no—
469C3×D3—42no—
470C3×D3—82no—
471C24—181no—
472#41—364no—
473C2×Q8—61no—
474C2×D4—31no—
475C2×D4—31no—
476C2×D4—32no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—182no—
480C2×D4—181no—
481C2×D4—182no—
482C2×D4—182no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—91no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—181no—
489C22×C4—181no—
490C22×C4—181no—
491C22×C4—182no—
492C22×C4—364no—
493D8—64no—
494D8—184no—
495C2×C8—92no—
496C2×C8C2×D3212yes—
497C4⋊C4—31no—
498C4⋊C4—32no—
499C4⋊C4—31no—
500C4⋊C4—61no—
501C4⋊C4—181no—
502C22⋊C4—61no—
503C22⋊C4—61no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C22⋊C4—182no—
507C22⋊C4—182no—
508C42—91no—
509C42—91no—
510C42—91no—
511C42C2×D3211yescharacteristic
512C22×C3—21no—
513C22×C3—62no—
514C22×C3—62no—
515C22×C3—121no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—121no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3—122no—
522C22×C3C2×D3×D411yescharacteristic
523C22×C3C2×D3×D411yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—32no—
527C2×D3—32no—
528C2×D3—41no—
529C2×D3—41no—
530C2×D3—41no—
531C2×D3—41no—
532C2×D3—42no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3—62no—
536C2×D3—61no—
537C2×D3—61no—
538C2×D3—61no—
539C2×D3—61no—
540C2×D3—121no—
541C2×D3—121no—
542C2×D3—128no—
543C2×D3—128no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—22no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—41no—
550C3×C4—121no—
551C3×C4—121no—
552C3×C4—122no—
553C3×C4D3×D812yes—
554C3×C4D3×D812yes—
555C3×C4C2×#23711yescharacteristic
556C3×C4C2×#23911yescharacteristic
557C3×C4D3×#4111yescharacteristic
558C3×C4D3×#4111yescharacteristic
559Dic3—32no—
560Dic3—32no—
561Dic3—42no—
562Dic3—41no—
563Dic3—41no—
564Dic3—62no—
565Dic3—62no—
566Dic3—61no—
567Dic3—61no—
568Dic3—61no—
569Dic3—61no—
570Dic3—121no—
571C32#310011yescharacteristic, complemented, Sylow
572C23—61no—
573C23—61no—
574C23—62no—
575C23—91no—
576C23—184no—
577C23—362no—
578C23—362no—
579Q8—122no—
580D4—32no—
581D4—32no—
582D4—61no—
583D4—62no—
584D4—61no—
585D4—62no—
586D4—122no—
587D4—122no—
588D4—184no—
589D4—364no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—62no—
593C2×C4—91no—
594C2×C4—94no—
595C2×C4—91no—
596C2×C4—91no—
597C2×C4—122no—
598C2×C4—122no—
599C2×C4—181no—
600C2×C4—181no—
601C2×C4—361no—
602C2×C4—362no—
603C2×C4—362no—
604C2×C4—364no—
605C2×C4—362no—
606C2×C4#380211yescharacteristic
607C2×C4#380211yescharacteristic
608C2×C4C22×D3211yescharacteristic
609C8—22no—
610C8—182no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—122no—
615C2×C3—122no—
616C2×C3—242no—
617C2×C3#560611yescharacteristic
618C2×C3#562711yescharacteristic
619C2×C3C2×D3×D811yescharacteristic
620C2×C3C2×D3×D811yescharacteristic
621C2×C3#577311yescharacteristic
622C2×C3#577711yescharacteristic
623D3—42no—
624D3—42no—
625D3—62no—
626D3—62no—
627D3—82no—
628D3—122no—
629C22—62no—
630C22—62no—
631C22—92no—
632C22—121no—
633C22—121no—
634C22—121no—
635C22—121no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22—181no—
640C22—181no—
641C22—368no—
642C22C2×#380211yescharacteristic
643C4—21no—
644C4—92no—
645C4—121no—
646C4—121no—
647C4—122no—
648C4—181no—
649C4—181no—
650C4#6379712yes—
651C4D3×#23711yescharacteristic
652C4D3×#23911yescharacteristic
653C3—21no—
654C3#8031211yescharacteristic, complemented
655C3#8094811yescharacteristic, complemented
656C2—122no—
657C2—122no—
658C2—182no—
659C2—242no—
660C2#1059463211yescharacteristic
661C2C2×#6379711yescharacteristic
662C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#3802C2semidirect
2. #10593907C2semidirect
3. #10592532C2semidirect
4. C3×#4846C2semidirect
5. C3×#4843C2semidirect
6. #10590945C2semidirect
7. #10590777C2semidirect
8. #10590740C2semidirect
9. #10590650C2semidirect
10. #10590347C2semidirect
11. #10590269C2semidirect
19. C3×#874C22semidirect
22. C3×#869C22semidirect
32. #63898C22semidirect
35. C32×C4⋊C8C22semidirect
37. C8×C3⋊Dic3C22semidirect
38. C4⋊(C3⋊(C3⋊C8))C22semidirect
40. C3×#821C22semidirect
41. C3×#818C22semidirect
42. #63576C22semidirect
44. #63562C22semidirect
59. #4846D3semidirect
60. #4843D3semidirect
146. #874C2×D3semidirect
152. #869C2×D3semidirect
155. C3×C4⋊C8C2×D3semidirect
156. C3×C4⋊C8C2×D3semidirect
162. #821C2×D3semidirect
166. #818C2×D3semidirect
193. C4×C3⋊D3D8semidirect
203. C3×D12#41semidirect
204. C3×D12#41semidirect
366. C4⋊C8D32semidirect
436. D12#237semidirect
437. D12#239semidirect
571. C32#3100semidirect
654. C3#80312semidirect
655. C3#80948semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105939072
#105925322
C3×#48462
C3×#48432
#105909452
#105907772
#105907402
#105906502
#105903472
#105902692
#809483
#803123