Finite Group Databasebeta

← #11868662

Subgroups — #11868662

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3802C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3#10592536C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4842C211yesmaximal, characteristic, complemented
6#10590941C212yesmaximal
7#10590782C212yesmaximal, complemented
8#10590780C212yesmaximal, complemented
9#10590688C212yesmaximal, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#81060—31nomaximal
13#80965—31nomaximal
14C2×#3802C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3743C2212yes—
17C42×C3⋊D3C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic, complemented
21C3×#869C2211yescharacteristic, complemented
22#63921—21no—
23#63902—21no—
24C4×#625—21no—
25#63900C2211yescharacteristic
26#63898C2211yescharacteristic
27#63898C2211yescharacteristic
28#63872C2212yescomplemented
29#63871—21no—
30#63871—21no—
31#63849C2212yes—
32#63843—21no—
33#63843—21no—
34C32×C4⋊C8C2211yescharacteristic, complemented
35#63641C2212yescomplemented
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
37C3×#821C2212yes—
38C3×#821C2212yes—
39C3×#818C2212yescomplemented
40C3×#817C2212yescomplemented
41#63576C2212yescomplemented
42#63574C2212yescomplemented
43#63562C2212yes—
44#63562C2212yes—
45#5728—31no—
46#5728—31no—
47C4×D3×D4—31no—
48C4×D3×D4—31no—
49C3×#476—31no—
50C3×#474—31no—
51#5087—31no—
52#5084—31no—
53#5008—31no—
54#5007—31no—
55#4891—32no—
56#4881—32no—
57#4871—32no—
58#4861—32no—
59#4846D311yescharacteristic, complemented
60#4842D311yescharacteristic, complemented
61#4837—31no—
62#4837—31no—
63#4837—61no—
64#4770—32no—
65#4770—32no—
66#4766—32no—
67#4763—32no—
68C22×D32—21no—
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—21no—
78C2×#625—21no—
79C2×#624—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82#3802—22no—
83#3802Q814yescomplemented
84C4×D32—44no—
85C2×C32×C8C2312yes—
86C32×C42C2311yescharacteristic
87C4×C3⋊Dic3D411yescharacteristic
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91#3743—24no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2312yes—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2311yescharacteristic
100#3724—21no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103#3722—22no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—22no—
107#3077—91noSylow
108C2×D3×D4—31no—
109C2×D3×D4—31no—
110C22×C4×D3—61no—
111C22×C4×D3—61no—
112C3×C4⋊Q8—31no—
113C3×C4⋊Q8—31no—
114C3×C4×D4—31no—
115C3×C4×D4—31no—
116#946—61no—
117#946—61no—
118Q8×Dic3—61no—
119Q8×Dic3—61no—
120D4×Dic3—31no—
121D4×Dic3—31no—
122C4×#67—61no—
123C4×#67—61no—
124C2×ΓL(1,𝔽25)—32no—
125C2×ΓL(1,𝔽25)—32no—
126C2×ΓL(1,𝔽25)—62no—
127#897—61no—
128#897—61no—
129#893—31no—
130#893—31no—
131#892—32no—
132#892—32no—
133D3×C4⋊C4—31no—
134D3×C4⋊C4—31no—
135#890—32no—
136#890—32no—
137#887—61no—
138#887—61no—
139#67⋊C4—61no—
140#67⋊C4—61no—
141D3×C22⋊C4—61no—
142D3×C22⋊C4—61no—
143C4×D12C2×D311yescharacteristic
144C4×D12C2×D311yescharacteristic
145C42×D3—31no—
146C42×D3—31no—
147C42×D3—61no—
148#869C2×D311yescharacteristic, complemented
149#869C2×D311yescharacteristic, complemented
150C3×#107—32no—
151C3×#106—32no—
152C3×C4⋊C8—21no—
153C3×C4⋊C8C2×D311yescharacteristic, complemented
154C3×C4⋊C8C2×D311yescharacteristic, complemented
155C3×#102—32no—
156C3×#102—32no—
157#832—32no—
158#832—32no—
159#821C2×D312yes—
160#821C2×D312yes—
161#818C2×D312yescomplemented
162#817C2×D312yescomplemented
163Dic3⋊C8—32no—
164Dic3⋊C8—32no—
165Dic3⋊C8—62no—
166#809—32no—
167#809—32no—
168#808—32no—
169#808—32no—
170#807—32no—
171#807—32no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C22×C3⋊D3C2×D411yescharacteristic
176C22×C3×D3—21no—
177C22×C3×D3—21no—
178C2×D32—24no—
179C2×D32—42no—
180C2×D32—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4×C3⋊D3—22no—
188C4×C3⋊D3—41no—
189C4×C3⋊D3C2×Q812yes—
190C4×C3⋊D3#4112yes—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C3×D12—21no—
196C3×D12—21no—
197C3×D12C2×Q812yes—
198C3×D12C2×Q812yes—
199C3×C4×D3—42no—
200C3×C4×D3—42no—
201C3×Dic6—42no—
202C3×Dic6—42no—
203#625—24no—
204#624—42no—
205D3×Dic3—42no—
206D3×Dic3—42no—
207C32×C8—22no—
208C3⋊(C3⋊C8)—22no—
209#533—91no—
210C2×C4×D4—91no—
211#478—92no—
212#478—92no—
213#476—31no—
214#476—91no—
215#474—31no—
216#474—91no—
217#428—92no—
218#423—91no—
219#418—92no—
220C23×D3—61no—
221C23×D3—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8—61no—
224C2×C3×D4—31no—
225C2×C3×D4—31no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C2×#67—61no—
229C2×#67—61no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232D3×D4—34no—
233D3×D4—34no—
234D3×D4—62no—
235D3×D4—62no—
236C2×D12C22×D311yescharacteristic
237C2×D12C22×D311yescharacteristic
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—31no—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×C4×D3—31no—
244C2×C4×D3—31no—
245C2×C4×D3—31no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—124no—
254C2×C4×D3—124no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×C3×C8—22no—
258C2×C3×C8C22×D312yes—
259C2×C3×C8C22×D312yes—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—61no—
268C3×C42—21no—
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D311yescharacteristic
271#217—61no—
272#217—61no—
273(C2×D3)⋊C4—21no—
274(C2×D3)⋊C4—21no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—61no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3C22×D311yescharacteristic
284C4⋊Dic3C22×D312yes—
285C4⋊Dic3C22×D311yescharacteristic
286C4⋊Dic3C22×D312yes—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291C4×Dic3—31no—
292C4×Dic3—31no—
293C4×Dic3—31no—
294C4×Dic3—31no—
295C4×Dic3—31no—
296C4×Dic3—31no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C4×Dic3—62no—
301C4×Dic3—62no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—62no—
305ΓL(1,𝔽25)—64no—
306ΓL(1,𝔽25)—64no—
307ΓL(1,𝔽25)—124no—
308C22×C32C22×D411yescharacteristic
309C2×C3⋊D3—21no—
310C2×C3⋊D3—21no—
311C2×C3⋊D3C22⋊Q812yes—
312C2×C3×D3—22no—
313C2×C3×D3—22no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318D32—48no—
319C32×C4—21no—
320C32×C4AGL(1,ℤ/8)12yes—
321C32×C4C22×Q811yescharacteristic
322C32×C4C2×#4111yescharacteristic
323C3⋊Dic3—21no—
324C3⋊Dic3—21no—
325C3⋊Dic3C22⋊Q812yes—
326C3×Dic3—41no—
327C3×Dic3—41no—
328C3×Dic3—42no—
329C3×Dic3—42no—
330C22×D4—91no—
331C23×C4—181no—
332C2×M16—92no—
333C4⋊Q8—31no—
334C4⋊Q8—31no—
335#125—92no—
336C22⋊Q8—181no—
337C22⋊Q8—181no—
338C4×Q8—181no—
339C4×Q8—181no—
340C4×D4—31no—
341C4×D4—31no—
342C4×D4—91no—
343C4×D4—91no—
344C4×D4—181no—
345C4×D4—181no—
346#117—92no—
347C2×C4⋊C4—91no—
348C2×C22⋊C4—181no—
349C2×C42—91no—
350#107—32no—
351#107—92no—
352#106—32no—
353#106—92no—
354C4⋊C8—92no—
355C4⋊C8—91no—
356C4⋊C8D3211yescharacteristic, complemented
357#102—32no—
358#102—32no—
359#102—92no—
360#102—92no—
361C23×C3—61no—
362C23×C3—61no—
363C22×D3—21no—
364C22×D3—21no—
365C22×D3—31no—
366C22×D3—31no—
367C22×D3—61no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—122no—
374C3×Q8—122no—
375C3×Q8—122no—
376C3×D4—32no—
377C3×D4—32no—
378C3×D4—61no—
379C3×D4—61no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—122no—
388C2×C3×C4—122no—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—64no—
396#67—64no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—31no—
404C2×Dic3—31no—
405C2×Dic3—31no—
406C2×Dic3—31no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412D12—21no—
413D12—21no—
414D12D3×Q812yes—
415D12D3×Q812yes—
416C4×D3—32no—
417C4×D3—32no—
418C4×D3—32no—
419C4×D3—32no—
420C4×D3—42no—
421C4×D3—42no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—122no—
427C4×D3—122no—
428C4×D3—122no—
429C4×D3—121no—
430C4×D3—121no—
431C4×D3—122no—
432C4×D3—122no—
433C4×D3—122no—
434Dic6—42no—
435Dic6—42no—
436C3×C8—22no—
437C3×C8—22no—
438C3×C8—42no—
439C3⋊C8—62no—
440C3⋊C8—62no—
441C3⋊C8—122no—
442C2×C32C2×C22⋊Q811yescharacteristic
443C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
444C2×C32#57511yescharacteristic
445C3⋊D3—22no—
446C3×D3—42no—
447C3×D3—42no—
448C24—181no—
449C2×Q8—61no—
450C2×Q8—61no—
451C2×D4—31no—
452C2×D4—31no—
453C2×D4—94no—
454C2×D4—182no—
455C2×D4—181no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—181no—
462C22×C4—181no—
463C22×C4—181no—
464C22×C4—364no—
465M16—184no—
466C2×C8—92no—
467C2×C8C2×D3212yes—
468C4⋊C4—32no—
469C4⋊C4—32no—
470C4⋊C4—31no—
471C4⋊C4—31no—
472C4⋊C4—61no—
473C4⋊C4—61no—
474C4⋊C4—181no—
475C4⋊C4—182no—
476C4⋊C4—182no—
477C22⋊C4—61no—
478C22⋊C4—61no—
479C22⋊C4—182no—
480C22⋊C4—181no—
481C22⋊C4—181no—
482C42—91no—
483C42—91no—
484C42—91no—
485C42—182no—
486C42C2×D3211yescharacteristic
487C22×C3—21no—
488C22×C3—62no—
489C22×C3—62no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3—121no—
493C22×C3—121no—
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—32no—
499C2×D3—32no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3—41no—
504C2×D3—62no—
505C2×D3—61no—
506C2×D3—61no—
507C2×D3—61no—
508C2×D3—61no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—128no—
512C2×D3—128no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—22no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—41no—
519C3×C4—121no—
520C3×C4—121no—
521C3×C4—122no—
522C3×C4—122no—
523C3×C4#91112yes—
524C3×C4#91412yes—
525C3×C4C2×D3×Q811yescharacteristic
526C3×C4C2×D3×Q811yescharacteristic
527C3×C4D3×#4111yescharacteristic
528C3×C4D3×#4111yescharacteristic
529Dic3—32no—
530Dic3—32no—
531Dic3—42no—
532Dic3—41no—
533Dic3—41no—
534Dic3—42no—
535Dic3—62no—
536Dic3—62no—
537Dic3—61no—
538Dic3—61no—
539Dic3—61no—
540Dic3—61no—
541Dic3—121no—
542C32#307711yescharacteristic, complemented, Sylow
543C23—61no—
544C23—61no—
545C23—91no—
546C23—184no—
547C23—362no—
548C23—362no—
549Q8—122no—
550Q8—122no—
551D4—32no—
552D4—32no—
553D4—61no—
554D4—61no—
555D4—184no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—91no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—91no—
564C2×C4—91no—
565C2×C4—122no—
566C2×C4—122no—
567C2×C4—182no—
568C2×C4—361no—
569C2×C4—362no—
570C2×C4—362no—
571C2×C4—362no—
572C2×C4#380211yescharacteristic
573C2×C4#380211yescharacteristic
574C2×C4C22×D3211yescharacteristic
575C8—22no—
576C8—182no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—122no—
581C2×C3—122no—
582C2×C3D3×C22⋊Q811yescharacteristic
583C2×C3D3×C22⋊Q811yescharacteristic
584C2×C3C2×#91111yescharacteristic
585C2×C3C2×#91411yescharacteristic
586C2×C3#577311yescharacteristic
587C2×C3#577711yescharacteristic
588D3—42no—
589D3—42no—
590D3—62no—
591D3—62no—
592D3—122no—
593C22—62no—
594C22—62no—
595C22—92no—
596C22—121no—
597C22—121no—
598C22—121no—
599C22—121no—
600C22—181no—
601C22—181no—
602C22—368no—
603C22C2×#380211yescharacteristic
604C4—21no—
605C4—92no—
606C4—121no—
607C4—121no—
608C4—122no—
609C4—122no—
610C4—181no—
611C4—181no—
612C4#6379812yes—
613C4#6431211yescharacteristic
614C4D32×Q811yescharacteristic
615C3—21no—
616C3#8096511yescharacteristic, complemented
617C3#8106011yescharacteristic, complemented
618C2—122no—
619C2—122no—
620C2—182no—
621C2#1059463111yescharacteristic
622C2C2×#6379811yescharacteristic
623C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊C8D32
hypocenterC32#3077
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. #10593866C2semidirect
3. #10592536C2semidirect
4. C3×#4846C2semidirect
5. C3×#4842C2semidirect
7. #10590782C2semidirect
8. #10590780C2semidirect
9. #10590688C2semidirect
10. #10590269C2semidirect
11. #10590266C2semidirect
20. C3×#869C22semidirect
21. C3×#869C22semidirect
28. #63872C22semidirect
34. C32×C4⋊C8C22semidirect
35. #63641C22semidirect
36. C4⋊(C3⋊(C3⋊C8))C22semidirect
39. C3×#818C22semidirect
40. C3×#817C22semidirect
41. #63576C22semidirect
42. #63574C22semidirect
59. #4846D3semidirect
60. #4842D3semidirect
83. #3802Q8semidirect
148. #869C2×D3semidirect
149. #869C2×D3semidirect
153. C3×C4⋊C8C2×D3semidirect
154. C3×C4⋊C8C2×D3semidirect
161. #818C2×D3semidirect
162. #817C2×D3semidirect
356. C4⋊C8D32semidirect
542. C32#3077semidirect
616. C3#80965semidirect
617. C3#81060semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105938662
#105925362
C3×#48462
C3×#48422
#105909412
#105907822
#105907802
#105906882
#105902692
#105902662
#810603
#809653