Finite Group Databasebeta

← #11887029

Subgroups — #11887029

Order 1152.

1202 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2#10593869C211yesmaximal, characteristic, complemented
3C3×C4×#213C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591456C212yesmaximal, complemented
6#10591416C212yesmaximal, complemented
7#10590509C212yesmaximal, complemented
8#10590442C212yesmaximal, complemented
9#10590349C211yesmaximal, characteristic, complemented
10#10590327C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#80980—31nomaximal
13#79608—31nomaximal
14C2×D4×C3⋊D3C2212yes—
15C22×C4⋊(C3⋊D3)—21no—
16C2×#3799—21no—
17C32×C4×D4C2211yescharacteristic
18#64139—21no—
19#64104C2212yes—
20#64091—22no—
21#64083C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic, complemented
25C3×#869C2211yescharacteristic, complemented
26#63916C2212yescomplemented
27#63900C2212yescomplemented
28#63856—21no—
29#63854—22no—
30C2×#3714C2212yescomplemented
31C2×#3710C2212yescomplemented
32C3×#832C2212yes—
33C3×#832C2211yescharacteristic
34C3×#809C2211yescharacteristic, complemented
35C3×#807C2212yescomplemented
36C3×#807C2211yescharacteristic, complemented
37C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
38C3×C4×C3⋊C8C2211yescharacteristic, complemented
39#63564C2212yescomplemented
40#63564C2212yescomplemented
41#63564C2212yescomplemented
42#63557C2212yescomplemented
43#5726—31no—
44#5551—31no—
45D4×D12—31no—
46D4×D12—31no—
47D4×D12—61no—
48C3×#474—31no—
49C3×C4×D8—31no—
50#5156—32no—
51#5088—31no—
52#5015—31no—
53C4×#213D311yescharacteristic, complemented
54#5007D311yescharacteristic, complemented
55#4883—32no—
56#4882—32no—
57#4882—32no—
58#4843—31no—
59#4834—31no—
60#4775—32no—
61#4773—32no—
62D3×#102—32no—
63D3×#102—32no—
64#4694—31no—
65C8×D12—31no—
66C23×C3⋊D3—22no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×#638—22no—
70D4×C3⋊D3—24no—
71D4×C3⋊D3—42no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)—21no—
75C2×C4⋊(C3⋊D3)—44no—
76C2×C4⋊(C3⋊D3)D411yescharacteristic
77C2×C4⋊(C3⋊D3)C2312yes—
78C2×C4×C3⋊D3C2312yes—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6—21no—
82C2×#626—22no—
83C2×#624—22no—
84#3799—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3752—22no—
89#3752D412yes—
90C4⋊(C3⋊Dic3)D411yescharacteristic
91C3×#213—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99#3724—22no—
100(C2×D3)⋊Dic3—22no—
101#3714—42no—
102#3710—42no—
103#3294—91noSylow
104C2×#239—61no—
105C2×D3×D4—32no—
106C2×D3×D4—32no—
107C2×D3×D4—62no—
108C2×#235—61no—
109C22×D12—61no—
110C22×D12—61no—
111C22×D12—62no—
112C2×C3×D8—31no—
113C3×C4⋊Q8—31no—
114C3×C4×D4—21no—
115C3×C4×D4—31no—
116C3×C4×D4C2×D311yescharacteristic
117C3×C4×D4C2×D311yescharacteristic
118#946—61no—
119#938—32no—
120C2×#213—32no—
121C2×#213C2×D311yescharacteristic
122#930—61no—
123#930—61no—
124#930—62no—
125#924—61no—
126C2×D24—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129#895—32no—
130#895—32no—
131#895—32no—
132#895—62no—
133#894—62no—
134D3×C4⋊C4—32no—
135D3×C4⋊C4—32no—
136#883—62no—
137#882—62no—
138#882—62no—
139#882—64no—
140#874—31no—
141#874—31no—
142#874—61no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—61no—
146C4×D12C2×D311yescharacteristic, complemented
147#869C2×D311yescharacteristic, complemented
148C3×#107—31no—
149C3×#107—32no—
150C3×C4⋊C8—31no—
151C3×#102—31no—
152C3×#102—32no—
153C3×#102—31no—
154C3×C4×C8—31no—
155#832C2×D312yes—
156#832C2×D311yescharacteristic
157#821—32no—
158#821—32no—
159#821—32no—
160(C2×D3)⋊C8—32no—
161(C2×D3)⋊C8—32no—
162#809—32no—
163#809—32no—
164#809—32no—
165#809C2×D311yescharacteristic, complemented
166#807C2×D311yescharacteristic, complemented
167#807C2×D312yescomplemented
168C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
169C4×C3⋊C8C2×D311yescharacteristic, complemented
170C23×C32—21no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—44no—
173C22×C3⋊D3—44no—
174C22×C3⋊D3—82no—
175C22×C3⋊D3C2×D412yes—
176C22×C3×D3—21no—
177C32×D4—21no—
178C32×D4#4112yescomplemented
179C2×C32×C4—21no—
180C2×C32×C4—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—44no—
185C2×C3⋊Dic3C2×D412yes—
186C4⋊(C3⋊D3)—22no—
187C4⋊(C3⋊D3)—22no—
188C4⋊(C3⋊D3)—44no—
189C4⋊(C3⋊D3)—42no—
190C4⋊(C3⋊D3)—81no—
191C4⋊(C3⋊D3)D814yescomplemented
192C4×C3⋊D3—22no—
193C4×C3⋊D3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C3×D12—21no—
197C3×D12—21no—
198C3×C4×D3—42no—
199C3×Dic6—42no—
200#626—44no—
201#624—44no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—21no—
204C3×C3⋊C8—22no—
205#547—91no—
206D42—91no—
207#486—91no—
208#480—92no—
209#474—31no—
210#466—92no—
211#459—91no—
212#447—92no—
213C4×D8—31no—
214C8×D4—91no—
215C2×#102—92no—
216C23×D3—62no—
217C23×D3—62no—
218C23×D3—64no—
219C2×C3×Q8—61no—
220C2×C3×D4—21no—
221C2×C3×D4—31no—
222C2×C3×D4C22×D311yescharacteristic
223C2×C3×D4C22×D311yescharacteristic
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—61no—
228C2×#67—62no—
229C2×#67—62no—
230C2×#67—62no—
231C2×#67—64no—
232#239—124no—
233D3×D4—64no—
234D3×D4—64no—
235D3×D4—124no—
236D3×D4—122no—
237D3×D4—122no—
238D3×D4—124no—
239#235—124no—
240C2×D12—31no—
241C2×D12—31no—
242C2×D12—32no—
243C2×D12—32no—
244C2×D12—61no—
245C2×D12—62no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—64no—
250C2×D12—62no—
251C2×D12—61no—
252C2×D12—61no—
253C2×D12—62no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—124no—
257C2×D12—124no—
258C2×D12—128no—
259C2×D12C22×D311yescharacteristic
260C2×C4×D3—21no—
261C2×C4×D3—32no—
262C2×C4×D3—32no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×Dic6—21no—
267C3×D8—62no—
268C2×C3×C8—31no—
269C2×C3×C8—32no—
270C2×C3×C8—31no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—31no—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—61no—
275C3×C4⋊C4C22×D311yescharacteristic
276C3×C4⋊C4C22×D311yescharacteristic
277C3×C22⋊C4—22no—
278C3×C22⋊C4—21no—
279C3×C22⋊C4—21no—
280C3×C22⋊C4—61no—
281C3×C42—21no—
282C3×C42C22×D311yescharacteristic
283C3×C42C22×D311yescharacteristic
284#217—62no—
285#213—22no—
286#213—122no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—32no—
289(C2×D3)⋊C4—32no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—64no—
295C4⋊Dic3—21no—
296C4⋊Dic3—31no—
297C4⋊Dic3—31no—
298C4⋊Dic3—61no—
299C4⋊Dic3C22×D312yes—
300C4⋊Dic3C22×D311yescharacteristic
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D311yescharacteristic
305C2×C3⋊C8C22×D312yes—
306D24—122no—
307D3×C8—122no—
308D3×C8—122no—
309C22×C32—22no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—42no—
316C2×C3⋊D3—42no—
317C2×C3⋊D3—42no—
318C2×C3⋊D3—88no—
319C2×C3⋊D3C2×D814yes—
320C2×C3×D3—41no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C32×C4—21no—
324C32×C4—41no—
325C32×C4C2×D812yes—
326C32×C4C2×#4111yescharacteristic
327C32×C4H(5,𝔽2)11yescharacteristic
328C3⋊Dic3—22no—
329C3×Dic3—41no—
330C3×Dic3—42no—
331C2×#41—181no—
332C22×D4—92no—
333C22×D4—181no—
334C2×D8—31no—
335C2×D8—92no—
336C22×C8—92no—
337C4⋊Q8—31no—
338#127—91no—
339#123—182no—
340C22⋊Q8—181no—
341#121—92no—
342#121—92no—
343#121—181no—
344#120—182no—
345C4×D4—31no—
346C4×D4—91no—
347C4×D4D3211yescharacteristic
348C2×C4⋊C4—92no—
349#107—31no—
350#107—32no—
351C4⋊C8—31no—
352#102—31no—
353#102—32no—
354#102—31no—
355#102—92no—
356#102—92no—
357#102—92no—
358C22⋊C8—92no—
359C4×C8—31no—
360C23×C3—22no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—61no—
364C22×D3—21no—
365C22×D3—32no—
366C22×D3—32no—
367C22×D3—62no—
368C22×D3—64no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—124no—
372C22×D3—124no—
373C22×D3—124no—
374C22×D3—124no—
375C22×D3—128no—
376C22×D3—128no—
377C22×D3—242no—
378C22×D3—242no—
379C22×D3—244no—
380C3×Q8—122no—
381C3×D4—22no—
382C3×D4—21no—
383C3×D4—21no—
384C3×D4—22no—
385C3×D4—61no—
386C3×D4—61no—
387C3×D4#23512yescomplemented
388C3×D4#23912yescomplemented
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—44no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—61no—
399C2×C3×C4—62no—
400C2×C3×C4—122no—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—124no—
408#67—124no—
409#67—124no—
410#67—128no—
411C2×Dic3—21no—
412C2×Dic3—22no—
413C2×Dic3—32no—
414C2×Dic3—32no—
415C2×Dic3—62no—
416D12—21no—
417D12—21no—
418D12—34no—
419D12—34no—
420D12—64no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12—62no—
425D12—122no—
426D12—122no—
427D12—124no—
428D12—124no—
429D12—124no—
430D12—128no—
431D12—124no—
432D12—122no—
433D12—122no—
434D12—241no—
435D12—241no—
436D12—242no—
437C4×D3—42no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—62no—
442C4×D3—122no—
443C4×D3—122no—
444C4×D3—124no—
445C4×D3—124no—
446Dic6—42no—
447C3×C8—61no—
448C3×C8—61no—
449C3×C8—62no—
450C3⋊C8—21no—
451C3⋊C8—21no—
452C3⋊C8—22no—
453C2×C32—42no—
454C2×C32#54611yescharacteristic
455C2×C32C22×D811yescharacteristic
456C2×C32#57711yescharacteristic
457C3⋊D3—24no—
458C3⋊D3—82no—
459C3×D3—81no—
460C24—182no—
461#41—364no—
462C2×Q8—61no—
463C2×D4—31no—
464C2×D4—92no—
465C2×D4—91no—
466C2×D4—182no—
467C2×D4—182no—
468C2×D4—182no—
469C2×D4—184no—
470C2×D4—181no—
471C2×D4—181no—
472C2×D4—364no—
473C2×D4—362no—
474C2×D4C2×D3211yescharacteristic
475C22×C4—21no—
476C22×C4—61no—
477C22×C4—92no—
478C22×C4—182no—
479D8—62no—
480D8—362no—
481C2×C8—31no—
482C2×C8—31no—
483C2×C8—32no—
484C2×C8—362no—
485C4⋊C4—31no—
486C4⋊C4—32no—
487C4⋊C4—61no—
488C4⋊C4—91no—
489C4⋊C4—182no—
490C4⋊C4C2×D3211yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—61no—
493C22⋊C4—92no—
494C22⋊C4—182no—
495C22⋊C4—182no—
496C42C2×D3211yescharacteristic
497C22×C3—24no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3C2×D3×D411yescharacteristic
511C22×C3C2×D3×D411yescharacteristic
512C2×D3—34no—
513C2×D3—34no—
514C2×D3—41no—
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—64no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—124no—
525C2×D3—124no—
526C2×D3—124no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—248no—
534C2×D3—248no—
535C2×D3—2416no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—41no—
542C3×C4—42no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—121no—
546C3×C4—122no—
547C3×C4D3×D812yes—
548C3×C4D3×D812yes—
549C3×C4C2×#23511yescharacteristic
550C3×C4C2×#23911yescharacteristic
551C3×C4#100911yescharacteristic
552C3×C4#100911yescharacteristic
553Dic3—42no—
554Dic3—41no—
555Dic3—62no—
556Dic3—62no—
557Dic3—122no—
558C32#329411yescharacteristic, complemented, Sylow
559C23—21no—
560C23—61no—
561C23—92no—
562C23—182no—
563C23—364no—
564C23—364no—
565C23—722no—
566Q8—122no—
567D4—21no—
568D4—61no—
569D4—61no—
570D4—94no—
571D4—182no—
572D4—182no—
573D4—364no—
574D4—364no—
575D4—364no—
576D4—362no—
577D4—721no—
578D4#379912yescomplemented
579C2×C4—21no—
580C2×C4—42no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—92no—
584C2×C4—122no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—364no—
588C2×C4#381111yescharacteristic
589C2×C4#381111yescharacteristic
590C2×C4C22×D3211yescharacteristic
591C8—61no—
592C8—61no—
593C8—62no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—44no—
598C2×C3—42no—
599C2×C3—42no—
600C2×C3—241no—
601C2×C3#555011yescharacteristic
602C2×C3#563011yescharacteristic
603C2×C3C2×D3×D811yescharacteristic
604C2×C3C2×D3×D811yescharacteristic
605C2×C3#577011yescharacteristic
606C2×C3#577811yescharacteristic
607D3—64no—
608D3—64no—
609D3—81no—
610D3—124no—
611D3—244no—
612D3—242no—
613D3—242no—
614C22—22no—
615C22—41no—
616C22—41no—
617C22—94no—
618C22—121no—
619C22—121no—
620C22—121no—
621C22—182no—
622C22—182no—
623C22—362no—
624C22—362no—
625C22—362no—
626C22—728no—
627C22C2×#381111yescharacteristic
628C4—21no—
629C4—41no—
630C4—121no—
631C4—122no—
632C4—182no—
633C4#6392612yes—
634C4C2×#379911yescharacteristic
635C4#6430811yescharacteristic
636C3—21no—
637C3#7960811yescharacteristic, complemented
638C3#8098011yescharacteristic, complemented
639C2—42no—
640C2—184no—
641C2—241no—
642C2—722no—
643C2#1059501811yescharacteristic
644C2C2×#6392611yescharacteristic
645C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×C4⋊(C3⋊D3)C2semidirect
2. #10593869C2semidirect
3. C3×C4×#213C2semidirect
4. C3×#5007C2semidirect
5. #10591456C2semidirect
6. #10591416C2semidirect
7. #10590509C2semidirect
8. #10590442C2semidirect
9. #10590349C2semidirect
10. #10590327C2semidirect
11. #10590281C2semidirect
24. C3×C4×D12C22semidirect
25. C3×#869C22semidirect
26. #63916C22semidirect
27. #63900C22semidirect
30. C2×#3714C22semidirect
31. C2×#3710C22semidirect
34. C3×#809C22semidirect
35. C3×#807C22semidirect
36. C3×#807C22semidirect
37. C3×C4⋊(C3⋊C8)C22semidirect
38. C3×C4×C3⋊C8C22semidirect
39. #63564C22semidirect
40. #63564C22semidirect
41. #63564C22semidirect
42. #63557C22semidirect
53. C4×#213D3semidirect
54. #5007D3semidirect
146. C4×D12C2×D3semidirect
147. #869C2×D3semidirect
165. #809C2×D3semidirect
166. #807C2×D3semidirect
167. #807C2×D3semidirect
168. C4⋊(C3⋊C8)C2×D3semidirect
169. C4×C3⋊C8C2×D3semidirect
178. C32×D4#41semidirect
191. C4⋊(C3⋊D3)D8semidirect
387. C3×D4#235semidirect
388. C3×D4#239semidirect
558. C32#3294semidirect
578. D4#3799semidirect
637. C3#79608semidirect
638. C3#80980semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊(C3⋊D3)2
#105938692
C3×C4×#2132
C3×#50072
#105914562
#105914162
#105905092
#105904422
#105903492
#105903272
#105902812
#809803
#796083