Finite Group Databasebeta

← #11887059

Subgroups — #11887059

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594004C211yesmaximal, characteristic, complemented
2#10593869C211yesmaximal, characteristic, complemented
3C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C4×D24C211yesmaximal, characteristic, complemented
6#10590945C212yesmaximal, complemented
7#10590940C212yesmaximal, complemented
8#10590839C212yesmaximal, complemented
9#10590650C212yesmaximal, complemented
10#10590347C211yesmaximal, characteristic, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#81576—31nomaximal
13#79608—31nomaximal
14C2×#3802C2212yes—
15C2×D3×D12—21no—
16C2×#3799—21no—
17C2×C8×C3⋊D3C2212yescomplemented
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20C3×#874C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic, complemented
23C3×#869C2211yescharacteristic, complemented
24#63922—22no—
25#63916C2212yes—
26#63916C2212yescomplemented
27#63908—21no—
28#63900C2212yescomplemented
29#63856—21no—
30#63854—22no—
31C2×#3713C2212yescomplemented
32C32×C4×C8C2211yescharacteristic, complemented
33#63647C2212yescomplemented
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic, complemented
37C3×#821C2212yescomplemented
38C3×#821C2212yescomplemented
39C3×#818C2211yescharacteristic, complemented
40#63576C2212yescomplemented
41#63562C2212yes—
42#63562C2212yescomplemented
43#5726—31no—
44#5717—31no—
45#5551—31no—
46D4×D12—31no—
47C3×#486—31no—
48C3×C4×D8—31no—
49#5156—32no—
50#5087—31no—
51#5072—31no—
52#5015—31no—
53#5007—31no—
54#4882—32no—
55#4775—32no—
56#4775—32no—
57#4774—32no—
58#4773—32no—
59D3×#102—32no—
60D3×#102—32no—
61#4694D311yescharacteristic, complemented
62C4×D24D311yescharacteristic, complemented
63C8×D12—31no—
64C8×D12—31no—
65C8×D12—61no—
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)D411yescharacteristic
68C2×C4×C3⋊D3C2312yes—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×D12C2312yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×#626—22no—
78C2×#626—22no—
79C2×#625—22no—
80C2×#624—22no—
81#3802—24no—
82#3802—42no—
83D3×D12—44no—
84#3799—44no—
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C42C2311yescharacteristic
88#3752D412yes—
89C4⋊(C3⋊Dic3)D411yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91C8×C3⋊D3—42no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×D24—22no—
99#3724—22no—
100(C2×D3)⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102#3713—42no—
103#3294—91noSylow
104C2×#239—61no—
105C2×D3×D4—32no—
106C2×D3×D4—32no—
107C2×D3×D4—61no—
108C2×#235—61no—
109C22×D12—61no—
110C2×C3×D8—31no—
111C3×C4⋊Q8—31no—
112C3×#127—31no—
113C3×C4×D4—31no—
114C3×C4×D4—31no—
115#946—61no—
116#938—32no—
117#938—32no—
118#938—61no—
119#937—62no—
120C2×#213—32no—
121C2×#213—32no—
122#930—61no—
123#924—61no—
124C2×D24C2×D311yescharacteristic
125C2×D3×C8—32no—
126C2×D3×C8—32no—
127C2×D3×C8—62no—
128#895—32no—
129#895—32no—
130#894—62no—
131D3×C4⋊C4—32no—
132D3×C4⋊C4—32no—
133#883—62no—
134#882—62no—
135#874C2×D311yescharacteristic
136C4×D12—31no—
137C4×D12—31no—
138C4×D12—61no—
139C4×D12C2×D311yescharacteristic
140C4×D12C2×D311yescharacteristic, complemented
141#869C2×D311yescharacteristic, complemented
142C3×#107—31no—
143C3×#102—31no—
144C3×#102—32no—
145C3×#102—32no—
146C3×#102—31no—
147C3×C4×C8—21no—
148C3×C4×C8C2×D311yescharacteristic, complemented
149C3×C4×C8C2×D311yescharacteristic, complemented
150#832—32no—
151#832—32no—
152#821C2×D311yescharacteristic
153#821C2×D312yescomplemented
154#821C2×D311yescharacteristic, complemented
155#821C2×D312yescomplemented
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8—32no—
158(C2×D3)⋊C8—62no—
159#818C2×D311yescharacteristic, complemented
160#809—32no—
161#809—32no—
162#807—32no—
163#807—32no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—31no—
166C4⋊(C3⋊C8)—61no—
167C22×C3⋊D3C2×D412yes—
168C22×C3×D3—21no—
169C22×C3×D3—22no—
170C22×C3×D3—21no—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—82no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3C2×D412yes—
178C4⋊(C3⋊D3)D814yescomplemented
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C3×D12—21no—
185C3×D12—22no—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12—22no—
189C3×D12—42no—
190C3×D12—81no—
191C3×D12#4112yescomplemented
192C3×C4×D3—42no—
193C3×C4×D3—42no—
194C3×Dic6—42no—
195#626—44no—
196#626—44no—
197#625—44no—
198#624—44no—
199C32×C8—21no—
200C32×C8—21no—
201C3⋊(C3⋊C8)—22no—
202#547—91no—
203D42—91no—
204#486—31no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—91no—
209#447—92no—
210C4×D8—31no—
211C8×D4—91no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C2×C3×Q8—61no—
216C2×C3×D4—31no—
217C2×C3×D4—32no—
218C2×C3×D4—31no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C2×#67—62no—
224C2×#67—62no—
225C2×#67—62no—
226C2×#67—62no—
227#239—124no—
228D3×D4—64no—
229D3×D4—64no—
230D3×D4—124no—
231D3×D4—122no—
232D3×D4—122no—
233#235—124no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—31no—
237C2×D12—31no—
238C2×D12—61no—
239C2×D12—62no—
240C2×D12—62no—
241C2×D12—124no—
242C2×D12C22×D312yes—
243C2×D12C22×D311yescharacteristic
244C2×D12C22×D311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—32no—
248C2×C4×D3—32no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×C4×D3—62no—
252C2×Dic6—21no—
253C3×D8—62no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8C22×D311yescharacteristic
257C2×C3×C8C22×D311yescharacteristic
258C2×C3×C8C22×D311yescharacteristic
259C2×C3×C8C22×D311yescharacteristic
260C3×C4⋊C4—31no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—61no—
264C3×C22⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C42—21no—
267C3×C42C22×D311yescharacteristic
268C3×C42C22×D311yescharacteristic
269#217—62no—
270#217—62no—
271#213—122no—
272#213—122no—
273(C2×D3)⋊C4—21no—
274(C2×D3)⋊C4—21no—
275(C2×D3)⋊C4—32no—
276(C2×D3)⋊C4—32no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280C4⋊Dic3—21no—
281C4⋊Dic3—31no—
282C4⋊Dic3—31no—
283C4⋊Dic3—61no—
284C4⋊Dic3C22×D311yescharacteristic
285C4⋊Dic3C22×D312yes—
286C4⋊Dic3C22×D311yescharacteristic
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289C2×C3⋊C8—32no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—62no—
292D24—22no—
293D3×C8—122no—
294D3×C8—122no—
295D3×C8—124no—
296C22×C32C22×D411yescharacteristic
297C2×C3⋊D3—22no—
298C2×C3⋊D3—22no—
299C2×C3⋊D3C2×D814yes—
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C2×C3×D3—42no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C2×C3×D3—41no—
309D32—88no—
310C32×C4—21no—
311C32×C4C2×D812yes—
312C32×C4C2×#4111yescharacteristic
313C32×C4H(5,𝔽2)11yescharacteristic
314C3⋊Dic3—22no—
315C3×Dic3—41no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C2×#41—181no—
319C22×D4—92no—
320C22×D4—181no—
321C2×D8—31no—
322C2×D8—92no—
323C22×C8—92no—
324C4⋊Q8—31no—
325#127—31no—
326#123—182no—
327C22⋊Q8—181no—
328#121—92no—
329#121—92no—
330#121—181no—
331#120—182no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4—91no—
335C2×C4⋊C4—92no—
336#107—31no—
337#107—92no—
338C4⋊C8—91no—
339#102—31no—
340#102—32no—
341#102—31no—
342#102—32no—
343#102—92no—
344#102—92no—
345C22⋊C8—92no—
346C4×C8D3211yescharacteristic, complemented
347C23×C3—61no—
348C23×C3—61no—
349C23×C3—62no—
350C22×D3—21no—
351C22×D3—21no—
352C22×D3—22no—
353C22×D3—32no—
354C22×D3—32no—
355C22×D3—62no—
356C22×D3—124no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—124no—
360C22×D3—242no—
361C22×D3—242no—
362C3×Q8—122no—
363C3×D4—32no—
364C3×D4—62no—
365C3×D4—61no—
366C3×D4—61no—
367C3×D4—61no—
368C3×D4—62no—
369C3×D4—122no—
370C3×D4—241no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—61no—
377C2×C3×C4—122no—
378C2×C3×C4—122no—
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385#67—124no—
386#67—124no—
387#67—124no—
388#67—124no—
389C2×Dic3—21no—
390C2×Dic3—22no—
391C2×Dic3—21no—
392C2×Dic3—32no—
393C2×Dic3—32no—
394C2×Dic3—62no—
395D12—21no—
396D12—22no—
397D12—21no—
398D12—21no—
399D12—22no—
400D12—34no—
401D12—34no—
402D12—42no—
403D12—64no—
404D12—81no—
405D12—124no—
406D12—124no—
407D12#23512yescomplemented
408C4×D3—42no—
409C4×D3—42no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—122no—
415C4×D3—122no—
416C4×D3—124no—
417C4×D3—124no—
418Dic6—42no—
419C3×C8—22no—
420C3×C8—21no—
421C3×C8—21no—
422C3×C8—21no—
423C3×C8—21no—
424C3×C8—41no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
428C2×C32#54611yescharacteristic
429C2×C32C22×D811yescharacteristic
430C2×C32#57711yescharacteristic
431C3⋊D3—24no—
432C3×D3—42no—
433C3×D3—82no—
434C3×D3—81no—
435C24—182no—
436#41—364no—
437C2×Q8—61no—
438C2×D4—31no—
439C2×D4—32no—
440C2×D4—31no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—91no—
444C2×D4—182no—
445C2×D4—182no—
446C2×D4—182no—
447C2×D4—184no—
448C2×D4—364no—
449C2×D4—362no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—92no—
453C22×C4—182no—
454D8—62no—
455D8—362no—
456C2×C8—92no—
457C2×C8—362no—
458C2×C8C2×D3211yescharacteristic
459C2×C8C2×D3211yescharacteristic
460C4⋊C4—32no—
461C4⋊C4—31no—
462C4⋊C4—31no—
463C4⋊C4—61no—
464C4⋊C4—91no—
465C4⋊C4—182no—
466C22⋊C4—61no—
467C22⋊C4—61no—
468C22⋊C4—92no—
469C22⋊C4—182no—
470C22⋊C4—182no—
471C42C2×D3211yescharacteristic
472C22×C3—21no—
473C22×C3—62no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3—122no—
479C22×C3—121no—
480C22×C3—122no—
481C22×C3—122no—
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C2×D3×D411yescharacteristic
484C2×D3—22no—
485C2×D3—34no—
486C2×D3—34no—
487C2×D3—41no—
488C2×D3—41no—
489C2×D3—42no—
490C2×D3—41no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—64no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—248no—
503C2×D3—248no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—41no—
510C3×C4—121no—
511C3×C4—122no—
512C3×C4—121no—
513C3×C4D3×D812yes—
514C3×C4D3×D812yes—
515C3×C4C2×#23511yescharacteristic
516C3×C4D3×#4111yescharacteristic
517C3×C4#100911yescharacteristic
518C3×C4#100911yescharacteristic
519Dic3—42no—
520Dic3—41no—
521Dic3—41no—
522Dic3—62no—
523Dic3—62no—
524Dic3—122no—
525C32#329411yescharacteristic, complemented, Sylow
526C23—61no—
527C23—61no—
528C23—62no—
529C23—92no—
530C23—364no—
531C23—364no—
532C23—722no—
533Q8—122no—
534D4—32no—
535D4—61no—
536D4—62no—
537D4—61no—
538D4—61no—
539D4—62no—
540D4—94no—
541D4—122no—
542D4—241no—
543D4—364no—
544D4—364no—
545D4—364no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—92no—
550C2×C4—122no—
551C2×C4—122no—
552C2×C4—182no—
553C2×C4—182no—
554C2×C4—364no—
555C2×C4#380211yescharacteristic
556C2×C4#380211yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—21no—
559C8—21no—
560C8—182no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—122no—
565C2×C3—241no—
566C2×C3—242no—
567C2×C3#555011yescharacteristic
568C2×C3#567611yescharacteristic
569C2×C3C2×D3×D811yescharacteristic
570C2×C3C2×D3×D811yescharacteristic
571C2×C3#576211yescharacteristic
572C2×C3#577011yescharacteristic
573D3—42no—
574D3—64no—
575D3—64no—
576D3—82no—
577D3—81no—
578D3—124no—
579C22—62no—
580C22—94no—
581C22—121no—
582C22—121no—
583C22—121no—
584C22—122no—
585C22—122no—
586C22—121no—
587C22—122no—
588C22—121no—
589C22—182no—
590C22—182no—
591C22—728no—
592C22C2×#380211yescharacteristic
593C4—21no—
594C4—121no—
595C4—121no—
596C4—122no—
597C4—182no—
598C4#6379712yes—
599C4D3×#23511yescharacteristic
600C4#6430811yescharacteristic
601C3—21no—
602C3#7960811yescharacteristic, complemented
603C3#8157611yescharacteristic, complemented
604C2—122no—
605C2—184no—
606C2—242no—
607C2—241no—
608C2#1059400711yescharacteristic
609C2C2×#6379711yescharacteristic
610C2#1059468611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3294
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. #10594004C2semidirect
2. #10593869C2semidirect
3. C8×C4⋊(C3⋊D3)C2semidirect
4. C3×#4694C2semidirect
5. C3×C4×D24C2semidirect
6. #10590945C2semidirect
7. #10590940C2semidirect
8. #10590839C2semidirect
9. #10590650C2semidirect
10. #10590347C2semidirect
11. #10590269C2semidirect
17. C2×C8×C3⋊D3C22semidirect
22. C3×C4×D12C22semidirect
23. C3×#869C22semidirect
26. #63916C22semidirect
28. #63900C22semidirect
31. C2×#3713C22semidirect
32. C32×C4×C8C22semidirect
33. #63647C22semidirect
34. C4⋊(C3⋊(C3⋊C8))C22semidirect
36. C3×#821C22semidirect
37. C3×#821C22semidirect
38. C3×#821C22semidirect
39. C3×#818C22semidirect
40. #63576C22semidirect
42. #63562C22semidirect
61. #4694D3semidirect
62. C4×D24D3semidirect
140. C4×D12C2×D3semidirect
141. #869C2×D3semidirect
148. C3×C4×C8C2×D3semidirect
149. C3×C4×C8C2×D3semidirect
153. #821C2×D3semidirect
154. #821C2×D3semidirect
155. #821C2×D3semidirect
159. #818C2×D3semidirect
178. C4⋊(C3⋊D3)D8semidirect
191. C3×D12#41semidirect
346. C4×C8D32semidirect
407. D12#235semidirect
525. C32#3294semidirect
602. C3#79608semidirect
603. C3#81576semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105938692
C8×C4⋊(C3⋊D3)2
C3×#46942
C3×C4×D242
#105909452
#105909402
#105908392
#105906502
#105903472
#105902692
#815763
#796083