Finite Group Databasebeta

← #11887573

Subgroups — #11887573

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2#10593869C211yesmaximal, characteristic
3C3×#5083C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591592C212yesmaximal, complemented
6#10591591C212yesmaximal, complemented
7#10591553C212yesmaximal, complemented
8#10591552C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic, complemented
10#10590327C211yesmaximal, characteristic, complemented
11#10590307C211yesmaximal, characteristic, complemented
12#81612—31nomaximal
13#80450—31nomaximal
14C2×Q8×C3⋊D3C2212yes—
15C2×#3799—21no—
16C32×C4⋊Q8C2211yescharacteristic
17#64155C2212yes—
18#64105—22no—
19#64102—21no—
20#64097—21no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#215C2212yes—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63916C2212yes—
27#63900C2212yes—
28#63856—21no—
29#63854—22no—
30C2×#3716C2211yescharacteristic
31C2×#3710C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38#63573C2212yes—
39#63567C2211yescharacteristic
40#63567C2212yes—
41#63563C2211yescharacteristic
42#63557C2212yes—
43#5727—31no—
44#5727—31no—
45#5727—61no—
46#5726—31no—
47#5551—31no—
48C3×#487—31no—
49C3×#461—31no—
50#5171—32no—
51#5170—32no—
52#5094—31no—
53#5083D311yescharacteristic, complemented
54#5079D311yescharacteristic, complemented
55C4×#214—31no—
56#4851—31no—
57#4834—31no—
58#4807—32no—
59#4806—32no—
60#4805—32no—
61#4805—32no—
62D3×#103—32no—
63D3×#103—32no—
64C4×#204—31no—
65C8×D12—31no—
66C2×C32×Q8C2312yes—
67Q8×C3⋊D3—24no—
68Q8×C3⋊D3—42no—
69C2×C4⋊(C3⋊D3)D411yescharacteristic
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3C2312yes—
72C2×#634—22no—
73C2×#634C2311yescharacteristic
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×#626—22no—
78C2×#624—22no—
79#3799—44no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3752—22no—
84#3752D412yes—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—22no—
89C4×C3⋊Dic3—21no—
90C3×#215—42no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3724—22no—
99(C2×D3)⋊Dic3—22no—
100#3716—22no—
101#3710—42no—
102#3298—91noSylow
103C2×#239—61no—
104C2×D3×Q8—32no—
105C2×D3×Q8—32no—
106C2×D3×Q8—62no—
107C2×#235—61no—
108C2×C3×SD16—32no—
109C3×C4⋊Q8—21no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8C2×D311yescharacteristic
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×C4×D4—31no—
114#946—32no—
115#946—32no—
116#946—62no—
117#946—61no—
118C2×#215C2×D312yes—
119#938—32no—
120C2×#214—31no—
121#924—61no—
122C2×#204—31no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125#896—62no—
126#896—62no—
127#896—64no—
128#895—32no—
129#894—62no—
130#893—61no—
131#893—61no—
132#893—62no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—32no—
135#888—61no—
136#888—61no—
137#888—62no—
138#883—62no—
139C4×D12—31no—
140C4×D12—31no—
141C4×D12—61no—
142C4×D12C2×D311yescharacteristic
143#869C2×D311yescharacteristic
144C4×Dic6—31no—
145C4×Dic6—31no—
146C4×Dic6—61no—
147C3×C4⋊C8—31no—
148C3×#103—32no—
149C3×#103—32no—
150C3×#103—32no—
151C3×C4×C8—31no—
152#835C2×D312yes—
153#835C2×D312yes—
154#835C2×D312yes—
155#832—31no—
156#821—31no—
157(C2×D3)⋊C8—32no—
158(C2×D3)⋊C8—32no—
159#817—32no—
160#817—31no—
161#816—32no—
162#816—31no—
163#810—31no—
164#810—32no—
165#808—31no—
166#808—32no—
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C4×C3⋊C8C2×D311yescharacteristic
169C22×C3⋊D3C2×D412yes—
170C22×C3×D3—21no—
171C32×Q8—22no—
172C32×Q8—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3C2×D412yes—
180C4⋊(C3⋊D3)SD1614yescomplemented
181C4×C3⋊D3—22no—
182C4×C3⋊D3—22no—
183C4×C3⋊D3—44no—
184#634—21no—
185#634—44no—
186#634#4112yescomplemented
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C3×D12—21no—
190C3×D12—21no—
191C3×C4×D3—42no—
192C3×Dic6—42no—
193#626—44no—
194#624—44no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197C3×C3⋊C8—22no—
198D4×Q8—91no—
199#547—91no—
200#487—31no—
201#483—92no—
202#475—91no—
203#465—92no—
204#461—31no—
205#448—92no—
206C4×SD16—91no—
207C8×D4—91no—
208C2×#103—92no—
209C2×C3×Q8—22no—
210C2×C3×Q8—61no—
211C2×C3×Q8C22×D312yes—
212C2×C3×Q8C22×D312yes—
213C2×C3×D4—31no—
214C22×C3×C4—61no—
215C2×#67—62no—
216#239—124no—
217D3×Q8—64no—
218D3×Q8—64no—
219D3×Q8—124no—
220D3×Q8—122no—
221D3×Q8—122no—
222D3×Q8—124no—
223#235—124no—
224C2×D12—31no—
225C2×D12—31no—
226C2×D12—61no—
227C2×D12—62no—
228C2×D12C22×D311yescharacteristic
229C2×C4×D3—21no—
230C2×C4×D3—32no—
231C2×C4×D3—32no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—64no—
238C2×Dic6—21no—
239C2×Dic6—31no—
240C2×Dic6—31no—
241C2×Dic6—61no—
242C2×Dic6—62no—
243C2×Dic6—62no—
244C2×Dic6—64no—
245C3×SD16—122no—
246C2×C3×C8—32no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—61no—
259C3×C42—21no—
260C3×C42C22×D311yescharacteristic
261C3×C42C22×D311yescharacteristic
262#217—62no—
263#215—42no—
264#214—62no—
265(C2×D3)⋊C4—21no—
266(C2×D3)⋊C4—32no—
267(C2×D3)⋊C4—32no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—64no—
273C4⋊Dic3—21no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—31no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3C22×D312yes—
281C4⋊Dic3C22×D311yescharacteristic
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—64no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290C4×Dic3—62no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D312yes—
296#204—62no—
297D3×C8—122no—
298D3×C8—122no—
299C22×C32C22×D411yescharacteristic
300C2×C3⋊D3—22no—
301C2×C3⋊D3—22no—
302C2×C3⋊D3C2×SD1614yes—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C32×C4—21no—
307C32×C4—42no—
308C32×C4C2×SD1612yes—
309C32×C4C2×#4111yescharacteristic
310C32×C4H(5,𝔽2)11yescharacteristic
311C3⋊Dic3—22no—
312C3⋊Dic3—22no—
313C3⋊Dic3—41no—
314C3×Dic3—41no—
315C3×Dic3—42no—
316C2×#41—181no—
317C22×Q8—92no—
318C2×SD16—32no—
319C2×SD16—91no—
320C22×C8—92no—
321C4⋊Q8—31no—
322C4⋊Q8—181no—
323C4⋊Q8D3211yescharacteristic
324#123—182no—
325C22⋊Q8—92no—
326C22⋊Q8—182no—
327C22⋊Q8—181no—
328#121—92no—
329C4×Q8—91no—
330C4×D4—31no—
331C4×D4—91no—
332C4×D4—181no—
333C2×C4⋊C4—92no—
334#106—91no—
335#106—92no—
336C4⋊C8—31no—
337#103—32no—
338#103—32no—
339#103—32no—
340#103—91no—
341#103—92no—
342#102—91no—
343C22⋊C8—92no—
344C4×C8—31no—
345C23×C3—61no—
346C22×D3—21no—
347C22×D3—32no—
348C22×D3—32no—
349C22×D3—62no—
350C3×Q8—22no—
351C3×Q8—22no—
352C3×Q8—22no—
353C3×Q8—22no—
354C3×Q8—42no—
355C3×Q8—42no—
356C3×Q8—122no—
357C3×D4—61no—
358C3×D4—61no—
359C2×C3×C4—24no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—122no—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—124no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—62no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386D12—21no—
387D12—21no—
388D12—34no—
389D12—34no—
390D12—64no—
391D12—124no—
392C4×D3—42no—
393C4×D3—62no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—122no—
398C4×D3—122no—
399C4×D3—124no—
400C4×D3—124no—
401C4×D3—124no—
402C4×D3—124no—
403C4×D3—128no—
404Dic6—32no—
405Dic6—32no—
406Dic6—42no—
407Dic6—62no—
408Dic6—62no—
409Dic6—61no—
410Dic6—61no—
411Dic6—124no—
412Dic6—124no—
413Dic6—128no—
414C3×C8—61no—
415C3×C8—61no—
416C3×C8—62no—
417C3⋊C8—22no—
418C3⋊C8—21no—
419C3⋊C8—21no—
420C2×C32#54611yescharacteristic
421C2×C32C22×SD1611yescharacteristic
422C2×C32#57811yescharacteristic
423C3⋊D3—24no—
424C3×D3—81no—
425#41—364no—
426C2×Q8—61no—
427C2×Q8—91no—
428C2×Q8—182no—
429C2×Q8—184no—
430C2×Q8—362no—
431C2×Q8C2×D3212yes—
432C2×D4—31no—
433C2×D4—91no—
434C2×D4—182no—
435C22×C4—61no—
436C22×C4—92no—
437C22×C4—182no—
438C22×C4—182no—
439SD16—122no—
440SD16—182no—
441C2×C8—31no—
442C2×C8—31no—
443C2×C8—32no—
444C2×C8—362no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—31no—
448C4⋊C4—32no—
449C4⋊C4—61no—
450C4⋊C4—91no—
451C4⋊C4—91no—
452C4⋊C4—182no—
453C4⋊C4—182no—
454C4⋊C4—181no—
455C22⋊C4—61no—
456C22⋊C4—92no—
457C22⋊C4—182no—
458C22⋊C4—182no—
459C42—181no—
460C42C2×D3211yescharacteristic
461C22×C3—21no—
462C22×C3—121no—
463C22×C3—121no—
464C22×C3—121no—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C2×D3×D411yescharacteristic
467C2×D3—34no—
468C2×D3—34no—
469C2×D3—41no—
470C2×D3—41no—
471C2×D3—41no—
472C2×D3—64no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—122no—
478C2×D3—122no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—22no—
484C3×C4—41no—
485C3×C4—44no—
486C3×C4—42no—
487C3×C4—42no—
488C3×C4—121no—
489C3×C4—122no—
490C3×C4D3×SD1612yes—
491C3×C4D3×SD1612yes—
492C3×C4#100411yescharacteristic
493C3×C4D3×#4111yescharacteristic
494C3×C4D3×#4111yescharacteristic
495C3×C4#100911yescharacteristic
496Dic3—42no—
497Dic3—41no—
498Dic3—64no—
499Dic3—62no—
500Dic3—62no—
501Dic3—62no—
502Dic3—62no—
503Dic3—122no—
504Dic3—122no—
505Dic3—121no—
506Dic3—121no—
507C32#329811yescharacteristic, complemented, Sylow
508C23—61no—
509C23—92no—
510Q8—22no—
511Q8—22no—
512Q8—92no—
513Q8—122no—
514Q8—181no—
515Q8—364no—
516D4—61no—
517D4—61no—
518D4—94no—
519D4—364no—
520C2×C4—22no—
521C2×C4—61no—
522C2×C4—62no—
523C2×C4—92no—
524C2×C4—122no—
525C2×C4—181no—
526C2×C4—182no—
527C2×C4—182no—
528C2×C4—181no—
529C2×C4—364no—
530C2×C4—364no—
531C2×C4#381111yescharacteristic
532C2×C4#381111yescharacteristic
533C2×C4C22×D3211yescharacteristic
534C8—61no—
535C8—61no—
536C8—62no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—241no—
541C2×C3#561211yescharacteristic
542C2×C3#567611yescharacteristic
543C2×C3C2×D3×SD1611yescharacteristic
544C2×C3C2×D3×SD1611yescharacteristic
545C2×C3#576611yescharacteristic
546C2×C3#577911yescharacteristic
547D3—64no—
548D3—64no—
549D3—81no—
550D3—124no—
551C22—94no—
552C22—121no—
553C22—121no—
554C22—121no—
555C22—182no—
556C22—182no—
557C22C2×#381111yescharacteristic
558C4—21no—
559C4—42no—
560C4—121no—
561C4—122no—
562C4—182no—
563C4—182no—
564C4—361no—
565C4#6394012yes—
566C4#6431211yescharacteristic
567C4#6431411yescharacteristic
568C3—21no—
569C3#8045011yescharacteristic, complemented
570C3#8161211yescharacteristic, complemented
571C2—184no—
572C2—241no—
573C2#1059524311yescharacteristic
574C2C2×#6394011yescharacteristic
575C2#1059533711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593869C2
hypercenterC4⋊Q8D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596198C2semidirect
3. C3×#5083C2semidirect
4. C3×#5079C2semidirect
5. #10591592C2semidirect
6. #10591591C2semidirect
7. #10591553C2semidirect
8. #10591552C2semidirect
9. C4×#3716C2semidirect
10. #10590327C2semidirect
11. #10590307C2semidirect
53. #5083D3semidirect
54. #5079D3semidirect
180. C4⋊(C3⋊D3)SD16semidirect
186. #634#41semidirect
507. C32#3298semidirect
569. C3#80450semidirect
570. C3#81612semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105938692
C3×#50832
C3×#50792
#105915922
#105915912
#105915532
#105915522
C4×#37162
#105903272
#105903072
#816123
#804503