Finite Group Databasebeta

← #11887567

Subgroups — #11887567

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 579 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596022C211yesmaximal, characteristic
2#10593903C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591518C212yesmaximal, complemented
6#10591465C212yesmaximal, complemented
7#10590601C212yesmaximal, complemented
8#10590529C212yesmaximal, complemented
9#10590327C211yesmaximal, characteristic, complemented
10#10590301C211yesmaximal, characteristic, complemented
11#10590287C211yesmaximal, characteristic, complemented
12#80450—31nomaximal
13#79678—31nomaximal
14C2×#3828—21no—
15C2×#3797C2212yes—
16C32×C4×D4C2211yescharacteristic
17#64147C2212yes—
18#64133—21no—
19C4⋊C4×C3⋊D3C2212yes—
20#64092—22no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22#64078C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#214C2212yes—
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63918—21no—
28#63895—22no—
29#63894—21no—
30#63871C2212yes—
31C2×#3710C2212yes—
32C3×#832C2211yescharacteristic
33C3×#810C2212yes—
34C3×#810C2211yescharacteristic
35C3×#808C2211yescharacteristic
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63566C2212yes—
42#63557C2212yes—
43#5727—31no—
44Q8×D12—31no—
45#5551—31no—
46#5551—31no—
47#5551—61no—
48C3×#461—31no—
49C3×C4×SD16—31no—
50#5171—32no—
51#5170—32no—
52#5170—32no—
53#5079—31no—
54#5020—31no—
55#5019D311yescharacteristic, complemented
56C4×#214D311yescharacteristic, complemented
57#4862—32no—
58#4851—31no—
59#4834—31no—
60#4805—32no—
61D3×#103—32no—
62D3×#103—32no—
63#4778—32no—
64C8×D12—31no—
65#4681—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#638—22no—
69#3828—44no—
70C2×C4⋊(C3⋊D3)D411yescharacteristic
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3C2312yes—
73C2×#634—21no—
74C2×C3×Dic6C2312yes—
75C2×C3×Dic6C2311yescharacteristic
76C2×#627—22no—
77C2×#624—22no—
78#3797—24no—
79#3797—42no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3757—22no—
84#3752D412yes—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88#3750—22no—
89C3×#214—22no—
90C3×#214—42no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3—21no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99Dic3⋊Dic3—22no—
100#3722—22no—
101#3710—42no—
102#3298—91noSylow
103C2×D3×Q8—32no—
104C2×D3×Q8—32no—
105C2×#235—61no—
106C2×#235—61no—
107C2×#235—62no—
108C2×C3×SD16—31no—
109C2×C3×SD16—32no—
110C3×C4⋊Q8—31no—
111C3×C4×Q8—31no—
112C3×C4×D4—21no—
113C3×C4×D4C2×D311yescharacteristic
114C3×C4×D4C2×D311yescharacteristic
115#946—32no—
116#938—32no—
117#938—32no—
118#938—62no—
119C2×#214C2×D311yescharacteristic
120C2×#214C2×D312yes—
121#924—61no—
122#924—61no—
123#924—62no—
124C2×D3×C8—32no—
125C2×D3×C8—32no—
126#897—32no—
127#897—62no—
128#896—62no—
129#893—61no—
130D3×C4⋊C4—32no—
131D3×C4⋊C4—32no—
132D3×C4⋊C4—62no—
133#888—61no—
134#883—62no—
135#883—62no—
136#883—64no—
137C4×D12—31no—
138C4×D12—31no—
139C4×D12—61no—
140C4×D12—61no—
141#869—31no—
142#869—31no—
143#869—61no—
144#869—61no—
145#869C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×#106—31no—
148C3×C4⋊C8—31no—
149C3×#103—31no—
150C3×#103—32no—
151C3×#102—31no—
152C3×C4×C8—31no—
153#835—32no—
154#835—32no—
155#835—32no—
156#832C2×D311yescharacteristic
157(C2×D3)⋊C8—32no—
158(C2×D3)⋊C8—32no—
159#817—32no—
160#816—32no—
161#816—32no—
162#816—32no—
163#810C2×D311yescharacteristic
164#810C2×D312yes—
165#808—32no—
166#808C2×D311yescharacteristic
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C4×C3⋊C8C2×D311yescharacteristic
169C23×C32—21no—
170C22×C3⋊D3C2×D412yes—
171C32×D4—21no—
172C32×D4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—42no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178#638—44no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3C2×D412yes—
181C4⋊(C3⋊D3)SD1614yescomplemented
182C4×C3⋊D3—22no—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—44no—
185#634—42no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C3×Dic6—21no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192C3×Dic6#4112yescomplemented
193#627—44no—
194#624—44no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197C3×C3⋊C8—22no—
198D4×Q8—91no—
199#547—91no—
200#487—91no—
201#483—92no—
202#475—91no—
203#465—92no—
204#461—31no—
205#448—92no—
206C4×SD16—31no—
207C8×D4—91no—
208C2×#103—92no—
209C2×C3×Q8—31no—
210C2×C3×Q8—32no—
211C2×C3×D4—21no—
212C2×C3×D4C22×D311yescharacteristic
213C2×C3×D4C22×D311yescharacteristic
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C2×#67—62no—
218C2×#67—62no—
219C2×#67—64no—
220D3×Q8—64no—
221D3×Q8—64no—
222D3×Q8—122no—
223D3×Q8—122no—
224#235—124no—
225#235—124no—
226#235—128no—
227C2×D12—31no—
228C2×D12—31no—
229C2×D12—61no—
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—62no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6C22×D312yes—
244C2×Dic6C22×D311yescharacteristic
245C3×SD16—62no—
246C3×SD16—122no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C2×C3×C8—32no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C22×D311yescharacteristic
257C3×C22⋊C4—22no—
258C3×C22⋊C4—21no—
259C3×C22⋊C4—21no—
260C3×C42—21no—
261C3×C42—61no—
262C3×C42C22×D311yescharacteristic
263C3×C42C22×D311yescharacteristic
264#217—62no—
265#217—62no—
266#217—64no—
267#214—22no—
268#214—42no—
269(C2×D3)⋊C4—32no—
270(C2×D3)⋊C4—32no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—31no—
277C4⋊Dic3—31no—
278C4⋊Dic3—32no—
279C4⋊Dic3—32no—
280C4⋊Dic3—62no—
281C4⋊Dic3—61no—
282C4⋊Dic3—62no—
283C4⋊Dic3—62no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3C22×D311yescharacteristic
287Dic3⋊C4—21no—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291Dic3⋊C4—64no—
292C4×Dic3—21no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D312yes—
296D3×C8—122no—
297D3×C8—122no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32—41no—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3C2×SD1614yes—
305C32×C4—21no—
306C32×C4—41no—
307C32×C4C2×SD1612yes—
308C32×C4C2×#4111yescharacteristic
309C32×C4H(5,𝔽2)11yescharacteristic
310C3⋊Dic3—22no—
311C3⋊Dic3—42no—
312C3×Dic3—22no—
313C3×Dic3—42no—
314C3×Dic3—41no—
315C2×#41—181no—
316C22×Q8—92no—
317C2×SD16—31no—
318C2×SD16—32no—
319C22×C8—92no—
320C4⋊Q8—31no—
321C4⋊Q8—91no—
322C4⋊Q8—181no—
323#123—182no—
324C22⋊Q8—92no—
325C22⋊Q8—182no—
326C22⋊Q8—181no—
327#121—92no—
328C4×Q8—31no—
329C4×D4—91no—
330C4×D4—181no—
331C4×D4D3211yescharacteristic
332C2×C4⋊C4—92no—
333#106—31no—
334#106—92no—
335C4⋊C8—31no—
336#103—31no—
337#103—32no—
338#103—92no—
339#103—92no—
340#103—92no—
341#102—31no—
342C22⋊C8—92no—
343C4×C8—31no—
344C23×C3—22no—
345C23×C3—21no—
346C23×C3—21no—
347C22×D3—32no—
348C22×D3—32no—
349C22×D3—62no—
350C3×Q8—32no—
351C3×Q8—61no—
352C3×Q8—62no—
353C3×Q8—62no—
354C3×D4—21no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—41no—
359C3×D4—41no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—44no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—61no—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—124no—
379#67—124no—
380#67—128no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—62no—
387C2×Dic3—64no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390D12—34no—
391D12—34no—
392D12—64no—
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—21no—
405Dic6—22no—
406Dic6—22no—
407Dic6—124no—
408Dic6—124no—
409Dic6—124no—
410Dic6—122no—
411Dic6—122no—
412Dic6#23512yescomplemented
413C3×C8—61no—
414C3×C8—61no—
415C3×C8—62no—
416C3⋊C8—21no—
417C3⋊C8—22no—
418C3⋊C8—21no—
419C2×C32—81no—
420C2×C32#54611yescharacteristic
421C2×C32C22×SD1611yescharacteristic
422C2×C32#57811yescharacteristic
423C3⋊D3—24no—
424#41—364no—
425C2×Q8—31no—
426C2×Q8—32no—
427C2×Q8—182no—
428C2×Q8—181no—
429C2×Q8—184no—
430C2×Q8—362no—
431C2×D4—91no—
432C2×D4—182no—
433C2×D4C2×D3211yescharacteristic
434C22×C4—21no—
435C22×C4—92no—
436C22×C4—182no—
437C22×C4—182no—
438SD16—62no—
439SD16—122no—
440C2×C8—31no—
441C2×C8—31no—
442C2×C8—32no—
443C2×C8—362no—
444C4⋊C4—31no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4—61no—
448C4⋊C4—91no—
449C4⋊C4—92no—
450C4⋊C4—182no—
451C4⋊C4—182no—
452C4⋊C4—181no—
453C4⋊C4C2×D3211yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—92no—
456C22⋊C4—182no—
457C22⋊C4—182no—
458C42—61no—
459C42C2×D3211yescharacteristic
460C22×C3—21no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3C2×D3×D411yescharacteristic
471C22×C3C2×D3×D411yescharacteristic
472C2×D3—34no—
473C2×D3—34no—
474C2×D3—64no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—122no—
480C2×D3—122no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—22no—
486C3×C4—41no—
487C3×C4—42no—
488C3×C4—41no—
489C3×C4—41no—
490C3×C4—62no—
491C3×C4—121no—
492C3×C4—122no—
493C3×C4D3×SD1612yes—
494C3×C4D3×SD1612yes—
495C3×C4C2×#23511yescharacteristic
496C3×C4#100411yescharacteristic
497C3×C4D3×#4111yescharacteristic
498C3×C4#100911yescharacteristic
499Dic3—22no—
500Dic3—41no—
501Dic3—42no—
502Dic3—62no—
503Dic3—62no—
504Dic3—122no—
505Dic3—124no—
506Dic3—122no—
507Dic3—122no—
508C32#329811yescharacteristic, complemented, Sylow
509C23—21no—
510C23—92no—
511Q8—32no—
512Q8—61no—
513Q8—62no—
514Q8—62no—
515Q8—364no—
516Q8—362no—
517D4—21no—
518D4—21no—
519D4—94no—
520D4—364no—
521C2×C4—21no—
522C2×C4—42no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—92no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—364no—
531C2×C4—364no—
532C2×C4#381111yescharacteristic
533C2×C4#381111yescharacteristic
534C2×C4C22×D3211yescharacteristic
535C8—61no—
536C8—61no—
537C8—62no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—82no—
542C2×C3—81no—
543C2×C3—81no—
544C2×C3#555011yescharacteristic
545C2×C3#561211yescharacteristic
546C2×C3C2×D3×SD1611yescharacteristic
547C2×C3C2×D3×SD1611yescharacteristic
548C2×C3#577111yescharacteristic
549C2×C3#577911yescharacteristic
550D3—64no—
551D3—64no—
552D3—124no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—94no—
557C22—182no—
558C22—182no—
559C22C2×#381111yescharacteristic
560C4—21no—
561C4—41no—
562C4—62no—
563C4—122no—
564C4—121no—
565C4—182no—
566C4—362no—
567C4#6393012yes—
568C4D3×#23511yescharacteristic
569C4#6430711yescharacteristic
570C3—21no—
571C3#7967811yescharacteristic, complemented
572C3#8045011yescharacteristic, complemented
573C2—81no—
574C2—184no—
575C2#1059507811yescharacteristic
576C2C2×#6393011yescharacteristic
577C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596022C2
hypercenterC4×D4D32
hypocenterC32#3298
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
2. #10593903C2semidirect
3. C3×#5019C2semidirect
4. C3×C4×#214C2semidirect
5. #10591518C2semidirect
6. #10591465C2semidirect
7. #10590601C2semidirect
8. #10590529C2semidirect
9. #10590327C2semidirect
10. #10590301C2semidirect
11. #10590287C2semidirect
55. #5019D3semidirect
56. C4×#214D3semidirect
181. C4⋊(C3⋊D3)SD16semidirect
192. C3×Dic6#41semidirect
412. Dic6#235semidirect
508. C32#3298semidirect
571. C3#79678semidirect
572. C3#80450semidirect

Maximal subgroups

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

subgroupindex
#105960222
#105939032
C3×#50192
C3×C4×#2142
#105915182
#105914652
#105906012
#105905292
#105903272
#105903012
#105902872
#804503
#796783