Finite Group Databasebeta

← #11887561

Subgroups — #11887561

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#10596197C211yesmaximal, characteristic
2#10593903C211yesmaximal, characteristic, complemented
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5#10590606C212yesmaximal, complemented
6#10590601C212yesmaximal, complemented
7#10590529C212yesmaximal, complemented
8#10590523C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11#10590327C211yesmaximal, characteristic, complemented
12#81612—31nomaximal
13#81022—31nomaximal
14C2×#3832—21no—
15C2×#3797C2212yes—
16C32×C4⋊Q8C2211yescharacteristic
17#64155—21no—
18#64104C2212yes—
19#64103—22no—
20C4⋊C4×C3⋊D3C2212yes—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63895—22no—
27#63894—21no—
28#63871C2212yes—
29C2×#3717C2211yescharacteristic
30C2×#3717C2212yes—
31C2×#3710C2212yes—
32C3×#810C2212yes—
33C3×#810C2212yes—
34C3×#810C2212yes—
35C3×#808C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63566C2212yes—
40#63566C2211yescharacteristic
41#63564C2211yescharacteristic
42#63557C2212yes—
43#5727—31no—
44#5726—31no—
45#5726—31no—
46#5726—61no—
47Q8×D12—31no—
48C3×#487—31no—
49C3×#475—31no—
50#5094D311yescharacteristic, complemented
51#5093D311yescharacteristic, complemented
52#5083—31no—
53C4×#215—31no—
54#4864—32no—
55#4862—32no—
56#4841—31no—
57#4834—31no—
58#4807—32no—
59#4806—32no—
60#4806—32no—
61#4805—32no—
62D3×#103—32no—
63D3×#103—32no—
64C4×#204—31no—
65C8×D12—31no—
66C2×C32×Q8—21no—
67#3832—44no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)D411yescharacteristic
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3C2312yes—
74C2×C3×Dic6C2312yes—
75C2×C3×Dic6C2311yescharacteristic
76C2×#627—22no—
77C2×#624—22no—
78#3797—24no—
79#3797—42no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83#3752—21no—
84#3752—22no—
85#3752D412yes—
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97Dic3⋊Dic3—22no—
98#3722—22no—
99#3717—22no—
100#3717—42no—
101#3710—42no—
102#3298—91noSylow
103C2×#239—61no—
104C2×#239—61no—
105C2×#239—62no—
106C2×D3×Q8—32no—
107C2×D3×Q8—32no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8C2×D311yescharacteristic
111C3×C4⋊Q8C2×D311yescharacteristic
112C3×C4×Q8—31no—
113#946—32no—
114#946—61no—
115#946—61no—
116#946—62no—
117C2×#215—31no—
118C2×#215—32no—
119C2×#204—31no—
120C2×#204—32no—
121C2×D3×C8—32no—
122C2×D3×C8—32no—
123#897—32no—
124#897—62no—
125#896—62no—
126#895—32no—
127#895—32no—
128#895—62no—
129#894—62no—
130#894—62no—
131#894—64no—
132#893—61no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—32no—
135D3×C4⋊C4—62no—
136#888—61no—
137C4×D12—31no—
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—31no—
141C4×D12—61no—
142C4×D12—61no—
143C4×D12—61no—
144#869—61no—
145#869C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×#106—32no—
148C3×C4⋊C8—31no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#103—32no—
152C3×C4×C8—31no—
153#835—31no—
154#835—32no—
155#821—31no—
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8—32no—
158#817—31no—
159#816—31no—
160#816—32no—
161#810C2×D312yes—
162#810C2×D312yes—
163#810C2×D312yes—
164#809—31no—
165#808—31no—
166#808C2×D312yes—
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C4×C3⋊C8C2×D311yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3⋊D3C2×D412yes—
171C32×Q8—42no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3C2×D412yes—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—44no—
181C4⋊(C3⋊D3)SD1614yescomplemented
182C4×C3⋊D3—22no—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—44no—
185C4×C3⋊D3—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—31no—
201#483—92no—
202#475—31no—
203#465—92no—
204#461—91no—
205#448—92no—
206C4×SD16—91no—
207C8×D4—91no—
208C2×#103—92no—
209C2×C3×Q8—22no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—31no—
213C2×C3×Q8—32no—
214#239—124no—
215#239—124no—
216#239—128no—
217D3×Q8—64no—
218D3×Q8—64no—
219D3×Q8—122no—
220D3×Q8—122no—
221C2×D12—31no—
222C2×D12—31no—
223C2×D12—31no—
224C2×D12—31no—
225C2×D12—61no—
226C2×D12—61no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—64no—
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—62no—
238C2×C4×D3—64no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×Dic6—62no—
242C2×Dic6—62no—
243C2×Dic6C22×D312yes—
244C2×Dic6C22×D311yescharacteristic
245C2×C3×C8—32no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4C22×D312yes—
257C3×C4⋊C4C22×D312yes—
258C3×C42—21no—
259C3×C42—61no—
260C3×C42C22×D311yescharacteristic
261C3×C42C22×D311yescharacteristic
262#215—62no—
263#215—122no—
264(C2×D3)⋊C4—32no—
265(C2×D3)⋊C4—32no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
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—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275C4⋊Dic3—21no—
276C4⋊Dic3—21no—
277C4⋊Dic3—31no—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—31no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283C4⋊Dic3—62no—
284C4⋊Dic3C22×D311yescharacteristic
285Dic3⋊C4—21no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—64no—
290C4×Dic3—21no—
291C2×C3⋊C8C22×D311yescharacteristic
292C2×C3⋊C8C22×D311yescharacteristic
293C2×C3⋊C8C22×D312yes—
294#204—62no—
295#204—122no—
296D3×C8—122no—
297D3×C8—122no—
298C22×C32C22×D411yescharacteristic
299C2×C3⋊D3—22no—
300C2×C3⋊D3—22no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3C2×SD1614yes—
305C32×C4—21no—
306C32×C4—42no—
307C32×C4C2×SD1612yes—
308C32×C4C2×#4111yescharacteristic
309C32×C4H(5,𝔽2)11yescharacteristic
310C3⋊Dic3—22no—
311C3⋊Dic3—41no—
312C3×Dic3—22no—
313C3×Dic3—42no—
314C3×Dic3—41no—
315C2×#41—181no—
316C22×Q8—92no—
317C2×SD16—91no—
318C2×SD16—92no—
319C22×C8—92no—
320C4⋊Q8—31no—
321C4⋊Q8—181no—
322C4⋊Q8D3211yescharacteristic
323#123—182no—
324C22⋊Q8—92no—
325C22⋊Q8—182no—
326C22⋊Q8—181no—
327#121—92no—
328C4×Q8—31no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—181no—
332C2×C4⋊C4—92no—
333#106—32no—
334#106—91no—
335C4⋊C8—31no—
336#103—32no—
337#103—32no—
338#103—32no—
339#103—91no—
340#103—92no—
341#102—91no—
342C22⋊C8—92no—
343C4×C8—31no—
344C22×D3—32no—
345C22×D3—32no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—61no—
349C22×D3—61no—
350C3×Q8—32no—
351C3×Q8—44no—
352C3×Q8—42no—
353C3×Q8—42no—
354C3×Q8—61no—
355C3×Q8—62no—
356C3×Q8—62no—
357C2×C3×C4—24no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381D12—34no—
382D12—34no—
383D12—64no—
384D12—61no—
385D12—61no—
386D12—61no—
387D12—61no—
388D12—121no—
389D12—121no—
390D12—124no—
391D12—124no—
392D12—128no—
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—124no—
404C4×D3—128no—
405C4×D3—122no—
406C4×D3—122no—
407Dic6—21no—
408Dic6—22no—
409Dic6—22no—
410Dic6—124no—
411Dic6—124no—
412Dic6#23912yescomplemented
413C3×C8—61no—
414C3×C8—61no—
415C3×C8—62no—
416C3⋊C8—21no—
417C3⋊C8—21no—
418C3⋊C8—22no—
419C2×C32#54611yescharacteristic
420C2×C32C22×SD1611yescharacteristic
421C2×C32#57811yescharacteristic
422C3⋊D3—24no—
423C3⋊D3—81no—
424#41—364no—
425C2×Q8—21no—
426C2×Q8—31no—
427C2×Q8—32no—
428C2×Q8—182no—
429C2×Q8—184no—
430C2×Q8—362no—
431C2×D4—91no—
432C2×D4—91no—
433C2×D4—182no—
434C22×C4—92no—
435C22×C4—182no—
436C22×C4—182no—
437C22×C4—181no—
438SD16—182no—
439SD16—362no—
440C2×C8—31no—
441C2×C8—31no—
442C2×C8—32no—
443C2×C8—362no—
444C4⋊C4—21no—
445C4⋊C4—31no—
446C4⋊C4—61no—
447C4⋊C4—61no—
448C4⋊C4—61no—
449C4⋊C4—91no—
450C4⋊C4—91no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C4⋊C4C2×D3212yes—
454C22⋊C4—92no—
455C22⋊C4—182no—
456C22⋊C4—182no—
457C22⋊C4—181no—
458C42—61no—
459C42C2×D3211yescharacteristic
460C22×C3—21no—
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C2×D3×D411yescharacteristic
463C2×D3—34no—
464C2×D3—34no—
465C2×D3—64no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—121no—
476C2×D3—121no—
477C2×D3—121no—
478C2×D3—121no—
479C2×D3—121no—
480C2×D3—121no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—22no—
486C3×C4—41no—
487C3×C4—44no—
488C3×C4—42no—
489C3×C4—42no—
490C3×C4—62no—
491C3×C4—121no—
492C3×C4—122no—
493C3×C4D3×SD1612yes—
494C3×C4D3×SD1612yes—
495C3×C4C2×#23911yescharacteristic
496C3×C4D3×#4111yescharacteristic
497C3×C4#100911yescharacteristic
498C3×C4#100911yescharacteristic
499Dic3—22no—
500Dic3—42no—
501Dic3—41no—
502Dic3—62no—
503Dic3—62no—
504Dic3—122no—
505Dic3—122no—
506Dic3—121no—
507Dic3—121no—
508C32#329811yescharacteristic, complemented, Sylow
509C23—92no—
510C23—181no—
511Q8—32no—
512Q8—42no—
513Q8—61no—
514Q8—62no—
515Q8—62no—
516Q8—364no—
517D4—94no—
518D4—181no—
519D4—181no—
520D4—364no—
521C2×C4—22no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—92no—
526C2×C4—182no—
527C2×C4—182no—
528C2×C4—181no—
529C2×C4—364no—
530C2×C4—364no—
531C2×C4—362no—
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#563011yescharacteristic
542C2×C3#567611yescharacteristic
543C2×C3C2×D3×SD1611yescharacteristic
544C2×C3C2×D3×SD1611yescharacteristic
545C2×C3#576611yescharacteristic
546C2×C3#577911yescharacteristic
547D3—64no—
548D3—64no—
549D3—124no—
550D3—242no—
551D3—241no—
552D3—241no—
553C22—94no—
554C22—182no—
555C22—182no—
556C22—361no—
557C22—361no—
558C22—361no—
559C22C2×#381111yescharacteristic
560C4—21no—
561C4—42no—
562C4—62no—
563C4—121no—
564C4—122no—
565C4—182no—
566C4—361no—
567C4#6393012yes—
568C4D3×#23911yescharacteristic
569C4#6432011yescharacteristic
570C3—21no—
571C3#8102211yescharacteristic, complemented
572C3#8161211yescharacteristic, complemented
573C2—184no—
574C2—721no—
575C2C2×#6393011yescharacteristic
576C2#1059533711yescharacteristic
577C2#1059543111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10596197C2
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
2. #10593903C2semidirect
3. C3×#5094C2semidirect
4. C3×#5093C2semidirect
5. #10590606C2semidirect
6. #10590601C2semidirect
7. #10590529C2semidirect
8. #10590523C2semidirect
9. #10590379C2semidirect
10. C4×#3717C2semidirect
11. #10590327C2semidirect
50. #5094D3semidirect
51. #5093D3semidirect
181. C4⋊(C3⋊D3)SD16semidirect
192. C3×Dic6#41semidirect
412. Dic6#239semidirect
508. C32#3298semidirect
571. C3#81022semidirect
572. C3#81612semidirect

Maximal subgroups

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

subgroupindex
#105961972
#105939032
C3×#50942
C3×#50932
#105906062
#105906012
#105905292
#105905232
#105903792
C4×#37172
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