Finite Group Databasebeta

← #11865054

Subgroups — #11865054

Order 1152.

1691 conjugacy classes of subgroups; only the 204 normal subgroups are shown.

normal subgroups only

This group has 1691 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2#10596301C211yesmaximal, characteristic, complemented
3C3×#5822C212yesmaximal, complemented
4#10591658C214yesmaximal, complemented
5#10591522C214yesmaximal, complemented
6#10591110C212yesmaximal, complemented
7C2×#63559C211yesmaximal, characteristic, complemented
8#84005—32nomaximal
9C2×C32×#41C2211yescharacteristic, complemented
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2212yes—
12C2×#3811—22no—
13#64308—22no—
14#64308—24no—
15#64308C2214yes—
16C2×D3×D12—22no—
17C2×#3799—22no—
18#64156C2212yescomplemented
19#64149C2212yescomplemented
20#64146—22no—
21#64139—22no—
22#64135C2211yescharacteristic, complemented
23C3×#951—22no—
24C3×#950—24no—
25C3×#949—22no—
26C3×#942C2214yescomplemented
27C3×#932C2214yescomplemented
28C2×C3×#208C2212yescomplemented
29#63568C2218yescomplemented
30#63559C2214yescomplemented
31C2×#1009—32no—
32C3×#575—32no—
33#5830—32no—
34#5830—61no—
35#5822D312yescomplemented
36#5236—32no—
37#5202—38no—
38#5198—38no—
39#5139—32no—
40C2×#823—32no—
41C23×C3⋊D3D412yes—
42C22×D32—22no—
43C32×#41—22no—
44C32×#41—22no—
45C2×C32×Q8C2311yescharacteristic, complemented
46C2×C32×D4—21no—
47C2×C32×D4C2311yescharacteristic, complemented
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#638—24no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)D412yes—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C3×#67—22no—
56C3×#235—22no—
57C3×#235—22no—
58C3×#235D414yescomplemented
59C3×#235C2314yes—
60C2×C3×D12D412yescomplemented
61C2×C3×C4×D3—22no—
62C2×C3×Dic6D412yescomplemented
63#3811—28no—
64#3811—28no—
65C2×#626—24no—
66C2×#624—22no—
67D3×D12—28no—
68D3×D12—28no—
69#3799—28no—
70#3799—28no—
71#3757—21no—
72#3752—24no—
73C4⋊(C3⋊Dic3)—21no—
74C4×C3⋊Dic3C2312yescomplemented
75C3×#216—24no—
76C3×#215—24no—
77C3×#214—24no—
78C3×#213—24no—
79C3×#208—22no—
80C3×#208C2314yescomplemented
81C2×C3×C3⋊C8—22no—
82#3019—91noSylow
83C2×C3×#41—21no—
84C2×C3×#41—32no—
85C2×C3×#41C2×D312yescomplemented
86#1009—38no—
87#1009—64no—
88#1009—64no—
89#1009—64no—
90C2×#239—62no—
91C2×D3×D4—62no—
92C2×D3×D4—64no—
93C2×#235—62no—
94C2×#235C2×D312yes—
95C22×D12—32no—
96C22×D12—61no—
97C22×D12—62no—
98C3×#137—34no—
99C3×#137—62no—
100C3×AGL(1,ℤ/8)—34no—
101C3×AGL(1,ℤ/8)—62no—
102C3×#135—64no—
103C2×C3×M16—32no—
104#951—22no—
105#950—24no—
106#949—22no—
107#947—34no—
108#947—62no—
109#942C2×D314yescomplemented
110#940—34no—
111#940—62no—
112#937—64no—
113#937—64no—
114#932C2×D314yescomplemented
115#930—64no—
116#930—64no—
117#926—32no—
118#926—61no—
119C2×#208C2×D312yescomplemented
120#837—38no—
121#825—38no—
122#823—38no—
123C23×C32—21no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—82no—
128C22×C3⋊D3C2×D414yes—
129C22×C3×D3—22no—
130C2×D32—28no—
131C2×D32—84no—
132C32×Q8—22no—
133C32×D4—22no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4—21no—
137C2×C32×C4—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2411yescharacteristic
142#638—84no—
143C2×C3⋊Dic3—22no—
144C4⋊(C3⋊D3)—24no—
145C4⋊(C3⋊D3)—24no—
146C3×#67—24no—
147C3×#67—24no—
148C2×C3×Dic3—22no—
149C3×D12—22no—
150C3×D12C2×D414yes—
151C3×C4×D3—24no—
152C3×C4×D3—24no—
153C3×Dic6—22no—
154C3×Dic6C2×D414yes—
155#626—216no—
156#624—28no—
157C3×C3⋊C8—24no—
158C2×H(5,𝔽2)—91no—
159#575—32no—
160#535—91no—
161#455—94no—
162#453—94no—
163#421—92no—
164C2×#100—91no—
165C23×D3—34no—
166C23×D3—62no—
167C23×D3—64no—
168C3×#41—22no—
169C3×#41—22no—
170C3×#41—22no—
171C3×#41—22no—
172C3×#41—34no—
173C3×#41—34no—
174C3×#41—42no—
175C3×#41—42no—
176C3×#41—62no—
177C3×#41—62no—
178C2×C3×Q8—21no—
179C2×C3×Q8—32no—
180C2×C3×Q8C22×D312yescomplemented
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—21no—
184C2×C3×D4—32no—
185C2×C3×D4—62no—
186C2×C3×D4C22×D312yescomplemented
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—62no—
191C22×C3×C4C22×D312yes—
192C2×#67—22no—
193C2×#67—64no—
194C2×#67—68no—
195C2×#67—68no—
196#239—68no—
197#239—68no—
198D3×D4—68no—
199D3×D4—68no—
200D3×D4—616no—
201D3×D4—616no—
202#235—22no—
203#235—22no—
204#235—68no—
205#235—68no—
206#235#6714yescomplemented
207#235C22×D314yes—
208C2×D12—34no—
209C2×D12—34no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—68no—
213C2×D12—64no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—68no—
219C2×D12—122no—
220C2×D12—122no—
221C2×D12#6712yescomplemented
222C2×C4×D3—22no—
223C2×C4×D3—64no—
224C2×Dic6#6712yescomplemented
225C3×Q16—64no—
226C3×SD16—64no—
227C3×SD16—64no—
228C3×D8—64no—
229C3×M16—34no—
230C3×M16—62no—
231C2×C3×C8—62no—
232#217—62no—
233#217—62no—
234#216—24no—
235#215—24no—
236#214—24no—
237#213—24no—
238(C2×D3)⋊C4—68no—
239(C2×D3)⋊C4—68no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4×Dic3—34no—
243C4×Dic3—62no—
244#208—22no—
245#208C22×D314yescomplemented
246C2×C3⋊C8—22no—
247C22×C32—41no—
248C22×C32—42no—
249C22×C32—41no—
250C22×C32#12011yescharacteristic
251C22×C32#12011yescharacteristic
252C22×C32C22×D411yescharacteristic
253C2×C3⋊D3—24no—
254C2×C3⋊D3—44no—
255C2×C3⋊D3—44no—
256C2×C3⋊D3—82no—
257C2×C3×D3—24no—
258C2×C3×D3—44no—
259D32—88no—
260C32×C4—41no—
261C32×C4#12012yes—
262C32×C4C22×D412yes—
263C3⋊Dic3—42no—
264C3×Dic3—24no—
265H(5,𝔽2)—94no—
266H(5,𝔽2)—182no—
267H(5,𝔽2)—184no—
268C2×#41—32no—
269C2×#41—182no—
270C2×#41D3211yescharacteristic, complemented
271C22×D4—91no—
272C22×D4—182no—
273C22×D4—182no—
274#137—34no—
275#137—62no—
276AGL(1,ℤ/8)—34no—
277AGL(1,ℤ/8)—62no—
278#135—64no—
279C2×M16—32no—
280#127—92no—
281#124—92no—
282#121—182no—
283#120—182no—
284#117—91no—
285#104—98no—
286#100—94no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—62no—
291C23×C3D3×D412yes—
292C22×D3—22no—
293C22×D3—38no—
294C22×D3—64no—
295C22×D3—616no—
296C22×D3—64no—
297C22×D3—64no—
298C22×D3—122no—
299C22×D3—122no—
300C22×D3—248no—
301C22×D3—244no—
302C22×D3—244no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—34no—
306C3×Q8—42no—
307C3×Q8—62no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—34no—
311C3×D4—42no—
312C3×D4—42no—
313C3×D4—42no—
314C3×D4—42no—
315C3×D4—42no—
316C3×D4—64no—
317C3×D4—64no—
318C3×D4—62no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—44no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—64no—
330C2×C3×C4—64no—
331C2×C3×C4D3×D412yes—
332C2×C3×C4D3×D412yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4C2×#6712yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C23×D312yes—
337#67—24no—
338#67—24no—
339#67—616no—
340#67—248no—
341#67—248no—
342C2×Dic3—22no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345D12—22no—
346D12—616no—
347D12—64no—
348D12—64no—
349D12—64no—
350D12—64no—
351D12—124no—
352D12—124no—
353D12C2×#6714yes—
354C4×D3—24no—
355C4×D3—24no—
356C4×D3—616no—
357Dic6—22no—
358Dic6C2×#6714yes—
359C3×C8—64no—
360C3⋊C8—24no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32—81no—
365C2×C32C2×#12011yescharacteristic
366C3⋊D3—44no—
367C3×D3—44no—
368C24—92no—
369C24—182no—
370#41—22no—
371#41—22no—
372#41—34no—
373#41—34no—
374#41—62no—
375#41—62no—
376#41—188no—
377#41—188no—
378C2×Q8—32no—
379C2×Q8C2×D3211yescharacteristic, complemented
380C2×D4—21no—
381C2×D4—32no—
382C2×D4—62no—
383C2×D4—92no—
384C2×D4—92no—
385C2×D4—188no—
386C2×D4—188no—
387C2×D4—184no—
388C2×D4—188no—
389C2×D4—188no—
390C2×D4—184no—
391C2×D4—182no—
392C2×D4—182no—
393C2×D4C2×D3211yescharacteristic, complemented
394C22×C4—21no—
395C22×C4—62no—
396C22×C4—182no—
397C22×C4C2×D3211yescharacteristic
398Q16—64no—
399SD16—64no—
400SD16—64no—
401D8—64no—
402M16—34no—
403M16—62no—
404C2×C8—62no—
405C4⋊C4—181no—
406C22⋊C4—184no—
407C22⋊C4—181no—
408C42—92no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—44no—
415C22×C3—44no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—64no—
419C22×C3—124no—
420C22×C3#93712yes—
421C22×C3#93712yes—
422C22×C3C2×D3×D412yes—
423C2×D3—24no—
424C2×D3—44no—
425C2×D3—68no—
426C2×D3—124no—
427C2×D3—128no—
428C2×D3—128no—
429C2×D3—128no—
430C2×D3—244no—
431C2×D3—2416no—
432C2×D3—244no—
433C2×D3—244no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—64no—
439C3×C4#93712yes—
440C3×C4#93712yes—
441C3×C4C2×D3×D412yes—
442C3×C4C22×#6712yes—
443Dic3—24no—
444Dic3—124no—
445Dic3—124no—
446C32#301911yescharacteristic, complemented, Sylow
447C23—21no—
448C23—62no—
449C23—94no—
450C23—188no—
451C23—182no—
452C23—182no—
453C23—722no—
454C23—724no—
455C23#381111yescharacteristic
456Q8—22no—
457Q8—34no—
458Q8—62no—
459D4—22no—
460D4—34no—
461D4—41no—
462D4—41no—
463D4—64no—
464D4—64no—
465D4—62no—
466D4—1816no—
467D4—184no—
468D4—184no—
469D4—724no—
470C2×C4—21no—
471C2×C4—42no—
472C2×C4—62no—
473C2×C4—64no—
474C2×C4—64no—
475C2×C4—188no—
476C2×C4—182no—
477C2×C4D3×#6712yes—
478C2×C4D3×#6712yes—
479C2×C4#381111yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—64no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—82no—
490C2×C3—82no—
491C2×C3—124no—
492C2×C3C2×#93712yes—
493D3—44no—
494D3—128no—
495D3—244no—
496C22—41no—
497C22—42no—
498C22—41no—
499C22—64no—
500C22—124no—
501C22—184no—
502C22—364no—
503C22—364no—
504C22—722no—
505C22—728no—
506C22#6398311yescharacteristic
507C22#6398311yescharacteristic
508C22C2×#381111yescharacteristic
509C4—41no—
510C4—64no—
511C4—362no—
512C4#6398312yes—
513C4C2×D3×#6712yes—
514C3—21no—
515C3#8400512yescomplemented
516C2—21no—
517C2—21no—
518C2—21no—
519C2—81no—
520C2—124no—
521C2—364no—
522C2C2×#6398311yescharacteristic
subgroupG/H
centerC2C2×#63983
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3019
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. #10596301C2semidirect
3. C3×#5822C2semidirect
4. #10591658C2semidirect
5. #10591522C2semidirect
6. #10591110C2semidirect
7. C2×#63559C2semidirect
9. C2×C32×#41C22semidirect
18. #64156C22semidirect
19. #64149C22semidirect
22. #64135C22semidirect
26. C3×#942C22semidirect
27. C3×#932C22semidirect
28. C2×C3×#208C22semidirect
29. #63568C22semidirect
30. #63559C22semidirect
35. #5822D3semidirect
45. C2×C32×Q8C23semidirect
47. C2×C32×D4C23semidirect
58. C3×#235D4semidirect
60. C2×C3×D12D4semidirect
62. C2×C3×Dic6D4semidirect
74. C4×C3⋊Dic3C23semidirect
80. C3×#208C23semidirect
85. C2×C3×#41C2×D3semidirect
109. #942C2×D3semidirect
114. #932C2×D3semidirect
119. C2×#208C2×D3semidirect
180. C2×C3×Q8C22×D3semidirect
186. C2×C3×D4C22×D3semidirect
206. #235#67semidirect
221. C2×D12#67semidirect
224. C2×Dic6#67semidirect
245. #208C22×D3semidirect
270. C2×#41D32semidirect
379. C2×Q8C2×D32semidirect
393. C2×D4C2×D32semidirect
446. C32#3019semidirect
515. C3#84005semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
#105963012
C3×#58222
#105916582
#105915222
#105911102
C2×#635592
#840053