Finite Group Databasebeta

← #11895970

Subgroups — #11895970

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596041C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic
3C3×#5027C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591622C212yesmaximal, complemented
6#10591572C212yesmaximal, complemented
7#10590554C212yesmaximal, complemented
8#10590474C212yesmaximal, complemented
9#10590296C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#80371—31nomaximal
13#79625—31nomaximal
14C2×#3795—21no—
15C32×C4×Q8C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17#64099—22no—
18#64099C2212yes—
19#64078—21no—
20#64078C2211yescharacteristic
21C4×#634—21no—
22C4×#634C2211yescharacteristic
23C2×C3×#215C2212yes—
24C2×C3×#215C2211yescharacteristic
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27#63914C2212yes—
28#63908—21no—
29#63898C2212yes—
30#63885—22no—
31C3×#835C2211yescharacteristic
32C3×#809C2212yes—
33C3×#809C2211yescharacteristic
34C3×#808C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2212yes—
38#63572C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#5718—31no—
44#5570—31no—
45#5570—31no—
46#5570—61no—
47#5553—31no—
48C3×#460—31no—
49C3×C4×SD16—31no—
50#5164—32no—
51#5163—32no—
52#5163—32no—
53#5070—31no—
54#5027D311yescharacteristic, complemented
55C4×#215D311yescharacteristic, complemented
56#5007—31no—
57#4871—32no—
58#4846—31no—
59#4831—31no—
60#4817—32no—
61#4766—32no—
62#4764—32no—
63#4764—32no—
64#4694—31no—
65#4679—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×#634D411yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×#625—22no—
75C2×#625—22no—
76C2×D3×Dic3—22no—
77#3795—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—22no—
88#3750D412yes—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3C2312yes—
91C3×#215—22no—
92C3×#215—24no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98(C2×D3)⋊Dic3—22no—
99#3368—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C2×C3×SD16—31no—
103C2×C3×SD16—32no—
104C3×#127—31no—
105C3×C4×Q8—21no—
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×D4—31no—
109Q8×Dic3—32no—
110Q8×Dic3—32no—
111Q8×Dic3—62no—
112C2×#215C2×D311yescharacteristic
113C2×#215C2×D312yes—
114#940—32no—
115#940—32no—
116#939—62no—
117#938—61no—
118D4×Dic3—32no—
119#930—61no—
120#893—32no—
121#890—32no—
122#890—32no—
123#890—62no—
124#890—62no—
125#890—62no—
126#890—64no—
127#884—62no—
128#874C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130#869—31no—
131#869—31no—
132#869—61no—
133#869—61no—
134#869—61no—
135#869—62no—
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6—62no—
142C3×#106—31no—
143C3×C4⋊C8—31no—
144C3×#103—31no—
145C3×#102—31no—
146C3×#102—32no—
147C3×C4×C8—31no—
148#835C2×D311yescharacteristic
149#832—32no—
150#832—32no—
151#832—32no—
152#821—32no—
153#821—32no—
154#821—32no—
155#818—32no—
156#815—32no—
157#815—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#809C2×D312yes—
161#809C2×D311yescharacteristic
162#808C2×D311yescharacteristic
163#807—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C32×Q8—21no—
169C32×Q8#4112yescomplemented
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—22no—
179#634—42no—
180C2×C3×Dic3—21no—
181C3×D12—21no—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—42no—
186C3×D12—81no—
187C3×C4×D3—42no—
188#625—44no—
189#625—82no—
190D3×Dic3—44no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—21no—
194#557—91no—
195#550—91no—
196#490—92no—
197#486—91no—
198#478—92no—
199#474—91no—
200#460—31no—
201#460—92no—
202#446—91no—
203#440—92no—
204C4×SD16—31no—
205C2×C3×Q8—21no—
206C2×C3×Q8C22×D311yescharacteristic
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×D4—32no—
209C2×C3×D4—31no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C22×C3×C4—61no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C22×Dic3—62no—
218#237—124no—
219#235—124no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12C22×D311yescharacteristic
223C2×D12C22×D312yes—
224C2×C4×D3—21no—
225C2×C4×D3—62no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C2×Dic6—62no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C3×SD16—64no—
233C3×SD16—62no—
234C2×C3×C8—31no—
235C2×C3×C8—32no—
236C2×C3×C8—31no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C22⋊C4—61no—
245C3×C42—22no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—21no—
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D311yescharacteristic
251#217—62no—
252#215—22no—
253#215—24no—
254(C2×D3)⋊C4—21no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—32no—
259C4⋊Dic3—32no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—64no—
267C4⋊Dic3—62no—
268C4⋊Dic3—64no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3C22×D311yescharacteristic
272Dic3⋊C4—32no—
273Dic3⋊C4—32no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—64no—
278C4×Dic3—32no—
279C4×Dic3—32no—
280C4×Dic3—62no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—64no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D312yes—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—41no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—42no—
294C32×C4—22no—
295C32×C4—21no—
296C32×C4—41no—
297C32×C4AGL(1,ℤ/8)12yes—
298C32×C4C2×#4111yescharacteristic
299C32×C42−1+411yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—42no—
303C3×Dic3—41no—
304C2×#41—181no—
305C2×SD16—31no—
306C2×SD16—32no—
307C4⋊Q8—91no—
308C4⋊Q8—181no—
309#127—31no—
310#127—92no—
311#125—92no—
312#125—182no—
313#121—182no—
314#121—181no—
315C4×Q8—91no—
316C4×Q8—92no—
317C4×Q8—181no—
318C4×Q8D3211yescharacteristic
319C4×D4—31no—
320C4×D4—92no—
321#107—92no—
322#106—31no—
323C4⋊C8—31no—
324C4⋊C8—92no—
325#103—31no—
326#102—31no—
327#102—32no—
328#102—92no—
329#102—92no—
330#102—92no—
331#97—92no—
332C4×C8—31no—
333C23×C3—62no—
334C23×C3—61no—
335C22×D3—21no—
336C22×D3—22no—
337C3×Q8—22no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×Q8—22no—
341C3×Q8#23512yescomplemented
342C3×Q8#23712yescomplemented
343C3×D4—62no—
344C3×D4—61no—
345C3×D4—62no—
346C3×D4—61no—
347C3×D4—122no—
348C3×D4—241no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—61no—
359C2×C3×C4—122no—
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366#67—124no—
367#67—124no—
368#67—242no—
369#67—242no—
370C2×Dic3—21no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—64no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—124no—
381D12—21no—
382D12—22no—
383D12—21no—
384D12—22no—
385D12—42no—
386D12—81no—
387C4×D3—42no—
388C4×D3—124no—
389Dic6—62no—
390Dic6—62no—
391Dic6—122no—
392Dic6—124no—
393Dic6—122no—
394Dic6—122no—
395C3×C8—62no—
396C3×C8—61no—
397C3×C8—61no—
398C3⋊C8—21no—
399C3⋊C8—22no—
400C3⋊C8—21no—
401C2×C32#54811yescharacteristic
402C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
403C2×C32#57711yescharacteristic
404C3×D3—81no—
405C3×D3—82no—
406#41—364no—
407C2×Q8—91no—
408C2×Q8—181no—
409C2×Q8C2×D3211yescharacteristic
410C2×D4—31no—
411C2×D4—32no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—182no—
415C2×D4—182no—
416C22×C4—61no—
417C22×C4—182no—
418SD16—62no—
419SD16—64no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8—32no—
423C4⋊C4—21no—
424C4⋊C4—31no—
425C4⋊C4—91no—
426C4⋊C4—92no—
427C4⋊C4—92no—
428C4⋊C4—182no—
429C4⋊C4—182no—
430C4⋊C4—182no—
431C4⋊C4—181no—
432C4⋊C4C2×D3211yescharacteristic
433C22⋊C4—61no—
434C22⋊C4—182no—
435C42—21no—
436C42—92no—
437C42—182no—
438C42C2×D3211yescharacteristic
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3—122no—
445C22×C3—121no—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C2×D3×D411yescharacteristic
448C2×D3—41no—
449C2×D3—42no—
450C2×D3—41no—
451C2×D3—42no—
452C2×D3—41no—
453C2×D3—42no—
454C3×C4—24no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—41no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—121no—
467C3×C4#91412yes—
468C3×C4#91412yes—
469C3×C4C2×#23511yescharacteristic
470C3×C4C2×#23711yescharacteristic
471C3×C4#101011yescharacteristic
472C3×C4#101011yescharacteristic
473Dic3—41no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—62no—
478Dic3—122no—
479Dic3—122no—
480Dic3—124no—
481Dic3—122no—
482Dic3—122no—
483C32#336811yescharacteristic, complemented, Sylow
484C23—61no—
485C23—62no—
486Q8—21no—
487Q8—182no—
488Q8—362no—
489Q8#379512yescomplemented
490D4—61no—
491D4—62no—
492D4—61no—
493D4—62no—
494D4—122no—
495D4—241no—
496D4—364no—
497D4—722no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—61no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—122no—
504C2×C4—182no—
505C2×C4—364no—
506C2×C4#381111yescharacteristic
507C2×C4#381111yescharacteristic
508C2×C4C22×D3211yescharacteristic
509C8—61no—
510C8—62no—
511C8—61no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—242no—
516C2×C3—241no—
517C2×C3#555211yescharacteristic
518C2×C3#559811yescharacteristic
519C2×C3C2×#91411yescharacteristic
520C2×C3C2×#91411yescharacteristic
521C2×C3#577011yescharacteristic
522C2×C3#577511yescharacteristic
523D3—81no—
524D3—82no—
525C22—121no—
526C22—122no—
527C22—122no—
528C22—121no—
529C22—121no—
530C22—122no—
531C22C2×#381111yescharacteristic
532C4—22no—
533C4—21no—
534C4—41no—
535C4—121no—
536C4—182no—
537C4—182no—
538C4—362no—
539C4#6394112yes—
540C4C2×#379511yescharacteristic
541C4#6429811yescharacteristic
542C3—21no—
543C3#7962511yescharacteristic, complemented
544C3#8037111yescharacteristic, complemented
545C2—242no—
546C2—241no—
547C2#1059491811yescharacteristic
548C2C2×#6394111yescharacteristic
549C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4×Q8D32
hypocenterC32#3368
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. #10596041C2semidirect
3. C3×#5027C2semidirect
4. C3×C4×#215C2semidirect
5. #10591622C2semidirect
6. #10591572C2semidirect
7. #10590554C2semidirect
8. #10590474C2semidirect
9. #10590296C2semidirect
10. #10590273C2semidirect
11. #10590272C2semidirect
54. #5027D3semidirect
55. C4×#215D3semidirect
169. C32×Q8#41semidirect
341. C3×Q8#235semidirect
342. C3×Q8#237semidirect
483. C32#3368semidirect
489. Q8#3795semidirect
543. C3#79625semidirect
544. C3#80371semidirect

Maximal subgroups

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

subgroupindex
#105960412
#105939062
C3×#50272
C3×C4×#2152
#105916222
#105915722
#105905542
#105904742
#105902962
#105902732
#105902722
#803713
#796253