Finite Group Databasebeta

← #11895160

Subgroups — #11895160

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic
3C3×#5083C211yesmaximal, characteristic
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591630C212yesmaximal, complemented
6#10591571C212yesmaximal
7#10591569C212yesmaximal
8#10591538C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic
10#10590307C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#81620—31nomaximal
13#80414—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4⋊Q8C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17#64153C2212yes—
18#64099—21no—
19#64098—22no—
20#64096—21no—
21C4×#634C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#215C2212yes—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63919C2212yes—
27#63899—22no—
28#63898C2212yes—
29#63856—21no—
30C2×#3716C2211yescharacteristic
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63573C2212yes—
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63567C2211yescharacteristic
40#63567C2212yes—
41#63563C2211yescharacteristic
42#63553C2212yes—
43#5727—31no—
44#5721—31no—
45#5721—31no—
46#5721—61no—
47D4×Dic6—31no—
48C3×#487—31no—
49C3×#461—31no—
50#5162—32no—
51Dic3×SD16—32no—
52#5094—31no—
53#5083D311yescharacteristic
54#5079D311yescharacteristic, complemented
55C4×#214—31no—
56#4851—31no—
57#4830—31no—
58#4818—32no—
59#4792—32no—
60#4792—32no—
61#4791—32no—
62#4791—32no—
63#4788—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2312yes—
67C2×#634D411yescharacteristic
68C2×#634C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×#627—22no—
73C2×D3×Dic3—22no—
74D3×Dic6—44no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—22no—
79C4⋊(C3⋊Dic3)D411yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82#3750—22no—
83#3750—22no—
84#3750D412yes—
85C4×C3⋊Dic3—21no—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3C2312yes—
88C3×#215—24no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96#3724—22no—
97(C2×D3)⋊Dic3—22no—
98#3716—22no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4×D4—31no—
108#946—61no—
109Q8×Dic3—32no—
110Q8×Dic3—32no—
111Q8×Dic3—62no—
112#944—32no—
113#944—32no—
114#944—62no—
115C2×#215C2×D312yes—
116D4×Dic3—32no—
117C2×#214—31no—
118#924—61no—
119C2×#204—31no—
120#896—62no—
121#893—32no—
122#890—61no—
123#890—61no—
124#890—62no—
125#889—62no—
126#889—62no—
127#889—64no—
128#888—32no—
129#888—32no—
130#887—61no—
131#887—61no—
132#887—62no—
133#878—62no—
134C4×D12C2×D311yescharacteristic
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C4×Dic6—61no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×C4×C8—31no—
147#835C2×D312yes—
148#835C2×D312yes—
149#835C2×D312yes—
150#832—31no—
151#821—31no—
152#817—32no—
153#817—31no—
154#816—32no—
155#816—31no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158C8×Dic3—32no—
159C8×Dic3—32no—
160#810—31no—
161#810—32no—
162#808—31no—
163#808—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3×D3—21no—
167C32×Q8—22no—
168C32×Q8—22no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×D412yes—
177#634—21no—
178#634—21no—
179#634SD1614yescomplemented
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12#4112yes—
184C3×C4×D3—42no—
185C3×Dic6—42no—
186#627—44no—
187D3×Dic3—44no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—21no—
191#557—91no—
192D4×Q8—91no—
193#487—31no—
194#487—92no—
195#475—92no—
196#475—91no—
197#461—31no—
198#461—92no—
199C8×Q8—91no—
200C4×SD16—91no—
201C4×SD16—92no—
202C2×C3×Q8—22no—
203C2×C3×Q8—61no—
204C2×C3×Q8C22×D312yes—
205C2×C3×Q8C22×D312yes—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C22×Dic3—62no—
209D3×Q8—124no—
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—62no—
213C2×Dic6—21no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—124no—
223C3×SD16—64no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—31no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—61no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#215—24no—
242#214—62no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—62no—
245C4⋊Dic3—21no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—64no—
255C4⋊Dic3C22×D312yes—
256C4⋊Dic3C22×D311yescharacteristic
257Dic3⋊C4—32no—
258Dic3⋊C4—32no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271C4×Dic3—32no—
272C4×Dic3—32no—
273C4×Dic3—62no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—64no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D312yes—
283#204—62no—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—22no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—42no—
290C32×C4C2×SD1612yes—
291C32×C4C2×#4111yescharacteristic
292C32×C42−1+411yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C3⋊Dic3C2×SD1614yes—
297C3×Dic3—42no—
298C3×Dic3—41no—
299C22×Q8—181no—
300C2×SD16—32no—
301C2×SD16—91no—
302C4⋊Q8—31no—
303C4⋊Q8—92no—
304C4⋊Q8—92no—
305C4⋊Q8D3211yescharacteristic
306#125—182no—
307#125—181no—
308C22⋊Q8—182no—
309C22⋊Q8—181no—
310C4×Q8—91no—
311C4×Q8—92no—
312C4×Q8—91no—
313C4×Q8—181no—
314C4×D4—31no—
315C4×D4—92no—
316#106—91no—
317#106—92no—
318C4⋊C8—31no—
319C4⋊C8—92no—
320#103—32no—
321#103—32no—
322#103—32no—
323#103—91no—
324#103—92no—
325#102—91no—
326C4×C8—31no—
327C4×C8—92no—
328C23×C3—61no—
329C22×D3—21no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—42no—
335C3×Q8—42no—
336C3×Q8—122no—
337C3×D4—32no—
338C3×D4—61no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—124no—
369D12—21no—
370D12#23712yes—
371C4×D3—42no—
372C4×D3—124no—
373Dic6—34no—
374Dic6—34no—
375Dic6—42no—
376Dic6—64no—
377Dic6—61no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—121no—
382Dic6—121no—
383Dic6—124no—
384Dic6—124no—
385C3×C8—61no—
386C3×C8—62no—
387C3×C8—61no—
388C3⋊C8—22no—
389C3⋊C8—21no—
390C3⋊C8—21no—
391C2×C32#54811yescharacteristic
392C2×C32C22×SD1611yescharacteristic
393C2×C32#57811yescharacteristic
394C3×D3—42no—
395C2×Q8—61no—
396C2×Q8—91no—
397C2×Q8—91no—
398C2×Q8—182no—
399C2×Q8—364no—
400C2×Q8C2×D3212yes—
401C2×D4—31no—
402C22×C4—61no—
403C22×C4—182no—
404SD16—64no—
405SD16—182no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8—32no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—31no—
412C4⋊C4—32no—
413C4⋊C4—61no—
414C4⋊C4—92no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—181no—
422C22⋊C4—61no—
423C22⋊C4—182no—
424C42—92no—
425C42—182no—
426C42—181no—
427C42C2×D3211yescharacteristic
428C22×C3—21no—
429C22×C3—62no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—22no—
435C2×D3—41no—
436C2×D3—41no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—41no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—121no—
447C3×C4—122no—
448C3×C4D3×SD1612yes—
449C3×C4D3×SD1612yes—
450C3×C4C2×#23711yescharacteristic
451C3×C4D3×#4111yescharacteristic
452C3×C4#101011yescharacteristic
453C3×C4#101011yescharacteristic
454Dic3—34no—
455Dic3—34no—
456Dic3—42no—
457Dic3—41no—
458Dic3—64no—
459Dic3—62no—
460Dic3—62no—
461Dic3—122no—
462Dic3—122no—
463Dic3—122no—
464Dic3—121no—
465Dic3—121no—
466Dic3—121no—
467Dic3—121no—
468C32#335911yescharacteristic, complemented, Sylow
469C23—61no—
470Q8—22no—
471Q8—22no—
472Q8—94no—
473Q8—122no—
474Q8—181no—
475Q8—181no—
476Q8—364no—
477D4—32no—
478D4—61no—
479C2×C4—22no—
480C2×C4—61no—
481C2×C4—62no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—122no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—364no—
488C2×C4#381111yescharacteristic
489C2×C4#381111yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—61no—
492C8—62no—
493C8—61no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—122no—
498C2×C3#559811yescharacteristic
499C2×C3#567711yescharacteristic
500C2×C3C2×D3×SD1611yescharacteristic
501C2×C3C2×D3×SD1611yescharacteristic
502C2×C3#576611yescharacteristic
503C2×C3#577911yescharacteristic
504D3—42no—
505C22—62no—
506C22—121no—
507C22—121no—
508C22C2×#381111yescharacteristic
509C4—21no—
510C4—42no—
511C4—94no—
512C4—121no—
513C4—122no—
514C4—182no—
515C4—361no—
516C4—361no—
517C4#6394012yes—
518C4#6430911yescharacteristic
519C4D3×#23711yescharacteristic
520C3—21no—
521C3#8041411yescharacteristic, complemented
522C3#8162011yescharacteristic, complemented
523C2—122no—
524C2#1059516111yescharacteristic
525C2C2×#6394011yescharacteristic
526C2#1059533711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊Q8D32
hypocenterC32#3359
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. #10596192C2semidirect
4. C3×#5079C2semidirect
5. #10591630C2semidirect
8. #10591538C2semidirect
10. #10590307C2semidirect
11. #10590254C2semidirect
54. #5079D3semidirect
179. #634SD16semidirect
468. C32#3359semidirect
521. C3#80414semidirect
522. C3#81620semidirect

Maximal subgroups

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

subgroupindex
#105961922
#105939042
C3×#50832
C3×#50792
#105916302
#105915712
#105915692
#105915382
C4×#37162
#105903072
#105902542
#816203
#804143