Finite Group Databasebeta

← #11887564

Subgroups — #11887564

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593903C211yesmaximal, characteristic, complemented
2#10593869C211yesmaximal, characteristic
3#10592533C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic, complemented
6#10590843C212yesmaximal, complemented
7#10590824C212yesmaximal, complemented
8#10590686C212yesmaximal, complemented
9#10590672C212yesmaximal, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590290C211yesmaximal, characteristic, complemented
12#81022—31nomaximal
13#80450—31nomaximal
14C2×#3799—21no—
15C2×#3797C2212yes—
16C2×C8×C3⋊D3C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63918—21no—
24#63916C2212yes—
25#63900C2212yes—
26#63895—22no—
27#63894—21no—
28#63871C2212yes—
29#63856—21no—
30#63854—22no—
31C2×#3715C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic
33#63647C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#817C2212yes—
36C3×#816C2212yes—
37C3×#816C2212yes—
38#63574C2211yescharacteristic
39#63565C2212yes—
40#63565C2212yes—
41#63565C2211yescharacteristic
42#63562C2211yescharacteristic
43#5727—31no—
44#5726—31no—
45Q8×D12—31no—
46#5551—31no—
47C3×#475—31no—
48C3×#461—31no—
49#5171—32no—
50#5170—32no—
51#5093—31no—
52#5079—31no—
53C4×#215—31no—
54C4×#214—31no—
55#4864—32no—
56#4862—32no—
57#4851D311yescharacteristic, complemented
58#4841D311yescharacteristic, complemented
59#4834—31no—
60#4834—31no—
61#4834—61no—
62#4806—32no—
63#4805—32no—
64D3×#103—32no—
65D3×#103—32no—
66C2×C4⋊(C3⋊D3)D411yescharacteristic
67C2×C4×C3⋊D3C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C2×#626—22no—
75C2×#624—22no—
76C2×#624—22no—
77#3799—44no—
78#3797—24no—
79#3797—42no—
80C2×C32×C8C2312yes—
81C32×C42C2311yescharacteristic
82#3752D412yes—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C8×C3⋊D3—42no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3—21no—
96C3×#204—42no—
97#3724—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3715—22no—
102#3298—91noSylow
103C2×#239—61no—
104C2×D3×Q8—32no—
105C2×D3×Q8—32no—
106C2×#235—61no—
107C2×C3×SD16—32no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8—31no—
110C3×C4×Q8—31no—
111C3×C4×D4—31no—
112#946—32no—
113#946—61no—
114C2×#215—31no—
115#938—32no—
116C2×#214—31no—
117#924—61no—
118C2×#204C2×D312yes—
119C2×D3×C8—32no—
120C2×D3×C8—32no—
121C2×D3×C8—62no—
122#897—32no—
123#897—62no—
124#896—62no—
125#895—32no—
126#894—62no—
127#893—61no—
128D3×C4⋊C4—32no—
129D3×C4⋊C4—32no—
130#888—61no—
131#883—62no—
132C4×D12—31no—
133C4×D12—31no—
134C4×D12—61no—
135C4×D12—61no—
136C4×D12C2×D311yescharacteristic
137#869—61no—
138#869C2×D311yescharacteristic
139#869C2×D311yescharacteristic
140C4×Dic6C2×D311yescharacteristic
141C3×#106—32no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8C2×D311yescharacteristic
144C3×C4⋊C8C2×D311yescharacteristic
145C3×#103—32no—
146C3×#103—32no—
147#835—32no—
148#835—32no—
149#835—31no—
150#832—31no—
151(C2×D3)⋊C8—32no—
152(C2×D3)⋊C8—32no—
153(C2×D3)⋊C8—62no—
154#817C2×D312yes—
155#816C2×D312yes—
156#816C2×D312yes—
157#810—32no—
158#810—31no—
159#810—32no—
160#809—31no—
161#808—31no—
162#808—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—61no—
166C22×C3⋊D3C2×D412yes—
167C22×C3×D3—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3C2×D412yes—
172C4⋊(C3⋊D3)SD1614yescomplemented
173C4×C3⋊D3—22no—
174C4×C3⋊D3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—42no—
183C3×Dic6—21no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—42no—
187C3×Dic6#4112yescomplemented
188#627—44no—
189#626—44no—
190#624—44no—
191#624—44no—
192C32×C8—22no—
193C3⋊(C3⋊C8)—21no—
194C3⋊(C3⋊C8)—21no—
195D4×Q8—91no—
196#547—91no—
197#487—91no—
198#483—92no—
199#475—31no—
200#465—92no—
201#461—31no—
202#448—92no—
203C4×SD16—91no—
204C8×D4—91no—
205C2×#103—92no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×Q8—61no—
209C2×C3×D4—31no—
210C22×C3×C4—61no—
211C2×#67—62no—
212#239—124no—
213D3×Q8—64no—
214D3×Q8—64no—
215D3×Q8—122no—
216D3×Q8—122no—
217#235—124no—
218C2×D12—31no—
219C2×D12—31no—
220C2×D12—61no—
221C2×D12—62no—
222C2×D12C22×D311yescharacteristic
223C2×C4×D3—21no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×Dic6—21no—
232C2×Dic6—62no—
233C2×Dic6—62no—
234C2×Dic6C22×D312yes—
235C2×Dic6C22×D311yescharacteristic
236C3×SD16—122no—
237C2×C3×C8—22no—
238C2×C3×C8C22×D312yes—
239C2×C3×C8C22×D312yes—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C42—21no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#217—62no—
253#215—62no—
254#214—62no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—32no—
257(C2×D3)⋊C4—32no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D311yescharacteristic
271C4⋊Dic3C22×D312yes—
272Dic3⋊C4—21no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—21no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8—61no—
283#204—42no—
284D3×C8—122no—
285D3×C8—122no—
286D3×C8—124no—
287C22×C32C22×D411yescharacteristic
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3C2×SD1614yes—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C32×C4—21no—
295C32×C4C2×SD1612yes—
296C32×C4C2×#4111yescharacteristic
297C32×C4H(5,𝔽2)11yescharacteristic
298C3⋊Dic3—22no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—41no—
302C3×Dic3—42no—
303C3×Dic3—41no—
304C2×#41—181no—
305C22×Q8—92no—
306C2×SD16—32no—
307C2×SD16—91no—
308C22×C8—92no—
309C4⋊Q8—31no—
310C4⋊Q8—31no—
311C4⋊Q8—181no—
312#123—182no—
313C22⋊Q8—92no—
314C22⋊Q8—182no—
315C22⋊Q8—181no—
316#121—92no—
317C4×Q8—31no—
318C4×D4—31no—
319C4×D4—91no—
320C4×D4—181no—
321C2×C4⋊C4—92no—
322#106—32no—
323#106—91no—
324C4⋊C8D3211yescharacteristic
325#103—32no—
326#103—32no—
327#103—91no—
328#103—92no—
329#103—92no—
330#102—91no—
331C22⋊C8—92no—
332C4×C8—91no—
333C23×C3—61no—
334C22×D3—21no—
335C22×D3—32no—
336C22×D3—32no—
337C22×D3—62no—
338C3×Q8—32no—
339C3×Q8—61no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×Q8—122no—
343C3×D4—61no—
344C3×D4—61no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—61no—
353C2×C3×C4—122no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—124no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—62no—
369D12—21no—
370D12—21no—
371D12—34no—
372D12—34no—
373D12—64no—
374D12—124no—
375C4×D3—42no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—122no—
381C4×D3—122no—
382C4×D3—124no—
383C4×D3—124no—
384C4×D3—124no—
385C4×D3—124no—
386Dic6—21no—
387Dic6—22no—
388Dic6—22no—
389Dic6—42no—
390Dic6—124no—
391Dic6—124no—
392Dic6#23912yescomplemented
393C3×C8—22no—
394C3×C8—22no—
395C3×C8—42no—
396C3⋊C8—62no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C3⋊C8—61no—
400C3⋊C8—61no—
401C3⋊C8—121no—
402C2×C32#54611yescharacteristic
403C2×C32C22×SD1611yescharacteristic
404C2×C32#57811yescharacteristic
405C3⋊D3—24no—
406C3×D3—81no—
407#41—364no—
408C2×Q8—31no—
409C2×Q8—32no—
410C2×Q8—61no—
411C2×Q8—182no—
412C2×Q8—184no—
413C2×Q8—362no—
414C2×D4—31no—
415C2×D4—91no—
416C2×D4—182no—
417C22×C4—61no—
418C22×C4—92no—
419C22×C4—182no—
420C22×C4—182no—
421SD16—122no—
422SD16—182no—
423C2×C8—91no—
424C2×C8—91no—
425C2×C8—362no—
426C2×C8C2×D3212yes—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—32no—
430C4⋊C4—61no—
431C4⋊C4—61no—
432C4⋊C4—61no—
433C4⋊C4—61no—
434C4⋊C4—91no—
435C4⋊C4—182no—
436C4⋊C4—182no—
437C22⋊C4—61no—
438C22⋊C4—92no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C42—61no—
442C42C2×D3211yescharacteristic
443C22×C3—21no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3—121no—
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C2×D3×D411yescharacteristic
449C2×D3—34no—
450C2×D3—34no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—64no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—62no—
459C2×D3—122no—
460C2×D3—122no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—62no—
468C3×C4—121no—
469C3×C4—122no—
470C3×C4—121no—
471C3×C4—122no—
472C3×C4D3×SD1612yes—
473C3×C4D3×SD1612yes—
474C3×C4#100411yescharacteristic
475C3×C4C2×#23911yescharacteristic
476C3×C4D3×#4111yescharacteristic
477C3×C4#100911yescharacteristic
478Dic3—22no—
479Dic3—42no—
480Dic3—41no—
481Dic3—41no—
482Dic3—42no—
483Dic3—62no—
484Dic3—62no—
485Dic3—122no—
486C32#329811yescharacteristic, complemented, Sylow
487C23—61no—
488C23—92no—
489Q8—32no—
490Q8—61no—
491Q8—62no—
492Q8—62no—
493Q8—122no—
494Q8—364no—
495D4—61no—
496D4—61no—
497D4—94no—
498D4—364no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—92no—
505C2×C4—122no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—364no—
509C2×C4—364no—
510C2×C4#380211yescharacteristic
511C2×C4#380211yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—22no—
514C8—181no—
515C8—181no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—241no—
520C2×C3#561211yescharacteristic
521C2×C3#563011yescharacteristic
522C2×C3C2×D3×SD1611yescharacteristic
523C2×C3C2×D3×SD1611yescharacteristic
524C2×C3#577911yescharacteristic
525C2×C3#577911yescharacteristic
526D3—64no—
527D3—64no—
528D3—81no—
529D3—124no—
530C22—94no—
531C22—121no—
532C22—121no—
533C22—121no—
534C22—182no—
535C22—182no—
536C22C2×#380211yescharacteristic
537C4—21no—
538C4—62no—
539C4—122no—
540C4—121no—
541C4—122no—
542C4—121no—
543C4—182no—
544C4#6379612yes—
545C4#6431411yescharacteristic
546C4D3×#23911yescharacteristic
547C3—21no—
548C3#8045011yescharacteristic, complemented
549C3#8102211yescharacteristic, complemented
550C2—184no—
551C2—241no—
552C2#1059463311yescharacteristic
553C2C2×#6379611yescharacteristic
554C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593869C2
hypercenterC4⋊C8D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593903C2semidirect
3. #10592533C2semidirect
4. C3×#4851C2semidirect
5. C3×#4841C2semidirect
6. #10590843C2semidirect
7. #10590824C2semidirect
8. #10590686C2semidirect
9. #10590672C2semidirect
10. C4×#3715C2semidirect
11. #10590290C2semidirect
57. #4851D3semidirect
58. #4841D3semidirect
172. C4⋊(C3⋊D3)SD16semidirect
187. C3×Dic6#41semidirect
392. Dic6#239semidirect
486. C32#3298semidirect
548. C3#80450semidirect
549. C3#81022semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105938692
#105925332
C3×#48512
C3×#48412
#105908432
#105908242
#105906862
#105906722
C4×#37152
#105902902
#810223
#804503