Finite Group Databasebeta

← #11887544

Subgroups — #11887544

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
1C3×#5555C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591179C212yesmaximal, complemented
5#10591171C212yesmaximal, complemented
6#10591101C212yesmaximal, complemented
7C2×#63565C212yesmaximal, complemented
8#10590363C211yesmaximal, characteristic, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10#10590290C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#83550—31nomaximal
13#83531—31nomaximal
14C2×C3×#237—21no—
15C22×C3×Dic6C2212yes—
16C32×C4×D4C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2212yes—
18C3×D4×Dic3—21no—
19C3×#930C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C3×#924C2212yes—
22C3×#897—21no—
23C3×#888—21no—
24C3×#886—22no—
25C3×#878—22no—
26C3×C4×D12C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C2×#3715C2211yescharacteristic
31C2×#3715C2212yes—
32#63657C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35#63574C2212yes—
36#63574C2211yescharacteristic
37#63565C2212yes—
38#63565C2212yes—
39#63565C2212yes—
40#63565C2211yescharacteristic
41#63565C2212yes—
42#63562C2211yescharacteristic
43C3×D4×Q8—31no—
44C3×#547—31no—
45#5555D311yescharacteristic
46D4×Dic6D311yescharacteristic, complemented
47#5227—32no—
48C2×#835—32no—
49#5094—31no—
50#5093—31no—
51#5083—31no—
52#5079—31no—
53#5048—32no—
54#5043—32no—
55#5041—32no—
56#5040—32no—
57C4×#215—31no—
58#5020—31no—
59#5019—31no—
60C4×#214—31no—
61D4×C3⋊C8—31no—
62D4×C3⋊C8—31no—
63D4×C3⋊C8—61no—
64#4971—32no—
65C2×#810—32no—
66C2×C32×D4D411yescharacteristic
67C22×C32×C4C2312yes—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—22no—
71C3×#237—44no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—24no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—42no—
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C32×C4⋊C4D411yescharacteristic
81C32×C22⋊C4D412yes—
82C32×C42C2311yescharacteristic
83C2×C3⋊(C3⋊C8)—42no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#217—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—22no—
99C3×C4×Dic3—21no—
100#3715—22no—
101#3715—42no—
102#3298—91noSylow
103C2×C3×#41—61no—
104C22×C3×Q8—32no—
105C2×#237—21no—
106C22×Dic6C2×D312yes—
107C3×C4⋊Q8—31no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8—61no—
110C3×#123—62no—
111C3×C22⋊Q8—32no—
112C3×C22⋊Q8—61no—
113C3×C22⋊Q8—62no—
114C3×#121—32no—
115C3×C4×Q8—31no—
116C3×C4×D4—21no—
117C3×C4×D4—31no—
118C3×C4×D4—61no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C2×D311yescharacteristic
121C2×C3×C4⋊C4—32no—
122C2×#215—31no—
123C2×#215—32no—
124D4×Dic3—21no—
125C2×#214—31no—
126C2×#214—32no—
127#930C2×D312yes—
128C2×C4⋊Dic3C2×D312yes—
129#924C2×D312yes—
130C22×C3⋊C8—32no—
131C22×C3⋊C8—32no—
132C22×C3⋊C8—62no—
133#897—21no—
134#888—21no—
135#886—22no—
136#878—22no—
137C4×D12C2×D311yescharacteristic
138#869C2×D311yescharacteristic
139#869C2×D311yescharacteristic
140C4×Dic6C2×D311yescharacteristic
141#835—31no—
142#835—32no—
143#835—32no—
144#835—32no—
145#835—32no—
146#832—31no—
147#830—32no—
148#830—32no—
149#830—62no—
150#810—31no—
151#810—32no—
152#810—32no—
153#810—32no—
154#810—32no—
155#809—31no—
156#808—31no—
157#808—32no—
158#808—32no—
159#808—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—61no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—61no—
166C23×C32C2×D412yes—
167C22×C3×D3—21no—
168C32×D4SD1614yescomplemented
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C3×#67—44no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—44no—
182C2×C3×Dic3—44no—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—21no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3×Dic6—44no—
190C3×Dic6—42no—
191C3×Dic6#4112yescomplemented
192C3⋊(C3⋊C8)—21no—
193C3⋊(C3⋊C8)—21no—
194C3⋊(C3⋊C8)—22no—
195D4×Q8—31no—
196#547—31no—
197#487—91no—
198#483—92no—
199#475—91no—
200#465—92no—
201#461—91no—
202#448—92no—
203C4×SD16—91no—
204C8×D4—91no—
205C2×#103—92no—
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—32no—
209C2×C3×Q8—64no—
210C2×C3×Q8—61no—
211C2×C3×Q8—62no—
212C2×C3×Q8—122no—
213C2×C3×D4—21no—
214C2×C3×D4—31no—
215C2×C3×D4—62no—
216C2×C3×D4#6711yescharacteristic
217C2×C3×D4#6711yescharacteristic
218C22×C3×C4—22no—
219C22×C3×C4—62no—
220C22×C3×C4—62no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C2×#67—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227#237—44no—
228C2×D12C22×D311yescharacteristic
229C2×C4×D3—21no—
230C2×Dic6—24no—
231C2×Dic6—21no—
232C2×Dic6—22no—
233C2×Dic6—42no—
234C2×Dic6C22×D312yes—
235C2×Dic6C22×D311yescharacteristic
236C3×C4⋊C4—21no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4#6711yescharacteristic
247C3×C4⋊C4#6711yescharacteristic
248C3×C22⋊C4—22no—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—61no—
251C3×C22⋊C4—62no—
252C3×C22⋊C4#6712yes—
253C3×C22⋊C4#6712yes—
254C3×C42—21no—
255C3×C42—61no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258#217—22no—
259#215—62no—
260#215—122no—
261#214—62no—
262#214—122no—
263(C2×D3)⋊C4—21no—
264(C2×D3)⋊C4—22no—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C4⋊Dic3—22no—
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D312yes—
271C4⋊Dic3C22×D311yescharacteristic
272Dic3⋊C4—21no—
273Dic3⋊C4—22no—
274C4×Dic3—21no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—32no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8—122no—
285C2×C3⋊C8—122no—
286C2×C3⋊C8—124no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32C2×SD1614yes—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C32×C4—22no—
295C32×C4—21no—
296C32×C4C2×SD1612yes—
297C32×C4C2×#4111yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C2×#41—61no—
305C22×Q8—32no—
306C2×SD16—91no—
307C2×SD16—92no—
308C22×C8—92no—
309C4⋊Q8—31no—
310C4⋊Q8—31no—
311C4⋊Q8—61no—
312#123—62no—
313C22⋊Q8—32no—
314C22⋊Q8—61no—
315C22⋊Q8—62no—
316#121—32no—
317C4×Q8—31no—
318C4×D4—31no—
319C4×D4—61no—
320C4×D4D3211yescharacteristic
321C2×C4⋊C4—32no—
322#106—91no—
323#106—92no—
324C4⋊C8—91no—
325#103—91no—
326#103—92no—
327#103—92no—
328#103—92no—
329#103—92no—
330#102—91no—
331C22⋊C8—92no—
332C4×C8—91no—
333C23×C3—22no—
334C23×C3—61no—
335C23×C3C2×#6712yes—
336C23×C3C2×#6712yes—
337C22×D3—21no—
338C3×Q8—32no—
339C3×Q8—61no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×Q8—124no—
343C3×Q8—122no—
344C3×D4—24no—
345C3×D4—61no—
346C3×D4—61no—
347C3×D4—124no—
348C3×D4#21414yescomplemented
349C3×D4#21514yescomplemented
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—124no—
366C2×C3×C4—124no—
367C2×C3×C4—122no—
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6712yes—
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6712yes—
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—44no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—21no—
382C2×Dic3—44no—
383C2×Dic3—44no—
384D12—21no—
385D12—21no—
386C4×D3—42no—
387Dic6—21no—
388Dic6—22no—
389Dic6—22no—
390Dic6—44no—
391Dic6—42no—
392Dic6#23712yescomplemented
393C3⋊C8—62no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C3⋊C8—62no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C3⋊C8—62no—
400C3⋊C8—121no—
401C3⋊C8—122no—
402C2×C32—24no—
403C2×C32#54611yescharacteristic
404C2×C32C22×SD1611yescharacteristic
405C2×C32#57811yescharacteristic
406C3×D3—81no—
407#41—124no—
408C2×Q8—31no—
409C2×Q8—32no—
410C2×Q8—64no—
411C2×Q8—61no—
412C2×Q8—62no—
413C2×Q8—122no—
414C2×D4—31no—
415C2×D4—62no—
416C2×D4#62511yescharacteristic
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—61no—
420C22×C4C2×D3212yes—
421SD16—182no—
422SD16—362no—
423C2×C8—91no—
424C2×C8—91no—
425C2×C8—92no—
426C2×C8—362no—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—32no—
430C4⋊C4—62no—
431C4⋊C4—61no—
432C4⋊C4—61no—
433C4⋊C4—62no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4#62511yescharacteristic
437C22⋊C4—62no—
438C22⋊C4—61no—
439C22⋊C4—62no—
440C22⋊C4#62512yes—
441C42—61no—
442C42C2×D3211yescharacteristic
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3—24no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3C2×#21414yes—
455C22×C3C2×#21514yes—
456C22×C3C22×#6711yescharacteristic
457C22×C3C22×#6711yescharacteristic
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—41no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—42no—
469C3×C4—41no—
470C3×C4—62no—
471C3×C4—121no—
472C3×C4—122no—
473C3×C4—122no—
474C3×C4—121no—
475C3×C4C2×#21412yes—
476C3×C4C2×#21512yes—
477C3×C4C2×#23711yescharacteristic
478C3×C4#100411yescharacteristic
479C3×C4D3×#4111yescharacteristic
480C3×C4#100911yescharacteristic
481Dic3—22no—
482Dic3—42no—
483Dic3—41no—
484Dic3—42no—
485Dic3—41no—
486C32#329811yescharacteristic, complemented, Sylow
487C23—61no—
488C23C2×#62512yes—
489Q8—32no—
490Q8—61no—
491Q8—62no—
492Q8—62no—
493Q8—124no—
494Q8—122no—
495D4—61no—
496D4—61no—
497D4—124no—
498D4#371514yescomplemented
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—124no—
507C2×C4—124no—
508C2×C4—122no—
509C2×C4C2×#62511yescharacteristic
510C2×C4C2×#62512yes—
511C2×C4C2×#62511yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—181no—
514C8—181no—
515C8—182no—
516C2×C3—24no—
517C2×C3—24no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—44no—
522C2×C3—241no—
523C2×C3C22×#21411yescharacteristic
524C2×C3#580611yescharacteristic
525C2×C3C22×#21511yescharacteristic
526C2×C3#582911yescharacteristic
527C2×C3#583811yescharacteristic
528C2×C3#583811yescharacteristic
529D3—81no—
530C22—22no—
531C22—22no—
532C22—121no—
533C22—121no—
534C22—121no—
535C22C2×#371514yes—
536C22C22×#62511yescharacteristic
537C4—21no—
538C4—22no—
539C4—62no—
540C4—121no—
541C4—122no—
542C4—121no—
543C4—122no—
544C4C2×#371512yes—
545C4D3×#23711yescharacteristic
546C4#6431411yescharacteristic
547C3—21no—
548C3#8353111yescharacteristic, complemented
549C3#8355011yescharacteristic, complemented
550C2—24no—
551C2—241no—
552C2C22×#371511yescharacteristic
553C2#1059524411yescharacteristic
554C2#1059544511yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5555C2
hypercenterC4×D4D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×Dic6C2semidirect
3. D4×C3⋊(C3⋊C8)C2semidirect
4. #10591179C2semidirect
5. #10591171C2semidirect
6. #10591101C2semidirect
7. C2×#63565C2semidirect
8. #10590363C2semidirect
9. C4×#3715C2semidirect
10. #10590290C2semidirect
11. #10590285C2semidirect
46. D4×Dic6D3semidirect
168. C32×D4SD16semidirect
191. C3×Dic6#41semidirect
348. C3×D4#214semidirect
349. C3×D4#215semidirect
392. Dic6#237semidirect
486. C32#3298semidirect
498. D4#3715semidirect
548. C3#83531semidirect
549. C3#83550semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C3×D4×Dic62
D4×C3⋊(C3⋊C8)2
#105911792
#105911712
#105911012
C2×#635652
#105903632
C4×#37152
#105902902
#105902852
#835503
#835313