Finite Group Databasebeta

← #11887566

Subgroups — #11887566

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5551C211yesmaximal, characteristic
2#10593904C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591517C212yesmaximal, complemented
6#10591499C212yesmaximal, complemented
7D3×#810C212yesmaximal, complemented
8#10590516C212yesmaximal, complemented
9#10590329C211yesmaximal, characteristic, complemented
10#10590307C211yesmaximal, characteristic, complemented
11#10590290C211yesmaximal, characteristic, complemented
12#83531—31nomaximal
13#80450—31nomaximal
14C2×C3×#235—21no—
15C2×D3×Dic6C2212yes—
16C32×C4×D4C2211yescharacteristic
17C2×#3754C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C3×#938C2212yes—
20C2×C3×#214C2212yes—
21C3×#924—21no—
22C3×D3×C4⋊C4C2212yes—
23C3×#883—22no—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27#63919—21no—
28#63899—22no—
29#63898—21no—
30#63856C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63659C2211yescharacteristic
33#63637C2211yescharacteristic
34#63635C2211yescharacteristic
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36C3×#810C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38#63573C2212yes—
39#63567C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#547—31no—
44#5727—31no—
45#5551D311yescharacteristic
46D4×Dic6—31no—
47C3×#461—31no—
48#5171—32no—
49#5170—32no—
50#5094—31no—
51#5093—31no—
52#5079—31no—
53#5041—32no—
54#5040—32no—
55#5019D311yescharacteristic, complemented
56C4×#214—31no—
57C4×#214—31no—
58C4×#214—61no—
59D4×C3⋊C8—31no—
60#4971—32no—
61C2×#810—32no—
62#4851—31no—
63#4834—31no—
64#4805—32no—
65D3×#103—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2311yescharacteristic
69C2×C3×#67—22no—
70C3×#235—44no—
71C2×C3×D12D411yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2312yes—
76C2×#627—22no—
77C2×D3×Dic3—22no—
78D3×Dic6—24no—
79D3×Dic6—42no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3754—22no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C4×C3⋊Dic3—21no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C3×#217—22no—
90C3×#214—42no—
91C3×(C2×D3)⋊C4D412yes—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—22no—
98C2×C3×C3⋊C8C2312yes—
99#3724—22no—
100(C2×D3)⋊Dic3—22no—
101D3×C3⋊C8—42no—
102#3298—91noSylow
103C2×C3×#41—61no—
104C2×D3×Q8—32no—
105C2×#235—21no—
106C22×Dic6—32no—
107C2×C3×SD16—32no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8—31no—
110C3×#123—62no—
111C3×C22⋊Q8—61no—
112C3×#121—32no—
113C3×C4×D4—21no—
114C3×C4×D4—31no—
115C3×C4×D4C2×D311yescharacteristic
116C3×C4×D4C2×D311yescharacteristic
117C2×C3×C4⋊C4—32no—
118#946—32no—
119#938C2×D312yes—
120D4×Dic3—61no—
121C2×#214—31no—
122C2×#214—31no—
123C2×#214—61no—
124C2×#214C2×D312yes—
125#924—21no—
126#924—32no—
127C22×C3⋊C8—32no—
128C2×D3×C8—32no—
129#896—62no—
130#893—61no—
131D3×C4⋊C4C2×D312yes—
132#888—61no—
133#888—61no—
134#883—22no—
135#878—62no—
136C4×D12C2×D311yescharacteristic
137#869C2×D311yescharacteristic
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144#835—32no—
145#835—32no—
146#832—31no—
147#832—31no—
148#832—61no—
149#830—32no—
150(C2×D3)⋊C8—32no—
151#817—32no—
152#816—32no—
153#810—32no—
154#810—32no—
155#810—31no—
156#810—31no—
157#810—32no—
158#810—61no—
159#810C2×D312yes—
160#808—31no—
161#808—31no—
162#808—32no—
163#808—61no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8—31no—
166C4×C3⋊C8—31no—
167C4×C3⋊C8—61no—
168C23×C32—21no—
169C22×C3×D3C2×D412yes—
170C32×D4—21no—
171C32×D4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—42no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179#634—21no—
180#634#4112yescomplemented
181C3×#67—44no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D412yes—
185C3×D12SD1614yescomplemented
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×C4×D3—44no—
189C3×Dic6—22no—
190C3×Dic6—22no—
191C3×Dic6—42no—
192#627—44no—
193D3×Dic3—44no—
194C3⋊(C3⋊C8)—21no—
195C3⋊(C3⋊C8)—21no—
196C3×C3⋊C8—22no—
197D4×Q8—91no—
198#547—31no—
199#487—91no—
200#483—92no—
201#475—91no—
202#465—92no—
203#461—31no—
204#448—92no—
205C4×SD16—91no—
206C8×D4—91no—
207C2×#103—92no—
208C3×#41—124no—
209C2×C3×Q8—32no—
210C2×C3×Q8—61no—
211C2×C3×D4—21no—
212C2×C3×D4—31no—
213C2×C3×D4—62no—
214C2×C3×D4C22×D311yescharacteristic
215C2×C3×D4C22×D311yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—32no—
219C22×C3×C4—41no—
220C22×C3×C4—62no—
221C2×#67—22no—
222C22×Dic3—62no—
223D3×Q8—64no—
224D3×Q8—122no—
225#235—44no—
226C2×D12#6711yescharacteristic
227C2×C4×D3—22no—
228C2×C4×D3—62no—
229C2×C4×D3C22×D312yes—
230C2×Dic6—21no—
231C2×Dic6—31no—
232C2×Dic6—31no—
233C2×Dic6—61no—
234C2×Dic6—64no—
235C2×Dic6—62no—
236C2×Dic6—62no—
237C2×Dic6—122no—
238C2×Dic6C22×D312yes—
239C3×SD16—122no—
240C2×C3×C8—32no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C22⋊C4—21no—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—32no—
253C3×C22⋊C4—41no—
254C3×C22⋊C4—62no—
255C3×C42—21no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258#217—22no—
259#217—62no—
260#214—42no—
261#214—62no—
262#214—62no—
263#214—64no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4#6712yes—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3#6711yescharacteristic
273C4⋊Dic3C22×D312yes—
274Dic3⋊C4—22no—
275Dic3⋊C4—62no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278Dic3⋊C4—62no—
279Dic3⋊C4—121no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—121no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—122no—
290C2×C3⋊C8C22×D312yes—
291D3×C8—122no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32C22×D411yescharacteristic
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3C2×SD1614yes—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4C2×SD1612yes—
302C32×C4C2×#4111yescharacteristic
303C32×C4H(5,𝔽2)11yescharacteristic
304C3⋊Dic3—22no—
305C3⋊Dic3—41no—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3—42no—
309C2×#41—61no—
310C22×Q8—92no—
311C2×SD16—32no—
312C2×SD16—91no—
313C22×C8—92no—
314C4⋊Q8—31no—
315C4⋊Q8—31no—
316C4⋊Q8—181no—
317#123—62no—
318C22⋊Q8—61no—
319C22⋊Q8—92no—
320C22⋊Q8—182no—
321#121—32no—
322C4×Q8—91no—
323C4×D4—31no—
324C4×D4—181no—
325C4×D4D3211yescharacteristic
326C2×C4⋊C4—32no—
327#106—92no—
328#106—91no—
329C4⋊C8—31no—
330#103—32no—
331#103—92no—
332#103—92no—
333#103—92no—
334#103—91no—
335#102—91no—
336C22⋊C8—92no—
337C4×C8—91no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—32no—
341C23×C3—41no—
342C22×D3C2×#6712yes—
343C3×Q8—62no—
344C3×Q8—62no—
345C3×Q8—122no—
346C3×D4—22no—
347C3×D4—21no—
348C3×D4—21no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—34no—
352C3×D4—41no—
353C3×D4—124no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—32no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—82no—
368C2×C3×C4—124no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375#67—44no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3—124no—
385C2×Dic3C2×#6712yes—
386D12#21414yescomplemented
387C4×D3—22no—
388C4×D3—22no—
389C4×D3—44no—
390C4×D3—124no—
391Dic6—22no—
392Dic6—22no—
393Dic6—32no—
394Dic6—32no—
395Dic6—42no—
396Dic6—62no—
397Dic6—61no—
398Dic6—61no—
399Dic6—121no—
400Dic6—124no—
401Dic6—124no—
402C3×C8—62no—
403C3⋊C8—22no—
404C3⋊C8—62no—
405C3⋊C8—61no—
406C3⋊C8—61no—
407C3⋊C8—61no—
408C3⋊C8—61no—
409C3⋊C8—121no—
410C2×C32—81no—
411C2×C32#54611yescharacteristic
412C2×C32C22×SD1611yescharacteristic
413C2×C32#57811yescharacteristic
414C3×D3—24no—
415#41—124no—
416C2×Q8—32no—
417C2×Q8—61no—
418C2×Q8—91no—
419C2×Q8—182no—
420C2×Q8—184no—
421C2×Q8—362no—
422C2×D4—31no—
423C2×D4—62no—
424C2×D4C2×D3211yescharacteristic
425C22×C4—21no—
426C22×C4—32no—
427C22×C4—62no—
428C22×C4—182no—
429SD16—122no—
430SD16—182no—
431C2×C8—32no—
432C2×C8—91no—
433C2×C8—91no—
434C2×C8—362no—
435C4⋊C4—31no—
436C4⋊C4—32no—
437C4⋊C4—62no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—91no—
442C4⋊C4—182no—
443C4⋊C4—181no—
444C4⋊C4C2×D3211yescharacteristic
445C22⋊C4—21no—
446C22⋊C4—32no—
447C22⋊C4—62no—
448C22⋊C4—182no—
449C42—181no—
450C42C2×D3211yescharacteristic
451C22×C3—21no—
452C22×C3—34no—
453C22×C3—42no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—62no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3C2×D3×D411yescharacteristic
465C22×C3C22×#6711yescharacteristic
466C2×D3—22no—
467C2×D3—22no—
468C2×D3C2×#21414yes—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—22no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—62no—
478C3×C4—81no—
479C3×C4—122no—
480C3×C4—122no—
481C3×C4D3×SD1612yes—
482C3×C4C2×#21412yes—
483C3×C4#100411yescharacteristic
484C3×C4D3×#4111yescharacteristic
485C3×C4D3×#4111yescharacteristic
486C3×C4#100911yescharacteristic
487Dic3—22no—
488Dic3—42no—
489Dic3—42no—
490Dic3—62no—
491Dic3—62no—
492Dic3—122no—
493Dic3—121no—
494Dic3—121no—
495Dic3—241no—
496C32#329811yescharacteristic, complemented, Sylow
497C23—21no—
498C23—32no—
499Q8—62no—
500Q8—62no—
501Q8—92no—
502Q8—122no—
503Q8—181no—
504Q8—364no—
505D4—21no—
506D4—21no—
507D4—34no—
508D4—124no—
509C2×C4—21no—
510C2×C4—32no—
511C2×C4—42no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—124no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—364no—
520C2×C4D3×#6711yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—62no—
524C8—181no—
525C8—181no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—64no—
530C2×C3—82no—
531C2×C3—81no—
532C2×C3—81no—
533C2×C3#561211yescharacteristic
534C2×C3C2×D3×SD1611yescharacteristic
535C2×C3#577911yescharacteristic
536C2×C3C22×#21411yescharacteristic
537C2×C3#582911yescharacteristic
538C2×C3#583811yescharacteristic
539D3—24no—
540C22—34no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—62no—
545C22—62no—
546C22C2×D3×#6711yescharacteristic
547C4—21no—
548C4—41no—
549C4—62no—
550C4—122no—
551C4—122no—
552C4—182no—
553C4—361no—
554C4D3×#21412yes—
555C4#6430611yescharacteristic
556C4#6430711yescharacteristic
557C3—21no—
558C3#8045011yescharacteristic, complemented
559C3#8353111yescharacteristic, complemented
560C2—64no—
561C2—81no—
562C2#1059507011yescharacteristic
563C2C2×D3×#21411yescharacteristic
564C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5551C2
hypercenterC4×D4D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593904C2semidirect
3. C4×#3754C2semidirect
4. C3×#5019C2semidirect
5. #10591517C2semidirect
6. #10591499C2semidirect
7. D3×#810C2semidirect
8. #10590516C2semidirect
9. #10590329C2semidirect
10. #10590307C2semidirect
11. #10590290C2semidirect
55. #5019D3semidirect
180. #634#41semidirect
185. C3×D12SD16semidirect
386. D12#214semidirect
496. C32#3298semidirect
558. C3#80450semidirect
559. C3#83531semidirect

Maximal subgroups

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

subgroupindex
C3×#55512
#105939042
C4×#37542
C3×#50192
#105915172
#105914992
D3×#8102
#105905162
#105903292
#105903072
#105902902
#835313
#804503