Finite Group Databasebeta

← #11898299

Subgroups — #11898299

Order 1152.

868 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic
3#10592782C211yesmaximal, characteristic, complemented
4C3×#5085C211yesmaximal, characteristic, complemented
5#10591618C212yesmaximal, complemented
6#10591617C212yesmaximal, complemented
7#10591564C212yesmaximal, complemented
8Dic3×#215C212yesmaximal, complemented
9#10590364C211yesmaximal, characteristic, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83685—31nomaximal
13#81755—31nomaximal
14C2×#3796—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C2×#3755C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C3×#944C2212yes—
20C2×C3×#215C2212yes—
21C2×C3×#215C2212yes—
22C3×#890—21no—
23C3×#889—22no—
24C3×#887—21no—
25C3×#874C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28#63916—21no—
29#63911C2212yes—
30Dic3×D12C2212yes—
31#63886—22no—
32C2×#3717C2211yescharacteristic
33C2×#3715C2212yes—
34#63662C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2211yescharacteristic
40#63564C2211yescharacteristic
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5721D311yescharacteristic, complemented
45#5718—31no—
46#5577—31no—
47C3×#492—31no—
48#5175—32no—
49#5163—32no—
50#5162—32no—
51Dic3×SD16—32no—
52#5085—32no—
53#5085D311yescharacteristic, complemented
54#5083—31no—
55#5083—31no—
56#5083—32no—
57#5083—61no—
58#5075—31no—
59#5027—32no—
60#5027—31no—
61C4×#215—32no—
62C4×#215—31no—
63Q8×C3⋊C8—31no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3755—42no—
82#3752—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#215—24no—
86C3×#215—42no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99(C2×D3)⋊Dic3—22no—
100#3717—22no—
101#3715—42no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#237—61no—
105C2×C3×SD16—32no—
106C2×C3×SD16—32no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—32no—
109C3×C4⋊Q8C2×D311yescharacteristic
110C3×C4⋊Q8C2×D311yescharacteristic
111C3×#127—31no—
112C3×#125—62no—
113C3×#125—61no—
114C3×C4×Q8—31no—
115C3×C4×Q8—32no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118Q8×Dic3C2×D312yes—
119#944C2×D312yes—
120C2×#215—32no—
121C2×#215—32no—
122C2×#215—32no—
123C2×#215—31no—
124C2×#215—62no—
125C2×#215C2×D312yes—
126C2×#215C2×D312yes—
127#940—32no—
128#939—62no—
129#938—61no—
130D4×Dic3—32no—
131C2×#214—32no—
132C2×#204—31no—
133#895—62no—
134#895—61no—
135#890—21no—
136#889—22no—
137#887—21no—
138#874—32no—
139#874C2×D311yescharacteristic
140C4×D12—32no—
141C4×D12—31no—
142C4×D12—31no—
143C4×D12—61no—
144C4×Dic6C2×D311yescharacteristic
145C4×Dic6C2×D311yescharacteristic
146C3×C4×C8—31no—
147#835—32no—
148#835—32no—
149#835—31no—
150#835—62no—
151#832—32no—
152#821—31no—
153#817—31no—
154#816—31no—
155Dic3⋊C8—32no—
156C8×Dic3—32no—
157#809—32no—
158#809—31no—
159#808—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8—32no—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C32×Q8—22no—
169C32×Q8—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)—21no—
177C4×C3⋊D3—42no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—42no—
185C3×D12—81no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188C3×Dic6SD1614yescomplemented
189#626—44no—
190#626—82no—
191D3×Dic3—44no—
192C3⋊(C3⋊C8)—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8#4112yescomplemented
195#557—31no—
196#550—91no—
197#492—31no—
198#492—92no—
199#461—92no—
200#461—91no—
201#460—91no—
202#460—92no—
203C8×Q8—91no—
204C4×SD16—91no—
205C4×SD16—92no—
206C2×C3×Q8—22no—
207C2×C3×Q8—31no—
208C2×C3×Q8—31no—
209C2×C3×Q8C22×D312yes—
210C2×C3×Q8C22×D312yes—
211C2×C3×D4—32no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×#67—62no—
215C2×#67—62no—
216C22×Dic3—62no—
217#239—124no—
218#237—124no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—31no—
222C2×D12—31no—
223C2×D12—61no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12C22×D312yes—
227C2×C4×D3—62no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—121no—
231C2×Dic6#6711yescharacteristic
232C2×Dic6C22×D311yescharacteristic
233C3×SD16—64no—
234C3×SD16—122no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—41no—
245C3×C4⋊C4—41no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—61no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42—62no—
253C3×C42—61no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#217—62no—
257#215—24no—
258#215—42no—
259#215—62no—
260#215—122no—
261#215—122no—
262#215—122no—
263#215—124no—
264#214—122no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—121no—
269C4⋊Dic3—22no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—61no—
273C4⋊Dic3#6711yescharacteristic
274C4⋊Dic3C22×D311yescharacteristic
275Dic3⋊C4—21no—
276Dic3⋊C4—22no—
277Dic3⋊C4—22no—
278Dic3⋊C4#6712yes—
279C4×Dic3—21no—
280C4×Dic3—22no—
281C4×Dic3C22×D312yes—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—32no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287#204—62no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C32×C4—21no—
296C32×C4—42no—
297C32×C4C2×SD1612yes—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—41no—
301C3×Dic3—22no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C3×Dic3C2×SD1614yes—
305C2×#41—181no—
306C2×SD16—32no—
307C2×SD16—32no—
308C2×SD16—91no—
309C2×SD16—92no—
310C2×SD16—92no—
311C4⋊Q8—32no—
312C4⋊Q8D3211yescharacteristic
313#127—31no—
314#127—92no—
315#125—62no—
316#125—61no—
317#121—181no—
318#121—182no—
319C4×Q8—31no—
320C4×Q8—32no—
321C4×Q8—31no—
322C4×Q8—61no—
323C4×D4—92no—
324C4×D4—91no—
325#106—91no—
326C4⋊C8—92no—
327C4⋊C8—91no—
328#103—91no—
329#103—92no—
330#102—91no—
331#102—92no—
332C4×C8—31no—
333C4×C8—92no—
334C23×C3—62no—
335C22×D3—22no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—121no—
339C3×Q8—22no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—34no—
344C3×Q8—42no—
345C3×Q8—42no—
346C3×Q8—61no—
347C3×Q8—61no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—122no—
351C3×D4—241no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—42no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368#67—124no—
369#67—242no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—121no—
375C2×Dic3—124no—
376C2×Dic3C2×#6712yes—
377C2×Dic3C2×#6712yes—
378D12—22no—
379D12—22no—
380D12—42no—
381D12—62no—
382D12—61no—
383D12—61no—
384D12—61no—
385D12—61no—
386D12—81no—
387D12—121no—
388D12—124no—
389D12—242no—
390C4×D3—124no—
391C4×D3—122no—
392C4×D3—122no—
393C4×D3—242no—
394Dic6—21no—
395Dic6—21no—
396Dic6#21514yescomplemented
397C3×C8—32no—
398C3×C8—61no—
399C3⋊C8—21no—
400C3⋊C8—62no—
401C3⋊C8—62no—
402C3⋊C8—122no—
403C3⋊C8#23712yescomplemented
404C2×C32#55011yescharacteristic
405C2×C32C22×SD1611yescharacteristic
406C2×C32#57711yescharacteristic
407C3⋊D3—81no—
408C3×D3—82no—
409#41—364no—
410C2×Q8—31no—
411C2×Q8—31no—
412C2×Q8C2×D3212yes—
413C2×D4—32no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4—91no—
417C2×D4—182no—
418C2×D4—182no—
419C22×C4—182no—
420C22×C4—181no—
421SD16—64no—
422SD16—122no—
423SD16—182no—
424SD16—362no—
425SD16—362no—
426C2×C8—31no—
427C2×C8—31no—
428C2×C8—92no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—32no—
432C4⋊C4—31no—
433C4⋊C4—31no—
434C4⋊C4—62no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C4⋊C4—61no—
438C4⋊C4—91no—
439C22⋊C4—182no—
440C22⋊C4—181no—
441C42—32no—
442C42—62no—
443C42—61no—
444C42C2×D3211yescharacteristic
445C22×C3—21no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C22×#6711yescharacteristic
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—122no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—241no—
462C2×D3—241no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—34no—
469C3×C4—41no—
470C3×C4—42no—
471C3×C4—42no—
472C3×C4—62no—
473C3×C4—82no—
474C3×C4—121no—
475C3×C4—121no—
476C3×C4D3×SD1612yes—
477C3×C4C2×#21512yes—
478C3×C4C2×#23711yescharacteristic
479C3×C4#100411yescharacteristic
480C3×C4D3×#4111yescharacteristic
481C3×C4#100911yescharacteristic
482Dic3—22no—
483Dic3—41no—
484Dic3—41no—
485Dic3—121no—
486Dic3—121no—
487Dic3—241no—
488Dic3C2×#21514yes—
489C32#339211yescharacteristic, complemented, Sylow
490C23—62no—
491C23—181no—
492Q8—22no—
493Q8—22no—
494Q8—34no—
495Q8—61no—
496Q8—61no—
497D4—62no—
498D4—62no—
499D4—122no—
500D4—181no—
501D4—181no—
502D4—241no—
503D4—364no—
504D4—722no—
505C2×C4—22no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—181no—
511C2×C4—364no—
512C2×C4—362no—
513C2×C4D3×#6711yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4C22×D3211yescharacteristic
516C8—32no—
517C8—61no—
518C8—182no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—242no—
523C2×C3#571811yescharacteristic
524C2×C3C2×D3×SD1611yescharacteristic
525C2×C3#576211yescharacteristic
526C2×C3C22×#21511yescharacteristic
527C2×C3#583411yescharacteristic
528C2×C3#583711yescharacteristic
529D3—82no—
530D3—242no—
531D3—241no—
532D3—241no—
533C22—122no—
534C22—122no—
535C22—122no—
536C22—361no—
537C22—361no—
538C22—361no—
539C22C2×D3×#6711yescharacteristic
540C4—21no—
541C4—34no—
542C4—42no—
543C4—62no—
544C4—121no—
545C4—121no—
546C4—361no—
547C4D3×#21512yes—
548C4D3×#23711yescharacteristic
549C4#6431411yescharacteristic
550C3—21no—
551C3#8175511yescharacteristic, complemented
552C3#8368511yescharacteristic, complemented
553C2—242no—
554C2—721no—
555C2#1059515811yescharacteristic
556C2C2×D3×#21511yescharacteristic
557C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4⋊Q8D32
hypocenterC32#3392
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. C3×#5721C2semidirect
3. #10592782C2semidirect
4. C3×#5085C2semidirect
5. #10591618C2semidirect
6. #10591617C2semidirect
7. #10591564C2semidirect
8. Dic3×#215C2semidirect
9. #10590364C2semidirect
10. C4×#3717C2semidirect
11. C3⋊C8×Dic6C2semidirect
44. #5721D3semidirect
53. #5085D3semidirect
188. C3×Dic6SD16semidirect
194. C3×C3⋊C8#41semidirect
396. Dic6#215semidirect
403. C3⋊C8#237semidirect
489. C32#3392semidirect
551. C3#81755semidirect
552. C3#83685semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
#105939002
#105927822
C3×#50852
#105916182
#105916172
#105915642
Dic3×#2152
#105903642
C4×#37172
C3⋊C8×Dic62
#836853
#817553