Finite Group Databasebeta

← #11898313

Subgroups — #11898313

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×#5553C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591490C212yesmaximal, complemented
6#10591439C212yesmaximal, complemented
7#10590559C212yesmaximal, complemented
8#10590479C212yesmaximal, complemented
9#10590369C211yesmaximal, characteristic, complemented
10#10590364C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83588—31nomaximal
13#79637—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3754C2212yes—
17#64078C2211yescharacteristic
18C3×#940C2212yes—
19C2×C3×#214C2211yescharacteristic
20C3×#930—21no—
21C3×#893C2212yes—
22C3×#884—22no—
23C3×#874C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63869—21no—
27#63866C2212yes—
28#63845—22no—
29#63844C2212yes—
30Dic3×Dic6—21no—
31C2×#3716C2212yes—
32C2×#3716C2212yes—
33C2×#3715C2212yes—
34#63637C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×#832C2211yescharacteristic
37C3×#810C2211yescharacteristic
38C3×#808C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5570—31no—
45#5567—31no—
46#5553D311yescharacteristic
47C3×C4×SD16—31no—
48#5175—32no—
49#5076—32no—
50#5076—31no—
51#5075—31no—
52#5075—32no—
53#5027—31no—
54Q8×C3⋊C8—31no—
55#5019—31no—
56#5019—31no—
57#5019—32no—
58#5019—61no—
59C4×#214—32no—
60C4×#214D311yescharacteristic, complemented
61#4852—32no—
62#4818—32no—
63#4762—32no—
64#4693—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2312yes—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3754—42no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—21no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#214—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98Dic32—22no—
99#3716—24no—
100#3716—42no—
101#3715—42no—
102#3392—91noSylow
103C2×C3×#41—61no—
104C2×#235—21no—
105C2×C3×SD16—31no—
106C3×#127—32no—
107C3×#127—31no—
108C3×#121—62no—
109C3×#121—61no—
110C3×C4×Q8—31no—
111C3×C4×Q8—31no—
112C3×C4×D4—21no—
113C3×C4×D4—32no—
114C3×C4×D4C2×D311yescharacteristic
115C3×C4×D4C2×D311yescharacteristic
116Q8×Dic3—61no—
117#944—32no—
118C2×#215—32no—
119#940C2×D312yes—
120C2×#214—32no—
121C2×#214—32no—
122C2×#214—32no—
123C2×#214—32no—
124C2×#214—32no—
125C2×#214—62no—
126C2×#214C2×D311yescharacteristic
127#930—21no—
128C2×#204—32no—
129C2×#204—32no—
130#893C2×D312yes—
131#890—61no—
132#890—62no—
133#889—62no—
134#887—32no—
135#884—22no—
136#874C2×D311yescharacteristic
137#870—61no—
138#869—32no—
139#869—31no—
140#869—31no—
141#869—61no—
142C4×Dic6—32no—
143C4×Dic6—61no—
144C4×Dic6C2×D311yescharacteristic
145C4×Dic6C2×D311yescharacteristic
146C3×#106—31no—
147C3×#103—31no—
148C3×#102—31no—
149C3×C4×C8—31no—
150#832—32no—
151#832C2×D311yescharacteristic
152Dic3⋊C8—32no—
153C8×Dic3—32no—
154#810—32no—
155#810—32no—
156#810—62no—
157#810C2×D311yescharacteristic
158#809—32no—
159#808C2×D311yescharacteristic
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8—32no—
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—21no—
167C22×C3×D3—22no—
168C32×D4—21no—
169C32×D4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176#634—22no—
177#634—22no—
178C3×#67—44no—
179C3×#67—82no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×D12—22no—
185C3×D12—22no—
186C3×D12—42no—
187C3×D12—81no—
188C3×C4×D3—44no—
189C3×Dic6—21no—
190C3×Dic6—21no—
191C3×Dic6SD1614yescomplemented
192C3⋊(C3⋊C8)—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8#4112yescomplemented
195#557—91no—
196#550—31no—
197#492—91no—
198#492—92no—
199#461—92no—
200#461—91no—
201#460—92no—
202#460—91no—
203C8×Q8—91no—
204C4×SD16—31no—
205C4×SD16—92no—
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—31no—
209C2×C3×D4—21no—
210C2×C3×D4—32no—
211C2×C3×D4—62no—
212C2×C3×D4—62no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4C22×D311yescharacteristic
216C2×C3×D4C22×D311yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—41no—
220C22×C3×C4—62no—
221C2×#67—22no—
222C2×#67—22no—
223#235—44no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12C22×D312yes—
227C2×C4×D3—22no—
228C2×Dic6—32no—
229C2×Dic6—32no—
230C2×Dic6—62no—
231C2×Dic6#6711yescharacteristic
232C2×Dic6C22×D311yescharacteristic
233C3×SD16—62no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—41no—
246C3×C22⋊C4—62no—
247C3×C42—21no—
248C3×C42—32no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#215—122no—
253#214—22no—
254#214—64no—
255#214—122no—
256#214—122no—
257#214—122no—
258#214—122no—
259#214—124no—
260(C2×D3)⋊C4—22no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—121no—
268C4⋊Dic3—121no—
269C4⋊Dic3#6711yescharacteristic
270C4⋊Dic3C22×D311yescharacteristic
271Dic3⋊C4—21no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4#6712yes—
277C4×Dic3—21no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C4×Dic3C22×D312yes—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D311yescharacteristic
286#204—64no—
287#204—122no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C22×D411yescharacteristic
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C32×C4—21no—
296C32×C4—41no—
297C32×C4C2×SD1612yes—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—42no—
301C3×Dic3—22no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C3×Dic3C2×SD1614yes—
305C2×#41—61no—
306C2×SD16—31no—
307C2×SD16—92no—
308C2×SD16—92no—
309C2×SD16—92no—
310C2×SD16—92no—
311C4⋊Q8—92no—
312C4⋊Q8—91no—
313#127—32no—
314#127—31no—
315#125—181no—
316#125—182no—
317#121—62no—
318#121—61no—
319C4×Q8—31no—
320C4×Q8—31no—
321C4×Q8—92no—
322C4×Q8—181no—
323C4×D4—32no—
324C4×D4D3211yescharacteristic
325#106—31no—
326C4⋊C8—92no—
327C4⋊C8—91no—
328#103—31no—
329#103—92no—
330#102—31no—
331#102—92no—
332C4×C8—31no—
333C4×C8—92no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—41no—
337C23×C3—62no—
338C22×D3—22no—
339C3×Q8—34no—
340C3×Q8—61no—
341C3×Q8—61no—
342C3×D4—22no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—41no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—124no—
351C3×D4—122no—
352C3×D4—241no—
353C3×D4—242no—
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—32no—
361C2×C3×C4—41no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—82no—
367C2×C3×C4—124no—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—44no—
375#67—82no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—122no—
381C2×Dic3C2×#6712yes—
382C2×Dic3C2×#6712yes—
383D12—22no—
384D12—22no—
385D12—42no—
386D12—81no—
387C4×D3—44no—
388Dic6—21no—
389Dic6—21no—
390Dic6—62no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—122no—
395Dic6—122no—
396Dic6#21414yescomplemented
397C3×C8—32no—
398C3×C8—61no—
399C3⋊C8—21no—
400C3⋊C8—62no—
401C3⋊C8—62no—
402C3⋊C8—122no—
403C3⋊C8#23512yescomplemented
404C2×C32—81no—
405C2×C32#55011yescharacteristic
406C2×C32C22×SD1611yescharacteristic
407C2×C32#57711yescharacteristic
408C3×D3—82no—
409#41—124no—
410C2×Q8—31no—
411C2×Q8—31no—
412C2×Q8—92no—
413C2×D4—32no—
414C2×D4—62no—
415C2×D4—62no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4C2×D3211yescharacteristic
419C22×C4—21no—
420C22×C4—62no—
421SD16—62no—
422SD16—184no—
423SD16—362no—
424SD16—362no—
425SD16—362no—
426C2×C8—31no—
427C2×C8—31no—
428C2×C8—92no—
429C4⋊C4—32no—
430C4⋊C4—31no—
431C4⋊C4—31no—
432C4⋊C4—61no—
433C4⋊C4—182no—
434C4⋊C4—182no—
435C4⋊C4—182no—
436C4⋊C4—181no—
437C4⋊C4—181no—
438C4⋊C4C2×D3211yescharacteristic
439C22⋊C4—21no—
440C22⋊C4—62no—
441C42—32no—
442C42—61no—
443C42—182no—
444C42C2×D3211yescharacteristic
445C22×C3—21no—
446C22×C3—42no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—81no—
454C22×C3—81no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3—122no—
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C22×#6711yescharacteristic
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—42no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—34no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—62no—
473C3×C4—81no—
474C3×C4—121no—
475C3×C4—121no—
476C3×C4D3×SD1612yes—
477C3×C4C2×#21412yes—
478C3×C4C2×#23511yescharacteristic
479C3×C4D3×#4111yescharacteristic
480C3×C4#100911yescharacteristic
481C3×C4#100911yescharacteristic
482Dic3—22no—
483Dic3—41no—
484Dic3—41no—
485Dic3—122no—
486Dic3—122no—
487Dic3—242no—
488Dic3C2×#21414yes—
489C32#339211yescharacteristic, complemented, Sylow
490C23—21no—
491C23—62no—
492Q8—34no—
493Q8—61no—
494Q8—61no—
495Q8—182no—
496Q8—182no—
497D4—21no—
498D4—21no—
499D4—62no—
500D4—62no—
501D4—124no—
502D4—122no—
503D4—241no—
504D4—242no—
505C2×C4—21no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—42no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—124no—
512C2×C4—182no—
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—82no—
523C2×C3—81no—
524C2×C3—81no—
525C2×C3—242no—
526C2×C3#555311yescharacteristic
527C2×C3C2×D3×SD1611yescharacteristic
528C2×C3#577011yescharacteristic
529C2×C3C22×#21411yescharacteristic
530C2×C3#583411yescharacteristic
531C2×C3#583611yescharacteristic
532D3—82no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—122no—
537C22—122no—
538C22—122no—
539C22C2×D3×#6711yescharacteristic
540C4—21no—
541C4—34no—
542C4—41no—
543C4—62no—
544C4—121no—
545C4—121no—
546C4—362no—
547C4D3×#21412yes—
548C4D3×#23511yescharacteristic
549C4#6430811yescharacteristic
550C3—21no—
551C3#7963711yescharacteristic, complemented
552C3#8358811yescharacteristic, complemented
553C2—81no—
554C2—242no—
555C2#1059500711yescharacteristic
556C2C2×D3×#21411yescharacteristic
557C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC4×D4D32
hypocenterC32#3392
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. #10593860C2semidirect
3. #10592718C2semidirect
4. C3×C4×#214C2semidirect
5. #10591490C2semidirect
6. #10591439C2semidirect
7. #10590559C2semidirect
8. #10590479C2semidirect
9. #10590369C2semidirect
10. #10590364C2semidirect
11. C3⋊C8×Dic6C2semidirect
60. C4×#214D3semidirect
191. C3×Dic6SD16semidirect
194. C3×C3⋊C8#41semidirect
396. Dic6#214semidirect
403. C3⋊C8#235semidirect
489. C32#3392semidirect
551. C3#79637semidirect
552. C3#83588semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105938602
#105927182
C3×C4×#2142
#105914902
#105914392
#105905592
#105904792
#105903692
#105903642
C3⋊C8×Dic62
#835883
#796373