Finite Group Databasebeta

← #11898322

Subgroups — #11898322

Order 1152.

879 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592775C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5#10591490C212yesmaximal, complemented
6#10591489C212yesmaximal, complemented
7#10591439C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83588—31nomaximal
13#80378—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16C2×#3754C2212yes—
17C2×#3754C2212yes—
18#64078C2211yescharacteristic
19C3×#940C2212yes—
20C3×#939—22no—
21C3×#938—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C3×C4×D12C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63869—21no—
28#63866C2212yes—
29#63845—22no—
30#63844C2212yes—
31Dic3×Dic6—21no—
32C2×#3716C2212yes—
33C2×#3715C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#832C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63565C2211yescharacteristic
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5718D311yescharacteristic
45#5570—31no—
46#5567—31no—
47C3×#460—31no—
48#5175—32no—
49#5162—32no—
50#5076—31no—
51#5076—31no—
52#5076—32no—
53#5076—61no—
54#5075—32no—
55#5075D311yescharacteristic, complemented
56C4×#215—31no—
57Q8×C3⋊C8—31no—
58#5019—32no—
59#5019—31no—
60C4×#214—31no—
61C4×#214—32no—
62#4841—31no—
63#4830—31no—
64#4762—32no—
65#4758—32no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3754—24no—
80#3754—42no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—22no—
86C3×#214—42no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—21no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99Dic32—22no—
100#3716—42no—
101#3715—22no—
102#3392—91noSylow
103C2×C3×#41—61no—
104C2×#237—21no—
105C2×C3×SD16—32no—
106C3×#127—21no—
107C3×#127—32no—
108C3×#127C2×D311yescharacteristic
109C3×#127C2×D311yescharacteristic
110C3×#121—61no—
111C3×#121—62no—
112C3×C4×Q8—31no—
113C3×C4×Q8—31no—
114C3×C4×D4—32no—
115C3×C4×D4—31no—
116Q8×Dic3—61no—
117#944—32no—
118C2×#215—31no—
119#940C2×D312yes—
120#939—22no—
121#938—21no—
122D4×Dic3C2×D312yes—
123C2×#214—32no—
124C2×#214—32no—
125C2×#214—31no—
126C2×#214—32no—
127C2×#214—32no—
128C2×#214—32no—
129C2×#214—62no—
130C2×#214—62no—
131C2×#214C2×D312yes—
132C2×#204—32no—
133#890—61no—
134#890—62no—
135#889—62no—
136#887—32no—
137C4×D12C2×D311yescharacteristic
138#870—61no—
139#869—32no—
140#869—31no—
141#869—31no—
142#869—61no—
143C4×Dic6—32no—
144C4×Dic6—61no—
145C4×Dic6C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×C4⋊C8—31no—
148C3×#102—32no—
149#835—31no—
150#832—31no—
151#832C2×D312yes—
152#816—32no—
153Dic3⋊C8—32no—
154C8×Dic3—32no—
155#810—31no—
156#810—32no—
157#809—31no—
158#808—31no—
159#808—31no—
160C4⋊(C3⋊C8)—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—32no—
165C4×C3⋊C8—61no—
166C23×C32—22no—
167C22×C3×D3—21no—
168C32×D4—22no—
169C32×D4—22no—
170C32×D4—42no—
171C32×D4—81no—
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×Dic3—21no—
183C2×C3×Dic3—44no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12—21no—
188C3×C4×D3—42no—
189C3×Dic6—21no—
190C3×Dic6—21no—
191C3×Dic6SD1614yescomplemented
192C3⋊(C3⋊C8)—21no—
193C3⋊(C3⋊C8)#4112yescomplemented
194C3×C3⋊C8—22no—
195#557—91no—
196#550—31no—
197#492—92no—
198#492—91no—
199#461—91no—
200#461—92no—
201#460—31no—
202#460—92no—
203C8×Q8—91no—
204C4×SD16—92no—
205C4×SD16—91no—
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—31no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—22no—
214C2×C3×D4—31no—
215C2×C3×D4—41no—
216C2×C3×D4—41no—
217C2×C3×D4—62no—
218C2×C3×D4—62no—
219C2×C3×D4C22×D312yes—
220C2×C3×D4C22×D312yes—
221C22×C3×C4—62no—
222C22×C3×C4—61no—
223C2×#67—22no—
224C2×#67—22no—
225C22×Dic3—22no—
226#237—44no—
227C2×D12C22×D311yescharacteristic
228C2×C4×D3—21no—
229C2×Dic6—32no—
230C2×Dic6—32no—
231C2×Dic6—62no—
232C2×Dic6#6711yescharacteristic
233C2×Dic6C22×D311yescharacteristic
234C3×SD16—122no—
235C2×C3×C8—32no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—61no—
241C3×C22⋊C4—62no—
242C3×C22⋊C4—61no—
243C3×C42—21no—
244C3×C42—32no—
245C3×C42—61no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—22no—
249#215—62no—
250#214—42no—
251#214—62no—
252#214—64no—
253#214—64no—
254#214—124no—
255#214—122no—
256#214—122no—
257#214—122no—
258#214—124no—
259(C2×D3)⋊C4—21no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—121no—
267C4⋊Dic3—121no—
268C4⋊Dic3#6711yescharacteristic
269C4⋊Dic3C22×D311yescharacteristic
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—31no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—61no—
286C2×C3⋊C8—61no—
287C2×C3⋊C8C22×D312yes—
288#204—122no—
289C22×C32—42no—
290C22×C32—42no—
291C22×C32—42no—
292C22×C32C22×D411yescharacteristic
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C32×C4—21no—
297C32×C4C2×SD1612yes—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—42no—
301C3×Dic3—22no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C3×Dic3—41no—
305C3×Dic3C2×SD1614yes—
306C2×#41—61no—
307C2×SD16—32no—
308C2×SD16—92no—
309C2×SD16—91no—
310C2×SD16—92no—
311C2×SD16—92no—
312C4⋊Q8—92no—
313C4⋊Q8—91no—
314#127—32no—
315#127D3211yescharacteristic
316#125—181no—
317#125—182no—
318#121—61no—
319#121—62no—
320C4×Q8—31no—
321C4×Q8—31no—
322C4×Q8—92no—
323C4×Q8—181no—
324C4×D4—32no—
325C4×D4—31no—
326#106—91no—
327C4⋊C8—31no—
328C4⋊C8—92no—
329#103—92no—
330#103—91no—
331#102—32no—
332#102—91no—
333C4×C8—92no—
334C4×C8—91no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—42no—
338C23×C3—61no—
339C22×D3—21no—
340C3×Q8—34no—
341C3×Q8—61no—
342C3×Q8—61no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—22no—
346C3×D4—22no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—42no—
350C3×D4—42no—
351C3×D4—61no—
352C3×D4—61no—
353C3×D4—82no—
354C3×D4—81no—
355C3×D4—81no—
356C3×D4—82no—
357C3×D4—124no—
358C3×D4—242no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—124no—
368C2×C3×C4—122no—
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—
376#67—82no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—44no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3C2×#6712yes—
385C2×Dic3C2×#6712yes—
386D12—21no—
387D12—21no—
388C4×D3—42no—
389Dic6—21no—
390Dic6—21no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—62no—
395Dic6—122no—
396Dic6—122no—
397Dic6#21414yescomplemented
398C3×C8—62no—
399C3⋊C8—22no—
400C3⋊C8—32no—
401C3⋊C8—32no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C3⋊C8—61no—
405C3⋊C8—61no—
406C2×C32—82no—
407C2×C32#55011yescharacteristic
408C2×C32C22×SD1611yescharacteristic
409C2×C32#57711yescharacteristic
410C3×D3—81no—
411#41—124no—
412C2×Q8—31no—
413C2×Q8—31no—
414C2×Q8—92no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—31no—
418C2×D4—62no—
419C2×D4—62no—
420C2×D4C2×D3212yes—
421C22×C4—62no—
422C22×C4—61no—
423SD16—122no—
424SD16—184no—
425SD16—182no—
426SD16—362no—
427SD16—362no—
428C2×C8—32no—
429C2×C8—91no—
430C2×C8—91no—
431C4⋊C4—32no—
432C4⋊C4—31no—
433C4⋊C4—31no—
434C4⋊C4—31no—
435C4⋊C4—61no—
436C4⋊C4—182no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C22⋊C4—62no—
442C22⋊C4—61no—
443C42—32no—
444C42—61no—
445C42—182no—
446C42C2×D3211yescharacteristic
447C22×C3—21no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—82no—
457C22×C3—121no—
458C22×C3—121no—
459C22×C3—121no—
460C22×C3C2×D3×D411yescharacteristic
461C22×C3C22×#6711yescharacteristic
462C2×D3—41no—
463C2×D3—41no—
464C2×D3—41no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—22no—
471C3×C4—34no—
472C3×C4—62no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—121no—
476C3×C4D3×SD1612yes—
477C3×C4C2×#21412yes—
478C3×C4#100411yescharacteristic
479C3×C4D3×#4111yescharacteristic
480C3×C4D3×#4111yescharacteristic
481C3×C4#100911yescharacteristic
482Dic3—22no—
483Dic3—41no—
484Dic3—41no—
485Dic3—41no—
486Dic3—122no—
487Dic3—122no—
488Dic3—242no—
489Dic3C2×#21414yes—
490C32#339211yescharacteristic, complemented, Sylow
491C23—22no—
492C23—61no—
493Q8—34no—
494Q8—61no—
495Q8—61no—
496Q8—182no—
497Q8—182no—
498D4—22no—
499D4—22no—
500D4—42no—
501D4—61no—
502D4—61no—
503D4—81no—
504D4—124no—
505D4—242no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—124no—
512C2×C4—122no—
513C2×C4—182no—
514C2×C4D3×#6711yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—62no—
518C8—92no—
519C8—181no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—82no—
524C2×C3—82no—
525C2×C3—162no—
526C2×C3—241no—
527C2×C3#559911yescharacteristic
528C2×C3C2×D3×SD1611yescharacteristic
529C2×C3#577511yescharacteristic
530C2×C3C22×#21411yescharacteristic
531C2×C3#583411yescharacteristic
532C2×C3#583611yescharacteristic
533D3—81no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—121no—
538C22—121no—
539C22—121no—
540C22C2×D3×#6711yescharacteristic
541C4—21no—
542C4—34no—
543C4—62no—
544C4—121no—
545C4—121no—
546C4—121no—
547C4—362no—
548C4D3×#21412yes—
549C4#6431211yescharacteristic
550C4#6431411yescharacteristic
551C3—21no—
552C3#8037811yescharacteristic, complemented
553C3#8358811yescharacteristic, complemented
554C2—82no—
555C2—241no—
556C2C2×D3×#21411yescharacteristic
557C2#1059510611yescharacteristic
558C2#1059523611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593860C2semidirect
3. #10592775C2semidirect
4. C3×#5075C2semidirect
5. #10591490C2semidirect
6. #10591489C2semidirect
7. #10591439C2semidirect
8. #10591401C2semidirect
9. #10590365C2semidirect
10. C4×#3715C2semidirect
11. #10590250C2semidirect
55. #5075D3semidirect
191. C3×Dic6SD16semidirect
193. C3⋊(C3⋊C8)#41semidirect
397. Dic6#214semidirect
490. C32#3392semidirect
552. C3#80378semidirect
553. C3#83588semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105938602
#105927752
C3×#50752
#105914902
#105914892
#105914392
#105914012
#105903652
C4×#37152
#105902502
#835883
#803783