Finite Group Databasebeta

← #11889816

Subgroups — #11889816

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596102C211yesmaximal, characteristic
2#10595984C211yesmaximal, characteristic, complemented
3C32×#484C211yesmaximal, characteristic, complemented
4#10592751C211yesmaximal, characteristic, complemented
5#10592665C211yesmaximal, characteristic, complemented
6#10592590C211yesmaximal, characteristic, complemented
7#10592588C211yesmaximal, characteristic, complemented
8#10592587C211yesmaximal, characteristic, complemented
9#10592586C211yesmaximal, characteristic, complemented
10#10592507C211yesmaximal, characteristic, complemented
11#10592503C211yesmaximal, characteristic, complemented
12#10592496C211yesmaximal, characteristic, complemented
13#10592494C211yesmaximal, characteristic, complemented
14#10592432C211yesmaximal, characteristic, complemented
15#10592427C211yesmaximal, characteristic, complemented
16#81474—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64153C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64138—21no—
24C4×#638C2211yescharacteristic
25#64135—21no—
26#64133C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C2×#3746C2211yescharacteristic
29C2×#3744C2211yescharacteristic
30C2×C8×C3⋊D3C2211yescharacteristic
31#64107—21no—
32#64106C2211yescharacteristic
33#64106C2211yescharacteristic
34#64103—21no—
35#64102C2211yescharacteristic
36#64101C2211yescharacteristic
37C4⋊C4×C3⋊D3—21no—
38#64099C2211yescharacteristic
39#64098—21no—
40#64096C2211yescharacteristic
41#64093—21no—
42#64092—21no—
43C32×#107C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48#63662C2211yescharacteristic
49#63648C2211yescharacteristic
50#63647C2211yescharacteristic
51#63643C2211yescharacteristic
52#63642C2211yescharacteristic
53#63641C2211yescharacteristic
54#63637C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63636C2211yescharacteristic
59#63635C2211yescharacteristic
60#5631—34no—
61#5513—34no—
62C3×#484D314yescomplemented
63#5052—34no—
64#4966—34no—
65#4891—34no—
66#4889—34no—
67#4888—34no—
68#4887—34no—
69#4808—34no—
70#4804—34no—
71#4797—34no—
72#4795—34no—
73#4733—34no—
74#4728—34no—
75C2×C32×Q8C2311yescharacteristic
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C2×#638D411yescharacteristic
80#3832—22no—
81#3832—41no—
82#3828—22no—
83#3828—41no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100#3757—21no—
101#3757D411yescharacteristic
102#3756—41no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752D411yescharacteristic
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121#3748—41no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3746—41no—
125#3744—22no—
126C8×C3⋊D3—41no—
127#3315—91noSylow
128C2×#239—34no—
129C2×#235—34no—
130C3×C22⋊Q8C2×D314yes—
131C2×C3×C4⋊C4C2×D314yes—
132#944—34no—
133C2×#216—34no—
134#929—64no—
135C4×#67—34no—
136#926—64no—
137#924—34no—
138C2×#208—34no—
139C2×Dic12—34no—
140C2×#204—34no—
141C2×D3×C8—34no—
142#898—64no—
143#897—34no—
144#897—34no—
145#894—64no—
146#893—34no—
147#892—34no—
148D3×C4⋊C4—64no—
149#890—34no—
150#889—64no—
151#887—34no—
152#884—64no—
153#883—64no—
154C3×#107C2×D314yes—
155C3×#107C2×D314yes—
156C3×#103C2×D314yes—
157C3×#103C2×D314yes—
158C3×C22⋊C8C2×D314yes—
159#835—34no—
160#821—34no—
161(C2×D3)⋊C8—34no—
162#816—34no—
163#815—34no—
164Dic3⋊C8—34no—
165#810—34no—
166#810—34no—
167#810—34no—
168#809—34no—
169#809—34no—
170#808—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3—21no—
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—42no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185#638—41no—
186#638—42no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—42no—
195C4⋊(C3⋊D3)#4112yes—
196C4×C3⋊D3—21no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—42no—
199C4×C3⋊D3—42no—
200C4×C3⋊D3—42no—
201#634—21no—
202#634—21no—
203#634—21no—
204#634—21no—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#552—91no—
210#547—91no—
211#491—91no—
212#485—91no—
213#484C3⋊D311yescharacteristic, complemented
214#478—91no—
215#470—91no—
216#467—91no—
217#462—91no—
218#452—91no—
219#452—91no—
220#440—91no—
221#435—91no—
222#417—91no—
223#416—91no—
224C2×C3×Q8C22×D314yes—
225C22×C3×C4—24no—
226C22×C3×C4C22×D314yes—
227C2×#67—34no—
228C2×#67—64no—
229#239—68no—
230#239—124no—
231#235—68no—
232#235—124no—
233C2×D12—34no—
234C2×D12—64no—
235C2×C4×D3—34no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×Dic6—34no—
240C2×Dic6—34no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—24no—
244C3×C4⋊C4—24no—
245C3×C4⋊C4C22×D314yes—
246C3×C4⋊C4C22×D314yes—
247C3×C4⋊C4C22×D314yes—
248C3×C22⋊C4—24no—
249#217—34no—
250#217—64no—
251#216—124no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—34no—
258C4⋊Dic3—64no—
259C4⋊Dic3—64no—
260C4⋊Dic3—64no—
261Dic3⋊C4—34no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—34no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270#208—124no—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—34no—
273Dic12—124no—
274#204—68no—
275D3×C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—21no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—21no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C2×#4111yescharacteristic
292C32×C4H(5,𝔽2)11yescharacteristic
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C2×#41—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8—91no—
307#126—181no—
308#125—91no—
309#125—181no—
310#123—181no—
311#123—181no—
312#123—181no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8—91no—
316C22⋊Q8C2×C3⋊D311yescharacteristic
317#121—181no—
318C4×Q8—91no—
319C4×D4—91no—
320C4×D4—91no—
321#117—91no—
322#117—181no—
323C2×C4⋊C4—181no—
324C2×C4⋊C4C2×C3⋊D311yescharacteristic
325#107C2×C3⋊D311yescharacteristic
326#107C2×C3⋊D311yescharacteristic
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8C2×C3⋊D311yescharacteristic
341#97—91no—
342C23×C3D3×D414yes—
343C22×D3—34no—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—48no—
354C2×C3×C4D3×D414yes—
355C2×C3×C4C23×D314yes—
356#67—124no—
357#67—128no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364D12—38no—
365D12—64no—
366D12—128no—
367C4×D3—64no—
368C4×D3—64no—
369C4×D3—128no—
370C4×D3—128no—
371C4×D3—128no—
372Dic6—64no—
373Dic6—64no—
374Dic6—64no—
375Dic6—64no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—41no—
381C2×C32#54611yescharacteristic
382C2×C32#57511yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—41no—
385C3⋊D3—42no—
386#41—182no—
387#41—182no—
388#41—361no—
389#41—361no—
390C2×Q8—91no—
391C2×Q8—91no—
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×D4—91no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4—181no—
397C22×C4—21no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—361no—
404Q16—361no—
405SD16—182no—
406M16—361no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4C22×C3⋊D311yescharacteristic
425C4⋊C4C22×C3⋊D311yescharacteristic
426C4⋊C4C22×C3⋊D311yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—91no—
429C22⋊C4—91no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C22⋊C4—181no—
435C42—91no—
436C42—181no—
437C42—181no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3C2×D3×D414yes—
442C2×D3—64no—
443C2×D3—68no—
444C2×D3—64no—
445C2×D3—64no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—44no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4—44no—
453C3×C4D3×#4114yes—
454C3×C4#100914yes—
455Dic3—64no—
456Dic3—64no—
457Dic3—64no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#331511yescharacteristic, complemented, Sylow
462C23—91no—
463C23—181no—
464C23D4×C3⋊D311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—181no—
471D4—92no—
472D4—181no—
473D4—362no—
474D4—361no—
475D4—362no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3—44no—
501C2×C3#565414yes—
502C2×C3#576614yes—
503C2×C3#577314yes—
504D3—124no—
505D3—128no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—181no—
510C22—182no—
511C22—181no—
512C22—181no—
513C22—361no—
514C22—361no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—181no—
522C4—181no—
523C4—181no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#41×C3⋊D311yescharacteristic
528C4#6436611yescharacteristic
529C3#8147414yescomplemented
530C2—41no—
531C2—361no—
532C2—362no—
533C2#1059612511yescharacteristic
534C2#1059623711yescharacteristic
535C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#484C2
socleC22×C32C22×D4
prime radical#10596102C2
hypercenter#484C3⋊D3
hypocenterC32#3315
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #10595984C2semidirect
3. C32×#484C2semidirect
4. #10592751C2semidirect
5. #10592665C2semidirect
6. #10592590C2semidirect
7. #10592588C2semidirect
8. #10592587C2semidirect
9. #10592586C2semidirect
10. #10592507C2semidirect
11. #10592503C2semidirect
12. #10592496C2semidirect
13. #10592494C2semidirect
14. #10592432C2semidirect
15. #10592427C2semidirect
62. C3×#484D3semidirect
213. #484C3⋊D3semidirect
461. C32#3315semidirect
529. C3#81474semidirect

Maximal subgroups

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

subgroupindex
#105961022
#105959842
C32×#4842
#105927512
#105926652
#105925902
#105925882
#105925872
#105925862
#105925072
#105925032
#105924962
#105924942
#105924322
#105924272
#814743