Finite Group Databasebeta

← #11887602

Subgroups — #11887602

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596103C211yesmaximal, characteristic
2#10595982C211yesmaximal, characteristic
3C32×#484C211yesmaximal, characteristic, complemented
4#10592750C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6#10592586C211yesmaximal, characteristic, complemented
7#10592583C211yesmaximal, characteristic, complemented
8#10592574C211yesmaximal, characteristic, complemented
9#10592572C211yesmaximal, characteristic, complemented
10#10592508C211yesmaximal, characteristic, complemented
11C3⋊D3×#103C211yesmaximal, characteristic, complemented
12#10592494C211yesmaximal, characteristic, complemented
13#10592491C211yesmaximal, characteristic, complemented
14#10592438C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic
16#81490—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64153C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C4×#638—21no—
24C4×#638C2211yescharacteristic
25#64133—21no—
26#64133C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28C2×#3746C2211yescharacteristic
29C2×#3746C2211yescharacteristic
30C2×C8×C3⋊D3C2211yescharacteristic
31#64106C2211yescharacteristic
32#64106C2211yescharacteristic
33#64105—21no—
34#64105—21no—
35C4⋊C4×C3⋊D3C2211yescharacteristic
36#64098—21no—
37#64097—21no—
38#64097C2211yescharacteristic
39#64096C2211yescharacteristic
40#64096C2211yescharacteristic
41#64090—21no—
42#64087—21no—
43C32×#107C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48#63662C2211yescharacteristic
49#63647C2211yescharacteristic
50#63643C2211yescharacteristic
51#63643C2211yescharacteristic
52#63641C2211yescharacteristic
53C8×C3⋊Dic3C2211yescharacteristic
54#63637C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63637C2211yescharacteristic
59#63634C2211yescharacteristic
60#5632—34no—
61#5511—34no—
62C3×#484D314yescomplemented
63#5051—34no—
64C2×#810—34no—
65#4887—34no—
66#4884—34no—
67#4875—34no—
68#4873—34no—
69#4809—34no—
70D3×#103—34no—
71#4795—34no—
72#4792—34no—
73#4739—34no—
74#67⋊C8—34no—
75C2×C32×Q8C2311yescharacteristic
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C2×#638D411yescharacteristic
79C22×C3⋊Dic3—21no—
80Q8×C3⋊D3—22no—
81Q8×C3⋊D3—41no—
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3C2311yescharacteristic
85C2×#634—22no—
86C2×#634—21no—
87C2×#634—21no—
88C2×#634—21no—
89C2×#634—41no—
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×#634C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101#3757—21no—
102#3757D411yescharacteristic
103#3756—41no—
104#3752—21no—
105#3752—21no—
106#3752D411yescharacteristic
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
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
121C2×C3⋊(C3⋊C8)—41no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3746—22no—
125#3746—41no—
126C8×C3⋊D3—41no—
127#3299—91noSylow
128C2×D3×Q8—34no—
129C22×Dic6—34no—
130C3×C22⋊Q8C2×D314yes—
131C2×C3×C4⋊C4C2×D314yes—
132#944—34no—
133C2×#216—34no—
134C4×#67—34no—
135C4×#67—64no—
136#924—34no—
137#924—64no—
138C22×C3⋊C8—34no—
139C2×Dic12—34no—
140C2×Dic12—34no—
141C2×D3×C8—34no—
142#897—34no—
143#897—34no—
144#896—64no—
145#896—64no—
146D3×C4⋊C4—34no—
147#889—64no—
148#888—34no—
149#888—64no—
150#887—34no—
151#887—34no—
152#67⋊C4—64no—
153#878—64no—
154C3×#107C2×D314yes—
155C3×#107C2×D314yes—
156C3×#103C2×D314yes—
157C3×#103C2×D314yes—
158C3×C22⋊C8C2×D314yes—
159#835—34no—
160(C2×D3)⋊C8—34no—
161#816—34no—
162#816—34no—
163Dic3⋊C8—34no—
164C8×Dic3—34no—
165#810—34no—
166#810—34no—
167#810—34no—
168#810—34no—
169#810—34no—
170#807—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3C2×D411yescharacteristic
173C32×Q8—21no—
174C32×Q8—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—81no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638Q1614yescomplemented
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—42no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4×C3⋊D3—21no—
194C4×C3⋊D3—21no—
195C4×C3⋊D3—42no—
196C4×C3⋊D3—81no—
197#634—21no—
198#634—21no—
199#634—21no—
200#634—21no—
201#634—21no—
202#634—42no—
203#634—42no—
204#634—81no—
205#634#4112yes—
206C32×C8—21no—
207C32×C8—21no—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210#554—91no—
211D4×Q8—91no—
212#487—91no—
213#484—91no—
214#484C3⋊D311yescharacteristic, complemented
215#477—91no—
216#467—91no—
217#467—91no—
218#462—91no—
219#451—91no—
220#451—91no—
221C4×Q16—91no—
222C8×D4—91no—
223C2×#103—91no—
224C2×#103—91no—
225C2×C3×Q8C22×D314yes—
226C22×C3×C4—24no—
227C22×C3×C4C22×D314yes—
228C2×#67—34no—
229C22×Dic3—64no—
230D3×Q8—68no—
231D3×Q8—124no—
232C2×C4×D3—34no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×Dic6—34no—
236C2×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—68no—
239C2×Dic6—64no—
240C2×Dic6—64no—
241C2×Dic6—64no—
242C2×Dic6—124no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—24no—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C4⋊C4C22×D314yes—
250C3×C22⋊C4—24no—
251#217—34no—
252#217—64no—
253#216—124no—
254(C2×D3)⋊C4—34no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—34no—
258C4⋊Dic3—64no—
259C4⋊Dic3—64no—
260Dic3⋊C4—34no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—34no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—124no—
274Dic12—68no—
275Dic12—124no—
276D3×C8—124no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C2×Q1612yes—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3C2×Q1612yes—
284C32×C4—21no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4C2×#4111yescharacteristic
290C32×C4H(5,𝔽2)11yescharacteristic
291C3⋊Dic3—22no—
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3C2×Q1612yes—
298C22×Q8—91no—
299C22×Q8—91no—
300C2×Q16—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C22×C8—91no—
304C22×C8—91no—
305C4⋊Q8—91no—
306C4⋊Q8—91no—
307C4⋊Q8—181no—
308#125—181no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—91no—
312C22⋊Q8—181no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C22⋊Q8—181no—
316C22⋊Q8C2×C3⋊D311yescharacteristic
317C4×Q8—91no—
318C4×Q8—91no—
319C4×D4—91no—
320C4×D4—181no—
321C4×D4—181no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4C2×C3⋊D311yescharacteristic
324#107—91no—
325#107C2×C3⋊D311yescharacteristic
326#107C2×C3⋊D311yescharacteristic
327C4⋊C8—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#103C2×C3⋊D311yescharacteristic
337#103C2×C3⋊D311yescharacteristic
338C22⋊C8—91no—
339C22⋊C8C2×C3⋊D311yescharacteristic
340C4×C8—91no—
341C23×C3D3×D414yes—
342C22×D3—34no—
343C3×Q8—24no—
344C3×Q8—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—84no—
352C2×C3×C4D3×D414yes—
353C2×C3×C4C23×D314yes—
354#67—316no—
355C2×Dic3—34no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—128no—
363C4×D3—64no—
364C4×D3—64no—
365C4×D3—128no—
366C4×D3—244no—
367Dic6—38no—
368Dic6—64no—
369Dic6—64no—
370Dic6—64no—
371Dic6—64no—
372Dic6—64no—
373Dic6—128no—
374Dic6—128no—
375Dic6—244no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—22no—
381C2×C32#54611yescharacteristic
382C2×C32C22×Q1611yescharacteristic
383C2×C32#57711yescharacteristic
384C3⋊D3—22no—
385C2×Q8—91no—
386C2×Q8—91no—
387C2×Q8—91no—
388C2×Q8—181no—
389C2×Q8—181no—
390C2×Q8—182no—
391C2×Q8—181no—
392C2×Q8—182no—
393C2×Q8—361no—
394C2×Q8—361no—
395C2×Q8C22×C3⋊D311yescharacteristic
396C2×D4—91no—
397C22×C4—21no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—182no—
404Q16—361no—
405Q16—361no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—361no—
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⋊C4—181no—
425C4⋊C4C22×C3⋊D311yescharacteristic
426C4⋊C4C22×C3⋊D311yescharacteristic
427C4⋊C4C22×C3⋊D311yescharacteristic
428C22⋊C4—21no—
429C22⋊C4—91no—
430C22⋊C4—91no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—91no—
435C42—181no—
436C42—181no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3D3×Q1618yes—
440C22×C3C2×D3×D414yes—
441C2×D3—38no—
442C2×D3—64no—
443C2×D3—64no—
444C3×C4—24no—
445C3×C4—44no—
446C3×C4—44no—
447C3×C4—44no—
448C3×C4—44no—
449C3×C4D3×#4114yes—
450C3×C4#100914yes—
451Dic3—38no—
452Dic3—68no—
453Dic3—64no—
454Dic3—64no—
455Dic3—124no—
456Dic3—124no—
457Dic3—124no—
458C32#329911yescharacteristic, complemented, Sylow
459C23—91no—
460C23D4×C3⋊D311yescharacteristic
461Q8—21no—
462Q8—21no—
463Q8—92no—
464Q8—181no—
465Q8—181no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—362no—
470Q8—362no—
471Q8—721no—
472D4—94no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—81no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4—721no—
492C2×C4D4×C3⋊D311yescharacteristic
493C2×C4C23×C3⋊D311yescharacteristic
494C8—21no—
495C8—21no—
496C8—181no—
497C8—181no—
498C2×C3—28no—
499C2×C3#565414yes—
500C2×C3C2×D3×Q1614yes—
501C2×C3#577514yes—
502D3—68no—
503C22—21no—
504C22—21no—
505C22—92no—
506C22—181no—
507C22—181no—
508C22Q16×C3⋊D312yes—
509C22C2×D4×C3⋊D311yescharacteristic
510C4—21no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—92no—
516C4—181no—
517C4—182no—
518C4—181no—
519C4—361no—
520C4—361no—
521C4—361no—
522C4#41×C3⋊D311yescharacteristic
523C4#6436611yescharacteristic
524C3#8149014yescomplemented
525C2—22no—
526C2—182no—
527C2#1059612511yescharacteristic
528C2C2×Q16×C3⋊D311yescharacteristic
529C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#484C2
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenter#484C3⋊D3
hypocenterC32#3299
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
3. C32×#484C2semidirect
4. #10592750C2semidirect
5. C2×#63637C2semidirect
6. #10592586C2semidirect
7. #10592583C2semidirect
8. #10592574C2semidirect
9. #10592572C2semidirect
10. #10592508C2semidirect
11. C3⋊D3×#103C2semidirect
12. #10592494C2semidirect
13. #10592491C2semidirect
14. #10592438C2semidirect
62. C3×#484D3semidirect
184. #638Q16semidirect
214. #484C3⋊D3semidirect
458. C32#3299semidirect
524. C3#81490semidirect

Maximal subgroups

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

subgroupindex
#105961032
#105959822
C32×#4842
#105927502
C2×#636372
#105925862
#105925832
#105925742
#105925722
#105925082
C3⋊D3×#1032
#105924942
#105924912
#105924382
#105924242
#814903