Finite Group Databasebeta

← #11887593

Subgroups — #11887593

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#10596106C211yesmaximal, characteristic
2#10596103C211yesmaximal, characteristic
3C32×#467C211yesmaximal, characteristic, complemented
4#10592885C211yesmaximal, characteristic, complemented
5#10592881C211yesmaximal, characteristic, complemented
6C8×#638C211yesmaximal, characteristic
7C2×#63643C211yesmaximal, characteristic, complemented
8#10592749C211yesmaximal, characteristic, complemented
9#10592743C211yesmaximal, characteristic, complemented
10#10592583C211yesmaximal, characteristic, complemented
11#10592574C211yesmaximal, characteristic, complemented
12#10592512C211yesmaximal, characteristic, complemented
13C3⋊D3×#103C211yesmaximal, characteristic, complemented
14#10592491C211yesmaximal, characteristic, complemented
15#10592489C211yesmaximal, characteristic, complemented
16#80781—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23#64155C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25#64153C2211yescharacteristic
26C2×#3756C2211yescharacteristic
27C2×#3756C2211yescharacteristic
28C4×#638C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C8×C3⋊D3C2211yescharacteristic
31#64106—21no—
32#64106C2211yescharacteristic
33#64105—21no—
34C4⋊C4×C3⋊D3C2211yescharacteristic
35#64098—21no—
36#64097—21no—
37#64097C2211yescharacteristic
38#64096C2211yescharacteristic
39#64090—21no—
40#64090—21no—
41#64087—21no—
42#64087—21no—
43C32×#107C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63657C2211yescharacteristic
49#63647C2211yescharacteristic
50#63643C2211yescharacteristic
51#63643C2211yescharacteristic
52#63643C2211yescharacteristic
53#63643C2211yescharacteristic
54#63641C2211yescharacteristic
55C8×C3⋊Dic3C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63634C2211yescharacteristic
59#63634C2211yescharacteristic
60#5635—34no—
61#5632—34no—
62C3×#467D314yescomplemented
63#5186—34no—
64#5182—34no—
65C8×#67—34no—
66C2×#816—34no—
67#5050—34no—
68#5044—34no—
69#4884—34no—
70#4875—34no—
71#4813—34no—
72D3×#103—34no—
73#4792—34no—
74#4790—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638D411yescharacteristic
79C22×C3⋊Dic3—21no—
80C22×C3⋊Dic3—21no—
81Q8×C3⋊D3—22no—
82Q8×C3⋊D3—41no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×#634—22no—
87C2×#634—21no—
88C2×#634—21no—
89C2×#634—21no—
90C2×#634—41no—
91C2×#634C2311yescharacteristic
92C2×#634C2311yescharacteristic
93C32×Q16—41no—
94C2×C32×C8—41no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4—21no—
98C32×C4⋊C4—21no—
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103#3757D411yescharacteristic
104#3756—22no—
105#3756—41no—
106#3752—21no—
107#3752—21no—
108#3752D411yescharacteristic
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750D411yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3299—91noSylow
128C2×D3×Q8—34no—
129C22×Dic6—34no—
130C2×C3×Q16C2×D314yes—
131C22×C3×C8C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133C3×C22⋊Q8C2×D314yes—
134#946—34no—
135Q8×Dic3—34no—
136#944—34no—
137C2×#216—34no—
138C2×#216—34no—
139C4×#67—34no—
140C2×C4⋊Dic3—34no—
141C2×D3×C8—34no—
142#897—34no—
143#897—64no—
144#896—64no—
145D3×C4⋊C4—34no—
146#889—64no—
147#888—34no—
148#888—64no—
149#887—34no—
150#67⋊C4—64no—
151#67⋊C4—64no—
152#878—64no—
153#878—64no—
154C3×#107C2×D314yes—
155C3×#103C2×D314yes—
156C3×#103C2×D314yes—
157#835—34no—
158#835—34no—
159#830—34no—
160(C2×D3)⋊C8—34no—
161#816—34no—
162#816—34no—
163#816—34no—
164#816—34no—
165Dic3⋊C8—34no—
166C8×Dic3—34no—
167#810—34no—
168#810—34no—
169#807—34no—
170#807—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3C2×D411yescharacteristic
173C32×Q8—21no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185#638Q1614yescomplemented
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—42no—
191C2×C3⋊Dic3—81no—
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C4×C3⋊D3—21no—
196C4×C3⋊D3—21no—
197C4×C3⋊D3—42no—
198C4×C3⋊D3—81no—
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#484—91no—
215#477—91no—
216#467—91no—
217#467C3⋊D311yescharacteristic, complemented
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—
226C2×C3×Q8C22×D314yes—
227C22×C3×C4C22×D314yes—
228C2×#67—34no—
229C22×Dic3—64no—
230C22×Dic3—64no—
231D3×Q8—68no—
232D3×Q8—124no—
233C2×C4×D3—34no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—68no—
239C2×Dic6—64no—
240C2×Dic6—64no—
241C2×Dic6—64no—
242C2×Dic6—124no—
243C3×Q16—44no—
244C2×C3×C8—44no—
245C2×C3×C8C22×D314yes—
246C2×C3×C8C22×D314yes—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—24no—
249C3×C4⋊C4C22×D314yes—
250C3×C4⋊C4C22×D314yes—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—24no—
253#217—34no—
254#216—68no—
255#216—124no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263C4⋊Dic3—64no—
264Dic3⋊C4—34no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271C4×Dic3—34no—
272C4×Dic3—64no—
273C4×Dic3—64no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—34no—
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×Q16C2×C3⋊D311yescharacteristic
303C22×C8—91no—
304C22×C8C2×C3⋊D311yescharacteristic
305C4⋊Q8—91no—
306C4⋊Q8—91no—
307C4⋊Q8—181no—
308#125—181no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—181no—
312C22⋊Q8—181no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C22⋊Q8C2×C3⋊D311yescharacteristic
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⋊C4—91no—
324#107—91no—
325#107—91no—
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⋊C8—91no—
340C4×C8—91no—
341C23×C3D3×D414yes—
342C22×D3—34no—
343C3×Q8—24no—
344C3×Q8—24no—
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×C4D3×D414yes—
354C2×C3×C4C23×D314yes—
355#67—316no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—128no—
364C2×Dic3—244no—
365C4×D3—64no—
366C4×D3—64no—
367C4×D3—128no—
368C4×D3—244no—
369Dic6—38no—
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—181no—
388C2×Q8—181no—
389C2×Q8—182no—
390C2×Q8—181no—
391C2×Q8—182no—
392C2×Q8—361no—
393C2×Q8—361no—
394C2×Q8C22×C3⋊D311yescharacteristic
395C2×Q8C22×C3⋊D311yescharacteristic
396C2×D4—91no—
397C22×C4—91no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—41no—
404Q16—182no—
405Q16—361no—
406C2×C8—41no—
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—91no—
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⋊C4—181no—
426C4⋊C4C22×C3⋊D311yescharacteristic
427C4⋊C4C22×C3⋊D311yescharacteristic
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—91no—
431C22⋊C4—91no—
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×C4#100414yes—
450C3×C4D3×#4114yes—
451Dic3—38no—
452Dic3—64no—
453Dic3—68no—
454Dic3—64no—
455Dic3—124no—
456Dic3—124no—
457Dic3—124no—
458C32#329911yescharacteristic, complemented, Sylow
459C23—91no—
460C23D4×C3⋊D311yescharacteristic
461Q8—21no—
462Q8—21no—
463Q8—21no—
464Q8—21no—
465Q8—92no—
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—91no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—721no—
491C2×C4—721no—
492C2×C4D4×C3⋊D311yescharacteristic
493C2×C4C23×C3⋊D311yescharacteristic
494C8—21no—
495C8—21no—
496C8—181no—
497C8—181no—
498C2×C3—28no—
499C2×C3#561014yes—
500C2×C3C2×D3×Q1614yes—
501C2×C3#577014yes—
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—181no—
518C4—182no—
519C4—361no—
520C4—361no—
521C4—361no—
522C4#6436111yescharacteristic
523C4#41×C3⋊D311yescharacteristic
524C3#8078114yescomplemented
525C2—22no—
526C2—182no—
527C2#1059608111yescharacteristic
528C2C2×Q16×C3⋊D311yescharacteristic
529C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#467C2
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenter#467C3⋊D3
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. C32×#467C2semidirect
4. #10592885C2semidirect
5. #10592881C2semidirect
7. C2×#63643C2semidirect
8. #10592749C2semidirect
9. #10592743C2semidirect
10. #10592583C2semidirect
11. #10592574C2semidirect
12. #10592512C2semidirect
13. C3⋊D3×#103C2semidirect
14. #10592491C2semidirect
15. #10592489C2semidirect
62. C3×#467D3semidirect
185. #638Q16semidirect
217. #467C3⋊D3semidirect
458. C32#3299semidirect
524. C3#80781semidirect

Maximal subgroups

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

subgroupindex
#105961062
#105961032
C32×#4672
#105928852
#105928812
C8×#6382
C2×#636432
#105927492
#105927432
#105925832
#105925742
#105925122
C3⋊D3×#1032
#105924912
#105924892
#807813