Finite Group Databasebeta

← #11889828

Subgroups — #11889828

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#10596197C211yesmaximal, characteristic
2#10596052C211yesmaximal, characteristic, complemented
3C32×#462C211yesmaximal, characteristic, complemented
4#10592888C211yesmaximal, characteristic, complemented
5#10592887C211yesmaximal, characteristic, complemented
6#10592886C211yesmaximal, characteristic, complemented
7#10592886C211yesmaximal, characteristic, complemented
8#10592781C211yesmaximal, characteristic, complemented
9#10592725C211yesmaximal, characteristic, complemented
10#10592546C211yesmaximal, characteristic, complemented
11#10592535C211yesmaximal, characteristic, complemented
12#10592514C211yesmaximal, characteristic, complemented
13#10592510C211yesmaximal, characteristic, complemented
14#10592503C211yesmaximal, characteristic, complemented
15#10592502C211yesmaximal, characteristic, complemented
16#80494—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3832C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C4⋊Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23#64155C2211yescharacteristic
24#64155C2211yescharacteristic
25#64155C2211yescharacteristic
26#64155C2211yescharacteristic
27C2×#3755C2211yescharacteristic
28C2×#3743C2211yescharacteristic
29C2×C8×C3⋊D3C2211yescharacteristic
30#64104—21no—
31#64103—21no—
32#64103—21no—
33#64103—21no—
34#64101C2211yescharacteristic
35C4⋊C4×C3⋊D3—21no—
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64098—21no—
38#64085—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41#64081—21no—
42#64079C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63662C2211yescharacteristic
50#63662C2211yescharacteristic
51#63648C2211yescharacteristic
52#63648C2211yescharacteristic
53#63647C2211yescharacteristic
54#63647C2211yescharacteristic
55#63645C2211yescharacteristic
56#63644C2211yescharacteristic
57#63636C2211yescharacteristic
58#63634C2211yescharacteristic
59#63630C2211yescharacteristic
60#5726—34no—
61#5581—34no—
62C3×#462D314yescomplemented
63#5189—34no—
64#5188—34no—
65#5187—34no—
66#5187—34no—
67#5082—34no—
68#5026—34no—
69#4847—34no—
70#4836—34no—
71#4815—34no—
72#4811—34no—
73#4804—34no—
74#4803—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C2×C32×Q8C2311yescharacteristic
78#3832—22no—
79#3832—22no—
80#3832—41no—
81#3832—41no—
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)—21no—
84C2×C4⋊(C3⋊D3)D411yescharacteristic
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×C4×C3⋊D3C2311yescharacteristic
92C32×Q16—41no—
93C32×Q16—41no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4—21no—
98C32×C4⋊C4—21no—
99C32×C4⋊C4C2311yescharacteristic
100C32×C42—21no—
101C32×C42C2311yescharacteristic
102#3755—22no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752D411yescharacteristic
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)D411yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750—21no—
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3743—41no—
126C8×C3⋊D3—41no—
127#3315—91noSylow
128C2×#239—34no—
129C2×#239—34no—
130C2×C3×Q16C2×D314yes—
131C2×C3×Q16C2×D314yes—
132C3×C4⋊Q8C2×D314yes—
133C3×C4×Q8C2×D314yes—
134#946—34no—
135#946—34no—
136#946—34no—
137#946—34no—
138C2×#215—34no—
139C2×ΓL(1,𝔽25)—34no—
140C2×D3×C8—34no—
141#895—64no—
142#894—64no—
143#894—64no—
144#894—64no—
145#892—34no—
146D3×C4⋊C4—34no—
147D3×C4⋊C4—64no—
148#889—64no—
149#876—64no—
150C4×D12—34no—
151C4×D12—34no—
152#872—64no—
153#870—34no—
154C3×C4⋊C8C2×D314yes—
155C3×#103C2×D314yes—
156C3×#103C2×D314yes—
157#835—34no—
158#835—34no—
159#835—34no—
160#835—34no—
161#835—34no—
162#821—34no—
163#821—34no—
164(C2×D3)⋊C8—34no—
165(C2×D3)⋊C8—34no—
166#818—34no—
167#817—34no—
168#809—34no—
169#807—34no—
170#803—34no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C32×Q8—21no—
179C32×Q8—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)—41no—
194C4⋊(C3⋊D3)—42no—
195C4⋊(C3⋊D3)—42no—
196C4⋊(C3⋊D3)#4112yes—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—21no—
200C4×C3⋊D3—21no—
201C4×C3⋊D3—42no—
202C4×C3⋊D3—42no—
203C4×C3⋊D3—42no—
204C4×C3⋊D3—42no—
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#484—91no—
214#478—91no—
215#470—91no—
216#467—91no—
217#462C3⋊D311yescharacteristic, complemented
218#452—91no—
219#452—91no—
220#440—91no—
221#435—91no—
222#417—91no—
223#416—91no—
224C2×C3×Q8C22×D314yes—
225C2×C3×Q8C22×D314yes—
226C2×C3×Q8C22×D314yes—
227#239—68no—
228#239—68no—
229#239—124no—
230#239—124no—
231C2×D12—34no—
232C2×D12—34no—
233C2×D12—64no—
234C2×D12—64no—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C3×Q16—44no—
242C3×Q16—44no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—24no—
247C3×C4⋊C4—24no—
248C3×C4⋊C4C22×D314yes—
249C3×C42—24no—
250C3×C42C22×D314yes—
251#215—68no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—34no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—34no—
263C4⋊Dic3—34no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271C4×Dic3—64no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274ΓL(1,𝔽25)—124no—
275D3×C8—124no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—21no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4—41no—
292C32×C4C2×#4111yescharacteristic
293C32×C4H(5,𝔽2)11yescharacteristic
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C2×#41—91no—
301C2×Q16C2×C3⋊D311yescharacteristic
302C2×Q16C2×C3⋊D311yescharacteristic
303C2×SD16—91no—
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8C2×C3⋊D311yescharacteristic
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⋊Q8—91no—
317#121—181no—
318C4×Q8C2×C3⋊D311yescharacteristic
319C4×D4—91no—
320C4×D4—91no—
321#117—91no—
322#117—181no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—181no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8C2×C3⋊D311yescharacteristic
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⋊C8—91no—
341#97—91no—
342C22×D3—34no—
343C22×D3—34no—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—24no—
349C3×Q8—24no—
350C3×Q8—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4D3×D414yes—
356C2×C3×C4D3×D414yes—
357C2×C3×C4C23×D314yes—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363D12—38no—
364D12—64no—
365D12—124no—
366D12—128no—
367D12—128no—
368C4×D3—64no—
369C4×D3—64no—
370C4×D3—64no—
371C4×D3—64no—
372C4×D3—128no—
373C4×D3—128no—
374C4×D3—128no—
375C4×D3—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32#54611yescharacteristic
381C2×C32#57511yescharacteristic
382C2×C32#57811yescharacteristic
383C3⋊D3—41no—
384C3⋊D3—41no—
385C3⋊D3—42no—
386#41—182no—
387#41—182no—
388#41—361no—
389#41—361no—
390C2×Q8C22×C3⋊D311yescharacteristic
391C2×Q8C22×C3⋊D311yescharacteristic
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×D4—91no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4—181no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403Q16—41no—
404Q16—41no—
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—21no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—91no—
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
427C22⋊C4—91no—
428C22⋊C4—91no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C22⋊C4—181no—
435C42—21no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3C2×D3×D414yes—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—68no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4#100414yes—
455C3×C4D3×#4114yes—
456Dic3—64no—
457Dic3—64no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#331511yescharacteristic, complemented, Sylow
462C23—91no—
463C23—91no—
464C23—181no—
465Q8—21no—
466Q8—21no—
467Q8—21no—
468Q8—21no—
469Q8—21no—
470Q8—21no—
471D4—92no—
472D4—181no—
473D4—361no—
474D4—362no—
475D4—362no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
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—181no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4D4×C3⋊D311yescharacteristic
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3#561214yes—
501C2×C3#576614yes—
502C2×C3#577714yes—
503D3—124no—
504D3—124no—
505D3—128no—
506C22—181no—
507C22—181no—
508C22—181no—
509C22—181no—
510C22—181no—
511C22—181no—
512C22—182no—
513C22—361no—
514C22—361no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—21no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—181no—
523C4—181no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#6436111yescharacteristic
528C4#41×C3⋊D311yescharacteristic
529C3#8049414yescomplemented
530C2—361no—
531C2—361no—
532C2—362no—
533C2#1059608311yescharacteristic
534C2#1059623711yescharacteristic
535C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radical#10596197C2
hypercenter#462C3⋊D3
hypocenterC32#3315
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #10596052C2semidirect
3. C32×#462C2semidirect
4. #10592888C2semidirect
5. #10592887C2semidirect
6. #10592886C2semidirect
7. #10592886C2semidirect
8. #10592781C2semidirect
9. #10592725C2semidirect
10. #10592546C2semidirect
11. #10592535C2semidirect
12. #10592514C2semidirect
13. #10592510C2semidirect
14. #10592503C2semidirect
15. #10592502C2semidirect
62. C3×#462D3semidirect
217. #462C3⋊D3semidirect
461. C32#3315semidirect
529. C3#80494semidirect

Maximal subgroups

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

subgroupindex
#105961972
#105960522
C32×#4622
#105928882
#105928872
#105928862
#105927812
#105927252
#105925462
#105925352
#105925142
#105925102
#105925032
#105925022
#804943