Finite Group Databasebeta

← #11889804

Subgroups — #11889804

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#10596165C211yesmaximal, characteristic, complemented
3C32×#491C211yesmaximal, characteristic, complemented
4#10592789C211yesmaximal, characteristic, complemented
5#10592765C211yesmaximal, characteristic, complemented
6#10592515C211yesmaximal, characteristic, complemented
7#10592513C211yesmaximal, characteristic, complemented
8#10592512C211yesmaximal, characteristic, complemented
9#10592510C211yesmaximal, characteristic, complemented
10#10592507C211yesmaximal, characteristic, complemented
11#10592507C211yesmaximal, characteristic, complemented
12#10592503C211yesmaximal, characteristic, complemented
13#10592502C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15#10592405C211yesmaximal, characteristic, complemented
16#81750—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3832C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C32×#125C2211yescharacteristic
21#64155C2211yescharacteristic
22#64155C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26C2×#3743C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic
28#64107—21no—
29#64106C2211yescharacteristic
30#64106C2211yescharacteristic
31#64104—21no—
32#64103—21no—
33#64103—21no—
34#64103—21no—
35#64101—21no—
36#64101C2211yescharacteristic
37C4⋊C4×C3⋊D3—21no—
38C4⋊C4×C3⋊D3C2211yescharacteristic
39#64099—21no—
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42C4×#634C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#97C2211yescharacteristic
48#63662C2211yescharacteristic
49#63662C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63647C2211yescharacteristic
53#63645C2211yescharacteristic
54#63643C2211yescharacteristic
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5726—34no—
61#5694—34no—
62C3×#491D314yescomplemented
63#5090—34no—
64#5066—34no—
65#4816—34no—
66#4814—34no—
67#4813—34no—
68#4811—34no—
69#4808—34no—
70#4808—34no—
71#4804—34no—
72#4803—34no—
73#4710—34no—
74#4706—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77#3832—22no—
78#3832—22no—
79#3832—41no—
80#3832—41no—
81C2×C4⋊(C3⋊D3)—21no—
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)D411yescharacteristic
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C42C2311yescharacteristic
101#3756—41no—
102#3756—41no—
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)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)D411yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3744—22no—
125#3743—41no—
126C8×C3⋊D3—41no—
127#3315—91noSylow
128C2×#239—34no—
129C2×#239—34no—
130C3×C4⋊Q8C2×D314yes—
131C3×#125C2×D314yes—
132#946—34no—
133#946—34no—
134C2×#216—34no—
135C2×#216—34no—
136C2×#204—34no—
137C2×ΓL(1,𝔽25)—34no—
138C2×D3×C8—34no—
139#898—64no—
140#897—34no—
141#897—34no—
142#895—64no—
143#894—64no—
144#894—64no—
145#894—64no—
146#892—34no—
147#892—64no—
148D3×C4⋊C4—34no—
149D3×C4⋊C4—64no—
150#890—64no—
151C4×D12—34no—
152C4×D12—34no—
153C4×Dic6—34no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×#103C2×D314yes—
157C3×#103C2×D314yes—
158C3×#97C2×D314yes—
159#835—34no—
160#835—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163(C2×D3)⋊C8—34no—
164#818—34no—
165#816—34no—
166#809—34no—
167#809—34no—
168#808—34no—
169#807—34no—
170C4⋊(C3⋊C8)—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—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—41no—
192C4⋊(C3⋊D3)—42no—
193C4⋊(C3⋊D3)—42no—
194C4⋊(C3⋊D3)#4112yes—
195C4×C3⋊D3—21no—
196C4×C3⋊D3—21no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—42no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—42no—
202C4×C3⋊D3—42no—
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#491C3⋊D311yescharacteristic, complemented
212#485—91no—
213#484—91no—
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—
225C2×C3×Q8C22×D314yes—
226#239—68no—
227#239—68no—
228#239—124no—
229#239—124no—
230C2×D12—34no—
231C2×D12—34no—
232C2×D12—64no—
233C2×D12—64no—
234C2×C4×D3—34no—
235C2×C4×D3—34no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×Dic6—34no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—24no—
244C3×C4⋊C4—24no—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—24no—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C42C22×D314yes—
250#216—124no—
251#216—124no—
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—64no—
264C4⋊Dic3—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—34no—
273#204—68no—
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×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8C2×C3⋊D311yescharacteristic
307#126—181no—
308#125—181no—
309#125C2×C3⋊D311yescharacteristic
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×Q8—91no—
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⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103C2×C3⋊D311yescharacteristic
333#103C2×C3⋊D311yescharacteristic
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341#97C2×C3⋊D311yescharacteristic
342C22×D3—34no—
343C22×D3—34no—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4D3×D414yes—
354C2×C3×C4D3×D414yes—
355C2×C3×C4C23×D314yes—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361D12—38no—
362D12—64no—
363D12—124no—
364D12—128no—
365D12—128no—
366C4×D3—64no—
367C4×D3—64no—
368C4×D3—64no—
369C4×D3—64no—
370C4×D3—128no—
371C4×D3—128no—
372C4×D3—128no—
373C4×D3—128no—
374Dic6—64no—
375Dic6—64no—
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×Q8—91no—
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—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—21no—
415C4⋊C4—21no—
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⋊C4C22×C3⋊D311yescharacteristic
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—181no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3C2×D3×D414yes—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—68no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—64no—
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×C4D3×#4114yes—
455C3×C4#100914yes—
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—181no—
470Q8—181no—
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#567614yes—
501C2×C3#577714yes—
502C2×C3#577914yes—
503D3—124no—
504D3—124no—
505D3—128no—
506C22—181no—
507C22—181no—
508C22—182no—
509C22—181no—
510C22—181no—
511C22—181no—
512C22—181no—
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#41×C3⋊D311yescharacteristic
528C4#6436611yescharacteristic
529C3#8175014yescomplemented
530C2—361no—
531C2—361no—
532C2—362no—
533C2#1059614711yescharacteristic
534C2#1059624811yescharacteristic
535C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#491C2
socleC22×C32C22×D4
prime radical#10596197C2
hypercenter#491C3⋊D3
hypocenterC32#3315
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #10596165C2semidirect
3. C32×#491C2semidirect
4. #10592789C2semidirect
5. #10592765C2semidirect
6. #10592515C2semidirect
7. #10592513C2semidirect
8. #10592512C2semidirect
9. #10592510C2semidirect
10. #10592507C2semidirect
11. #10592507C2semidirect
12. #10592503C2semidirect
13. #10592502C2semidirect
14. #10592409C2semidirect
15. #10592405C2semidirect
62. C3×#491D3semidirect
211. #491C3⋊D3semidirect
461. C32#3315semidirect
529. C3#81750semidirect

Maximal subgroups

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

subgroupindex
#105961972
#105961652
C32×#4912
#105927892
#105927652
#105925152
#105925132
#105925122
#105925102
#105925072
#105925032
#105925022
#105924092
#105924052
#817503