Finite Group Databasebeta

← #11889813

Subgroups — #11889813

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#10596022C211yesmaximal, characteristic
2#10596012C211yesmaximal, characteristic, complemented
3C32×#435C211yesmaximal, characteristic, complemented
4#10592836C211yesmaximal, characteristic, complemented
5#10592832C211yesmaximal, characteristic, complemented
6#10592815C211yesmaximal, characteristic, complemented
7#10592812C211yesmaximal, characteristic, complemented
8#10592548C211yesmaximal, characteristic, complemented
9#10592546C211yesmaximal, characteristic, complemented
10#10592432C211yesmaximal, characteristic, complemented
11#10592432C211yesmaximal, characteristic, complemented
12#10592422C211yesmaximal, characteristic, complemented
13#10592421C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15#10592402C211yesmaximal, characteristic, complemented
16#79504—34nomaximal
17C2×#3828C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×C32×M16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22#64147—21no—
23#64144—21no—
24#64135C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26#64133C2211yescharacteristic
27#64133C2211yescharacteristic
28#64133C2211yescharacteristic
29#64133C2211yescharacteristic
30C2×#3746C2211yescharacteristic
31C2×#3746C2211yescharacteristic
32C2×#3744C2211yescharacteristic
33C4⋊C4×C3⋊D3—21no—
34#64098—21no—
35#64092—21no—
36#64092—21no—
37#64088—21no—
38#64086—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40#64079C2211yescharacteristic
41#64078C2211yescharacteristic
42C4×#634C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×#97C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63645C2211yescharacteristic
51#63645C2211yescharacteristic
52#63644C2211yescharacteristic
53#63643C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63643C2211yescharacteristic
57#63643C2211yescharacteristic
58#63643C2211yescharacteristic
59#63643C2211yescharacteristic
60#5551—34no—
61#5541—34no—
62C3×#435D314yescomplemented
63#5137—34no—
64#5133—34no—
65#5116—34no—
66#5113—34no—
67#4849—34no—
68#4847—34no—
69#4733—34no—
70#4733—34no—
71#4723—34no—
72#4722—34no—
73#4710—34no—
74#4703—34no—
75C2×C32×D4D411yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C2×#638—21no—
80C22×C3⋊Dic3—21no—
81#3828—22no—
82#3828—22no—
83#3828—41no—
84#3828—41no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×#634C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C32×M16—41no—
93C2×C32×C8—41no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C2×C32×C8C2311yescharacteristic
98C32×C4⋊C4D411yescharacteristic
99C32×C22⋊C4D411yescharacteristic
100C32×C22⋊C4D411yescharacteristic
101C32×C42C2311yescharacteristic
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106#3757—21no—
107#3752—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
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—
123C4×C3⋊Dic3—21no—
124#3746—41no—
125#3746—41no—
126#3744—22no—
127#3315—91noSylow
128C2×#235—34no—
129C2×#235—34no—
130C2×C3×M16C2×D314yes—
131C22×C3×C8C2×D314yes—
132C3×C4×D4C2×D314yes—
133#938—64no—
134#935—64no—
135#926—34no—
136C2×C4⋊Dic3—34no—
137#924—34no—
138#924—34no—
139#924—34no—
140#924—34no—
141C2×Dic12—34no—
142C2×Dic12—34no—
143C2×#204—34no—
144D3×C4⋊C4—64no—
145#889—64no—
146#883—64no—
147#883—64no—
148#879—64no—
149#877—64no—
150C4×D12—34no—
151#870—34no—
152#869—34no—
153C4×Dic6—34no—
154C3×C4⋊C8C2×D314yes—
155C3×C22⋊C8C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157C3×#97C2×D314yes—
158#821—34no—
159#821—34no—
160#821—34no—
161#818—34no—
162#818—34no—
163#817—34no—
164#816—34no—
165#816—34no—
166#816—34no—
167#816—34no—
168#816—34no—
169#816—34no—
170#816—34no—
171C23×C32C2×D411yescharacteristic
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C32×D4—41no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—42no—
185#638—42no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—42no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)#4112yes—
196C4×C3⋊D3—42no—
197C4×C3⋊D3—42no—
198C4×C3⋊D3—42no—
199#634—21no—
200#634—21no—
201#634—21no—
202#634—21no—
203#634—21no—
204#634—21no—
205C32×C8—21no—
206C32×C8—21no—
207C32×C8—21no—
208C32×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#462—91no—
218#452—91no—
219#452—91no—
220#440—91no—
221#435C3⋊D311yescharacteristic, complemented
222#417—91no—
223#416—91no—
224C2×C3×D4D1214yes—
225C22×C3×C4C22×D314yes—
226C22×C3×C4C22×D314yes—
227C2×#67—64no—
228C2×#67—64no—
229C22×Dic3—64no—
230#235—68no—
231#235—68no—
232#235—124no—
233#235—124no—
234C2×D12—34no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×Dic6—34no—
239C2×Dic6—34no—
240C2×Dic6—34no—
241C3×M16—44no—
242C2×C3×C8—44no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C2×C3×C8C22×D314yes—
246C2×C3×C8C22×D314yes—
247C3×C4⋊C4D1214yes—
248C3×C22⋊C4D1214yes—
249C3×C22⋊C4D1214yes—
250C3×C42C22×D314yes—
251#217—64no—
252#217—64no—
253#217—64no—
254#217—64no—
255#217—64no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—34no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263C4⋊Dic3—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273Dic12—124no—
274Dic12—124no—
275#204—68no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—22no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
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×M16C2×C3⋊D311yescharacteristic
305C22×C8C2×C3⋊D311yescharacteristic
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⋊Q8—91no—
317#121—181no—
318C4×Q8—91no—
319C4×D4—91no—
320C4×D4C2×C3⋊D311yescharacteristic
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#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8C2×C3⋊D311yescharacteristic
340C22⋊C8C2×C3⋊D311yescharacteristic
341#97C2×C3⋊D311yescharacteristic
342C23×C3C2×D1214yes—
343C23×C3C2×D1214yes—
344C22×D3—64no—
345C3×D4—44no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4C2×D1214yes—
351C2×C3×C4C2×D1214yes—
352C2×C3×C4C2×D1214yes—
353C2×C3×C4C2×D1214yes—
354C2×C3×C4C23×D314yes—
355#67—128no—
356#67—128no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—128no—
365D12—38no—
366D12—64no—
367C4×D3—128no—
368C4×D3—128no—
369C4×D3—128no—
370Dic6—64no—
371Dic6—64no—
372Dic6—64no—
373Dic6—64no—
374Dic6—64no—
375Dic6—64no—
376C3×C8—24no—
377C3×C8—24no—
378C3×C8—24no—
379C3×C8—24no—
380C2×C32—41no—
381C2×C32—41no—
382C2×C32#54611yescharacteristic
383C2×C32#57511yescharacteristic
384C2×C32#57811yescharacteristic
385C3⋊D3—42no—
386#41—182no—
387#41—182no—
388#41—361no—
389#41—361no—
390C2×Q8—91no—
391C2×Q8—91no—
392C2×Q8—91no—
393C2×D4—91no—
394C2×D4—181no—
395C2×D4—181no—
396C2×D4C4⋊(C3⋊D3)11yescharacteristic
397C22×C4—181no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4C22×C3⋊D311yescharacteristic
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—361no—
404Q16—361no—
405SD16—182no—
406M16—41no—
407C2×C8—41no—
408C2×C8C22×C3⋊D311yescharacteristic
409C2×C8C22×C3⋊D311yescharacteristic
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
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⋊C4—181no—
426C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
434C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
435C42—181no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3C22×D1214yes—
445C2×D3—68no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4#100414yes—
453C3×C4D3×#4114yes—
454Dic3—124no—
455Dic3—124no—
456Dic3—124no—
457Dic3—124no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#331511yescharacteristic, complemented, Sylow
462C23—181no—
463C23C2×C4⋊(C3⋊D3)11yescharacteristic
464C23C2×C4⋊(C3⋊D3)11yescharacteristic
465Q8—181no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—181no—
471D4—41no—
472D4—92no—
473D4—181no—
474D4—362no—
475D4—362no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—362no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
492C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
493C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
494C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—21no—
499C8—21no—
500C2×C3—44no—
501C2×C3—44no—
502C2×C3#555414yes—
503C2×C3#574814yes—
504C2×C3#575314yes—
505D3—128no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—182no—
513C22—361no—
514C22—361no—
515C22C22×C4⋊(C3⋊D3)11yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—361no—
521C4—361no—
522C4—361no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#6436111yescharacteristic
528C4#41×C3⋊D311yescharacteristic
529C3#7950414yescomplemented
530C2—41no—
531C2—41no—
532C2—362no—
533C2#1059602511yescharacteristic
534C2#1059621911yescharacteristic
535C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#435C2
socleC22×C32C22×D4
prime radical#10596022C2
hypercenter#435C3⋊D3
hypocenterC32#3315
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #10596012C2semidirect
3. C32×#435C2semidirect
4. #10592836C2semidirect
5. #10592832C2semidirect
6. #10592815C2semidirect
7. #10592812C2semidirect
8. #10592548C2semidirect
9. #10592546C2semidirect
10. #10592432C2semidirect
11. #10592432C2semidirect
12. #10592422C2semidirect
13. #10592421C2semidirect
14. #10592409C2semidirect
15. #10592402C2semidirect
62. C3×#435D3semidirect
221. #435C3⋊D3semidirect
461. C32#3315semidirect
529. C3#79504semidirect

Maximal subgroups

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

subgroupindex
#105960222
#105960122
C32×#4352
#105928362
#105928322
#105928152
#105928122
#105925482
#105925462
#105924322
#105924222
#105924212
#105924092
#105924022
#795043