Finite Group Databasebeta

← #11889478

Subgroups — #11889478

Order 1152.

1140 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#10596288C211yesmaximal, characteristic
2#10596112C211yesmaximal, characteristic, complemented
3C32×#451C211yesmaximal, characteristic, complemented
4#10592924C211yesmaximal, characteristic, complemented
5#10592887C211yesmaximal, characteristic, complemented
6#10592886C211yesmaximal, characteristic, complemented
7#10592884C211yesmaximal, characteristic, complemented
8#10592883C211yesmaximal, characteristic, complemented
9#10592748C211yesmaximal, characteristic, complemented
10#10592514C211yesmaximal, characteristic, complemented
11#10592503C211yesmaximal, characteristic, complemented
12#10592493C211yesmaximal, characteristic, complemented
13#10592492C211yesmaximal, characteristic, complemented
14#10592436C211yesmaximal, characteristic, complemented
15#10592427C211yesmaximal, characteristic, complemented
16#80197—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C2×#3832C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22#64156—21no—
23#64156C2211yescharacteristic
24#64155—21no—
25#64155C2211yescharacteristic
26#64155C2211yescharacteristic
27Q8×C3⋊Dic3C2211yescharacteristic
28Q8×C3⋊Dic3C2211yescharacteristic
29C2×#3755C2211yescharacteristic
30#64139—21no—
31#64139C2211yescharacteristic
32C4×#638—21no—
33C4×#638C2211yescharacteristic
34#64135C2211yescharacteristic
35C2×#3748C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37#64107—21no—
38#64101C2211yescharacteristic
39#64097C2211yescharacteristic
40#64096—21no—
41#64094—21no—
42#64088—21no—
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63662C2211yescharacteristic
50#63662C2211yescharacteristic
51#63648C2211yescharacteristic
52#63648C2211yescharacteristic
53#63647C2211yescharacteristic
54#63645C2211yescharacteristic
55#63644C2211yescharacteristic
56#63642C2211yescharacteristic
57#63641C2211yescharacteristic
58#63636C2211yescharacteristic
59#63634C2211yescharacteristic
60#5817—34no—
61#5641—34no—
62C3×#451D314yescomplemented
63#5225—34no—
64#5188—34no—
65#5187—34no—
66#5185—34no—
67#5184—34no—
68#5049—34no—
69#4815—34no—
70#4804—34no—
71#4794—34no—
72#4793—34no—
73#4737—34no—
74#4728—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8—22no—
77C2×C32×Q8—41no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638D411yescharacteristic
85#3832—22no—
86#3832—41no—
87C2×C4⋊(C3⋊D3)—21no—
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634—21no—
92C32×Q16—22no—
93C32×Q16—41no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C22⋊C4—21no—
99#3757—21no—
100#3757D411yescharacteristic
101#3755—41no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752D411yescharacteristic
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123#3748—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3313—91noSylow
128C22×C3×Q8C2×D314yes—
129C2×#239—34no—
130C2×C3×Q16C2×D314yes—
131C2×C3×Q16C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133#947—34no—
134#947—64no—
135#946—34no—
136#946—34no—
137#946—64no—
138Q8×Dic3—34no—
139Q8×Dic3—34no—
140C2×#215—34no—
141#930—34no—
142#930—64no—
143C4×#67—34no—
144C4×#67—64no—
145#926—34no—
146C2×#208—34no—
147C2×D3×C8—34no—
148#898—64no—
149#892—34no—
150#888—34no—
151#887—64no—
152#885—64no—
153#879—64no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×C22⋊C8C2×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#818—34no—
166#817—34no—
167#815—34no—
168Dic3⋊C8—34no—
169#809—34no—
170#807—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3—21no—
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C32×Q8—21no—
179C32×Q8—42no—
180C32×Q8#4112yes—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—42no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190#638—41no—
191#638—42no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)—42no—
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—42no—
204#634—42no—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#556—91no—
210#548—91no—
211#489—91no—
212#485—91no—
213#482—91no—
214#477—91no—
215#468—91no—
216#467—91no—
217#464—91no—
218#452—91no—
219#451C3⋊D311yescharacteristic, complemented
220#441—91no—
221#435—91no—
222#419—91no—
223#416—91no—
224C2×C3×Q8—24no—
225C2×C3×Q8—28no—
226C2×C3×Q8—44no—
227C2×C3×Q8C22×D314yes—
228C2×C3×Q8C22×D314yes—
229C2×C3×Q8C22×D314yes—
230C22×C3×C4—24no—
231C22×C3×C4C22×D314yes—
232C2×#67—34no—
233C2×#67—64no—
234#239—68no—
235#239—124no—
236C2×D12—34no—
237C2×D12—64no—
238C2×C4×D3—34no—
239C2×C4×D3—64no—
240C2×Dic6—64no—
241C3×Q16—28no—
242C3×Q16—44no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4C22×D314yes—
247C3×C22⋊C4—24no—
248#217—34no—
249#217—64no—
250#215—124no—
251(C2×D3)⋊C4—34no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263Dic3⋊C4—34no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—34no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272#208—124no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275D3×C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—21no—
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C2×#4111yescharacteristic
292C32×C4H(5,𝔽2)11yescharacteristic
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C22×Q8C2×C3⋊D311yescharacteristic
301C2×Q16C2×C3⋊D311yescharacteristic
302C2×Q16C2×C3⋊D311yescharacteristic
303C2×SD16—91no—
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8—91no—
307#126—181no—
308#126—181no—
309#124—91no—
310#124—181no—
311#124—181no—
312C22⋊Q8—91no—
313C22⋊Q8—91no—
314C22⋊Q8—181no—
315C22⋊Q8C2×C3⋊D311yescharacteristic
316#121—91no—
317#121—181no—
318C4×Q8—91no—
319C4×Q8—91no—
320C4×Q8—181no—
321C4×D4—91no—
322C4×D4—181no—
323#117—91no—
324#117—91no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
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⋊C8C2×C3⋊D311yescharacteristic
341#97—91no—
342C23×C3D3×D414yes—
343C22×D3—34no—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—24no—
349C3×Q8—24no—
350C3×Q8—48no—
351C3×Q8#23718yes—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—48no—
359C2×C3×C4D3×D414yes—
360C2×C3×C4C23×D314yes—
361#67—124no—
362#67—128no—
363C2×Dic3—34no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369D12—64no—
370D12—64no—
371D12—128no—
372C4×D3—64no—
373C4×D3—64no—
374C4×D3—128no—
375Dic6—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—41no—
381C2×C32#54611yescharacteristic
382C2×C32#57511yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—41no—
385C3⋊D3—81no—
386#41—182no—
387#41—361no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—41no—
391C2×Q8—181no—
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×Q8C22×C3⋊D311yescharacteristic
395C2×D4—91no—
396C2×D4—91no—
397C2×D4—181no—
398C2×D4—181no—
399C22×C4—21no—
400C22×C4—91no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—22no—
404Q16—41no—
405SD16—361no—
406M16—361no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
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⋊C4C22×C3⋊D311yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—91no—
425C22⋊C4—91no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C42—91no—
434C42—181no—
435C42—181no—
436C42—181no—
437C42—181no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3C2×D3×D414yes—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—28no—
449C3×C4—24no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4—44no—
453C3×C4C2×#23714yes—
454C3×C4#100414yes—
455Dic3—64no—
456Dic3—64no—
457Dic3—64no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#331311yescharacteristic, complemented, Sylow
462C23—91no—
463C23—181no—
464C23D4×C3⋊D311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—21no—
468Q8—21no—
469Q8—21no—
470Q8—42no—
471Q8—362no—
472Q8#383012yes—
473D4—181no—
474D4—181no—
475D4—362no—
476D4—361no—
477D4—362no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—91no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3—44no—
501C2×C3#559114yes—
502C2×C3#576614yes—
503C2×C3#577714yes—
504D3—124no—
505D3—244no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—181no—
510C22—181no—
511C22—181no—
512C22—361no—
513C22—361no—
514C22—361no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—22no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—181no—
522C4—181no—
523C4—181no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4C2×#383011yescharacteristic
528C4#6436111yescharacteristic
529C3#8019714yescomplemented
530C2—41no—
531C2—361no—
532C2—721no—
533C2#1059606211yescharacteristic
534C2#1059623711yescharacteristic
535C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radical#10596288C2
hypercenter#451C3⋊D3
hypocenterC32#3313
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #10596112C2semidirect
3. C32×#451C2semidirect
4. #10592924C2semidirect
5. #10592887C2semidirect
6. #10592886C2semidirect
7. #10592884C2semidirect
8. #10592883C2semidirect
9. #10592748C2semidirect
10. #10592514C2semidirect
11. #10592503C2semidirect
12. #10592493C2semidirect
13. #10592492C2semidirect
14. #10592436C2semidirect
15. #10592427C2semidirect
62. C3×#451D3semidirect
219. #451C3⋊D3semidirect
461. C32#3313semidirect
529. C3#80197semidirect

Maximal subgroups

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

subgroupindex
#105962882
#105961122
C32×#4512
#105929242
#105928872
#105928862
#105928842
#105928832
#105927482
#105925142
#105925032
#105924932
#105924922
#105924362
#105924272
#801973