Finite Group Databasebeta

← #11895832

Subgroups — #11895832

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2#10596039C211yesmaximal, characteristic, complemented
3C32×#477C211yesmaximal, characteristic, complemented
4#10592788C211yesmaximal, characteristic, complemented
5#10592725C211yesmaximal, characteristic, complemented
6#10592589C211yesmaximal, characteristic, complemented
7#10592588C211yesmaximal, characteristic, complemented
8#10592574C211yesmaximal, characteristic, complemented
9#10592571C211yesmaximal, characteristic
10#10592543C211yesmaximal, characteristic
11#10592527C211yesmaximal, characteristic, complemented
12#10592518C211yesmaximal, characteristic
13#10592517C211yesmaximal, characteristic, complemented
14#10592493C211yesmaximal, characteristic, complemented
15#10592491C211yesmaximal, characteristic, complemented
16#81100—34nomaximal
17C2×Q8×C3⋊D3—21no—
18C32×C4⋊Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64156C2211yescharacteristic
21#64155—21no—
22#64153C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3745C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26#64107—21no—
27#64105—21no—
28#64105—21no—
29#64105—21no—
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64102C2211yescharacteristic
33#64097C2211yescharacteristic
34#64097C2211yescharacteristic
35#64096C2211yescharacteristic
36#64085—21no—
37#64084C2211yescharacteristic
38C4×C4⋊(C3⋊D3)C2211yescharacteristic
39#64081—21no—
40C4×#634C2211yescharacteristic
41C32×#107C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46#63662C2211yescharacteristic
47#63648C2211yescharacteristic
48#63643C2211yescharacteristic
49#63642C2211yescharacteristic
50#63641C2211yescharacteristic
51#63641C2211yescharacteristic
52C8×C3⋊Dic3C2211yescharacteristic
53#63637C2211yescharacteristic
54#63637C2211yescharacteristic
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63634C2211yescharacteristic
59#63630C2211yescharacteristic
60#5727—34no—
61#5568—34no—
62C3×#477D314yescomplemented
63#5089—34no—
64#5026—34no—
65#4890—34no—
66#4889—34no—
67#4875—34no—
68#4872—34no—
69#4844—34no—
70#4828—34no—
71#4819—34no—
72#4818—34no—
73#4794—34no—
74#4792—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8C2311yescharacteristic
77Q8×C3⋊D3—44no—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4×C3⋊D3—21no—
81C2×C4×C3⋊D3—21no—
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×#634—21no—
85C2×#634—21no—
86C2×#634D411yescharacteristic
87C2×#634C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C42—21no—
96C32×C42C2311yescharacteristic
97#3755—22no—
98#3752—21no—
99#3752—21no—
100#3752—21no—
101#3752—21no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)D411yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750D411yescharacteristic
114#3750D411yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3745—22no—
121#3744—22no—
122#3367—91noSylow
123C2×D3×Q8—64no—
124C3×C4⋊Q8C2×D314yes—
125C3×C4×Q8C2×D314yes—
126#947—34no—
127#946—64no—
128#944—34no—
129C2×#215—34no—
130C2×D24—34no—
131C2×#204—34no—
132#898—64no—
133#896—64no—
134#896—64no—
135#896—64no—
136#893—34no—
137#893—34no—
138#893—34no—
139#888—34no—
140#888—34no—
141#887—34no—
142#876—64no—
143#875—34no—
144C4×D12—34no—
145#872—64no—
146C4×Dic6—34no—
147C3×#107C2×D314yes—
148C3×#107C2×D314yes—
149C3×C4⋊C8C2×D314yes—
150C3×#103C2×D314yes—
151C3×#103C2×D314yes—
152#835—34no—
153#821—34no—
154#816—34no—
155#815—34no—
156Dic3⋊C8—34no—
157Dic3⋊C8—34no—
158C8×Dic3—34no—
159#810—34no—
160#810—34no—
161#809—34no—
162#809—34no—
163#809—34no—
164#807—34no—
165#803—34no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C32×Q8—21no—
169C32×Q8—21no—
170C32×Q8—42no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)#4112yes—
188C4×C3⋊D3—42no—
189C4×C3⋊D3—42no—
190C4×C3⋊D3—42no—
191C4×C3⋊D3—42no—
192#634—22no—
193#634—21no—
194#634—21no—
195#634—42no—
196#634—42no—
197C32×C8—21no—
198C32×C8—21no—
199C3⋊(C3⋊C8)—21no—
200C3⋊(C3⋊C8)—21no—
201#556—91no—
202D4×Q8—91no—
203#489—91no—
204#489—91no—
205#487—91no—
206#477—91no—
207#477C3⋊D311yescharacteristic, complemented
208#474—91no—
209#463—91no—
210#463—91no—
211#461—91no—
212#446—91no—
213#440—91no—
214#440—91no—
215C4×D8—91no—
216C2×C3×Q8—24no—
217C2×C3×Q8C22×D314yes—
218D3×Q8—1216no—
219C2×D12—34no—
220C2×D12—34no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×Dic6—34no—
226C2×Dic6—34no—
227C2×Dic6—64no—
228C2×Dic6—64no—
229C2×C3×C8C22×D314yes—
230C2×C3×C8C22×D314yes—
231C3×C4⋊C4—24no—
232C3×C4⋊C4—24no—
233C3×C4⋊C4C22×D314yes—
234C3×C4⋊C4C22×D314yes—
235C3×C4⋊C4C22×D314yes—
236C3×C42—24no—
237C3×C42C22×D314yes—
238#215—68no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—34no—
248C4⋊Dic3—34no—
249Dic3⋊C4—34no—
250Dic3⋊C4—34no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256C4×Dic3—34no—
257C4×Dic3—34no—
258C4×Dic3—64no—
259C2×C3⋊C8—34no—
260C2×C3⋊C8—34no—
261D24—68no—
262#204—68no—
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—22no—
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—41no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—41no—
273C32×C4—41no—
274C32×C4—41no—
275C32×C4—41no—
276C32×C4C2×#4111yescharacteristic
277C32×C42−1+411yescharacteristic
278C3⋊Dic3—21no—
279C3⋊Dic3—21no—
280C3⋊Dic3—21no—
281C3⋊Dic3—41no—
282C3⋊Dic3—41no—
283C3⋊Dic3AGL(1,ℤ/8)12yes—
284C22×Q8—181no—
285C2×SD16—91no—
286C2×SD16—91no—
287C2×D8—91no—
288C4⋊Q8—91no—
289C4⋊Q8—91no—
290C4⋊Q8—91no—
291C4⋊Q8C2×C3⋊D311yescharacteristic
292#126—181no—
293#126—181no—
294#124—91no—
295#124—91no—
296C22⋊Q8—181no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C22⋊Q8—181no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8C2×C3⋊D311yescharacteristic
303C4×D4—91no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—91no—
307#117—181no—
308#107—91no—
309#107C2×C3⋊D311yescharacteristic
310#107C2×C3⋊D311yescharacteristic
311C4⋊C8—91no—
312C4⋊C8—91no—
313C4⋊C8C2×C3⋊D311yescharacteristic
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103C2×C3⋊D311yescharacteristic
319#103C2×C3⋊D311yescharacteristic
320#102—91no—
321#102—91no—
322#102—91no—
323#102—91no—
324#97—91no—
325#97—91no—
326C4×C8—91no—
327C22×D3—64no—
328C22×D3—64no—
329C3×Q8—24no—
330C3×Q8—24no—
331C3×Q8—48no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4D3×D414yes—
337C2×C3×C4D3×D414yes—
338C2×C3×C4C23×D314yes—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345D12—38no—
346D12—64no—
347D12—64no—
348D12—64no—
349C4×D3—128no—
350C4×D3—128no—
351C4×D3—128no—
352C4×D3—128no—
353Dic6—68no—
354Dic6—64no—
355Dic6—64no—
356Dic6—128no—
357Dic6—128no—
358C3×C8—24no—
359C3×C8—24no—
360C3⋊C8—64no—
361C3⋊C8—64no—
362C2×C32#54811yescharacteristic
363C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
364C2×C32#57811yescharacteristic
365C3⋊D3—42no—
366C3⋊D3—81no—
367C2×Q8—21no—
368C2×Q8—91no—
369C2×Q8—91no—
370C2×Q8—181no—
371C2×Q8—181no—
372C2×Q8—364no—
373C2×Q8C22×C3⋊D311yescharacteristic
374C2×D4—91no—
375C2×D4—91no—
376C22×C4—181no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4—181no—
380SD16—182no—
381SD16—182no—
382D8—182no—
383C2×C8—91no—
384C2×C8—91no—
385C2×C8C22×C3⋊D311yescharacteristic
386C2×C8C22×C3⋊D311yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—91no—
390C4⋊C4—91no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4C22×C3⋊D311yescharacteristic
399C4⋊C4C22×C3⋊D311yescharacteristic
400C4⋊C4C22×C3⋊D311yescharacteristic
401C22⋊C4—181no—
402C22⋊C4—181no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C42—21no—
410C42—91no—
411C42—91no—
412C42—181no—
413C42C22×C3⋊D311yescharacteristic
414C22×C3C2×D3×D414yes—
415C2×D3—68no—
416C2×D3—124no—
417C2×D3—124no—
418C2×D3—124no—
419C2×D3—124no—
420C2×D3—124no—
421C3×C4—24no—
422C3×C4—24no—
423C3×C4—44no—
424C3×C4—44no—
425C3×C4—44no—
426C3×C4—44no—
427C3×C4#100714yes—
428C3×C4D3×#4114yes—
429Dic3—38no—
430Dic3—64no—
431Dic3—64no—
432Dic3—64no—
433Dic3—124no—
434Dic3—124no—
435C32#336711yescharacteristic, complemented, Sylow
436C23—181no—
437C23—181no—
438Q8—21no—
439Q8—21no—
440Q8—42no—
441Q8—182no—
442Q8—181no—
443Q8—181no—
444Q8—362no—
445Q8—362no—
446D4—92no—
447D4—181no—
448D4—181no—
449D4—181no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—91no—
455C2×C4—91no—
456C2×C4—91no—
457C2×C4—91no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—362no—
461C2×C4—362no—
462C2×C4—362no—
463C2×C4—362no—
464C2×C4D4×C3⋊D311yescharacteristic
465C2×C4D4×C3⋊D311yescharacteristic
466C2×C4C23×C3⋊D311yescharacteristic
467C8—21no—
468C8—21no—
469C8—181no—
470C8—181no—
471C2×C3#563314yes—
472C2×C3#576614yes—
473C2×C3D3×AGL(1,ℤ/8)14yes—
474D3—128no—
475D3—244no—
476C22—182no—
477C22—361no—
478C22—361no—
479C22—361no—
480C22—361no—
481C22—361no—
482C22C2×D4×C3⋊D311yescharacteristic
483C4—21no—
484C4—21no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—92no—
490C4—181no—
491C4—181no—
492C4—181no—
493C4—361no—
494C4—361no—
495C4#6436411yescharacteristic
496C4#41×C3⋊D311yescharacteristic
497C3#8110014yescomplemented
498C2—362no—
499C2—721no—
500C2#1059610411yescharacteristic
501C2#1059623711yescharacteristic
502C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenter#477C3⋊D3
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #10596198C2semidirect
2. #10596039C2semidirect
3. C32×#477C2semidirect
4. #10592788C2semidirect
5. #10592725C2semidirect
6. #10592589C2semidirect
7. #10592588C2semidirect
8. #10592574C2semidirect
11. #10592527C2semidirect
13. #10592517C2semidirect
14. #10592493C2semidirect
15. #10592491C2semidirect
62. C3×#477D3semidirect
207. #477C3⋊D3semidirect
435. C32#3367semidirect
497. C3#81100semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105960392
C32×#4772
#105927882
#105927252
#105925892
#105925882
#105925742
#105925712
#105925432
#105925272
#105925182
#105925172
#105924932
#105924912
#811003