Finite Group Databasebeta

← #11895814

Subgroups — #11895814

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#10596142C211yesmaximal, characteristic, complemented
3C32×#489C211yesmaximal, characteristic, complemented
4#10592790C211yesmaximal, characteristic, complemented
5#10592756C211yesmaximal, characteristic
6#10592517C211yesmaximal, characteristic, complemented
7#10592516C211yesmaximal, characteristic, complemented
8#10592492C211yesmaximal, characteristic, complemented
9#10592491C211yesmaximal, characteristic, complemented
10#10592486C211yesmaximal, characteristic
11#10592464C211yesmaximal, characteristic, complemented
12#10592458C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic
14#10592409C211yesmaximal, characteristic, complemented
15#10592400C211yesmaximal, characteristic, complemented
16#81670—34nomaximal
17C2×Q8×C3⋊D3—21no—
18C32×C4⋊Q8C2211yescharacteristic
19C32×#124C2211yescharacteristic
20#64155—21no—
21Q8×C3⋊Dic3C2211yescharacteristic
22#64153C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24#64145C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C2×#3744C2211yescharacteristic
28#64105—21no—
29#64105—21no—
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64097C2211yescharacteristic
33#64097C2211yescharacteristic
34#64088—21no—
35#64088—21no—
36#64087—21no—
37#64086—21no—
38C4×C4⋊(C3⋊D3)C2211yescharacteristic
39C4×#634C2211yescharacteristic
40C4×#634C2211yescharacteristic
41C32×#103C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#97C2211yescharacteristic
46#63662C2211yescharacteristic
47#63659C2211yescharacteristic
48#63648C2211yescharacteristic
49#63645C2211yescharacteristic
50#63643C2211yescharacteristic
51#63642C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54C8×C3⋊Dic3C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63634C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5727—34no—
61#5671—34no—
62C3×#489D314yescomplemented
63#5091—34no—
64#5057—34no—
65#4818—34no—
66#4817—34no—
67#4793—34no—
68#4792—34no—
69#4787—34no—
70#4765—34no—
71#4759—34no—
72#4756—34no—
73#4710—34no—
74#4701—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C22×C3⋊Dic3—21no—
79Q8×C3⋊D3—44no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
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⋊C4C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C22⋊C4—21no—
94C32×C22⋊C4—21no—
95C32×C42C2311yescharacteristic
96#3757—21no—
97#3757—21no—
98#3757—21no—
99#3755—22no—
100#3753—22no—
101#3752—21no—
102#3752—21no—
103#3752—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)D411yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
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⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3744—22no—
122#3367—91noSylow
123C2×D3×Q8—64no—
124C3×C4⋊Q8C2×D314yes—
125C3×#124C2×D314yes—
126#946—64no—
127Q8×Dic3—34no—
128#944—34no—
129C2×#215—34no—
130#936—34no—
131D4×Dic3—34no—
132C2×#213—34no—
133C2×#204—34no—
134#896—64no—
135#896—64no—
136#893—34no—
137#893—34no—
138#888—34no—
139#888—34no—
140#879—64no—
141#879—64no—
142#878—64no—
143#877—64no—
144C4×D12—34no—
145C4×Dic6—34no—
146C4×Dic6—34no—
147C3×#103C2×D314yes—
148C3×#103C2×D314yes—
149C3×#102C2×D314yes—
150C3×#102C2×D314yes—
151C3×#97C2×D314yes—
152#835—34no—
153#832—34no—
154#821—34no—
155#818—34no—
156#816—34no—
157#815—34no—
158Dic3⋊C8—34no—
159Dic3⋊C8—34no—
160C8×Dic3—34no—
161#810—34no—
162#810—34no—
163#807—34no—
164#807—34no—
165C4⋊(C3⋊C8)—34no—
166C23×C32—21no—
167C22×C3⋊D3—21no—
168C32×Q8—21no—
169C32×Q8—21no—
170C32×Q8—42no—
171C32×D4—21no—
172C32×D4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—42no—
183C2×C3⋊Dic3C2×D411yescharacteristic
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)#4112yes—
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#489C3⋊D311yescharacteristic, complemented
205#487—91no—
206#477—91no—
207#477—91no—
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—
218C2×C3×D4C22×D314yes—
219C22×Dic3—64no—
220D3×Q8—1216no—
221C2×D12—34no—
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⋊C4C22×D314yes—
233C3×C4⋊C4C22×D314yes—
234C3×C22⋊C4—24no—
235C3×C22⋊C4—24no—
236C3×C42C22×D314yes—
237#217—64no—
238#217—64no—
239#217—64no—
240#215—68no—
241#213—68no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—34no—
246C4⋊Dic3—34no—
247C4⋊Dic3—34no—
248C4⋊Dic3—64no—
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—
259C4×Dic3—64no—
260C2×C3⋊C8—34no—
261C2×C3⋊C8—34no—
262#204—68no—
263C22×C32—41no—
264C22×C32—41no—
265C22×C32—41no—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—41no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—41no—
273C32×C4—41no—
274C32×C4—41no—
275C32×C4C2×#4111yescharacteristic
276C32×C42−1+411yescharacteristic
277C3⋊Dic3—21no—
278C3⋊Dic3—21no—
279C3⋊Dic3—21no—
280C3⋊Dic3—41no—
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#124C2×C3⋊D311yescharacteristic
296C22⋊Q8—181no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C22⋊Q8—181no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×D4—91no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—91no—
307#117—181no—
308#107—91no—
309#107—91no—
310#107—91no—
311C4⋊C8—91no—
312C4⋊C8—91no—
313C4⋊C8—91no—
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#102C2×C3⋊D311yescharacteristic
323#102C2×C3⋊D311yescharacteristic
324#97—91no—
325#97C2×C3⋊D311yescharacteristic
326C4×C8—91no—
327C23×C3—24no—
328C22×D3—64no—
329C3×Q8—24no—
330C3×Q8—24no—
331C3×Q8—48no—
332C3×D4—24no—
333C3×D4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4D3×D414yes—
338C2×C3×C4D3×D414yes—
339C2×C3×C4C23×D314yes—
340C2×Dic3—34no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—128no—
348D12—38no—
349D12—64no—
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—81no—
363C2×C32#54811yescharacteristic
364C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
365C2×C32#57811yescharacteristic
366C3⋊D3—42no—
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×D4C22×C3⋊D311yescharacteristic
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—91no—
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⋊C4—181no—
399C4⋊C4C22×C3⋊D311yescharacteristic
400C4⋊C4C22×C3⋊D311yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C42—91no—
410C42—91no—
411C42—181no—
412C42—181no—
413C42C22×C3⋊D311yescharacteristic
414C22×C3—44no—
415C22×C3—44no—
416C22×C3—44no—
417C22×C3C2×D3×D414yes—
418C2×D3—68no—
419C2×D3—124no—
420C2×D3—124no—
421C3×C4—24no—
422C3×C4—24no—
423C3×C4—44no—
424C3×C4—44no—
425C3×C4—44no—
426C3×C4D3×#4114yes—
427C3×C4#101014yes—
428Dic3—38no—
429Dic3—64no—
430Dic3—64no—
431Dic3—64no—
432Dic3—124no—
433Dic3—124no—
434Dic3—124no—
435C32#336711yescharacteristic, complemented, Sylow
436C23—21no—
437C23—181no—
438Q8—21no—
439Q8—21no—
440Q8—42no—
441Q8—182no—
442Q8—181no—
443Q8—181no—
444Q8—362no—
445Q8—362no—
446D4—21no—
447D4—21no—
448D4—92no—
449D4—181no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—91no—
454C2×C4—91no—
455C2×C4—91no—
456C2×C4—91no—
457C2×C4—181no—
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—84no—
472C2×C3#567714yes—
473C2×C3D3×AGL(1,ℤ/8)14yes—
474C2×C3#577914yes—
475D3—128no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—182no—
480C22—361no—
481C22—361no—
482C22C2×D4×C3⋊D311yescharacteristic
483C4—21no—
484C4—21no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—92no—
489C4—181no—
490C4—181no—
491C4—181no—
492C4—361no—
493C4—361no—
494C4—361no—
495C4#41×C3⋊D311yescharacteristic
496C4#6436711yescharacteristic
497C3#8167014yescomplemented
498C2—81no—
499C2—362no—
500C2#1059614811yescharacteristic
501C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
502C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#489C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#489C3⋊D3
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #10596198C2semidirect
2. #10596142C2semidirect
3. C32×#489C2semidirect
4. #10592790C2semidirect
6. #10592517C2semidirect
7. #10592516C2semidirect
8. #10592492C2semidirect
9. #10592491C2semidirect
11. #10592464C2semidirect
12. #10592458C2semidirect
14. #10592409C2semidirect
15. #10592400C2semidirect
62. C3×#489D3semidirect
204. #489C3⋊D3semidirect
435. C32#3367semidirect
497. C3#81670semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105961422
C32×#4892
#105927902
#105927562
#105925172
#105925162
#105924922
#105924912
#105924862
#105924642
#105924582
#105924552
#105924092
#105924002
#816703