Finite Group Databasebeta

← #11860485

Subgroups — #11860485

Order 1152.

1518 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic
3#10595992C211yesmaximal, characteristic, complemented
4C32×#416C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic, complemented
6#10592800C211yesmaximal, characteristic, complemented
7#10592694C211yesmaximal, characteristic, complemented
8#10592516C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10#10592484C212yesmaximal, complemented
11#10592455C212yesmaximal, complemented
12#78820—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64158C418yescomplemented
18Q8×C3⋊Dic3C2212yescomplemented
19C2×#3755C2212yes—
20D4×C3⋊Dic3—22no—
21D4×C3⋊Dic3C2212yescomplemented
22C2×#3753C2212yes—
23#64135—21no—
24#64135C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)—21no—
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28#64102C2212yes—
29#64102C2212yes—
30C22⋊C4×C3⋊D3—22no—
31C4×C4⋊(C3⋊D3)—21no—
32C4×C4⋊(C3⋊D3)—21no—
33C32×#103C2211yescharacteristic, complemented
34C32×#103C2211yescharacteristic, complemented
35C32×#102C2211yescharacteristic, complemented
36C32×#102C2211yescharacteristic, complemented
37#63648C2212yes—
38#63648C2212yes—
39#63642C2212yescomplemented
40C8×C3⋊Dic3C2212yescomplemented
41#63635C2212yescomplemented
42#63634C2212yescomplemented
43#5827—34no—
44C2×#949—34no—
45#5521—34no—
46C3×#416D314yescomplemented
47C2×#821—34no—
48#5101—34no—
49#4995—34no—
50#4817—38no—
51#4788—38no—
52#4785—38no—
53#4756—38no—
54C23×C3⋊D3—21no—
55C32×#41—22no—
56C32×#41C2×C414yescomplemented
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3—22no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)C2×C414yescomplemented
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C32×C8—22no—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42—21no—
77#3757—22no—
78#3757D412yes—
79#3755C2×C418yescomplemented
80#3753C2×C418yescomplemented
81#3752—22no—
82#3752—22no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3C2312yes—
90#3748C2×C414yescomplemented
91C2×C3⋊(C3⋊C8)C2312yes—
92#2946—91noSylow
93C2×C3×#41C2×D314yes—
94C22×D12—34no—
95C22×C3×C8C2×D314yes—
96C3×#117C2×D314yes—
97#949—332no—
98Q8×Dic3—38no—
99C2×#215—38no—
100D4×Dic3—38no—
101D4×Dic3—68no—
102C2×#213—38no—
103#926—34no—
104#926—64no—
105C2×C4⋊Dic3—34no—
106C2×C4⋊Dic3—64no—
107C2×#208—34no—
108#893—38no—
109#893—38no—
110D3×C22⋊C4—68no—
111C4×D12—64no—
112C4×D12—64no—
113C3×#103C2×D314yescomplemented
114C3×#103C2×D314yescomplemented
115C3×#102C2×D314yescomplemented
116C3×#102C2×D314yescomplemented
117#821—38no—
118#821—38no—
119#815—38no—
120C8×Dic3—38no—
121#808—38no—
122#807—38no—
123C23×C32—21no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—24no—
127C22×C3⋊D3—81no—
128C22×C3⋊D3—81no—
129C32×Q8—21no—
130C32×Q8C22×C412yes—
131C32×D4—24no—
132C32×D4—21no—
133C32×D4C22×C412yes—
134C2×C32×C4—21no—
135C2×C32×C4—24no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—82no—
144C2×C3⋊Dic3—81no—
145C2×C3⋊Dic3C2×D412yes—
146C2×C3⋊Dic3C2×D412yes—
147C4⋊(C3⋊D3)—24no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)C22×C414yes—
150C4×C3⋊D3—82no—
151C4×C3⋊D3—82no—
152C32×C8—21no—
153C32×C8—21no—
154C3⋊(C3⋊C8)C22×C414yes—
155C2×AGL(1,ℤ/8)—91no—
156#520—91no—
157#518—91no—
158#442—92no—
159#440—92no—
160C4×SD16—92no—
161C4×D8—92no—
162#428—91no—
163#416C3⋊D311yescharacteristic, complemented
164C2×#102—91no—
165#405—91no—
166C23×D3—64no—
167C3×#41—28no—
168C3×#41C4×D3116yescomplemented
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—24no—
171C2×C3×D4C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4C22×D314yes—
174C22×Dic3—68no—
175C22×Dic3—64no—
176C2×D12—316no—
177C2×D12—38no—
178C2×D12—64no—
179C2×D12—68no—
180C2×C4×D3—68no—
181C2×C4×D3—68no—
182C2×C3×C8—28no—
183C2×C3×C8C22×D314yes—
184C2×C3×C8C22×D314yes—
185C3×C4⋊C4C22×D314yes—
186C3×C4⋊C4C22×D314yes—
187C3×C22⋊C4—24no—
188C3×C42—24no—
189#217—38no—
190#217—68no—
191#215—332no—
192#213—332no—
193(C2×D3)⋊C4—68no—
194(C2×D3)⋊C4—68no—
195C4⋊Dic3—34no—
196C4⋊Dic3—34no—
197C4⋊Dic3—38no—
198C4⋊Dic3—68no—
199C4⋊Dic3—64no—
200C4×Dic3—38no—
201C4×Dic3—68no—
202#208—316no—
203C2×C3⋊C8—38no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32—22no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32C4×D412yes—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—24no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3—42no—
214C2×C3⋊D3—84no—
215C32×C4—22no—
216C32×C4—41no—
217C32×C4—41no—
218C32×C4C4×D412yes—
219C32×C4C23×C411yescharacteristic
220C32×C4C2×#4111yescharacteristic
221C3⋊Dic3—22no—
222C3⋊Dic3—22no—
223C3⋊Dic3—42no—
224C2×#41C2×C3⋊D311yescharacteristic
225C22×D4—91no—
226AGL(1,ℤ/8)—98no—
227C2×SD16—92no—
228C2×D8—92no—
229C2×M16—91no—
230C22×C8C2×C3⋊D311yescharacteristic
231C4×Q8—92no—
232C4×D4—92no—
233C4×D4—92no—
234C4×D4—92no—
235C4×D4—181no—
236C4×D4—181no—
237C4×D4—182no—
238#117—91no—
239#117—181no—
240#117C2×C3⋊D311yescharacteristic
241C2×C4⋊C4—91no—
242C2×C4⋊C4—181no—
243C2×C22⋊C4—182no—
244#107—92no—
245#106—92no—
246#103C2×C3⋊D311yescharacteristic, complemented
247#103C2×C3⋊D311yescharacteristic, complemented
248#102—92no—
249#102—92no—
250#102C2×C3⋊D311yescharacteristic, complemented
251#102C2×C3⋊D311yescharacteristic, complemented
252#97—92no—
253C4×C8—92no—
254C23×C3—24no—
255C23×C3D3×D414yes—
256C22×D3—68no—
257C22×D3—616no—
258C22×D3—244no—
259C22×D3—244no—
260C3×Q8—24no—
261C3×Q8C2×C4×D318yes—
262C3×D4—216no—
263C3×D4—24no—
264C3×D4C2×C4×D318yes—
265C2×C3×C4—24no—
266C2×C3×C4—216no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4C2×C4×D318yes—
270C2×C3×C4D3×D414yes—
271C2×C3×C4#23718yes—
272C2×C3×C4C23×D314yes—
273C2×Dic3—38no—
274C2×Dic3—38no—
275C2×Dic3—68no—
276C2×Dic3—248no—
277C2×Dic3—244no—
278D12—316no—
279D12—616no—
280D12—68no—
281C4×D3—248no—
282C4×D3—248no—
283C3×C8—24no—
284C3×C8—24no—
285C3⋊C8—316no—
286C2×C32—22no—
287C2×C32—42no—
288C2×C32C2×C4×D411yescharacteristic
289C2×C32#57611yescharacteristic
290C2×C32#57711yescharacteristic
291C3⋊D3—44no—
292C24—181no—
293#41—22no—
294#41C4×C3⋊D314yescomplemented
295C2×Q8C22×C3⋊D311yescharacteristic
296C2×D4—21no—
297C2×D4—92no—
298C2×D4—94no—
299C2×D4—181no—
300C2×D4—182no—
301C2×D4C22×C3⋊D311yescharacteristic
302C22×C4—21no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4—182no—
306C22×C4—181no—
307C22×C4C22×C3⋊D311yescharacteristic
308SD16—98no—
309D8—98no—
310M16—94no—
311C2×C8—22no—
312C2×C8—92no—
313C2×C8C22×C3⋊D311yescharacteristic
314C2×C8C22×C3⋊D311yescharacteristic
315C4⋊C4—91no—
316C4⋊C4—91no—
317C4⋊C4—92no—
318C4⋊C4—182no—
319C4⋊C4—181no—
320C4⋊C4C22×C3⋊D311yescharacteristic
321C4⋊C4C22×C3⋊D311yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—92no—
324C22⋊C4—182no—
325C22⋊C4—182no—
326C22⋊C4—182no—
327C42—21no—
328C42—92no—
329C42—182no—
330C22×C3—24no—
331C22×C3—24no—
332C22×C3—28no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3#67⋊C418yes—
336C22×C3C2×D3×D414yes—
337C2×D3—616no—
338C2×D3—128no—
339C2×D3—128no—
340C2×D3—2416no—
341C3×C4—28no—
342C3×C4—44no—
343C3×C4—44no—
344C3×C4#67⋊C418yes—
345C3×C4C22×C4×D314yes—
346C3×C4C2×#23714yes—
347Dic3—68no—
348Dic3—68no—
349Dic3—128no—
350C32#294611yescharacteristic, complemented, Sylow
351C23—21no—
352C23—182no—
353C23—184no—
354C23—721no—
355C23—721no—
356C23D4×C3⋊D311yescharacteristic
357Q8—21no—
358Q8C2×C4×C3⋊D312yes—
359D4—24no—
360D4—21no—
361D4—94no—
362D4—184no—
363D4—182no—
364D4C2×C4×C3⋊D312yes—
365C2×C4—21no—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—92no—
370C2×C4—92no—
371C2×C4—182no—
372C2×C4—722no—
373C2×C4—722no—
374C2×C4—722no—
375C2×C4—721no—
376C2×C4C2×C4×C3⋊D312yes—
377C2×C4D4×C3⋊D311yescharacteristic
378C2×C4#383012yes—
379C2×C4C23×C3⋊D311yescharacteristic
380C8—21no—
381C8—21no—
382C8—94no—
383C2×C3—28no—
384C2×C3—48no—
385C2×C3C2×#67⋊C414yes—
386C2×C3#576914yes—
387C2×C3#577014yes—
388D3—1216no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—184no—
395C22—362no—
396C22—362no—
397C22—724no—
398C22#6409012yes—
399C22C2×D4×C3⋊D311yescharacteristic
400C4—22no—
401C4—41no—
402C4—41no—
403C4—182no—
404C4—182no—
405C4—362no—
406C4#6409012yes—
407C4C22×C4×C3⋊D311yescharacteristic
408C4C2×#383011yescharacteristic
409C3#7882014yescomplemented
410C2—22no—
411C2—42no—
412C2—364no—
413C2C2×#6409011yescharacteristic
414C2#1059624011yescharacteristic
415C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radicalC2×#64158C2
cosocleC2×C32×C4C24
hypercenter#416C3⋊D3
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #10596298C2semidirect
3. #10595992C2semidirect
4. C32×#416C2semidirect
5. C2×#63648C2semidirect
6. #10592800C2semidirect
7. #10592694C2semidirect
8. #10592516C2semidirect
9. #10592487C2semidirect
10. #10592484C2semidirect
11. #10592455C2semidirect
17. #64158C4semidirect
18. Q8×C3⋊Dic3C22semidirect
21. D4×C3⋊Dic3C22semidirect
33. C32×#103C22semidirect
34. C32×#103C22semidirect
35. C32×#102C22semidirect
36. C32×#102C22semidirect
39. #63642C22semidirect
40. C8×C3⋊Dic3C22semidirect
41. #63635C22semidirect
42. #63634C22semidirect
46. C3×#416D3semidirect
56. C32×#41C2×C4semidirect
66. C2×C4⋊(C3⋊D3)C2×C4semidirect
79. #3755C2×C4semidirect
80. #3753C2×C4semidirect
90. #3748C2×C4semidirect
113. C3×#103C2×D3semidirect
114. C3×#103C2×D3semidirect
115. C3×#102C2×D3semidirect
116. C3×#102C2×D3semidirect
163. #416C3⋊D3semidirect
168. C3×#41C4×D3semidirect
246. #103C2×C3⋊D3semidirect
247. #103C2×C3⋊D3semidirect
250. #102C2×C3⋊D3semidirect
251. #102C2×C3⋊D3semidirect
294. #41C4×C3⋊D3semidirect
350. C32#2946semidirect
409. C3#78820semidirect

Maximal subgroups

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

subgroupindex
#105962982
C2×#641582
#105959922
C32×#4162
C2×#636482
#105928002
#105926942
#105925162
#105924872
#105924842
#105924552
#788203