Finite Group Databasebeta

← #11860578

Subgroups — #11860578

Order 1152.

1410 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic
3#10595994C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5#10592729C212yesmaximal, complemented
6C4×#3756C212yesmaximal, complemented
7#10592725C212yesmaximal, complemented
8C4×#3755C212yesmaximal, complemented
9#10592701C211yesmaximal, characteristic
10#10592696C211yesmaximal, characteristic, complemented
11#10592694C211yesmaximal, characteristic, complemented
12#82547—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C32×C4×Q8—21no—
16C32×C4×Q8—21no—
17C32×C4×Q8C2212yes—
18C32×C4×Q8C2212yes—
19C32×#117—22no—
20C32×#117C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C2×#3756C2212yes—
23#64151C418yescomplemented
24C2×#3755C2212yes—
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3748C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28#64101—21no—
29C4⋊C4×C3⋊D3—21no—
30#64090—22no—
31C4×C4⋊(C3⋊D3)C2212yes—
32C4×#634C2212yes—
33#63662C2212yes—
34#63662C2212yes—
35#63637C2211yescharacteristic
36#63637C2211yescharacteristic
37#63636C2211yescharacteristic
38#63636C2211yescharacteristic
39#63635C2212yes—
40#63634C2212yes—
41#63630C2212yes—
42C4×C3⋊(C3⋊C8)C2212yes—
43C3×#519D314yescomplemented
44C2×#942—34no—
45#5523—34no—
46C2×#835—34no—
47#5030—38no—
48C4×#216—38no—
49#5026—38no—
50C4×#215—38no—
51#5002—34no—
52#4997—34no—
53#4995—34no—
54C2×C32×Q8—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8C2×C414yescomplemented
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61C22×C3⋊Dic3—21no—
62#3828—22no—
63#3828C2×C414yes—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—22no—
67C2×#634C2311yescharacteristic
68C32×C4⋊C4—22no—
69C32×C4⋊C4—22no—
70C32×C4⋊C4D411yescharacteristic
71C32×C4⋊C4D411yescharacteristic
72C32×C4⋊C4C2311yescharacteristic
73C32×C4⋊C4C2311yescharacteristic
74C32×C22⋊C4—21no—
75C32×C22⋊C4D412yes—
76C32×C42—22no—
77C32×C42—22no—
78C32×C42—21no—
79C32×C42C2312yes—
80#3756C2×C418yescomplemented
81#3755C2×C418yescomplemented
82#3752—22no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—22no—
86C4×C3⋊Dic3—22no—
87#3748C2×C414yescomplemented
88C2×C3⋊(C3⋊C8)—22no—
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2312yes—
92#2947—91noSylow
93C22×C3×Q8C2×D314yes—
94C2×#235—34no—
95C3×C4×Q8—24no—
96C3×C4×Q8—24no—
97C3×C4×Q8C2×D318yes—
98C3×C4×Q8C2×D318yes—
99C3×#117—28no—
100C3×#117C2×D314yes—
101C3×#117C2×D314yes—
102C2×#216—38no—
103#942—332no—
104C2×#215—38no—
105C2×C4⋊Dic3—34no—
106C2×#208—34no—
107C22×C3⋊C8—34no—
108#892—64no—
109D3×C4⋊C4—64no—
110#67⋊C4—68no—
111C4×D12—38no—
112C4×Dic6—38no—
113#835—38no—
114#835—38no—
115#810—34no—
116#810—34no—
117#809—34no—
118#809—34no—
119#808—38no—
120#807—38no—
121#803—38no—
122C4×C3⋊C8—38no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—21no—
125C32×Q8—24no—
126C32×Q8—22no—
127C32×Q8C22×C414yes—
128C2×C32×C4—24no—
129C2×C32×C4—22no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4C2411yescharacteristic
138#638—24no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—81no—
142C4⋊(C3⋊D3)—21no—
143C4⋊(C3⋊D3)C22×C412yes—
144C4×C3⋊D3—24no—
145C4×C3⋊D3—82no—
146#634—21no—
147#634C22×C412yes—
148C3⋊(C3⋊C8)—21no—
149C3⋊(C3⋊C8)—21no—
150C3⋊(C3⋊C8)C22×C414yes—
151C2×#137—91no—
152#520—91no—
153#519C3⋊D311yescharacteristic, complemented
154#441—92no—
155#440—92no—
156C4×Q16—92no—
157C4×SD16—92no—
158#428—91no—
159#416—91no—
160C2×#103—91no—
161#405—91no—
162C2×C3×Q8—28no—
163C2×C3×Q8—24no—
164C2×C3×Q8C4×D3116yescomplemented
165C2×C3×Q8C22×D318yes—
166C22×C3×C4—24no—
167C22×C3×C4C22×D314yes—
168C2×#67—64no—
169C22×Dic3—64no—
170#235—316no—
171#235—68no—
172C2×D12—34no—
173C2×C4×D3—64no—
174C2×C4×D3—68no—
175C2×Dic6—34no—
176C3×C4⋊C4—28no—
177C3×C4⋊C4—28no—
178C3×C4⋊C4#6714yes—
179C3×C4⋊C4#6714yes—
180C3×C4⋊C4C22×D314yes—
181C3×C4⋊C4C22×D314yes—
182C3×C22⋊C4—24no—
183C3×C22⋊C4#6718yes—
184C3×C42—28no—
185C3×C42—28no—
186C3×C42—24no—
187C3×C42C22×D318yes—
188#216—332no—
189#215—332no—
190(C2×D3)⋊C4—68no—
191C4⋊Dic3—38no—
192C4⋊Dic3—64no—
193Dic3⋊C4—68no—
194C4×Dic3—68no—
195#208—316no—
196C2×C3⋊C8—38no—
197C2×C3⋊C8—34no—
198C2×C3⋊C8—34no—
199C2×C3⋊C8—68no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32C4×D412yes—
203C22×C32C22×D411yescharacteristic
204C2×C3⋊D3—22no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C32×C4—24no—
208C32×C4—22no—
209C32×C4—22no—
210C32×C4—41no—
211C32×C4—41no—
212C32×C4C4×D412yes—
213C32×C4C23×C411yescharacteristic
214C32×C4C2×#4111yescharacteristic
215C3⋊Dic3—22no—
216C3⋊Dic3—42no—
217C2×#41—91no—
218C22×Q8C2×C3⋊D311yescharacteristic
219#137—98no—
220C2×Q16—92no—
221C2×SD16—92no—
222C2×M16—91no—
223C22×C8—91no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—92no—
227C4×Q8C2×C3⋊D312yes—
228C4×Q8C2×C3⋊D312yes—
229C4×D4—92no—
230C4×D4—182no—
231#117—22no—
232#117—181no—
233#117C2×C3⋊D311yescharacteristic
234#117C2×C3⋊D311yescharacteristic
235C2×C4⋊C4—91no—
236C2×C4⋊C4—181no—
237#107—92no—
238#106—92no—
239#103—92no—
240#103—92no—
241#103—91no—
242#103—91no—
243#102—91no—
244#102—91no—
245#97—92no—
246C4×C8—92no—
247C23×C3C2×#6714yes—
248C22×D3—64no—
249C3×Q8—216no—
250C3×Q8—28no—
251C3×Q8C2×C4×D3116yes—
252C2×C3×C4—216no—
253C2×C3×C4—28no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4C2×C4×D318yes—
257C2×C3×C4#23518yes—
258C2×C3×C4C2×#6718yes—
259C2×C3×C4C2×#6718yes—
260C2×C3×C4C2×#6714yes—
261C2×C3×C4C23×D314yes—
262#67—616no—
263C2×Dic3—64no—
264C2×Dic3—68no—
265C2×Dic3—244no—
266D12—38no—
267D12—64no—
268C4×D3—616no—
269C4×D3—248no—
270Dic6—38no—
271Dic6—64no—
272C3⋊C8—316no—
273C3⋊C8—64no—
274C3⋊C8—64no—
275C2×C32—22no—
276C2×C32C2×C4×D411yescharacteristic
277C2×C32#57711yescharacteristic
278C2×C32#57811yescharacteristic
279C3⋊D3—42no—
280#41—94no—
281#41—182no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—91no—
285C2×Q8C4×C3⋊D314yescomplemented
286C2×Q8C22×C3⋊D312yes—
287C2×D4—91no—
288C2×D4—181no—
289C22×C4—21no—
290C22×C4—181no—
291C22×C4—181no—
292C22×C4—182no—
293C22×C4C22×C3⋊D311yescharacteristic
294Q16—98no—
295SD16—98no—
296M16—94no—
297C2×C8—92no—
298C2×C8—91no—
299C2×C8—91no—
300C2×C8—182no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—92no—
304C4⋊C4—181no—
305C4⋊C4—182no—
306C4⋊C4#63811yescharacteristic
307C4⋊C4#63811yescharacteristic
308C4⋊C4C22×C3⋊D311yescharacteristic
309C4⋊C4C22×C3⋊D311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—182no—
312C22⋊C4#63812yes—
313C42—22no—
314C42—22no—
315C42—21no—
316C42—182no—
317C42C22×C3⋊D312yes—
318C22×C3—24no—
319C22×C3—24no—
320C22×C3C4×#6718yes—
321C22×C3C22×#6714yes—
322C2×D3—68no—
323C2×D3—124no—
324C2×D3—124no—
325C3×C4—216no—
326C3×C4—28no—
327C3×C4—28no—
328C3×C4—44no—
329C3×C4—44no—
330C3×C4C4×#6718yes—
331C3×C4C22×C4×D314yes—
332C3×C4C2×#23514yes—
333Dic3—68no—
334Dic3—128no—
335C32#294711yescharacteristic, complemented, Sylow
336C23—181no—
337C23C2×#63811yescharacteristic
338Q8—22no—
339Q8—24no—
340Q8—92no—
341Q8—181no—
342Q8C2×C4×C3⋊D314yes—
343D4—92no—
344D4—184no—
345D4—181no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—181no—
351C2×C4—184no—
352C2×C4—182no—
353C2×C4—722no—
354C2×C4—721no—
355C2×C4C2×C4×C3⋊D312yes—
356C2×C4#382812yes—
357C2×C4C2×#63812yes—
358C2×C4C2×#63812yes—
359C2×C4C2×#63811yescharacteristic
360C2×C4C23×C3⋊D311yescharacteristic
361C8—94no—
362C8—181no—
363C8—181no—
364C2×C3—28no—
365C2×C3C2×C4×#6714yes—
366C2×C3#583714yes—
367C2×C3#583814yes—
368D3—128no—
369C22—21no—
370C22—21no—
371C22—182no—
372C22—361no—
373C22—361no—
374C22C4×#63812yes—
375C22C22×#63811yescharacteristic
376C4—24no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—182no—
382C4—362no—
383C4C4×#63812yes—
384C4C22×C4×C3⋊D311yescharacteristic
385C4C2×#382811yescharacteristic
386C3#8254714yescomplemented
387C2—22no—
388C2—362no—
389C2C2×C4×#63811yescharacteristic
390C2#1059630811yescharacteristic
391C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#519C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#519C3⋊D3
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
4. C2×#63662C2semidirect
5. #10592729C2semidirect
6. C4×#3756C2semidirect
7. #10592725C2semidirect
8. C4×#3755C2semidirect
10. #10592696C2semidirect
11. #10592694C2semidirect
23. #64151C4semidirect
43. C3×#519D3semidirect
56. C2×C32×Q8C2×C4semidirect
80. #3756C2×C4semidirect
81. #3755C2×C4semidirect
87. #3748C2×C4semidirect
153. #519C3⋊D3semidirect
164. C2×C3×Q8C4×D3semidirect
285. C2×Q8C4×C3⋊D3semidirect
335. C32#2947semidirect
386. C3#82547semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
C2×#641512
#105959942
C2×#636622
#105927292
C4×#37562
#105927252
C4×#37552
#105927012
#105926962
#105926942
#825473