Finite Group Databasebeta

← #11897608

Subgroups — #11897608

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×Q82C211yesmaximal, characteristic, complemented
2#10596050C211yesmaximal, characteristic
3#10592786C212yesmaximal
4#10592783C211yesmaximal, characteristic
5#10592780C212yesmaximal, complemented
6#10592777C211yesmaximal, characteristic, complemented
7#10592725C212yesmaximal
8C4×#3755C211yesmaximal, characteristic
9#10592723C211yesmaximal, characteristic, complemented
10#10592721C212yesmaximal, complemented
11#10592720C211yesmaximal, characteristic, complemented
12#83706—34nomaximal
13C32×C4⋊Q8—21no—
14C32×C4⋊Q8—22no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4⋊Q8C2212yes—
17C32×C4×Q8—21no—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×Q8C2212yes—
20C32×C4×Q8C2211yescharacteristic
21#64155—21no—
22C2×#3755C2211yescharacteristic
23#64105—22no—
24C4⋊C4×C3⋊D3—21no—
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2212yes—
27#64079C2212yes—
28#64078C2211yescharacteristic
29#63662C2212yes—
30#63662C2211yescharacteristic
31#63636C2212yes—
32#63636C2211yescharacteristic
33#63635C2211yescharacteristic
34#63635C2212yes—
35#63634C2212yes—
36#63634C2212yes—
37#63634C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40#63630C2212yes—
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42C3×Q82D314yescomplemented
43#5579—34no—
44#5087—38no—
45#5084—34no—
46#5081—38no—
47#5078—34no—
48#5026—38no—
49C4×#215—34no—
50#5024—34no—
51#5022—38no—
52#5021—34no—
53C2×C32×Q8—22no—
54C2×C32×Q8—21no—
55C2×C32×Q8D411yescharacteristic
56C2×C32×Q8C2311yescharacteristic
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—22no—
60C2×#634—21no—
61C32×C4⋊C4—22no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—22no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4D411yescharacteristic
66C32×C4⋊C4D412yes—
67C32×C4⋊C4C2312yes—
68C32×C4⋊C4C2311yescharacteristic
69C32×C42—22no—
70C32×C42—21no—
71C32×C42C2311yescharacteristic
72C32×C42C2312yes—
73#3755Q814yescomplemented
74#3752—21no—
75#3752—22no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2312yes—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—22no—
80#3750—22no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3385—91noSylow
85C3×C4⋊Q8—24no—
86C3×C4⋊Q8—28no—
87C3×C4⋊Q8C2×D314yes—
88C3×C4⋊Q8C2×D318yes—
89C3×C4×Q8—24no—
90C3×C4×Q8C2×D314yes—
91C3×C4×Q8C2×D318yes—
92C3×C4×Q8C2×D314yes—
93#946—64no—
94C2×#215—34no—
95#896—68no—
96D3×C4⋊C4—64no—
97C4×D12—34no—
98C4×D12—38no—
99#870—38no—
100#869—34no—
101#835—38no—
102#835—34no—
103#809—34no—
104#809—38no—
105#808—38no—
106#808—34no—
107#807—38no—
108#807—38no—
109#807—38no—
110C4⋊(C3⋊C8)—34no—
111C4⋊(C3⋊C8)—38no—
112#803—38no—
113C4×C3⋊C8—34no—
114C22×C3⋊D3—21no—
115C32×Q8—22no—
116C32×Q8—21no—
117C32×Q8—81no—
118C32×Q8—82no—
119C32×Q8C2×Q812yes—
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—21no—
123C2×C32×C4C2×D412yes—
124C2×C32×C4C2×D412yes—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—22no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)C2×Q812yes—
132C4×C3⋊D3—42no—
133C4×C3⋊D3—82no—
134#634—81no—
135C3⋊(C3⋊C8)—21no—
136C3⋊(C3⋊C8)—22no—
137C3⋊(C3⋊C8)C2×Q812yes—
138Q82C3⋊D311yescharacteristic, complemented
139#554—91no—
140#501—92no—
141#500—91no—
142#479—92no—
143#477—91no—
144#476—91no—
145#474—92no—
146#446—91no—
147#440—92no—
148C4×SD16—91no—
149C2×C3×Q8—28no—
150C2×C3×Q8—24no—
151C2×C3×Q8#6714yes—
152C2×C3×Q8C22×D314yes—
153C2×D12—34no—
154C2×C4×D3—64no—
155C2×C4×D3—68no—
156C2×Dic6—64no—
157C3×C4⋊C4—28no—
158C3×C4⋊C4—24no—
159C3×C4⋊C4—28no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4#6714yes—
162C3×C4⋊C4#6718yes—
163C3×C4⋊C4C22×D314yes—
164C3×C4⋊C4C22×D318yes—
165C3×C42—28no—
166C3×C42—24no—
167C3×C42C22×D314yes—
168C3×C42C22×D318yes—
169#215—316no—
170(C2×D3)⋊C4—64no—
171(C2×D3)⋊C4—68no—
172C4⋊Dic3—38no—
173C4⋊Dic3—34no—
174C4⋊Dic3—64no—
175Dic3⋊C4—68no—
176Dic3⋊C4—68no—
177C2×C3⋊C8—34no—
178C2×C3⋊C8—34no—
179C2×C3⋊C8—38no—
180C22×C32C22×D411yescharacteristic
181C2×C3⋊D3—22no—
182C2×C3⋊D3—41no—
183C2×C3⋊D3—41no—
184C32×C4—22no—
185C32×C4—22no—
186C32×C4—21no—
187C32×C4—22no—
188C32×C4—42no—
189C32×C4—41no—
190C32×C4#13712yes—
191C32×C4C22×Q811yescharacteristic
192C32×C42−1+411yescharacteristic
193C3⋊Dic3—41no—
194C3⋊Dic3—42no—
195C2×SD16—91no—
196C4⋊Q8—21no—
197C4⋊Q8—22no—
198C4⋊Q8—91no—
199C4⋊Q8C2×C3⋊D312yes—
200C4⋊Q8C2×C3⋊D311yescharacteristic
201#125—92no—
202C22⋊Q8—181no—
203C22⋊Q8—182no—
204C4×Q8—21no—
205C4×Q8C2×C3⋊D311yescharacteristic
206C4×Q8C2×C3⋊D312yes—
207C4×Q8C2×C3⋊D311yescharacteristic
208C4×D4—91no—
209C4×D4—92no—
210C2×C4⋊C4—181no—
211#107—92no—
212#107—92no—
213#107—92no—
214#106—91no—
215#106—92no—
216C4⋊C8—92no—
217C4⋊C8—91no—
218#103—91no—
219#103—92no—
220#102—91no—
221#102—92no—
222#97—92no—
223C4×C8—91no—
224C22×D3—64no—
225C3×Q8—28no—
226C3×Q8—24no—
227C3×Q8—84no—
228C3×Q8—88no—
229C3×Q8D3×Q818yes—
230C2×C3×C4—24no—
231C2×C3×C4—28no—
232C2×C3×C4—24no—
233C2×C3×C4C2×#6718yes—
234C2×C3×C4C2×#6718yes—
235C2×C3×C4C2×#6714yes—
236C2×C3×C4C2×#6714yes—
237C2×C3×C4C23×D314yes—
238C2×Dic3—64no—
239C2×Dic3—68no—
240D12—38no—
241D12—64no—
242C4×D3—128no—
243C4×D3—248no—
244Dic6—244no—
245C3⋊C8—38no—
246C3⋊C8—64no—
247C3⋊C8—68no—
248C2×C32D4×Q811yescharacteristic
249C2×C32C2×#13711yescharacteristic
250C2×C32#57611yescharacteristic
251C3⋊D3—42no—
252C2×Q8—21no—
253C2×Q8—22no—
254C2×Q8—181no—
255C2×Q8#63811yescharacteristic
256C2×Q8C22×C3⋊D311yescharacteristic
257C2×D4—91no—
258C22×C4—181no—
259C22×C4—182no—
260SD16—94no—
261C2×C8—91no—
262C2×C8—91no—
263C2×C8—92no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—91no—
269C4⋊C4—92no—
270C4⋊C4—182no—
271C4⋊C4—181no—
272C4⋊C4—182no—
273C4⋊C4#63811yescharacteristic
274C4⋊C4#63812yes—
275C4⋊C4C22×C3⋊D311yescharacteristic
276C4⋊C4C22×C3⋊D312yes—
277C22⋊C4—181no—
278C22⋊C4—182no—
279C42—22no—
280C42—21no—
281C42C22×C3⋊D311yescharacteristic
282C42C22×C3⋊D312yes—
283C22×C3C22×#6714yes—
284C2×D3—68no—
285C2×D3—124no—
286C2×D3—124no—
287C3×C4—28no—
288C3×C4—28no—
289C3×C4—24no—
290C3×C4—28no—
291C3×C4—48no—
292C3×C4—44no—
293C3×C4#94218yes—
294C3×C4C2×D3×Q814yes—
295C3×C4#100714yes—
296Dic3—124no—
297Dic3—128no—
298C32#338511yescharacteristic, complemented, Sylow
299C23—181no—
300Q8—21no—
301Q8—22no—
302Q8—82no—
303Q8—81no—
304Q8—721no—
305Q8Q8×C3⋊D312yes—
306D4—92no—
307D4—181no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—181no—
312C2×C4—182no—
313C2×C4—362no—
314C2×C4—722no—
315C2×C4C2×#63812yes—
316C2×C4C2×#63811yescharacteristic
317C2×C4C2×#63812yes—
318C2×C4C2×#63811yescharacteristic
319C2×C4C23×C3⋊D311yescharacteristic
320C8—92no—
321C8—181no—
322C8—182no—
323C2×C3C2×#94214yes—
324C2×C3Q8×#6714yes—
325C2×C3#583514yes—
326D3—128no—
327C22—182no—
328C22—361no—
329C22—361no—
330C22C22×#63811yescharacteristic
331C4—22no—
332C4—22no—
333C4—22no—
334C4—21no—
335C4—41no—
336C4—42no—
337C4—361no—
338C4—362no—
339C4#6415112yes—
340C4C2×Q8×C3⋊D311yescharacteristic
341C4#6436411yescharacteristic
342C3#8370614yescomplemented
343C2—362no—
344C2C2×#6415111yescharacteristic
345C2Q8×#63811yescharacteristic
346C2#1059630611yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×Q82C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterQ82C3⋊D3
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
1. C32×Q82C2semidirect
5. #10592780C2semidirect
6. #10592777C2semidirect
9. #10592723C2semidirect
10. #10592721C2semidirect
11. #10592720C2semidirect
42. C3×Q82D3semidirect
73. #3755Q8semidirect
138. Q82C3⋊D3semidirect
298. C32#3385semidirect
342. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C32×Q822
#105960502
#105927862
#105927832
#105927802
#105927772
#105927252
C4×#37552
#105927232
#105927212
#105927202
#837063