Finite Group Databasebeta

← #11788514

Subgroups — #11788514

Order 1152.

930 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic
3#10592924C211yesmaximal, characteristic, complemented
4#10592705C211yesmaximal, characteristic
5#10592704C211yesmaximal, characteristic
6#10589399C211yesmaximal, characteristic, complemented
7#10589397C211yesmaximal, characteristic, complemented
8#71662—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C32×C4×Q8—22no—
12C32×C4×Q8—22no—
13C32×#117—22no—
14C32×#117C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3756C412yescomplemented
17#64151—22no—
18#64151—22no—
19C2×#3755C412yescomplemented
20#64135C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C2×#3748C2211yescharacteristic
23#63662—22no—
24#63633—22no—
25#63632—22no—
26C3×#519D314yescomplemented
27C2×#942—34no—
28#5225—34no—
29#5006—34no—
30#5005—34no—
31#4533—34no—
32#4531—34no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8C2×C412yes—
37C2×C32×Q8D412yes—
38C2×C32×Q8D412yes—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×#634C2×C411yescharacteristic
49C32×C4⋊C4—24no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4D412yes—
54C32×C42—24no—
55C32×C42—21no—
56C32×C42D412yes—
57#3757—21no—
58#3756—24no—
59#3755—24no—
60C4⋊(C3⋊Dic3)—21no—
61C4×C3⋊Dic3—21no—
62#3748—21no—
63#3748—21no—
64#3748—21no—
65#3748—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)C2×C412yes—
68#1905—91noSylow
69C22×C3×Q8C2×D314yes—
70C2×#235—34no—
71C3×C4×Q8—28no—
72C3×C4×Q8—28no—
73C3×#117—28no—
74C3×#117C2×D314yes—
75C3×#117C2×D314yes—
76C2×#216—38no—
77#942—68no—
78#942—68no—
79C2×#215—38no—
80#926—34no—
81C2×#208—34no—
82C2×#208—34no—
83#835—68no—
84#806—68no—
85#805—68no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—21no—
88C32×Q8—22no—
89C32×Q8—22no—
90C32×Q8—22no—
91C32×Q8C22⋊C414yes—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103#638—41no—
104#638—41no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—41no—
107C4⋊(C3⋊D3)—21no—
108C4⋊(C3⋊D3)—21no—
109C4×C3⋊D3—41no—
110C4×C3⋊D3—41no—
111#634—21no—
112#634—21no—
113C3⋊(C3⋊C8)—22no—
114C3⋊(C3⋊C8)—41no—
115C2×#137—91no—
116#519C3⋊D311yescharacteristic, complemented
117#421—91no—
118#419—91no—
119#410—91no—
120#344—91no—
121H(3,ℤ/4)—91no—
122C2×C3×Q8—24no—
123C2×C3×Q8—24no—
124C2×C3×Q8—24no—
125C2×C3×Q8C4×D318yes—
126C2×C3×Q8D1218yes—
127C2×C3×Q8#6718yes—
128C22×C3×C4—24no—
129C22×C3×C4C22×D314yes—
130C2×#67—64no—
131#235—64no—
132#235—64no—
133#235—64no—
134#235—64no—
135C2×D12—34no—
136C2×C4×D3—64no—
137C2×Dic6—34no—
138C3×C4⋊C4—216no—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—24no—
141C3×C22⋊C4—24no—
142C3×C22⋊C4#6718yes—
143C3×C42—216no—
144C3×C42—24no—
145C3×C42#6718yes—
146#217—64no—
147#216—616no—
148#215—616no—
149C4⋊Dic3—64no—
150C4×Dic3—64no—
151#208—64no—
152#208—64no—
153#208—64no—
154#208—64no—
155C2×C3⋊C8—38no—
156C2×C3⋊C8—64no—
157C22×C32—41no—
158C22×C32C4×D411yescharacteristic
159C22×C32#12011yescharacteristic
160C22×C32#12111yescharacteristic
161C2×C3⋊D3—41no—
162C2×C3⋊D3—81no—
163C32×C4—24no—
164C32×C4—42no—
165C32×C4—42no—
166C32×C4C2×C22⋊C411yescharacteristic
167C32×C4C4×D411yescharacteristic
168C32×C4#12111yescharacteristic
169C32×C4#12311yescharacteristic
170C3⋊Dic3—41no—
171C3⋊Dic3—81no—
172C2×#41—91no—
173C22×Q8C2×C3⋊D311yescharacteristic
174#137—182no—
175#137—182no—
176C2×Q16—92no—
177C2×SD16—92no—
178C2×M16—91no—
179C2×M16—91no—
180C4×Q8—22no—
181C4×Q8—22no—
182#117—22no—
183#117—91no—
184#117C2×C3⋊D311yescharacteristic
185#117C2×C3⋊D311yescharacteristic
186#104—182no—
187#103—182no—
188#99—182no—
189C23×C3C2×#6714yes—
190C22×D3—64no—
191C3×Q8—28no—
192C3×Q8—28no—
193C3×Q8—28no—
194C3×Q8(C2×D3)⋊C4116yes—
195C2×C3×C4—28no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—28no—
199C2×C3×C4—28no—
200C2×C3×C4C2×C4×D314yes—
201C2×C3×C4C2×D1214yes—
202C2×C3×C4#23514yes—
203C2×C3×C4#23514yes—
204C2×C3×C4C2×#6714yes—
205C2×C3×C4C2×#6714yes—
206#67—124no—
207#67—124no—
208C2×Dic3—64no—
209C2×Dic3—124no—
210D12—64no—
211D12—64no—
212C4×D3—124no—
213C4×D3—124no—
214Dic6—64no—
215Dic6—64no—
216C3⋊C8—68no—
217C3⋊C8—124no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32#38611yescharacteristic
222C3⋊D3—81no—
223#41—181no—
224#41—181no—
225#41—181no—
226#41—181no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—91no—
231C2×Q8C4×C3⋊D312yes—
232C2×Q8C4⋊(C3⋊D3)12yes—
233C2×Q8#63812yes—
234C2×D4—91no—
235C2×D4—181no—
236C22×C4—21no—
237C22×C4—181no—
238C22×C4C22×C3⋊D311yescharacteristic
239Q16—184no—
240SD16—184no—
241M16—181no—
242M16—181no—
243M16—181no—
244M16—181no—
245C2×C8—92no—
246C2×C8—181no—
247C4⋊C4—24no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—181no—
251C22⋊C4—21no—
252C22⋊C4—181no—
253C22⋊C4#63812yes—
254C42—24no—
255C42—21no—
256C42—181no—
257C42#63812yes—
258C22×C3—44no—
259C22×C3C4×#6714yes—
260C22×C3#93014yes—
261C22×C3#95314yes—
262C2×D3—124no—
263C2×D3—244no—
264C3×C4—216no—
265C3×C4—48no—
266C3×C4—48no—
267C3×C4C2×(C2×D3)⋊C414yes—
268C3×C4C4×#6714yes—
269C3×C4#92914yes—
270C3×C4#93014yes—
271Dic3—124no—
272Dic3—244no—
273C32#190511yescharacteristic, complemented, Sylow
274C23—181no—
275C23C2×#63811yescharacteristic
276Q8—22no—
277Q8—22no—
278Q8—22no—
279Q8—181no—
280Q8—181no—
281Q8#375214yes—
282D4—181no—
283D4—181no—
284D4—361no—
285D4—361no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—181no—
292C2×C4—361no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4C2×C4×C3⋊D311yescharacteristic
296C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
297C2×C4#382811yescharacteristic
298C2×C4#382811yescharacteristic
299C2×C4C2×#63811yescharacteristic
300C2×C4C2×#63811yescharacteristic
301C8—182no—
302C8—361no—
303C2×C3—24no—
304C2×C3—24no—
305C2×C3—24no—
306C2×C3#521314yes—
307D3—244no—
308C22—41no—
309C22—361no—
310C22—721no—
311C22C4×#63811yescharacteristic
312C22#6413911yescharacteristic
313C22#6416211yescharacteristic
314C4—24no—
315C4—42no—
316C4—42no—
317C4—361no—
318C4—721no—
319C4C2×#375211yescharacteristic
320C4C4×#63811yescharacteristic
321C4#6413811yescharacteristic
322C4#6413911yescharacteristic
323C3#7166214yescomplemented
324C2—21no—
325C2—21no—
326C2—21no—
327C2—721no—
328C2#1059291211yescharacteristic
subgroupG/H
centerC2#10592912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#519C2
socleC2×C32#386
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#519C3⋊D3
hypocenterC32#1905
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
3. #10592924C2semidirect
6. #10589399C2semidirect
7. #10589397C2semidirect
16. C2×#3756C4semidirect
19. C2×#3755C4semidirect
26. C3×#519D3semidirect
116. #519C3⋊D3semidirect
273. C32#1905semidirect
323. C3#71662semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
C2×#641512
#105929242
#105927052
#105927042
#105893992
#105893972
#716623