Finite Group Databasebeta

← #11775113

Subgroups — #11775113

Order 1152.

1002 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 193 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
1#10596262C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic, complemented
3C2×#63658C211yesmaximal, characteristic, complemented
4#10589336C212yesmaximal, complemented
5#10589333C212yesmaximal, complemented
6#69976—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3—21no—
9C2×#3828C411yescharacteristic, complemented
10C2×C32×M16—21no—
11#64162—21no—
12#64139C411yescharacteristic, complemented
13#64139C2211yescharacteristic
14#64138—21no—
15C4×#638—21no—
16C4×#638—21no—
17#64135C411yescharacteristic, complemented
18#64133C411yescharacteristic, complemented
19#64133C2211yescharacteristic
20C32×C22⋊C8—21no—
21C32×C22⋊C8C2212yes—
22#63658—21no—
23#63658C2212yes—
24#5791—34no—
25C3×#407D314yescomplemented
26C2×C3⋊#95—34no—
27#4470—38no—
28#4467—38no—
29C24×C32D411yescharacteristic
30C22×C32×C4—42no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C2×#638—21no—
38C2×#638—21no—
39C2×#638—21no—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—42no—
43C22×C3⋊Dic3—42no—
44#3828—42no—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
46C2×C4×C3⋊D3—21no—
47C2×#634C2×C411yescharacteristic, complemented
48C32×M16—42no—
49C2×C32×C8—22no—
50#3757—21no—
51#3757—21no—
52#3757—21no—
53#3752—21no—
54#3752—21no—
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
56C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
57#3750—21no—
58#3750—21no—
59C4×C3⋊Dic3—21no—
60#1504—91noSylow
61C23×C3×C4C2×D314yes—
62C23×Dic3—64no—
63C2×#235—34no—
64C2×C3×M16—24no—
65#953—64no—
66#930—34no—
67#930—34no—
68#929—64no—
69C4×#67—64no—
70C4×#67—64no—
71#926—34no—
72#924—34no—
73#924—34no—
74C3×C22⋊C8—24no—
75C3×C22⋊C8C2×D318yes—
76C3⋊#95—38no—
77C3⋊#95—64no—
78C23×C32—22no—
79C23×C32—22no—
80C23×C32—21no—
81C23×C32—21no—
82C23×C32C22⋊C411yescharacteristic
83C23×C32C22⋊C411yescharacteristic
84C23×C32C2×D411yescharacteristic
85C22×C3⋊D3—21no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96#638—42no—
97#638—42no—
98#638—41no—
99#638—41no—
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—48no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3—42no—
107C4⋊(C3⋊D3)—41no—
108C4×C3⋊D3—42no—
109#634—41no—
110C32×C8—42no—
111#525—91no—
112#407C3⋊D311yescharacteristic, complemented
113C2×#95—91no—
114#328—92no—
115#327—92no—
116C24×C3D1214yes—
117C22×C3×C4—48no—
118C22×C3×C4C4×D314yes—
119C22×C3×C4C4×D314yes—
120C22×C3×C4D1214yes—
121C22×C3×C4#6714yes—
122C22×C3×C4#6714yes—
123C22×C3×C4C22×D314yes—
124C2×#67—64no—
125C2×#67—64no—
126C2×#67—64no—
127C22×Dic3—616no—
128C22×Dic3—68no—
129C22×Dic3—128no—
130C22×Dic3—128no—
131#235—128no—
132C2×D12—34no—
133C2×C4×D3—64no—
134C2×Dic6—34no—
135C3×M16—48no—
136C2×C3×C8—28no—
137#217—64no—
138#217—64no—
139#217—64no—
140(C2×D3)⋊C4—64no—
141(C2×D3)⋊C4—64no—
142C4⋊Dic3—34no—
143C4⋊Dic3—34no—
144Dic3⋊C4—64no—
145Dic3⋊C4—64no—
146C4×Dic3—64no—
147C22×C32—24no—
148C22×C32—24no—
149C22×C32—21no—
150C22×C32—21no—
151C22×C32—21no—
152C22×C32—21no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32#9912yes—
156C22×C32#10412yes—
157C22×C32C2×C22⋊C411yescharacteristic
158C22×C32AGL(1,ℤ/8)11yescharacteristic
159C22×C32#13711yescharacteristic
160C2×C3⋊D3—41no—
161C2×C3⋊D3—41no—
162C2×C3⋊D3—41no—
163C32×C4—21no—
164C32×C4—21no—
165C32×C4—21no—
166C32×C4—21no—
167C3⋊Dic3—44no—
168C3⋊Dic3—41no—
169C3⋊Dic3—41no—
170C3⋊Dic3—41no—
171C2×#41—91no—
172C23×C4—181no—
173C23×C4C2×C3⋊D311yescharacteristic
174C2×M16—21no—
175#123—181no—
176C22⋊Q8—91no—
177C22⋊Q8—91no—
178#121—91no—
179#121—91no—
180#120—181no—
181C4×D4—181no—
182C4×D4—181no—
183#117—91no—
184C22⋊C8—21no—
185C22⋊C8C2×C3⋊D312yes—
186#95—92no—
187#95—181no—
188C23×C3—28no—
189C23×C3—28no—
190C23×C3—24no—
191C23×C3—24no—
192C23×C3(C2×D3)⋊C414yes—
193C23×C3(C2×D3)⋊C414yes—
194C23×C3C2×D1214yes—
195C22×D3—64no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—44no—
199C2×C3×C4—44no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4(C2×D3)⋊C414yes—
203C2×C3×C4(C2×D3)⋊C414yes—
204C2×C3×C4C2×C4×D314yes—
205C2×C3×C4C2×#6714yes—
206#67—128no—
207#67—128no—
208#67—124no—
209#67—124no—
210C2×Dic3—616no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—1232no—
215C2×Dic3—128no—
216C2×Dic3—128no—
217D12—124no—
218C4×D3—128no—
219Dic6—124no—
220C3×C8—48no—
221C2×C32—21no—
222C2×C32—22no—
223C2×C32—22no—
224C2×C32—21no—
225C2×C32C2×#9911yescharacteristic
226C2×C32#41711yescharacteristic
227C2×C32C2×#10411yescharacteristic
228C3⋊D3—81no—
229C24C4⋊(C3⋊D3)11yescharacteristic
230#41—362no—
231C2×Q8—91no—
232C2×D4—91no—
233C2×D4—181no—
234C2×D4—181no—
235C2×D4—181no—
236C22×C4—42no—
237C22×C4—184no—
238C22×C4—182no—
239C22×C4—181no—
240C22×C4—362no—
241C22×C4—362no—
242C22×C4C4×C3⋊D311yescharacteristic
243C22×C4C4×C3⋊D311yescharacteristic
244C22×C4C4⋊(C3⋊D3)11yescharacteristic
245C22×C4#63811yescharacteristic
246C22×C4#63811yescharacteristic
247C22×C4C22×C3⋊D311yescharacteristic
248M16—42no—
249C2×C8—22no—
250C4⋊C4—91no—
251C4⋊C4—91no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C22⋊C4—181no—
255C22⋊C4—181no—
256C22⋊C4—181no—
257C22⋊C4—181no—
258C22⋊C4—181no—
259C42—181no—
260C22×C3—216no—
261C22×C3—216no—
262C22×C3—24no—
263C22×C3—24no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—24no—
267C22×C3—24no—
268C22×C3#80618yes—
269C22×C3#82518yes—
270C22×C3#90814yes—
271C22×C3#90914yes—
272C22×C3C2×(C2×D3)⋊C414yes—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—124no—
276C3×C4—24no—
277C3×C4—24no—
278C3×C4—24no—
279C3×C4—24no—
280Dic3—1216no—
281Dic3—124no—
282Dic3—124no—
283Dic3—124no—
284C32#150411yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—22no—
288C23—22no—
289C23—181no—
290C23#375211yescharacteristic
291C23#375211yescharacteristic
292C23C2×C4⋊(C3⋊D3)11yescharacteristic
293Q8—361no—
294D4—361no—
295D4—361no—
296D4—361no—
297D4—362no—
298D4—362no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—184no—
306C2×C4—181no—
307C2×C4—181no—
308C2×C4—181no—
309C2×C4—362no—
310C2×C4—368no—
311C2×C4—362no—
312C2×C4—362no—
313C2×C4#375211yescharacteristic
314C2×C4#375211yescharacteristic
315C2×C4C2×C4×C3⋊D311yescharacteristic
316C2×C4C2×#63811yescharacteristic
317C8—42no—
318C2×C3—24no—
319C2×C3—28no—
320C2×C3—28no—
321C2×C3—24no—
322C2×C3C2×#80614yes—
323C2×C3#513314yes—
324C2×C3C2×#82514yes—
325D3—244no—
326C22—24no—
327C22—24no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—361no—
335C22—361no—
336C22—361no—
337C22#6363312yes—
338C22#6365212yes—
339C22#6411711yescharacteristic
340C22#6411811yescharacteristic
341C22C2×#375211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—364no—
347C4—361no—
348C4—361no—
349C4—361no—
350C3#6997614yescomplemented
351C2—21no—
352C2—21no—
353C2—22no—
354C2—22no—
355C2—721no—
356C2C2×#6363311yescharacteristic
357C2#1059283211yescharacteristic
358C2C2×#6365211yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenter#407C3⋊D3
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C32×#407C2semidirect
3. C2×#63658C2semidirect
4. #10589336C2semidirect
5. #10589333C2semidirect
9. C2×#3828C4semidirect
12. #64139C4semidirect
17. #64135C4semidirect
18. #64133C4semidirect
25. C3×#407D3semidirect
45. C2×C4⋊(C3⋊D3)C2×C4semidirect
47. C2×#634C2×C4semidirect
55. C4⋊(C3⋊Dic3)C2×C4semidirect
56. C4⋊(C3⋊Dic3)C2×C4semidirect
112. #407C3⋊D3semidirect
284. C32#1504semidirect
350. C3#69976semidirect

Maximal subgroups

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

subgroupindex
#105962622
C32×#4072
C2×#636582
#105893362
#105893332
#699763