Finite Group Databasebeta

← #11778542

Subgroups — #11778542

Order 1152.

762 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 119 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#10596068C211yesmaximal, characteristic
2C32×#480C211yesmaximal, characteristic, complemented
3#10592682C211yesmaximal, characteristic, complemented
4#10592666C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589336C211yesmaximal, characteristic, complemented
7#10589335C211yesmaximal, characteristic, complemented
8#71167—34nomaximal
9C2×#3830—21no—
10C32×#121C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12#64148—21no—
13#64148—21no—
14#64139C2211yescharacteristic
15C2×#3750—21no—
16C2×#3750C2211yescharacteristic
17#64105—21no—
18#64093—21no—
19#64087—21no—
20C32×#107—21no—
21C32×#102—21no—
22C32×C22⋊C8C2211yescharacteristic
23#63658—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26#63636—21no—
27#63634—21no—
28#5597—34no—
29C3×#480D314yescomplemented
30#4983—34no—
31#4967—34no—
32#4537—34no—
33#4470—34no—
34#4469—34no—
35C2×C32×D4—21no—
36C2×C32×D4D411yescharacteristic
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40C2×#638—21no—
41C2×#638—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46#3830—42no—
47#3830—42no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56#3757—21no—
57#3752—21no—
58#3752—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60#3750—21no—
61#3750—21no—
62#3750—21no—
63#3750—42no—
64C2×C3⋊(C3⋊C8)—21no—
65#1610—91noSylow
66C2×#237—64no—
67C3×#121C2×D314yes—
68C2×C3×C4⋊C4C2×D314yes—
69#939—64no—
70#939—64no—
71#930—34no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—64no—
74#896—64no—
75#884—64no—
76#878—64no—
77C3×#107—24no—
78C3×#102—24no—
79C3×C22⋊C8C2×D314yes—
80C3⋊#95—34no—
81C3⋊#95—64no—
82#830—34no—
83#809—64no—
84#807—64no—
85C23×C32—21no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—21no—
88C32×D4—41no—
89C32×D4—41no—
90C32×D4—41no—
91C2×C32×C4—21no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98#638—42no—
99#638—41no—
100#638—41no—
101#638—81no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3D812yes—
112C4⋊(C3⋊D3)—41no—
113C4×C3⋊D3—42no—
114#634—42no—
115C32×C8—41no—
116C3⋊(C3⋊C8)—41no—
117#537—91no—
118#480—91no—
119#480C3⋊D311yescharacteristic, complemented
120#398—91no—
121#327—91no—
122#327—91no—
123#324—91no—
124C2×C3×D4—24no—
125C2×C3×D4#6714yes—
126C22×C3×C4—24no—
127C22×C3×C4C22×D314yes—
128C2×#67—64no—
129C2×#67—64no—
130C2×#67—64no—
131C22×Dic3—34no—
132C22×Dic3—34no—
133C22×Dic3—64no—
134C22×Dic3—64no—
135#237—128no—
136#237—128no—
137C2×D12—34no—
138C2×C4×D3—64no—
139C2×Dic6—64no—
140C2×C3×C8—24no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143C3×C4⋊C4#6714yes—
144C3×C22⋊C4—24no—
145#217—64no—
146(C2×D3)⋊C4—64no—
147(C2×D3)⋊C4—64no—
148C4⋊Dic3—34no—
149Dic3⋊C4—64no—
150Dic3⋊C4—64no—
151Dic3⋊C4—64no—
152Dic3⋊C4—128no—
153C2×C3⋊C8—64no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—41no—
157C22×C32—41no—
158C22×C32—41no—
159C22×C32#12011yescharacteristic
160C22×C32C2×D811yescharacteristic
161C22×C32AGL(1,ℤ/8)11yescharacteristic
162C2×C3⋊D3—41no—
163C2×C3⋊D3—41no—
164C2×C3⋊D3—41no—
165C32×C4—21no—
166C32×C4—21no—
167C32×C4—41no—
168C32×C4—81no—
169C3⋊Dic3—22no—
170C3⋊Dic3—42no—
171C3⋊Dic3—41no—
172C3⋊Dic3—41no—
173C2×#41—181no—
174C22⋊Q8—181no—
175C22⋊Q8—181no—
176#121—91no—
177#121—181no—
178#121—181no—
179#121—181no—
180#121C2×C3⋊D311yescharacteristic
181C2×C4⋊C4—91no—
182C2×C4⋊C4—181no—
183C2×C4⋊C4C2×C3⋊D311yescharacteristic
184#107—21no—
185#107—181no—
186#102—21no—
187#102—181no—
188C22⋊C8—91no—
189C22⋊C8C2×C3⋊D311yescharacteristic
190#95—91no—
191#95—181no—
192C23×C3—24no—
193C23×C3D3×D414yes—
194C22×D3—64no—
195C3×D4—44no—
196C3×D4—44no—
197C3×D4—44no—
198C2×C3×C4—24no—
199C2×C3×C4—44no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—44no—
203C2×C3×C4D3×D414yes—
204C2×C3×C4C2×#6714yes—
205#67—128no—
206#67—124no—
207#67—124no—
208#67—244no—
209C2×Dic3—38no—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—68no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—128no—
216C2×Dic3—124no—
217C2×Dic3—124no—
218C2×Dic3—124no—
219D12—124no—
220C4×D3—128no—
221Dic6—128no—
222C3×C8—44no—
223C3⋊C8—124no—
224C2×C32—21no—
225C2×C32—21no—
226C2×C32—81no—
227C2×C32#44711yescharacteristic
228C2×C32#45611yescharacteristic
229C2×C32#45811yescharacteristic
230C3⋊D3—81no—
231#41—362no—
232#41—362no—
233C2×Q8—181no—
234C2×D4—21no—
235C2×D4—91no—
236C2×D4—181no—
237C2×D4—181no—
238C2×D4—181no—
239C2×D4#63811yescharacteristic
240C22×C4—21no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4—181no—
246C22×C4C22×C3⋊D311yescharacteristic
247C2×C8—21no—
248C2×C8—181no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—91no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—362no—
256C4⋊C4#63811yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—181no—
259C22⋊C4—181no—
260C22⋊C4—181no—
261C22×C3—24no—
262C22×C3—24no—
263C22×C3—44no—
264C22×C3—44no—
265C22×C3—44no—
266C22×C3D3×D814yes—
267C22×C3#91114yes—
268C22×C3#93714yes—
269C2×D3—124no—
270C2×D3—124no—
271C2×D3—124no—
272C3×C4—24no—
273C3×C4—24no—
274C3×C4—44no—
275C3×C4—84no—
276Dic3—68no—
277Dic3—128no—
278Dic3—124no—
279Dic3—124no—
280C32#161011yescharacteristic, complemented, Sylow
281C23—21no—
282C23—181no—
283C23D4×C3⋊D311yescharacteristic
284Q8—362no—
285D4—41no—
286D4—41no—
287D4—41no—
288D4—361no—
289D4—362no—
290D4—361no—
291D4—361no—
292D4—721no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—92no—
299C2×C4—181no—
300C2×C4—181no—
301C2×C4—182no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—362no—
305C2×C4—362no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4—361no—
309C2×C4D4×C3⋊D311yescharacteristic
310C2×C4C2×#63811yescharacteristic
311C8—41no—
312C8—361no—
313C2×C3—24no—
314C2×C3—24no—
315C2×C3—84no—
316C2×C3#505314yes—
317C2×C3#515614yes—
318C2×C3#520514yes—
319D3—244no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—361no—
326C22—361no—
327C22—361no—
328C22D8×C3⋊D311yescharacteristic
329C22#6412011yescharacteristic
330C22#6414611yescharacteristic
331C4—21no—
332C4—21no—
333C4—41no—
334C4—81no—
335C4—182no—
336C4—362no—
337C4—361no—
338C4—361no—
339C3#7116714yescomplemented
340C2—21no—
341C2—21no—
342C2—81no—
343C2—721no—
344C2#1059275211yescharacteristic
345C2#1059285511yescharacteristic
346C2#1059290411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#480C2
socleC22×C32#120
prime radical#10596068C2
hypercenter#480C3⋊D3
hypocenterC32#1610
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C32×#480C2semidirect
3. #10592682C2semidirect
4. #10592666C2semidirect
5. #10589403C2semidirect
6. #10589336C2semidirect
7. #10589335C2semidirect
29. C3×#480D3semidirect
119. #480C3⋊D3semidirect
280. C32#1610semidirect
339. C3#71167semidirect

Maximal subgroups

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

subgroupindex
#105960682
C32×#4802
#105926822
#105926662
#105894032
#105893362
#105893352
#711673