Finite Group Databasebeta

← #11775413

Subgroups — #11775413

Order 1152.

756 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 129 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#10596067C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic, complemented
3#10592350C211yesmaximal, characteristic, complemented
4C32×#327C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589336C211yesmaximal, characteristic, complemented
7#10589317C211yesmaximal, characteristic, complemented
8#68281—34nomaximal
9C2×#3830—21no—
10C32×#121C2211yescharacteristic
11#64149C411yescharacteristic, complemented
12#64148—21no—
13D4×C3⋊Dic3C411yescharacteristic, complemented
14#64139C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64102C411yescharacteristic, complemented
17#64097C411yescharacteristic, complemented
18#64094—21no—
19#64090—21no—
20C32×C22⋊C8C2211yescharacteristic
21C32×#95C2211yescharacteristic
22#63658—21no—
23#63658—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26#63642—21no—
27#63641—21no—
28#5596—34no—
29#4719—34no—
30#4651—34no—
31C3×#327D314yescomplemented
32#4537—34no—
33#4470—34no—
34#4451—34no—
35C2×C32×D4—21no—
36C2×C32×D4C2×C411yescharacteristic
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)C2×C411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4C2×C411yescharacteristic
53C32×C22⋊C4—21no—
54#3757—21no—
55#3752—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3C2×C411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C2×C3⋊(C3⋊C8)—21no—
64#1514—91noSylow
65C2×#237—64no—
66C3×#121C2×D314yes—
67#940—34no—
68#939—64no—
69D4×Dic3—34no—
70#930—34no—
71C2×C4×Dic3—34no—
72#893—34no—
73#888—34no—
74#885—64no—
75#67⋊C4—64no—
76C3×C22⋊C8C2×D314yes—
77C3×#95C2×D314yes—
78C3⋊#95—34no—
79C3⋊#95—64no—
80C3⋊#95—64no—
81#830—34no—
82#815—64no—
83Dic3⋊C8—64no—
84C23×C32—21no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—21no—
87C32×D4—41no—
88C32×D4—41no—
89C32×D4—41no—
90C2×C32×C4—21no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97#638—42no—
98#638—42no—
99#638—41no—
100#638—41no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C2×C3⋊Dic3C22⋊C411yescharacteristic
112C2×C3⋊Dic3C22⋊C411yescharacteristic
113C4⋊(C3⋊D3)—41no—
114C4×C3⋊D3—42no—
115#634—42no—
116C32×C8—41no—
117C3⋊(C3⋊C8)—41no—
118#532—91no—
119#432—91no—
120#383—91no—
121#327—91no—
122#327—91no—
123#327—91no—
124#327C3⋊D311yescharacteristic, complemented
125C2×C3×D4—24no—
126C2×C3×D4C4×D314yes—
127C22×C3×C4—24no—
128C22×C3×C4C22×D314yes—
129C2×#67—64no—
130C2×#67—64no—
131C2×#67—64no—
132C22×Dic3—34no—
133C22×Dic3—34no—
134C22×Dic3—64no—
135C22×Dic3—64no—
136#237—128no—
137#237—128no—
138C2×D12—34no—
139C2×C4×D3—64no—
140C2×Dic6—64no—
141C2×C3×C8—24no—
142C3×C4⋊C4C4×D314yes—
143C3×C22⋊C4—24no—
144#217—64no—
145(C2×D3)⋊C4—64no—
146(C2×D3)⋊C4—64no—
147C4⋊Dic3—34no—
148Dic3⋊C4—64no—
149C4×Dic3—34no—
150C4×Dic3—34no—
151C4×Dic3—34no—
152C4×Dic3—34no—
153C2×C3⋊C8—64no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—41no—
157C22×C32—41no—
158C22×C32—41no—
159C22×C32C2×C22⋊C411yescharacteristic
160C22×C32AGL(1,ℤ/8)11yescharacteristic
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—21no—
170C3⋊Dic3—21no—
171C3⋊Dic3—21no—
172C3⋊Dic3—21no—
173C3⋊Dic3—41no—
174C3⋊Dic3—81no—
175C2×#41—181no—
176C4⋊Q8—91no—
177#127—91no—
178#124—181no—
179#121—91no—
180#121—181no—
181#121C2×C3⋊D311yescharacteristic
182C4×D4—91no—
183C4×D4—91no—
184C4×D4—181no—
185C2×C42—91no—
186C4⋊C8—181no—
187C22⋊C8—91no—
188C22⋊C8C2×C3⋊D311yescharacteristic
189#97—181no—
190#95—91no—
191#95—181no—
192#95—181no—
193#95C2×C3⋊D311yescharacteristic
194C23×C3—24no—
195C23×C3D3×D414yes—
196C22×D3—64no—
197C3×D4—44no—
198C3×D4—44no—
199C3×D4—44no—
200C2×C3×C4—24no—
201C2×C3×C4—44no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4—44no—
205C2×C3×C4C2×C4×D314yes—
206C2×C3×C4D3×D414yes—
207#67—128no—
208#67—128no—
209#67—124no—
210#67—124no—
211C2×Dic3—34no—
212C2×Dic3—34no—
213C2×Dic3—34no—
214C2×Dic3—34no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—124no—
219C2×Dic3—128no—
220C2×Dic3—124no—
221C2×Dic3—124no—
222C2×Dic3—124no—
223D12—124no—
224C4×D3—128no—
225Dic6—128no—
226C3×C8—44no—
227C3⋊C8—124no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32—81no—
231C2×C32#41011yescharacteristic
232C2×C32#41811yescharacteristic
233C2×C32#42111yescharacteristic
234C3⋊D3—81no—
235#41—362no—
236#41—362no—
237C2×Q8—181no—
238C2×D4—21no—
239C2×D4—91no—
240C2×D4—181no—
241C2×D4—181no—
242C2×D4—181no—
243C2×D4C4×C3⋊D311yescharacteristic
244C22×C4—21no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—181no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4C22×C3⋊D311yescharacteristic
251C2×C8—21no—
252C2×C8—181no—
253C4⋊C4—91no—
254C4⋊C4—181no—
255C4⋊C4C4×C3⋊D311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—181no—
258C22⋊C4—181no—
259C22⋊C4—181no—
260C42—91no—
261C42—91no—
262C42—91no—
263C42—91no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—44no—
267C22×C3—44no—
268C22×C3—44no—
269C22×C3D3×C22⋊C414yes—
270C22×C3#91114yes—
271C22×C3#91414yes—
272C2×D3—124no—
273C2×D3—124no—
274C2×D3—124no—
275C3×C4—24no—
276C3×C4—24no—
277C3×C4—44no—
278C3×C4—84no—
279Dic3—64no—
280Dic3—64no—
281Dic3—64no—
282Dic3—64no—
283Dic3—124no—
284Dic3—244no—
285C32#151411yescharacteristic, complemented, Sylow
286C23—21no—
287C23—181no—
288C23D4×C3⋊D311yescharacteristic
289Q8—362no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—361no—
294D4—362no—
295D4—362no—
296D4—361no—
297D4—361no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—181no—
308C2×C4—181no—
309C2×C4—181no—
310C2×C4—362no—
311C2×C4—361no—
312C2×C4—362no—
313C2×C4—361no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4C2×C4×C3⋊D311yescharacteristic
317C2×C4D4×C3⋊D311yescharacteristic
318C8—41no—
319C8—361no—
320C2×C3—24no—
321C2×C3—24no—
322C2×C3—84no—
323C2×C3#474014yes—
324C2×C3#477014yes—
325C2×C3#482114yes—
326D3—244no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—361no—
333C22—361no—
334C22—361no—
335C22C22⋊C4×C3⋊D311yescharacteristic
336C22#6412011yescharacteristic
337C22#6412311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—81no—
342C4—181no—
343C4—181no—
344C4—181no—
345C4—181no—
346C4—361no—
347C4—721no—
348C3#6828114yescomplemented
349C2—21no—
350C2—21no—
351C2—81no—
352C2—721no—
353C2#1059243911yescharacteristic
354C2#1059246911yescharacteristic
355C2#1059252011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#327C2
socleC22×C32C2×C22⋊C4
prime radical#10596067C2
cosocleC22×C32×C4C23
hypercenter#327C3⋊D3
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #10592418C2semidirect
3. #10592350C2semidirect
4. C32×#327C2semidirect
5. #10589403C2semidirect
6. #10589336C2semidirect
7. #10589317C2semidirect
11. #64149C4semidirect
13. D4×C3⋊Dic3C4semidirect
16. #64102C4semidirect
17. #64097C4semidirect
31. C3×#327D3semidirect
124. #327C3⋊D3semidirect
285. C32#1514semidirect
348. C3#68281semidirect

Maximal subgroups

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

subgroupindex
#105960672
#105924182
#105923502
C32×#3272
#105894032
#105893362
#105893172
#682813