Finite Group Databasebeta

← #11777640

Subgroups — #11777640

Order 1152.

397 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 397 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C4×#3713C211yesmaximal, characteristic
2#10590339C211yesmaximal, characteristic, complemented
3#10590329C211yesmaximal, characteristic, complemented
4#10589321C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589098C211yesmaximal, characteristic, complemented
8#68158—31nomaximal
9#68157—31nomaximal
10C3×C4×D12C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C2×#3713C411yescharacteristic
13C2×#3711—21no—
14C2×D3×C3⋊C8—21no—
15C32×C4×C8C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20#63576C411yescharacteristic
21#63562C411yescharacteristic
22#63562C411yescharacteristic
23(C2×D3)⋊(C3⋊C8)—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C4×#213—31no—
26C4×#213—31no—
27#5012—31no—
28D4×C3⋊C8—31no—
29#4838—31no—
30#4834—31no—
31C3×D4⋊C8—31no—
32C3×D4⋊C8—31no—
33#4480—31no—
34#4480—31no—
35#4459D311yescharacteristic, complemented
36#4459D311yescharacteristic, complemented
37#4455—31no—
38#4455—31no—
39#4455—61no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×C4×D3—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
47C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3C2×C411yescharacteristic
53C3×C4⋊Dic3C2×C411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3713—22no—
57#3711—42no—
58D3×C3⋊C8—42no—
59#1586—91noSylow
60C3×C4×D4—31no—
61C3×C4×D4—31no—
62C2×#213—31no—
63C2×#213—31no—
64C2×#208—61no—
65C22×C3⋊C8—61no—
66C2×ΓL(1,𝔽25)—61no—
67C2×D3×C8—61no—
68C4×D12C2×D311yescharacteristic
69C4×D12C2×D311yescharacteristic
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C4×C8—21no—
73C3×C4×C8C2×D311yescharacteristic
74C3×C4×C8C2×D311yescharacteristic
75#832—31no—
76#832—31no—
77#830—61no—
78#830—61no—
79(C2×D3)⋊C8—61no—
80(C2×D3)⋊C8—61no—
81#809—31no—
82#809—31no—
83#807—31no—
84#807—31no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4×C3⋊C8—31no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C4×C3⋊C8—61no—
93C22×C3×D3—21no—
94C22×C3×D3—21no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C3×D12—21no—
101C3×D12—21no—
102C3×D12—21no—
103C3×D12M1612yescomplemented
104C3×C4×D3—41no—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C32×C8—22no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C4×D8—91no—
116#436—91no—
117C8×D4—91no—
118#334—91no—
119D4⋊C8—31no—
120D4⋊C8—31no—
121#322—91no—
122C2×C3×D4—31no—
123C2×C3×D4—31no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C2×D12C4×D311yescharacteristic
127C2×D12C4×D311yescharacteristic
128C2×C4×D3—21no—
129C2×C4×D3—21no—
130C2×C3×C8—22no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—61no—
134C2×C3×C8—61no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—31no—
137C3×C22⋊C4—61no—
138C3×C22⋊C4—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#213—62no—
143#213—62no—
144(C2×D3)⋊C4—21no—
145(C2×D3)⋊C4—21no—
146C4⋊Dic3C4×D311yescharacteristic
147C4⋊Dic3C4×D311yescharacteristic
148#208—122no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—122no—
164ΓL(1,𝔽25)—122no—
165D3×C8—122no—
166C22×C32C4×D411yescharacteristic
167C2×C3×D3—22no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C2×C3×D3—41no—
171C2×C3×D3—41no—
172C2×C3×D3—41no—
173C32×C4—21no—
174C32×C4C2×M1611yescharacteristic
175C32×C4#13111yescharacteristic
176C32×C4AGL(1,ℤ/8)11yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C3×Dic3—41no—
179C3×Dic3—41no—
180C2×D8—91no—
181C2×M16—181no—
182C22×C8—181no—
183C4×D4—31no—
184C4×D4—31no—
185#107—91no—
186C4⋊C8—31no—
187C4⋊C8—31no—
188#102—91no—
189#102—91no—
190C22⋊C8—181no—
191C22⋊C8—181no—
192C4×C8—91no—
193C4×C8—91no—
194C4×C8D3211yescharacteristic
195C23×C3—61no—
196C23×C3—61no—
197C22×D3—21no—
198C22×D3—21no—
199C3×D4—32no—
200C3×D4—61no—
201C3×D4—61no—
202C3×D4—61no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—61no—
207C2×C3×C4—61no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4C2×C4×D311yescharacteristic
213C2×C3×C4C2×C4×D311yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4#23711yescharacteristic
217C2×C3×C4#23711yescharacteristic
218C2×Dic3—21no—
219C2×Dic3—21no—
220D12—21no—
221D12—21no—
222D12—21no—
223D12ΓL(1,𝔽25)12yescomplemented
224C4×D3—41no—
225C4×D3—41no—
226C4×D3—41no—
227C4×D3—41no—
228C3×C8—24no—
229C3×C8—22no—
230C3×C8—22no—
231C3×C8—121no—
232C3×C8—121no—
233C3⋊C8—41no—
234C3⋊C8—41no—
235C3⋊C8—61no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C3⋊C8—61no—
239C3⋊C8—61no—
240C3⋊C8—61no—
241C3⋊C8—61no—
242C3⋊C8—61no—
243C3⋊C8—121no—
244C3⋊C8—121no—
245C3⋊C8—121no—
246C3⋊C8—121no—
247C2×C32#43511yescharacteristic
248C2×C32#44211yescharacteristic
249C2×C32#44311yescharacteristic
250C3×D3—42no—
251C3×D3—81no—
252C2×D4—31no—
253C2×D4—31no—
254C22×C4—61no—
255C22×C4—61no—
256D8—182no—
257M16—362no—
258C2×C8—21no—
259C2×C8—61no—
260C2×C8—61no—
261C2×C8—91no—
262C2×C8—91no—
263C2×C8—91no—
264C2×C8—91no—
265C2×C8—362no—
266C4⋊C4—31no—
267C4⋊C4—31no—
268C22⋊C4—61no—
269C22⋊C4—61no—
270C42C2×D3211yescharacteristic
271C22×C3—21no—
272C22×C3—62no—
273C22×C3—121no—
274C22×C3—121no—
275C22×C3—121no—
276C22×C3—121no—
277C22×C3—121no—
278C22×C3#67⋊C411yescharacteristic
279C22×C3#67⋊C411yescharacteristic
280C2×D3—22no—
281C2×D3—41no—
282C2×D3—41no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—121no—
294C3×C4—121no—
295C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
296C3×C4#90111yescharacteristic
297C3×C4D3×M1611yescharacteristic
298C3×C4#90711yescharacteristic
299C3×C4#91111yescharacteristic
300C3×C4#91111yescharacteristic
301C3×C4#91411yescharacteristic
302C3×C4#91411yescharacteristic
303Dic3—41no—
304Dic3—41no—
305C32#158611yescharacteristic, complemented, Sylow
306C23—61no—
307C23—61no—
308D4—32no—
309D4—61no—
310D4—61no—
311D4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4—121no—
317C2×C4—121no—
318C2×C4C4×D3211yescharacteristic
319C2×C4#380211yescharacteristic
320C2×C4#380511yescharacteristic
321C8—22no—
322C8—121no—
323C8—121no—
324C8—181no—
325C8—181no—
326C8—181no—
327C8—181no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—122no—
332C2×C3—241no—
333C2×C3#472811yescharacteristic
334C2×C3#473011yescharacteristic
335C2×C3#478511yescharacteristic
336C2×C3#478511yescharacteristic
337C2×C3#482411yescharacteristic
338C2×C3#482411yescharacteristic
339D3—42no—
340D3—81no—
341C22—62no—
342C22—121no—
343C22—121no—
344C22—121no—
345C22—121no—
346C22—121no—
347C22#6390211yescharacteristic
348C4—21no—
349C4—121no—
350C4—121no—
351C4D3×ΓL(1,𝔽25)11yescharacteristic
352C4#6379811yescharacteristic
353C4#6379811yescharacteristic
354C4#6380411yescharacteristic
355C3—21no—
356C3#6815711yescharacteristic, complemented
357C3#6815811yescharacteristic, complemented
358C2—122no—
359C2—241no—
360C2#1059038911yescharacteristic
361C2#1059072511yescharacteristic
362C2#1059074111yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C4×D4
prime radicalC2×#3713C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1586
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10590339C2semidirect
3. #10590329C2semidirect
4. #10589321C2semidirect
5. C3×#4459C2semidirect
6. C3×#4459C2semidirect
7. #10589098C2semidirect
35. #4459D3semidirect
36. #4459D3semidirect
103. C3×D12M16semidirect
223. D12ΓL(1,𝔽25)semidirect
305. C32#1586semidirect
356. C3#68157semidirect
357. C3#68158semidirect

Maximal subgroups

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

subgroupindex
C4×#37132
#105903392
#105903292
#105893212
C3×#44592
#105890982
#681583
#681573