Finite Group Databasebeta

← #11777643

Subgroups — #11777643

Order 1152.

425 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592711C211yesmaximal, characteristic, complemented
2C3×C4×#213C211yesmaximal, characteristic
3#10590329C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic, complemented
7#10589078C211yesmaximal, characteristic, complemented
8#70880—31nomaximal
9#68158—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3748—21no—
12C2×C3×#213C411yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C2×D3×C3⋊C8—21no—
15#63657—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#832C411yescharacteristic
19C3×#809C411yescharacteristic
20C3×#807C411yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×C4×D8—31no—
26C4×#213D311yescharacteristic
27#5012—31no—
28#5012—31no—
29#5012—61no—
30D4×C3⋊C8—31no—
31#4834—31no—
32C3×D4⋊C8—31no—
33D4⋊(C3⋊C8)—31no—
34D4⋊(C3⋊C8)D311yescharacteristic, complemented
35#4480—31no—
36#4459—31no—
37#4457—31no—
38#4455—31no—
39#4454—31no—
40C2×C32×D4C2×C411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×D12C2×C411yescharacteristic
43C2×C3×C4×D3—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3748—42no—
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×#213—22no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3C2×C411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8C2×C411yescharacteristic
57C2×C3×C3⋊C8C2×C411yescharacteristic
58D3×C3⋊C8—42no—
59#1586—91noSylow
60C2×C3×D8—31no—
61C3×C4×D4—21no—
62C3×C4×D4—31no—
63C3×C4×D4C2×D311yescharacteristic
64C3×C4×D4C2×D311yescharacteristic
65C2×#213Dic311yescharacteristic
66C2×#208—61no—
67C2×#208—61no—
68C2×#208—62no—
69C22×C3⋊C8—61no—
70C2×D3×C8—61no—
71C4×D12C2×D311yescharacteristic
72C3×#107—31no—
73C3×C4⋊C8—31no—
74C3×#102—31no—
75C3×#102—31no—
76C3×C4×C8—31no—
77C3×C4×C8—31no—
78#832Dic311yescharacteristic
79#830—61no—
80#830—61no—
81#830—61no—
82#830—62no—
83(C2×D3)⋊C8—61no—
84#809Dic311yescharacteristic
85#807Dic311yescharacteristic
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C4×C3⋊C8C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C23×C32—21no—
96C22×C3×D3—21no—
97C32×D4—21no—
98C32×D4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—21no—
106C3×D12—21no—
107C3×D12M1612yescomplemented
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—22no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C4×D8—31no—
118#436—91no—
119C8×D4—91no—
120#334—91no—
121D4⋊C8—31no—
122D4⋊C8—91no—
123#322—91no—
124C2×C3×D4—21no—
125C2×C3×D4—31no—
126C2×C3×D4C4×D311yescharacteristic
127C2×C3×D4C2×Dic311yescharacteristic
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—61no—
132C2×D12C2×Dic311yescharacteristic
133C2×C4×D3—21no—
134C3×D8—62no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4C4×D311yescharacteristic
142C3×C4⋊C4C2×Dic311yescharacteristic
143C3×C22⋊C4—22no—
144C3×C22⋊C4—21no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4—61no—
147C3×C42—21no—
148C3×C42C22×D311yescharacteristic
149C3×C42C22×D311yescharacteristic
150#213—22no—
151(C2×D3)⋊C4—21no—
152C4⋊Dic3C2×Dic311yescharacteristic
153#208—124no—
154#208—122no—
155#208—122no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—62no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—122no—
168C2×C3⋊C8C2×Dic311yescharacteristic
169C2×C3⋊C8C2×Dic311yescharacteristic
170D3×C8—122no—
171C22×C32—41no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32C4×D411yescharacteristic
175C2×C3×D3—22no—
176C2×C3×D3—41no—
177C2×C3×D3—41no—
178C32×C4—21no—
179C32×C4—41no—
180C32×C4C2×M1611yescharacteristic
181C32×C4#13111yescharacteristic
182C32×C4AGL(1,ℤ/8)11yescharacteristic
183C32×C4AGL(1,ℤ/8)11yescharacteristic
184C3×Dic3—41no—
185C2×D8—31no—
186C2×M16—181no—
187C22×C8—181no—
188C4×D4—31no—
189C4×D4D3211yescharacteristic
190#107—31no—
191C4⋊C8—31no—
192C4⋊C8—91no—
193#102—31no—
194#102—31no—
195C22⋊C8—181no—
196C22⋊C8—181no—
197C4×C8—31no—
198C4×C8—31no—
199C4×C8—91no—
200C23×C3—22no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—61no—
204C22×D3—21no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—21no—
208C3×D4—21no—
209C3×D4—32no—
210C3×D4—41no—
211C3×D4—41no—
212C3×D4—61no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4—42no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—61no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4#23711yescharacteristic
232C2×C3×C4#23711yescharacteristic
233C2×C3×C4C22×Dic311yescharacteristic
234C2×Dic3—21no—
235D12—21no—
236D12#20812yescomplemented
237C4×D3—41no—
238C4×D3—41no—
239C3×C8—62no—
240C3×C8—61no—
241C3×C8—61no—
242C3×C8—121no—
243C3⋊C8—22no—
244C3⋊C8—21no—
245C3⋊C8—21no—
246C3⋊C8—41no—
247C3⋊C8—62no—
248C3⋊C8—61no—
249C3⋊C8—61no—
250C3⋊C8—61no—
251C3⋊C8—61no—
252C3⋊C8—121no—
253C3⋊C8—122no—
254C3⋊C8—121no—
255C3⋊C8—121no—
256C2×C32—81no—
257C2×C32#43511yescharacteristic
258C2×C32#44211yescharacteristic
259C2×C32#44311yescharacteristic
260C3×D3—42no—
261C2×D4—31no—
262C2×D4D3×Dic311yescharacteristic
263C22×C4—21no—
264C22×C4—61no—
265D8—62no—
266M16—362no—
267C2×C8—31no—
268C2×C8—31no—
269C2×C8—61no—
270C2×C8—61no—
271C2×C8—91no—
272C2×C8—91no—
273C2×C8—181no—
274C2×C8—362no—
275C4⋊C4—31no—
276C4⋊C4D3×Dic311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—61no—
279C42C2×D3211yescharacteristic
280C22×C3—21no—
281C22×C3—42no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—41no—
290C22×C3—62no—
291C22×C3—121no—
292C22×C3—121no—
293C22×C3#67⋊C411yescharacteristic
294C22×C3D4×Dic311yescharacteristic
295C2×D3—22no—
296C2×D3—41no—
297C2×D3—41no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4—42no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—121no—
309C3×C4#90111yescharacteristic
310C3×C4D3×M1611yescharacteristic
311C3×C4#91111yescharacteristic
312C3×C4#91111yescharacteristic
313C3×C4#91111yescharacteristic
314C3×C4#91411yescharacteristic
315C3×C4C2×#20811yescharacteristic
316C3×C4#94811yescharacteristic
317Dic3—41no—
318C32#158611yescharacteristic, complemented, Sylow
319C23—21no—
320C23—61no—
321D4—21no—
322D4—21no—
323D4—32no—
324D4—61no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—61no—
329C2×C4—121no—
330C2×C4—121no—
331C2×C4C2×D3×Dic311yescharacteristic
332C2×C4#380511yescharacteristic
333C2×C4#381111yescharacteristic
334C8—62no—
335C8—61no—
336C8—61no—
337C8—121no—
338C8—181no—
339C8—181no—
340C8—361no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—82no—
345C2×C3—81no—
346C2×C3—81no—
347C2×C3—122no—
348C2×C3#472811yescharacteristic
349C2×C3#478511yescharacteristic
350C2×C3#482411yescharacteristic
351C2×C3#501111yescharacteristic
352C2×C3#515211yescharacteristic
353C2×C3#519611yescharacteristic
354D3—42no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—62no—
359C22—121no—
360C22—121no—
361C22#67⋊Dic311yescharacteristic
362C4—21no—
363C4—41no—
364C4—121no—
365C4D3×#20811yescharacteristic
366C4#6381411yescharacteristic
367C4#6392711yescharacteristic
368C4#6393711yescharacteristic
369C3—21no—
370C3#6815811yescharacteristic, complemented
371C3#7088011yescharacteristic, complemented
372C2—81no—
373C2—122no—
374C2#1059115111yescharacteristic
375C2#1059143611yescharacteristic
376C2#1059167511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C4×D4
prime radicalC2×C3×#213C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1586
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10592711C2semidirect
3. #10590329C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589097C2semidirect
6. #10589081C2semidirect
7. #10589078C2semidirect
34. D4⋊(C3⋊C8)D3semidirect
107. C3×D12M16semidirect
236. D12#208semidirect
318. C32#1586semidirect
370. C3#68158semidirect
371. C3#70880semidirect

Maximal subgroups

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

subgroupindex
#105927112
C3×C4×#2132
#105903292
C3×D4⋊(C3⋊C8)2
#105890972
#105890812
#105890782
#708803
#681583