Finite Group Databasebeta

← #11777402

Subgroups — #11777402

Order 1152.

405 conjugacy classes of subgroups.

The subgroup lattice has 373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#213C211yesmaximal, characteristic
2C3×#5012C211yesmaximal, characteristic, complemented
3C3⋊C8×D12C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589080C211yesmaximal, characteristic, complemented
7#10589078C211yesmaximal, characteristic, complemented
8#70879—31nomaximal
9#70862—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×C3×#213C411yescharacteristic
12C2×C3×#208—21no—
13C3×C4×D12C2211yescharacteristic
14C2×D3×C3⋊C8—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#832C411yescharacteristic
18C3×#830—21no—
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—
26C3×#436—31no—
27C4×#213D311yescharacteristic
28#5012D311yescharacteristic, complemented
29D4×C3⋊C8—31no—
30C8×D12—31no—
31D4⋊(C3⋊C8)—31no—
32D4⋊(C3⋊C8)—31no—
33D4⋊(C3⋊C8)—31no—
34D4⋊(C3⋊C8)—61no—
35#4483—31no—
36#4479—31no—
37#4458—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
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×#213—22no—
50C3×(C2×D3)⋊C4—21no—
51C3×C4⋊Dic3C2×C411yescharacteristic
52C3×#208—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58D3×C3⋊C8—42no—
59#1581—91noSylow
60C2×C3×D8—31no—
61C2×C3×M16—61no—
62C3×C4×D4—21no—
63C3×C4×D4—31no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C2×D311yescharacteristic
66C2×#213Dic311yescharacteristic
67C2×#208—21no—
68C22×C3⋊C8—61no—
69C2×D3×C8—61no—
70C4×D12C2×D311yescharacteristic
71C3×#107—31no—
72C3×C4⋊C8—31no—
73C3×#102—31no—
74C3×#102—31no—
75C3×C22⋊C8—61no—
76C3×C4×C8—31no—
77C3×C4×C8—31no—
78#832Dic311yescharacteristic
79#830—21no—
80#830—61no—
81(C2×D3)⋊C8—61no—
82#809Dic311yescharacteristic
83#807Dic311yescharacteristic
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4×C3⋊C8—31no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—61no—
91C4×C3⋊C8C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C23×C32—21no—
94C22×C3×D3—21no—
95C32×D4—21no—
96C32×D4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—21no—
104C3×D12—21no—
105C3×D12M1612yescomplemented
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C3⋊(C3⋊C8)—41no—
109C3⋊(C3⋊C8)—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8D812yescomplemented
115C4×D8—31no—
116#436—31no—
117C8×D4—91no—
118#335—91no—
119D4⋊C8—91no—
120D4⋊C8—91no—
121#322—91no—
122C2×C3×D4—21no—
123C2×C3×D4—31no—
124C2×C3×D4C4×D311yescharacteristic
125C2×C3×D4C2×Dic311yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—41no—
129C22×C3×C4—61no—
130C2×D12C2×Dic311yescharacteristic
131C2×C4×D3—21no—
132C3×D8—62no—
133C3×M16—122no—
134C2×C3×C8—31no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—31no—
138C2×C3×C8—61no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4C4×D311yescharacteristic
142C3×C4⋊C4C2×Dic311yescharacteristic
143C3×C22⋊C4—21no—
144C3×C22⋊C4—21no—
145C3×C22⋊C4—41no—
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—42no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—121no—
160C2×C3⋊C8—121no—
161C2×C3⋊C8—122no—
162C2×C3⋊C8C2×Dic311yescharacteristic
163C2×C3⋊C8C2×Dic311yescharacteristic
164C2×C3⋊C8#6711yescharacteristic
165C2×C3⋊C8#6711yescharacteristic
166D3×C8—122no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32C4×D411yescharacteristic
171C2×C3×D3—22no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C32×C4—21no—
175C32×C4—41no—
176C32×C4C2×M1611yescharacteristic
177C32×C4#13111yescharacteristic
178C32×C4C2×D811yescharacteristic
179C32×C4#13511yescharacteristic
180C3×Dic3—41no—
181C2×D8—31no—
182C2×M16—61no—
183C22×C8—181no—
184C4×D4—31no—
185C4×D4D3211yescharacteristic
186#107—31no—
187C4⋊C8—31no—
188C4⋊C8—91no—
189#102—31no—
190#102—31no—
191C22⋊C8—61no—
192C22⋊C8—181no—
193C4×C8—31no—
194C4×C8—31no—
195C4×C8—91no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—41no—
199C23×C3—61no—
200C22×D3—21no—
201C3×D4—22no—
202C3×D4—21no—
203C3×D4—21no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—32no—
207C3×D4—41no—
208C3×D4—61no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—61no—
220C2×C3×C4—81no—
221C2×C3×C4—81no—
222C2×C3×C4—121no—
223C2×C3×C4—121no—
224C2×C3×C4C2×C4×D311yescharacteristic
225C2×C3×C4#23511yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4#23711yescharacteristic
228C2×C3×C4C22×Dic311yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×Dic3—21no—
231D12—21no—
232D12#20812yescomplemented
233C4×D3—41no—
234C4×D3—41no—
235C3×C8—32no—
236C3×C8—61no—
237C3×C8—61no—
238C3×C8—61no—
239C3×C8—121no—
240C3⋊C8—21no—
241C3⋊C8—21no—
242C3⋊C8—21no—
243C3⋊C8—41no—
244C3⋊C8—121no—
245C3⋊C8—121no—
246C3⋊C8—122no—
247C3⋊C8—121no—
248C3⋊C8—121no—
249C3⋊C8—241no—
250C3⋊C8#21312yescomplemented
251C2×C32—81no—
252C2×C32#43511yescharacteristic
253C2×C32C4×D811yescharacteristic
254C2×C32#44411yescharacteristic
255C3×D3—42no—
256C2×D4—31no—
257C2×D4D3×Dic311yescharacteristic
258C22×C4—21no—
259C22×C4—61no—
260D8—62no—
261M16—122no—
262C2×C8—31no—
263C2×C8—31no—
264C2×C8—31no—
265C2×C8—31no—
266C2×C8—61no—
267C2×C8—181no—
268C2×C8—181no—
269C2×C8—362no—
270C4⋊C4—31no—
271C4⋊C4D3×Dic311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—61no—
274C42C2×D3211yescharacteristic
275C22×C3—21no—
276C22×C3—42no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—62no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3—121no—
287C22×C3—121no—
288C22×C3C4×#6711yescharacteristic
289C22×C3D4×Dic311yescharacteristic
290C2×D3—22no—
291C2×D3—41no—
292C2×D3—41no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—81no—
303C3×C4—121no—
304C3×C4D3×M1611yescharacteristic
305C3×C4#90711yescharacteristic
306C3×C4D3×D811yescharacteristic
307C3×C4#91211yescharacteristic
308C3×C4C2×#20811yescharacteristic
309C3×C4C2×#21311yescharacteristic
310C3×C4#94811yescharacteristic
311C3×C4#95011yescharacteristic
312Dic3—41no—
313C32#158111yescharacteristic, complemented, Sylow
314C23—21no—
315C23—61no—
316D4—21no—
317D4—21no—
318D4—32no—
319D4—61no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—61no—
324C2×C4—121no—
325C2×C4—121no—
326C2×C4C2×D3×Dic311yescharacteristic
327C2×C4#380411yescharacteristic
328C2×C4D3×#6711yescharacteristic
329C8—32no—
330C8—61no—
331C8—61no—
332C8—61no—
333C8—121no—
334C8—361no—
335C8—361no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—82no—
340C2×C3—81no—
341C2×C3—81no—
342C2×C3—122no—
343C2×C3#501111yescharacteristic
344C2×C3C4×#21311yescharacteristic
345C2×C3#512711yescharacteristic
346C2×C3#514511yescharacteristic
347C2×C3Dic3×D811yescharacteristic
348C2×C3#519711yescharacteristic
349D3—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—62no—
354C22—121no—
355C22—121no—
356C22Dic3×#6711yescharacteristic
357C4—21no—
358C4—41no—
359C4—121no—
360C4D3×#20811yescharacteristic
361C4#6381511yescharacteristic
362C4D3×#21311yescharacteristic
363C4#6393311yescharacteristic
364C3—21no—
365C3#7086211yescharacteristic, complemented
366C3#7087911yescharacteristic, complemented
367C2—81no—
368C2—122no—
369C2#1059114711yescharacteristic
370C2Dic3×#21311yescharacteristic
371C2#1059167411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C4×D4
prime radicalC2×C3×#213C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1581
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
2. C3×#5012C2semidirect
3. C3⋊C8×D12C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
5. #10589099C2semidirect
6. #10589080C2semidirect
7. #10589078C2semidirect
28. #5012D3semidirect
105. C3×D12M16semidirect
114. C3×C3⋊C8D8semidirect
232. D12#208semidirect
250. C3⋊C8#213semidirect
313. C32#1581semidirect
365. C3#70862semidirect
366. C3#70879semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2132
C3×#50122
C3⋊C8×D122
D4⋊(C3⋊(C3⋊C8))2
#105890992
#105890802
#105890782
#708793
#708623