Finite Group Databasebeta

← C8×#3699 #11861532

Subgroups — C8×#3699 #11861532

Order 1152.

684 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
1C4×#3699C211yesmaximal, characteristic
2C8×D4×C9C211yesmaximal, characteristic, complemented
3C8×#611C212yesmaximal, complemented
4C2×C8×Dic9C212yesmaximal, complemented
5D4×C9⋊C8C211yesmaximal, characteristic, complemented
6#10588517C211yesmaximal, characteristic, complemented
7#10588508C211yesmaximal, characteristic, complemented
8#611⋊C8C212yesmaximal, complemented
9#10588398C212yesmaximal, complemented
10C4×C8×D9C211yesmaximal, characteristic, complemented
11C8×Dic18C211yesmaximal, characteristic, complemented
12C8×#237—31nomaximal
13C2×#3699C411yescharacteristic
14C22×C8×C9C2212yes—
15C4×D4×C9C2211yescharacteristic
16D4×Dic9C411yescharacteristic
17C4×#611C2212yes—
18C2×C4×Dic9C2212yes—
19C22×C9⋊C8C2212yes—
20C2×C8×D9C2211yescharacteristic
21C2×C8×D9C2211yescharacteristic
22#63454C411yescharacteristic
23#63449C411yescharacteristic
24#611⋊C4C412yes—
25#63439C412yes—
26C42×D9C2211yescharacteristic
27C4×Dic18C2211yescharacteristic
28C9×C4⋊C8C2211yescharacteristic
29C9×C22⋊C8C2212yes—
30C4×C8×C9C2211yescharacteristic
31#63389C2212yes—
32(C2×D9)⋊C8C2212yes—
33Dic9⋊C8C2212yes—
34Dic9⋊C8C2212yes—
35C8×Dic9C2212yes—
36C8×Dic9C2212yes—
37C8×Dic9C2211yescharacteristic
38C8×Dic9C2212yes—
39C8×Dic9C2211yescharacteristic
40C4⋊(C9⋊C8)C2211yescharacteristic
41C4×C9⋊C8C2211yescharacteristic
42C4×#237—31no—
43C3×C8×D4D311yescharacteristic
44C8×#67—32no—
45C2×C8×Dic3—32no—
46D4×C3⋊C8—31no—
47#4833—31no—
48#4830—31no—
49#67⋊C8—32no—
50#4718—32no—
51C4×D3×C8—31no—
52C8×Dic6—31no—
53C2×D4×C9C2×C411yescharacteristic
54C22×C4×C9C2312yes—
55C2×#611C2×C412yes—
56C22×Dic9C2×C412yes—
57C22×Dic9C2×C412yes—
58#3699C818yesdirect product factor
59C2×C4×D9C2×C411yescharacteristic
60C2×C4×D9C2×C411yescharacteristic
61C2×C4×D9C2311yescharacteristic
62C2×Dic18C2×C411yescharacteristic
63C2×C8×C9—24no—
64C2×C8×C9C2312yes—
65C2×C8×C9C2311yescharacteristic
66C2×C8×C9C2311yescharacteristic
67C9×C4⋊C4C2×C411yescharacteristic
68C9×C22⋊C4C2×C412yes—
69C42×C9C2311yescharacteristic
70#3676C2×C412yes—
71(C2×D9)⋊C4C2×C412yes—
72C4⋊Dic9C2×C411yescharacteristic
73Dic9⋊C4C2×C412yes—
74Dic9⋊C4C2×C412yes—
75C4×Dic9C2×C411yescharacteristic
76C4×Dic9C2×C411yescharacteristic
77C4×Dic9C2×C412yes—
78C4×Dic9C2×C412yes—
79C4×Dic9C2312yes—
80C4×Dic9C2311yescharacteristic
81C2×C9⋊C8—24no—
82C2×C9⋊C8C2311yescharacteristic
83C2×C9⋊C8C2312yes—
84C2×C9⋊C8C2311yescharacteristic
85C8×D9—22no—
86C8×D9—22no—
87C8×#41—91noSylow
88C2×#237—31no—
89C22×C3×C8C2×D312yes—
90C3×C4×D4C2×D311yescharacteristic
91D4×Dic3—31no—
92C4×#67—32no—
93C2×C4×Dic3—32no—
94C22×C3⋊C8—32no—
95C2×D3×C8—31no—
96C2×D3×C8—31no—
97#892—31no—
98#887—31no—
99#67⋊C4—32no—
100#877—32no—
101C42×D3—31no—
102C4×Dic6—31no—
103C3×C4⋊C8C2×D311yescharacteristic
104C3×C22⋊C8C2×D312yes—
105C3×C4×C8C2×D311yescharacteristic
106#830—32no—
107(C2×D3)⋊C8—32no—
108Dic3⋊C8—32no—
109Dic3⋊C8—32no—
110C8×Dic3—32no—
111C8×Dic3—31no—
112C8×Dic3—31no—
113C8×Dic3—32no—
114C8×Dic3—32no—
115C4⋊(C3⋊C8)—31no—
116C4×C3⋊C8—31no—
117C23×C9C22×C412yes—
118C22×D9C22×C411yescharacteristic
119D4×C9C2×C814yescomplemented
120C2×C4×C9—22no—
121C2×C4×C9—22no—
122C2×C4×C9C22×C412yes—
123C2×C4×C9C22×C411yescharacteristic
124C2×C4×C9C22×C411yescharacteristic
125C2×C4×C9C2411yescharacteristic
126#611C2×C818yescomplemented
127C2×Dic9—24no—
128C2×Dic9C2×C818yescomplemented
129C2×Dic9C22×C411yescharacteristic
130C2×Dic9C22×C412yes—
131C2×Dic9C22×C411yescharacteristic
132C2×Dic9C22×C412yes—
133C2×Dic9C22×C411yescharacteristic
134C4×D9—21no—
135C4×D9—21no—
136C4×D9—22no—
137C4×D9C2×C814yescomplemented
138Dic18C2×C814yescomplemented
139C8×C9—21no—
140C8×C9—22no—
141C8×C9#4112yescomplemented
142C9⋊C8—21no—
143C9⋊C8—22no—
144C9⋊C8#4112yescomplemented
145C4×#41—91no—
146C8×Q8—91no—
147C8×Q8—91no—
148C8×D4—92no—
149C8×D4—91no—
150C8×D4—92no—
151C8×D4D911yescharacteristic, complemented
152#431—91no—
153#431—92no—
154C2×C4×C8—92no—
155C2×C4×C8—91no—
156C2×C3×D4C4×D311yescharacteristic
157C22×C3×C4C22×D312yes—
158C2×#67—32no—
159C22×Dic3—32no—
160C22×Dic3—32no—
161#237—38no—
162C2×C4×D3—31no—
163C2×C4×D3—31no—
164C2×C4×D3—31no—
165C2×Dic6—31no—
166C2×C3×C8—24no—
167C2×C3×C8C22×D312yes—
168C2×C3×C8C22×D311yescharacteristic
169C2×C3×C8C22×D311yescharacteristic
170C3×C4⋊C4C4×D311yescharacteristic
171C3×C22⋊C4C4×D312yes—
172C3×C42C22×D311yescharacteristic
173#217—32no—
174(C2×D3)⋊C4—32no—
175C4⋊Dic3—31no—
176Dic3⋊C4—32no—
177Dic3⋊C4—32no—
178C4×Dic3—31no—
179C4×Dic3—31no—
180C4×Dic3—32no—
181C4×Dic3—32no—
182C4×Dic3—31no—
183C4×Dic3—32no—
184C2×C3⋊C8—31no—
185C2×C3⋊C8—31no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—64no—
188D3×C8—62no—
189D3×C8—62no—
190C22×C9—22no—
191C22×C9—22no—
192C22×C9C22×C814yes—
193C22×C9C23×C411yescharacteristic
194C2×D9—21no—
195C2×D9—21no—
196C2×D9C22×C812yes—
197C4×C9—22no—
198C4×C9—21no—
199C4×C9C22×C812yes—
200C4×C9C2×#4111yescharacteristic
201C4×C9C2×#4111yescharacteristic
202Dic9—21no—
203Dic9—22no—
204Dic9C22×C814yes—
205Dic9C22×C812yes—
206Dic9#13112yes—
207C2×#41—91no—
208C22×C8—92no—
209C22×C8—91no—
210C22×C8—91no—
211C22×C8C2×D912yes—
212C4×Q8—91no—
213C4×Q8—91no—
214C4×D4—91no—
215C4×D4—92no—
216C4×D4—92no—
217C4×D4C2×D911yescharacteristic
218#117—91no—
219#117—92no—
220C2×C42—92no—
221C2×C42—91no—
222C4⋊C8—92no—
223C4⋊C8—92no—
224C4⋊C8—91no—
225C4⋊C8C2×D911yescharacteristic
226C22⋊C8—92no—
227C22⋊C8—92no—
228C22⋊C8C2×D912yes—
229C4×C8—92no—
230C4×C8—91no—
231C4×C8—92no—
232C4×C8—91no—
233C4×C8—92no—
234C4×C8—91no—
235C4×C8C2×D911yescharacteristic
236C23×C3C2×C4×D312yes—
237C22×D3—31no—
238C3×D4D3×C814yes—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4C2×C4×D312yes—
242C2×C3×C4C2×C4×D311yescharacteristic
243C2×C3×C4C2×C4×D311yescharacteristic
244C2×C3×C4C23×D311yescharacteristic
245#67—38no—
246C2×Dic3—38no—
247C2×Dic3—31no—
248C2×Dic3—31no—
249C2×Dic3—32no—
250C2×Dic3—31no—
251C2×Dic3—32no—
252C2×Dic3—64no—
253C4×D3—34no—
254C4×D3—62no—
255C4×D3—61no—
256C4×D3—61no—
257Dic6—34no—
258C3×C8—22no—
259C3×C8—21no—
260C3×C8#23712yes—
261C3⋊C8—32no—
262C3⋊C8—61no—
263C3⋊C8—62no—
264C2×C9—24no—
265C2×C9C4×#4111yescharacteristic
266C2×C9C23×C811yescharacteristic
267C2×C9C2×#13111yescharacteristic
268D9—22no—
269#41—98no—
270C2×Q8—91no—
271C2×D4—92no—
272C2×D4C4×D911yescharacteristic
273C22×C4—92no—
274C22×C4—91no—
275C22×C4—92no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4C22×D912yes—
279C2×C8—24no—
280C2×C8—91no—
281C2×C8—91no—
282C2×C8—92no—
283C2×C8—182no—
284C2×C8—184no—
285C2×C8—182no—
286C2×C8C22×D912yes—
287C2×C8C22×D911yescharacteristic
288C2×C8C22×D911yescharacteristic
289C4⋊C4—92no—
290C4⋊C4—92no—
291C4⋊C4—91no—
292C4⋊C4C4×D911yescharacteristic
293C22⋊C4—92no—
294C22⋊C4—92no—
295C22⋊C4C4×D912yes—
296C42—92no—
297C42—91no—
298C42—92no—
299C42—91no—
300C42—91no—
301C42—92no—
302C42C22×D911yescharacteristic
303C22×C3—22no—
304C22×C3—22no—
305C22×C3C2×D3×C814yes—
306C22×C3C22×C4×D311yescharacteristic
307C2×D3—32no—
308C2×D3—61no—
309C2×D3—61no—
310C3×C4—21no—
311C3×C4—22no—
312C3×C4C2×D3×C812yes—
313C3×C4C2×#23711yescharacteristic
314C3×C4D3×#4111yescharacteristic
315Dic3—34no—
316Dic3—32no—
317Dic3—32no—
318Dic3—62no—
319Dic3—61no—
320C9C8×#4111yescharacteristic, complemented, Sylow
321C23—91no—
322C23C2×C4×D912yes—
323Q8—94no—
324D4—98no—
325D4C8×D914yescomplemented
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—92no—
331C2×C4—98no—
332C2×C4—94no—
333C2×C4—92no—
334C2×C4—91no—
335C2×C4—182no—
336C2×C4—184no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4C2×C4×D912yes—
340C2×C4C2×C4×D911yescharacteristic
341C2×C4C2×C4×D911yescharacteristic
342C2×C4C23×D911yescharacteristic
343C8—22no—
344C8—21no—
345C8—92no—
346C8—181no—
347C8—182no—
348C8#369912yesdirect product factor
349C2×C3—24no—
350C2×C3C4×#23711yescharacteristic
351C2×C3C22×D3×C811yescharacteristic
352C2×C3D3×#13111yescharacteristic
353D3—62no—
354C22—22no—
355C22—22no—
356C22—92no—
357C22—181no—
358C22—181no—
359C22C2×C8×D914yes—
360C22C22×C4×D911yescharacteristic
361C4—21no—
362C4—22no—
363C4—92no—
364C4—94no—
365C4—92no—
366C4—182no—
367C4—181no—
368C4C2×C8×D912yes—
369C4C2×#369911yescharacteristic
370C4#41×D911yescharacteristic
371C3C8×#23711yescharacteristic
372C2—24no—
373C2—182no—
374C2C4×#369911yescharacteristic
375C2C22×C8×D911yescharacteristic
376C2D9×#13111yescharacteristic
subgroupG/H
centerC2×C8C22×D9
commutatorC2×C9C23×C8
FrattiniC2×C3×C4C23×D3
FittingC8×D4×C9C2
socleC22×C3C22×C4×D3
prime radicalC2×#3699C4
cosocleC2×C4×C9C24
hypercenterC8×D4D9
hypocenterC9C8×#41
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. C8×D4×C9C2semidirect
3. C8×#611C2semidirect
4. C2×C8×Dic9C2semidirect
5. D4×C9⋊C8C2semidirect
6. #10588517C2semidirect
7. #10588508C2semidirect
8. #611⋊C8C2semidirect
9. #10588398C2semidirect
10. C4×C8×D9C2semidirect
11. C8×Dic18C2semidirect
58. #3699C8direct (N × H)
119. D4×C9C2×C8semidirect
126. #611C2×C8semidirect
128. C2×Dic9C2×C8semidirect
137. C4×D9C2×C8semidirect
138. Dic18C2×C8semidirect
141. C8×C9#41semidirect
144. C9⋊C8#41semidirect
151. C8×D4D9semidirect
320. C9C8×#41semidirect
325. D4C8×D9semidirect
348. C8#3699direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#36992
C8×D4×C92
C8×#6112
C2×C8×Dic92
D4×C9⋊C82
#105885172
#105885082
#611⋊C82
#105883982
C4×C8×D92
C8×Dic182
C8×#2373