Finite Group Databasebeta

← C2×#10588415 #11863764

Subgroups — C2×#10588415 #11863764

Order 1152.

1140 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3697C211yesmaximal, characteristic
2C2×#63486C211yesmaximal, characteristic, complemented
3C22×#3664C211yesmaximal, characteristic, complemented
4C22×Dic36C211yesmaximal, characteristic, complemented
5C2×C9×C22⋊C8C211yesmaximal, characteristic, complemented
6C2×#63380C211yesmaximal, characteristic, complemented
7C2×#63376C211yesmaximal, characteristic, complemented
8#10588415C218yesmaximal, direct product factor
9C2×#4733—31nomaximal
10C23×C4×C9C2211yescharacteristic
11C22×#611—21no—
12C2×#3697—22no—
13C2×#3697—24no—
14C2×#3697—24no—
15C2×#3697C2214yes—
16C22×D36C2211yescharacteristic
17C22×C4×D9—21no—
18C22×Dic18C2211yescharacteristic
19C22×Dic18C2211yescharacteristic
20C22×C8×C9C2211yescharacteristic
21C22×C8×C9C2211yescharacteristic
22C2×#3676—21no—
23C2×C4⋊Dic9C2211yescharacteristic
24#63486—22no—
25#63486C2214yescomplemented
26C2×Dic9⋊C4—21no—
27C2×#3664—24no—
28C2×#3664C2214yescomplemented
29C2×Dic36—24no—
30C2×Dic36C2214yescomplemented
31C9×C22⋊C8C2214yescomplemented
32#63380C2214yescomplemented
33#63376C2214yescomplemented
34C22×#235—31no—
35C2×#924—31no—
36C22×Dic12—31no—
37C22×#204—31no—
38C2×C3×C22⋊C8D311yescharacteristic
39C2×#821—31no—
40C2×#816—31no—
41#4733—38no—
42C24×C9D411yescharacteristic
43C23×D9—21no—
44C22×C4×C9—22no—
45C22×C4×C9—22no—
46C22×C4×C9D411yescharacteristic
47C22×C4×C9D412yes—
48C22×C4×C9C2312yes—
49C22×C4×C9C2311yescharacteristic
50C2×#611—28no—
51C2×#611—24no—
52C22×Dic9—21no—
53C22×Dic9—21no—
54C22×Dic9—21no—
55#3697—216no—
56#3697—28no—
57#3697—28no—
58C2×D36—21no—
59C2×D36—22no—
60C2×D36D414yes—
61C2×D36C2312yes—
62C2×C4×D9—28no—
63C2×C4×D9—24no—
64C2×Dic18—21no—
65C2×Dic18—22no—
66C2×Dic18—22no—
67C2×Dic18—22no—
68C2×Dic18—21no—
69C2×Dic18D414yes—
70C2×Dic18C2312yes—
71C2×Dic18C2312yes—
72C2×C8×C9—22no—
73C2×C8×C9—22no—
74C2×C8×C9C2312yes—
75C2×C8×C9C2312yes—
76#3676—24no—
77C4⋊Dic9—21no—
78C4⋊Dic9C2312yes—
79Dic9⋊C4—24no—
80#3664—28no—
81Dic36—28no—
82C2×#452—91noSylow
83C23×C3×C4C2×D311yescharacteristic
84C22×#67—61no—
85C2×#235—34no—
86C2×#235—64no—
87C2×#235—64no—
88C2×#235—62no—
89C22×D12—31no—
90C22×C4×D3—61no—
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C2×#217—61no—
96C2×C4⋊Dic3—31no—
97#924—34no—
98#924—62no—
99C2×Dic3⋊C4—61no—
100C2×Dic12—34no—
101C2×Dic12—64no—
102C2×#204—34no—
103C2×#204—64no—
104C3×C22⋊C8C2×D314yes—
105#821—34no—
106#816—34no—
107C23×C9—22no—
108C23×C9—22no—
109C23×C9—22no—
110C23×C9C2×D412yes—
111C23×C9C2×D411yescharacteristic
112C22×D9—24no—
113C22×D9—22no—
114C22×D9—42no—
115C22×D9—42no—
116C2×C4×C9—22no—
117C2×C4×C9—24no—
118C2×C4×C9—22no—
119C2×C4×C9—22no—
120C2×C4×C9C2×D412yes—
121C2×C4×C9C2×D411yescharacteristic
122C2×C4×C9C2×D412yes—
123C2×C4×C9C2×D412yes—
124C2×C4×C9C2411yescharacteristic
125#611—216no—
126C2×Dic9—24no—
127C2×Dic9—22no—
128C2×Dic9—22no—
129C2×Dic9—22no—
130C2×Dic9—42no—
131C2×Dic9—42no—
132D36—24no—
133D36—22no—
134D36C2×D414yes—
135C4×D9—216no—
136Dic18—24no—
137Dic18—22no—
138Dic18—22no—
139Dic18—22no—
140Dic18—42no—
141Dic18C2×D414yes—
142C8×C9—22no—
143C8×C9—22no—
144C22×#41—91no—
145C22×Q16—91no—
146C22×SD16—91no—
147C2×C22⋊Q8—91no—
148#452—98no—
149C2×#103—91no—
150C2×#102—91no—
151C2×C22⋊C8D911yescharacteristic, complemented
152C24×C3D1211yescharacteristic
153C23×D3—61no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4D1211yescharacteristic
157C22×C3×C4D1212yes—
158C22×C3×C4C22×D312yes—
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—68no—
161C2×#67—64no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165#235—68no—
166#235—68no—
167#235—616no—
168C2×D12—34no—
169C2×D12—32no—
170C2×D12—61no—
171C2×D12—62no—
172C2×C4×D3—68no—
173C2×C4×D3—64no—
174C2×Dic6—34no—
175C2×Dic6—32no—
176C2×Dic6—32no—
177C2×Dic6—61no—
178C2×Dic6—62no—
179C2×Dic6—62no—
180C2×Dic6—62no—
181C2×Dic6—61no—
182C2×C3×C8—22no—
183C2×C3×C8—22no—
184C2×C3×C8C22×D312yes—
185C2×C3×C8C22×D312yes—
186#217—64no—
187C4⋊Dic3—32no—
188C4⋊Dic3—61no—
189Dic3⋊C4—64no—
190Dic12—68no—
191#204—68no—
192C22×C9—22no—
193C22×C9—22no—
194C22×C9—22no—
195C22×C9—44no—
196C22×C9#12012yes—
197C22×C9#13512yes—
198C22×C9#13712yes—
199C22×C9C22×D411yescharacteristic
200C2×D9—24no—
201C2×D9—42no—
202C2×D9—42no—
203C2×D9—48no—
204C4×C9—22no—
205C4×C9#12012yes—
206C4×C9C22×D411yescharacteristic
207C4×C9C22×D411yescharacteristic
208Dic9—24no—
209Dic9—42no—
210Dic9—42no—
211C2×#41—94no—
212C2×#41—184no—
213C2×#41—184no—
214C2×#41—182no—
215C22×Q8—91no—
216C22×Q8—91no—
217C22×D4—91no—
218C22×D4—181no—
219C23×C4—181no—
220C23×C4C2×D911yescharacteristic
221C2×Q16—94no—
222C2×Q16—184no—
223C2×SD16—94no—
224C2×SD16—184no—
225C22×C8C2×D911yescharacteristic
226C22×C8C2×D911yescharacteristic
227C22⋊Q8—94no—
228C22⋊Q8—182no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—181no—
231C2×C22⋊C4—181no—
232#103—94no—
233#102—94no—
234C22⋊C8C2×D914yescomplemented
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3C2×D1212yes—
239C23×C3C2×D1211yescharacteristic
240C22×D3—64no—
241C22×D3—62no—
242C22×D3—122no—
243C22×D3—122no—
244C2×C3×C4—22no—
245C2×C3×C4—24no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4C2×D1212yes—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4D3×D412yes—
251C2×C3×C4D3×D412yes—
252C2×C3×C4C23×D311yescharacteristic
253#67—616no—
254C2×Dic3—64no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—122no—
259C2×Dic3—122no—
260D12—34no—
261D12—64no—
262D12—62no—
263C4×D3—616no—
264Dic6—34no—
265Dic6—64no—
266Dic6—62no—
267Dic6—62no—
268Dic6—62no—
269Dic6—122no—
270C3×C8—22no—
271C3×C8—22no—
272C2×C9—42no—
273C2×C9#45214yescomplemented
274C2×C9C2×#12011yescharacteristic
275C2×C9C2×#13511yescharacteristic
276C2×C9C2×#13711yescharacteristic
277D9—44no—
278C24—181no—
279C24D3611yescharacteristic
280#41—188no—
281#41—188no—
282#41—1816no—
283C2×Q8—94no—
284C2×Q8—92no—
285C2×Q8—92no—
286C2×Q8—181no—
287C2×Q8—181no—
288C2×Q8—182no—
289C2×Q8—182no—
290C2×Q8—182no—
291C2×D4—94no—
292C2×D4—92no—
293C2×D4—188no—
294C2×D4—184no—
295C2×D4—181no—
296C2×D4—182no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—188no—
300C22×C4—181no—
301C22×C4—184no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4D3612yes—
305C22×C4D3611yescharacteristic
306C22×C4C22×D912yes—
307C22×C4C22×D911yescharacteristic
308Q16—188no—
309SD16—188no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8C22×D912yes—
313C2×C8C22×D912yes—
314C4⋊C4—92no—
315C4⋊C4—181no—
316C4⋊C4—184no—
317C22⋊C4—184no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—44no—
322C22×C3#88212yes—
323C22×C3#90412yes—
324C22×C3#90912yes—
325C22×C3C22×D1211yescharacteristic
326C2×D3—64no—
327C2×D3—122no—
328C2×D3—122no—
329C2×D3—128no—
330C3×C4—22no—
331C3×C4#88212yes—
332C3×C4C2×D3×D411yescharacteristic
333C3×C4C2×D3×D411yescharacteristic
334Dic3—64no—
335Dic3—122no—
336Dic3—122no—
337C9C2×#45211yescharacteristic, complemented, Sylow
338C23—22no—
339C23—22no—
340C23—22no—
341C23—184no—
342C23—182no—
343C23—362no—
344C23—362no—
345C23C2×D3612yes—
346C23C2×D3611yescharacteristic
347Q8—94no—
348Q8—184no—
349Q8—182no—
350Q8—182no—
351Q8—182no—
352Q8—362no—
353D4—94no—
354D4—1816no—
355D4—184no—
356D4—182no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—1816no—
362C2×C4—184no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—362no—
367C2×C4—362no—
368C2×C4C2×D3612yes—
369C2×C4C2×D3611yescharacteristic
370C2×C4D4×D912yes—
371C2×C4D4×D912yes—
372C2×C4C23×D911yescharacteristic
373C8—22no—
374C8—22no—
375C2×C3—42no—
376C2×C3#473314yes—
377C2×C3C2×#88211yescharacteristic
378C2×C3C2×#90411yescharacteristic
379C2×C3C2×#90911yescharacteristic
380D3—124no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—44no—
385C22—184no—
386C22—362no—
387C22—362no—
388C22—368no—
389C22#6344412yes—
390C22#6346712yes—
391C22#6347112yes—
392C22C22×D3611yescharacteristic
393C4—22no—
394C4—184no—
395C4—362no—
396C4—362no—
397C4#6344412yes—
398C4C2×D4×D911yescharacteristic
399C4C2×D4×D911yescharacteristic
400C3C2×#473311yescharacteristic
401C2—42no—
402C2—364no—
403C2#1058841514yesdirect product factor
404C2C2×#6344411yescharacteristic
405C2C2×#6346711yescharacteristic
406C2C2×#6347111yescharacteristic
subgroupG/H
centerC23C2×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×C22⋊C8C2
socleC23×C3C2×D12
prime radicalC22×#3697C2
hypercenterC2×C22⋊C8D9
hypocenterC9C2×#452
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63486C2semidirect
3. C22×#3664C2semidirect
4. C22×Dic36C2semidirect
5. C2×C9×C22⋊C8C2semidirect
6. C2×#63380C2semidirect
7. C2×#63376C2semidirect
8. #10588415C2direct (N × H)
25. #63486C22semidirect
28. C2×#3664C22semidirect
30. C2×Dic36C22semidirect
31. C9×C22⋊C8C22semidirect
32. #63380C22semidirect
33. #63376C22semidirect
151. C2×C22⋊C8D9semidirect
234. C22⋊C8C2×D9semidirect
273. C2×C9#452semidirect
337. C9C2×#452semidirect
403. C2#10588415direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36972
C2×#634862
C22×#36642
C22×Dic362
C2×C9×C22⋊C82
C2×#633802
C2×#633762
#105884152
C2×#47333