Finite Group Databasebeta

← C2×#10588866 #11863640

Subgroups — C2×#10588866 #11863640

Order 1152.

1110 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D9C211yesmaximal, characteristic
2C22×C9×Q16C211yesmaximal, characteristic, complemented
3C2×#63508C211yesmaximal, characteristic
4C22×#3674C211yesmaximal, characteristic, complemented
5C2×#63395C211yesmaximal, characteristic, complemented
6#10588866C218yesmaximal, direct product factor
7C2×(C2×D9)⋊C8C211yesmaximal, characteristic
8C2×#63376C211yesmaximal, characteristic, complemented
9C2×#5186—31nomaximal
10C22×Q8×C9C2211yescharacteristic
11C22×Q8×C9C2211yescharacteristic
12C2×Q8×D9—24no—
13C2×Q8×D9—22no—
14C2×Q8×D9—24no—
15C2×Q8×D9C2214yes—
16C22×C4×D9—21no—
17C22×C4×D9C2211yescharacteristic
18C22×Dic18—21no—
19C22×Dic18C2211yescharacteristic
20C2×C9×Q16—24no—
21C2×C9×Q16C2214yescomplemented
22C22×C8×C9C2211yescharacteristic
23#63508—22no—
24#63508C2214yes—
25C2×#3674—24no—
26C2×#3674C2214yescomplemented
27C2×(C2×D9)⋊C4—21no—
28C2×C4⋊Dic9C2211yescharacteristic
29C2×Dic9⋊C4—21no—
30C22×C9⋊C8C2211yescharacteristic
31#63395C2214yescomplemented
32(C2×D9)⋊C8C2214yes—
33#63376C2214yescomplemented
34C22×D3×Q8—31no—
35C22×C3×Q16D311yescharacteristic
36C2×#946—31no—
37C22×#216—31no—
38C2×#835—31no—
39#5186—38no—
40C2×(C2×D3)⋊C8—31no—
41C2×#816—31no—
42C23×D9D411yescharacteristic
43C2×Q8×C9—22no—
44C2×Q8×C9—21no—
45C2×Q8×C9—21no—
46C2×Q8×C9—22no—
47C2×Q8×C9—22no—
48C2×Q8×C9D414yes—
49C2×Q8×C9C2312yes—
50C2×Q8×C9C2312yes—
51C22×C4×C9—21no—
52C22×C4×C9—21no—
53C22×C4×C9C2311yescharacteristic
54C22×Dic9—21no—
55C22×Dic9—21no—
56C22×Dic9D411yescharacteristic
57Q8×D9—216no—
58Q8×D9—28no—
59Q8×D9—28no—
60C2×C4×D9—28no—
61C2×C4×D9—24no—
62C2×C4×D9—22no—
63C2×C4×D9—22no—
64C2×C4×D9D412yes—
65C2×C4×D9C2312yes—
66C2×Dic18—28no—
67C2×Dic18—21no—
68C2×Dic18—22no—
69C2×Dic18—24no—
70C2×Dic18D414yes—
71C2×Dic18C2312yes—
72C9×Q16—28no—
73C2×C8×C9—22no—
74C2×C8×C9C2312yes—
75#3674—28no—
76(C2×D9)⋊C4—24no—
77C4⋊Dic9—21no—
78C4⋊Dic9C2312yes—
79Dic9⋊C4—24no—
80C2×C9⋊C8—22no—
81C2×C9⋊C8C2312yes—
82C2×#451—91noSylow
83C22×C3×Q8C2×D311yescharacteristic
84C22×C3×Q8C2×D311yescharacteristic
85C2×D3×Q8—34no—
86C2×D3×Q8—64no—
87C2×D3×Q8—62no—
88C2×D3×Q8—64no—
89C22×C4×D3—31no—
90C22×C4×D3—61no—
91C22×Dic6—31no—
92C22×Dic6—61no—
93C2×C3×Q16—24no—
94C2×C3×Q16C2×D314yes—
95C22×C3×C8C2×D311yescharacteristic
96#946—34no—
97#946—62no—
98C2×#216—34no—
99C2×#216—64no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3—31no—
102C2×Dic3⋊C4—61no—
103C22×C3⋊C8—31no—
104#835—34no—
105(C2×D3)⋊C8—34no—
106#816—34no—
107C23×C9C2×D411yescharacteristic
108C22×D9—22no—
109C22×D9—22no—
110C22×D9Q1614yescomplemented
111C22×D9C2×D412yes—
112Q8×C9—24no—
113Q8×C9—22no—
114Q8×C9—22no—
115Q8×C9—22no—
116Q8×C9—42no—
117Q8×C9C2×D414yes—
118C2×C4×C9—24no—
119C2×C4×C9—22no—
120C2×C4×C9—22no—
121C2×C4×C9—42no—
122C2×C4×C9C2×D411yescharacteristic
123C2×C4×C9C2×D412yes—
124C2×C4×C9C2×D412yes—
125C2×C4×C9C2411yescharacteristic
126C2×Dic9—22no—
127C2×Dic9—24no—
128C2×Dic9—22no—
129C2×Dic9—22no—
130C2×Dic9—42no—
131C2×Dic9C2×D412yes—
132C4×D9—216no—
133C4×D9—24no—
134C4×D9—22no—
135C4×D9—22no—
136Dic18—216no—
137Dic18—24no—
138Dic18—22no—
139Dic18C2×D414yes—
140C8×C9—22no—
141C9⋊C8—22no—
142C23×Q8—91no—
143C22×Q16—91no—
144C22×Q16D911yescharacteristic, complemented
145C2×C22⋊Q8—91no—
146#451—98no—
147C2×#103—91no—
148C2×#103—91no—
149C2×C22⋊C8—91no—
150C23×D3—31no—
151C2×C3×Q8—22no—
152C2×C3×Q8—21no—
153C2×C3×Q8—21no—
154C2×C3×Q8—22no—
155C2×C3×Q8—22no—
156C2×C3×Q8#6714yes—
157C2×C3×Q8C22×D312yes—
158C2×C3×Q8C22×D312yes—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—31no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165D3×Q8—68no—
166D3×Q8—616no—
167D3×Q8—68no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—64no—
171C2×C4×D3—68no—
172C2×C4×D3—62no—
173C2×C4×D3—62no—
174C2×Dic6—34no—
175C2×Dic6—32no—
176C2×Dic6—64no—
177C2×Dic6—68no—
178C2×Dic6—61no—
179C2×Dic6—62no—
180C3×Q16—28no—
181C2×C3×C8—22no—
182C2×C3×C8C22×D312yes—
183#216—68no—
184(C2×D3)⋊C4—64no—
185C4⋊Dic3—32no—
186C4⋊Dic3—61no—
187Dic3⋊C4—64no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—62no—
190C22×C9#12012yes—
191C22×C9C2×Q1612yes—
192C22×C9#13712yes—
193C22×C9C22×D411yescharacteristic
194C2×D9—22no—
195C2×D9—22no—
196C2×D9—28no—
197C2×D9C2×Q1614yescomplemented
198C4×C9—24no—
199C4×C9—42no—
200C4×C9#12012yes—
201C4×C9C22×D411yescharacteristic
202C4×C9C22×D411yescharacteristic
203Dic9—22no—
204Dic9—24no—
205Dic9—42no—
206C22×Q8—94no—
207C22×Q8—91no—
208C22×Q8—181no—
209C22×Q8—182no—
210C22×Q8—184no—
211C22×Q8—184no—
212C22×Q8C2×D911yescharacteristic
213C22×Q8C2×D911yescharacteristic
214C23×C4—91no—
215C23×C4—181no—
216C2×Q16—24no—
217C2×Q16—94no—
218C2×Q16—184no—
219C2×Q16C2×D914yescomplemented
220C22×C8—91no—
221C22×C8C2×D911yescharacteristic
222C22⋊Q8—94no—
223C22⋊Q8—182no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—181no—
226C2×C22⋊C4—181no—
227#103—94no—
228#103—94no—
229C22⋊C8—94no—
230C23×C3D3×D411yescharacteristic
231C22×D3—34no—
232C22×D3—32no—
233C22×D3—62no—
234C22×D3—62no—
235C3×Q8—24no—
236C3×Q8—22no—
237C3×Q8—22no—
238C3×Q8—22no—
239C3×Q8—42no—
240C3×Q8C2×#6714yes—
241C2×C3×C4—24no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—42no—
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D412yes—
247C2×C3×C4C2×#6712yes—
248C2×C3×C4C23×D311yescharacteristic
249C2×Dic3—32no—
250C2×Dic3—64no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—122no—
255C4×D3—616no—
256C4×D3—64no—
257C4×D3—62no—
258C4×D3—62no—
259Dic6—34no—
260Dic6—616no—
261Dic6—64no—
262Dic6—62no—
263C3×C8—22no—
264C3⋊C8—62no—
265C2×C9#45114yescomplemented
266C2×C9C2×#12011yescharacteristic
267C2×C9C22×Q1611yescharacteristic
268C2×C9C2×#13711yescharacteristic
269D9—24no—
270C24—91no—
271C2×Q8—22no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—94no—
277C2×Q8—92no—
278C2×Q8—184no—
279C2×Q8—188no—
280C2×Q8—188no—
281C2×Q8—1816no—
282C2×Q8—188no—
283C2×Q8—181no—
284C2×Q8—182no—
285C2×Q8#61114yes—
286C2×Q8C22×D912yes—
287C2×Q8C22×D912yes—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—91no—
291C22×C4—92no—
292C22×C4—92no—
293C22×C4—184no—
294C22×C4—188no—
295C22×C4—181no—
296C22×C4—182no—
297C22×C4—182no—
298C22×C4—181no—
299C22×C4C22×D911yescharacteristic
300Q16—28no—
301Q16—188no—
302C2×C8—22no—
303C2×C8—92no—
304C2×C8—182no—
305C2×C8C22×D912yes—
306C4⋊C4—92no—
307C4⋊C4—184no—
308C4⋊C4—181no—
309C22⋊C4—184no—
310C22×C3D3×Q1612yes—
311C22×C3#91812yes—
312C22×C3#93712yes—
313C22×C3C2×D3×D411yescharacteristic
314C2×D3—34no—
315C2×D3—68no—
316C2×D3—62no—
317C2×D3—62no—
318C3×C4—24no—
319C3×C4—42no—
320C3×C4#93712yes—
321C3×C4C2×D3×D411yescharacteristic
322C3×C4C22×#6711yescharacteristic
323Dic3—64no—
324Dic3—62no—
325Dic3—122no—
326C9C2×#45111yescharacteristic, complemented, Sylow
327C23—92no—
328C23—94no—
329C23—182no—
330C23—182no—
331C23D4×D911yescharacteristic
332Q8—24no—
333Q8—22no—
334Q8—22no—
335Q8—22no—
336Q8—42no—
337Q8—94no—
338Q8—1816no—
339Q8—184no—
340Q8—182no—
341Q8C2×#61114yes—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—92no—
347C2×C4—1816no—
348C2×C4—182no—
349C2×C4—184no—
350C2×C4—182no—
351C2×C4—184no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—362no—
356C2×C4D4×D911yescharacteristic
357C2×C4D4×D912yes—
358C2×C4C2×#61112yes—
359C2×C4C23×D911yescharacteristic
360C8—22no—
361C8—182no—
362C2×C3#518614yes—
363C2×C3C2×D3×Q1611yescharacteristic
364C2×C3C2×#91811yescharacteristic
365C2×C3C2×#93711yescharacteristic
366D3—64no—
367C22—94no—
368C22—182no—
369C22—188no—
370C22—182no—
371C22Q16×D912yes—
372C22#6348012yes—
373C22#6349912yes—
374C22C2×D4×D911yescharacteristic
375C4—24no—
376C4—42no—
377C4—182no—
378C4—184no—
379C4—362no—
380C4#6349912yes—
381C4C2×D4×D911yescharacteristic
382C4C22×#61111yescharacteristic
383C3C2×#518611yescharacteristic
384C2—184no—
385C2#1058886614yesdirect product factor
386C2C2×Q16×D911yescharacteristic
387C2C2×#6348011yescharacteristic
388C2C2×#6349911yescharacteristic
subgroupG/H
centerC23D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC22×C9×Q16C2
socleC23×C3D3×D4
prime radicalC23×D9D4
hypercenterC22×Q16D9
hypocenterC9C2×#451
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C22×C9×Q16C2semidirect
4. C22×#3674C2semidirect
5. C2×#63395C2semidirect
6. #10588866C2direct (N × H)
8. C2×#63376C2semidirect
21. C2×C9×Q16C22semidirect
26. C2×#3674C22semidirect
31. #63395C22semidirect
33. #63376C22semidirect
110. C22×D9Q16semidirect
144. C22×Q16D9semidirect
197. C2×D9C2×Q16semidirect
219. C2×Q16C2×D9semidirect
265. C2×C9#451semidirect
326. C9C2×#451semidirect
385. C2#10588866direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D92
C22×C9×Q162
C2×#635082
C22×#36742
C2×#633952
#105888662
C2×(C2×D9)⋊C82
C2×#633762
C2×#51863