Finite Group Databasebeta

← C2×#10588741 #11864806

Subgroups — C2×#10588741 #11864806

Order 1152.

1140 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63710C211yesmaximal, characteristic
2C2×C9×#124C211yesmaximal, characteristic, complemented
3C2×#63505C212yesmaximal, complemented
4C2×#63391C211yesmaximal, characteristic, complemented
5#10588741C218yesmaximal, direct product factor
6C2×#63364C212yesmaximal, complemented
7C2×#5061—31nomaximal
8C22×Q8×C9C2211yescharacteristic, complemented
9C22×D4×C9C2211yescharacteristic
10C22×#611—22no—
11#63710—22no—
12#63710—24no—
13#63710C2214yes—
14C2×#3699—22no—
15C2×D4×D9—22no—
16C2×#3697C2212yes—
17C9×#124—22no—
18C9×#124C2214yescomplemented
19C2×C9×C22⋊C4—22no—
20C2×C42×C9C2211yescharacteristic, complemented
21#63505—24no—
22#63505C2218yescomplemented
23C2×#3675—22no—
24C2×#3674—22no—
25C2×#3667C2212yescomplemented
26#63391C2214yescomplemented
27#63364C2218yescomplemented
28C2×#1004—31no—
29C2×C3×#124D311yescharacteristic
30C2×#942—32no—
31C2×#833—31no—
32#5061—38no—
33C2×#805—32no—
34C24×C9D412yes—
35C23×D9—22no—
36C2×Q8×C9—21no—
37C2×Q8×C9—22no—
38C2×Q8×C9—22no—
39C2×Q8×C9C2312yescomplemented
40C2×D4×C9—22no—
41C2×D4×C9—22no—
42C2×D4×C9D412yes—
43C2×D4×C9C2312yes—
44C22×C4×C9—21no—
45C22×C4×C9—21no—
46C22×C4×C9C2311yescharacteristic
47C2×#611—24no—
48C2×#611—28no—
49C2×#611—22no—
50C2×#611—28no—
51C22×Dic9—22no—
52#3699—28no—
53#3699—28no—
54D4×D9—28no—
55D4×D9—28no—
56#3697—22no—
57#3697—22no—
58#3697D414yes—
59#3697C2314yes—
60C2×D36D412yes—
61C2×C4×D9—22no—
62C2×Dic18D412yes—
63C9×C22⋊C4—28no—
64C42×C9—21no—
65C42×C9C2312yescomplemented
66#3675—28no—
67#3674—28no—
68#3667—22no—
69#3667C2314yescomplemented
70C2×C9⋊C8—22no—
71C2×#455—91noSylow
72C22×C3×Q8C2×D311yescharacteristic
73C22×C3×D4C2×D311yescharacteristic
74C22×#67—62no—
75#1004—34no—
76#1004—64no—
77#1004—62no—
78C2×#237—62no—
79C2×D3×D4—62no—
80C2×#235—32no—
81C3×#124—22no—
82C3×#124C2×D314yes—
83C2×C3×C22⋊C4—22no—
84C2×C3×C42C2×D311yescharacteristic
85C2×#216—62no—
86#942—38no—
87#942—64no—
88C2×#215—62no—
89C2×#208—32no—
90#833—34no—
91#805—38no—
92C23×C9—22no—
93C23×C9—22no—
94C23×C9—44no—
95C23×C9C2×D411yescharacteristic
96C23×C9C2×D414yes—
97C22×D9—22no—
98C22×D9—28no—
99C22×D9—84no—
100Q8×C9—24no—
101Q8×C9—42no—
102D4×C9—24no—
103D4×C9—24no—
104C2×C4×C9—22no—
105C2×C4×C9—22no—
106C2×C4×C9—42no—
107C2×C4×C9—41no—
108C2×C4×C9—41no—
109C2×C4×C9C2×D412yes—
110C2×C4×C9C2×D412yes—
111C2×C4×C9C2×D411yescharacteristic
112C2×C4×C9C2411yescharacteristic
113#611—216no—
114#611—24no—
115#611—24no—
116C2×Dic9—28no—
117C2×Dic9—22no—
118D36—22no—
119D36C2×D414yes—
120C4×D9—24no—
121C4×D9—24no—
122Dic18—22no—
123Dic18C2×D414yes—
124C9⋊C8—24no—
125C2×H(5,𝔽2)—91no—
126C2×#137—92no—
127C2×#124D911yescharacteristic, complemented
128#455—98no—
129C2×#104—92no—
130C2×#100—91no—
131C24×C3#6712yes—
132C23×D3—62no—
133C2×C3×Q8—21no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8C22×D312yes—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4#6712yes—
140C2×C3×D4C22×D312yes—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4C22×D311yescharacteristic
144C2×#67—64no—
145C2×#67—68no—
146C2×#67—62no—
147C2×#67—68no—
148C22×Dic3—62no—
149#237—68no—
150#237—68no—
151D3×D4—68no—
152D3×D4—68no—
153#235—34no—
154#235—34no—
155#235—62no—
156#235—62no—
157C2×D12—32no—
158C2×C4×D3—62no—
159C2×Dic6—32no—
160C3×C22⋊C4—28no—
161C3×C42—21no—
162C3×C42C22×D312yes—
163#216—68no—
164#215—68no—
165#208—34no—
166#208—62no—
167C2×C3⋊C8—62no—
168C22×C9—22no—
169C22×C9—24no—
170C22×C9—44no—
171C22×C9—44no—
172C22×C9—82no—
173C22×C9#12011yescharacteristic
174C22×C9#12011yescharacteristic
175C22×C9C22×D411yescharacteristic
176C2×D9—24no—
177C2×D9—44no—
178C2×D9—88no—
179C4×C9—42no—
180C4×C9—42no—
181C4×C9#12012yes—
182C4×C9C22×D412yes—
183Dic9—24no—
184H(5,𝔽2)—94no—
185H(5,𝔽2)—184no—
186H(5,𝔽2)—182no—
187C2×#41—92no—
188C2×#41—182no—
189C22×Q8C2×D911yescharacteristic, complemented
190C22×D4—182no—
191C22×D4—182no—
192C22×D4C2×D911yescharacteristic
193#137—98no—
194#137—184no—
195C2×Q16—182no—
196C2×SD16—182no—
197C2×M16—92no—
198#124—22no—
199#124C2×D914yescomplemented
200C2×C22⋊C4—22no—
201C2×C42C2×D911yescharacteristic, complemented
202#104—98no—
203#100—94no—
204C23×C3—22no—
205C23×C3—22no—
206C23×C3—44no—
207C23×C3C2×#6711yescharacteristic
208C23×C3C2×#6714yes—
209C22×D3—62no—
210C22×D3—68no—
211C22×D3—244no—
212C3×Q8—24no—
213C3×Q8—42no—
214C3×D4—24no—
215C3×D4—24no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—42no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4D3×D412yes—
222C2×C3×C4D3×D412yes—
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C23×D311yescharacteristic
225#67—616no—
226#67—64no—
227#67—64no—
228C2×Dic3—68no—
229C2×Dic3—62no—
230D12—34no—
231D12—62no—
232C4×D3—64no—
233C4×D3—64no—
234Dic6—34no—
235Dic6—62no—
236C3⋊C8—64no—
237C2×C9—21no—
238C2×C9—21no—
239C2×C9—44no—
240C2×C9#45512yescomplemented
241C2×C9C2×#12011yescharacteristic
242D9—44no—
243C24—182no—
244C24#61112yes—
245#41—94no—
246#41—94no—
247#41—188no—
248#41—188no—
249#41—182no—
250#41—182no—
251C2×Q8—21no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—92no—
255C2×Q8C22×D912yescomplemented
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—92no—
259C2×D4—188no—
260C2×D4—188no—
261C2×D4—184no—
262C2×D4—188no—
263C2×D4—182no—
264C2×D4—188no—
265C2×D4#61112yes—
266C2×D4C22×D912yes—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—182no—
270C22×C4—182no—
271C22×C4C22×D911yescharacteristic
272Q16—188no—
273SD16—188no—
274M16—94no—
275M16—182no—
276C2×C8—182no—
277C22⋊C4—28no—
278C42—21no—
279C42C22×D912yescomplemented
280C22×C3—22no—
281C22×C3—24no—
282C22×C3—44no—
283C22×C3—44no—
284C22×C3—82no—
285C22×C3#93711yescharacteristic
286C22×C3#93711yescharacteristic
287C22×C3C22×#6711yescharacteristic
288C2×D3—64no—
289C2×D3—124no—
290C2×D3—248no—
291C3×C4—42no—
292C3×C4—42no—
293C3×C4#93712yes—
294C3×C4C2×D3×D412yes—
295Dic3—64no—
296C9C2×#45511yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—44no—
300C23—188no—
301C23—182no—
302C23—724no—
303C23C2×#61111yescharacteristic
304C23C2×#61114yes—
305Q8—24no—
306Q8—42no—
307Q8—94no—
308Q8—182no—
309D4—24no—
310D4—24no—
311D4—94no—
312D4—1816no—
313D4—184no—
314D4—184no—
315D4—182no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—188no—
322C2×C4—182no—
323C2×C4—184no—
324C2×C4—184no—
325C2×C4D4×D912yes—
326C2×C4D4×D912yes—
327C2×C4C2×#61111yescharacteristic
328C2×C4C23×D911yescharacteristic
329C8—184no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—44no—
333C2×C3#506112yes—
334C2×C3C2×#93711yescharacteristic
335D3—124no—
336C22—22no—
337C22—24no—
338C22—44no—
339C22—44no—
340C22—82no—
341C22—184no—
342C22—364no—
343C22—728no—
344C22#6349911yescharacteristic
345C22#6349911yescharacteristic
346C22C22×#61111yescharacteristic
347C4—42no—
348C4—42no—
349C4—184no—
350C4#6349912yes—
351C4C2×D4×D912yes—
352C3C2×#506111yescharacteristic
353C2—21no—
354C2—21no—
355C2—44no—
356C2—364no—
357C2#1058874112yesdirect product factor
358C2C2×#6349911yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×#124C2
socleC22×C3#937
prime radicalC2×#63710C2
hypercenterC2×#124D9
hypocenterC9C2×#455
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×C9×#124C2semidirect
3. C2×#63505C2semidirect
4. C2×#63391C2semidirect
5. #10588741C2direct (N × H)
6. C2×#63364C2semidirect
8. C22×Q8×C9C22semidirect
18. C9×#124C22semidirect
20. C2×C42×C9C22semidirect
22. #63505C22semidirect
25. C2×#3667C22semidirect
26. #63391C22semidirect
27. #63364C22semidirect
39. C2×Q8×C9C23semidirect
65. C42×C9C23semidirect
69. #3667C23semidirect
127. C2×#124D9semidirect
189. C22×Q8C2×D9semidirect
199. #124C2×D9semidirect
201. C2×C42C2×D9semidirect
240. C2×C9#455semidirect
255. C2×Q8C22×D9semidirect
279. C42C22×D9semidirect
296. C9C2×#455semidirect
357. C2#10588741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#637102
C2×C9×#1242
C2×#635052
C2×#633912
#105887412
C2×#633642
C2×#50613