Finite Group Databasebeta

← C2×#10589533 #11920431

Subgroups — C2×#10589533 #11920431

Order 1152.

557 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 557 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×2−1+4⋊C9C211yesmaximal, characteristic, complemented
2C2×#63692C211yesmaximal, characteristic, complemented
3#10589533C214yesmaximal, direct product factor
4C2×#63422C211yesmaximal, characteristic, complemented
5C2×#5245—31nomaximal
62−1+4⋊C9—21no—
72−1+4⋊C9C2212yescomplemented
8C2×#41⋊C9C2211yescharacteristic
9C22×Q8⋊C9—21no—
10#63692—21no—
11#63692C2212yescomplemented
12C2×#3689—21no—
13C2×#3673—41nomaximal
14#63422C2212yescomplemented
15C2×C3×2−1+4D311yescharacteristic
16C2×#949—31no—
17C2×#949—31no—
18C2×#947—31no—
19#5245—34no—
20#5245—34no—
21C2×#837—31no—
22C2×#837—31no—
23C2×#836—31no—
24C2×D4×C9—41no—
25C2×D36—41no—
26#41⋊C9D411yescharacteristic
27#41⋊C9C2311yescharacteristic
28C2×Q8⋊C9—22no—
29C2×Q8⋊C9D411yescharacteristic
30#3689—22no—
31#3673—44no—
32C2×C9⋊C8—41no—
33C2×#454—91noSylow
34C3×2−1+4—21no—
35C3×2−1+4—32no—
36C3×2−1+4—61no—
37C3×2−1+4C2×D312yes—
38C2×C3×#41—31no—
39C2×C3×#41—61no—
40C2×C3×#41C2×D311yescharacteristic
41C22×C3×Q8—21no—
42C22×C3×Q8—31no—
43C22×D12—31no—
44#949—32no—
45#949—34no—
46#949—32no—
47#949—61no—
48#949—62no—
49#949—61no—
50#947—34no—
51#947—62no—
52C2×#215—61no—
53C2×#215—61no—
54C2×#213—61no—
55C2×#213—61no—
56C2×(C2×D3)⋊C4—62no—
57C2×C4×Dic3—31no—
58C2×#208—31no—
59C2×#208—31no—
60#837—32no—
61#837—34no—
62#837—32no—
63#836—34no—
64C23×C9—81no—
65C22×D9—81no—
66D4×C9—42no—
67D4×C9—81no—
68C2×C4×C9—41no—
69D36—42no—
70D36—81no—
71Q8⋊C9C2×D411yescharacteristic
72C9⋊C8—42no—
73C2×2−1+4D911yescharacteristic, complemented
74C2×AGL(1,ℤ/8)—91no—
75C2×AGL(1,ℤ/8)—91no—
76C2×#124—91no—
77#454—94no—
78#454—94no—
79C2×#104—91no—
80C2×#104—91no—
81C2×#101—91no—
82C23×D3—61no—
83C3×#41—31no—
84C3×#41—31no—
85C3×#41—32no—
86C3×#41—32no—
87C3×#41—62no—
88C3×#41—61no—
89C3×#41—61no—
90C3×#41—64no—
91C3×#41—62no—
92C3×#41#6711yescharacteristic
93C3×#41C22×D311yescharacteristic
94C2×C3×Q8—22no—
95C2×C3×Q8—32no—
96C2×C3×Q8—32no—
97C2×C3×Q8—31no—
98C2×C3×Q8—61no—
99C2×C3×Q8—61no—
100C2×C3×Q8—61no—
101C2×C3×Q8—62no—
102C2×C3×Q8#6711yescharacteristic
103C2×C3×D4—31no—
104C2×C3×D4—61no—
105C2×C3×D4S411yescharacteristic
106C22×C3×C4—31no—
107C22×C3×C4—32no—
108C22×C3×C4—61no—
109C22×Dic3—61no—
110C2×D12—32no—
111C2×D12—61no—
112C2×D12—61no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116#215—62no—
117#215—64no—
118#215—62no—
119#213—62no—
120#213—62no—
121#213—64no—
122(C2×D3)⋊C4—68no—
123C4×Dic3—32no—
124C4×Dic3—61no—
125#208—32no—
126#208—32no—
127#208—61no—
128#208—61no—
129C2×C3⋊C8—61no—
130C2×C3⋊C8—61no—
131C22×C9—41no—
132C22×C9—82no—
133C22×C9—162no—
134C2×D9—82no—
135C2×D9—162no—
136C4×C9—41no—
137C4×C9—41no—
1382−1+4—21no—
1392−1+4—32no—
1402−1+4—61no—
1412−1+4C2×D912yescomplemented
142C2×#41—31no—
143C2×#41—61no—
144C2×#41C2×D911yescharacteristic
145C22×Q8—21no—
146C22×Q8—31no—
147C22×D4—91no—
148AGL(1,ℤ/8)—92no—
149AGL(1,ℤ/8)—94no—
150AGL(1,ℤ/8)—92no—
151AGL(1,ℤ/8)—181no—
152AGL(1,ℤ/8)—182no—
153AGL(1,ℤ/8)—181no—
154C2×SD16—181no—
155C2×SD16—181no—
156C2×D8—181no—
157C2×D8—181no—
158C2×M16—91no—
159C2×M16—91no—
160#124—94no—
161#124—182no—
162C2×C22⋊C4—182no—
163C2×C42—91no—
164#104—92no—
165#104—94no—
166#104—92no—
167#101—94no—
168C23×C3—21no—
169C23×C3—31no—
170C22×D3—62no—
171C22×D3—121no—
172C22×D3—124no—
173C22×D3—121no—
174C3×Q8—31no—
175C3×Q8—32no—
176C3×Q8—62no—
177C3×Q8—62no—
178C3×Q8—61no—
179C3×Q8C2×#6711yescharacteristic
180C3×D4—21no—
181C3×D4—31no—
182C3×D4—31no—
183C3×D4—61no—
184C3×D4—62no—
185C3×D4—62no—
186C3×D4C2×S412yes—
187C2×C3×C4—31no—
188C2×C3×C4—31no—
189C2×C3×C4—31no—
190C2×C3×C4—31no—
191C2×C3×C4—31no—
192C2×C3×C4—34no—
193C2×C3×C4—62no—
194C2×C3×C4—62no—
195C2×C3×C4—62no—
196C2×C3×C4—61no—
197C2×C3×C4C2×S411yescharacteristic
198C2×Dic3—62no—
199C2×Dic3—122no—
200D12—62no—
201D12—62no—
202D12—121no—
203D12—121no—
204C3⋊C8—62no—
205C3⋊C8—62no—
206C2×C9—41no—
207C2×C9—42no—
208C2×C9—162no—
209D9—162no—
210C24—181no—
211#41—31no—
212#41—31no—
213#41—32no—
214#41—32no—
215#41—62no—
216#41—61no—
217#41—61no—
218#41—64no—
219#41—62no—
220#41#61111yescharacteristic
221#41C22×D911yescharacteristic
222C2×Q8—22no—
223C2×Q8—32no—
224C2×Q8—32no—
225C2×Q8—31no—
226C2×Q8—61no—
227C2×Q8—61no—
228C2×Q8—61no—
229C2×Q8—62no—
230C2×Q8#61111yescharacteristic
231C2×D4—31no—
232C2×D4—61no—
233C2×D4—92no—
234C2×D4—181no—
235C2×D4—181no—
236C2×D4—181no—
237C2×D4—181no—
238C2×D4—181no—
239C2×D4(C22⋊C9)⋊C211yescharacteristic
240C22×C4—31no—
241C22×C4—32no—
242C22×C4—61no—
243C22×C4—181no—
244SD16—182no—
245SD16—184no—
246SD16—182no—
247D8—182no—
248D8—182no—
249D8—184no—
250M16—92no—
251M16—92no—
252M16—181no—
253M16—181no—
254C2×C8—181no—
255C2×C8—181no—
256C22⋊C4—188no—
257C42—92no—
258C42—181no—
259C22×C3—22no—
260C22×C3—31no—
261C22×C3—31no—
262C22×C3—42no—
263C22×C3—62no—
264C22×C3GL(2,ℤ/4)11yescharacteristic
265C2×D3—124no—
266C2×D3—122no—
267C2×D3—242no—
268C2×D3—242no—
269C3×C4—31no—
270C3×C4—31no—
271C3×C4—62no—
272C3×C4GL(2,ℤ/4)11yescharacteristic
273C3×C4C22×S411yescharacteristic
274Dic3—122no—
275C9—41noSylow
276C23—21no—
277C23—31no—
278C23—182no—
279C23—361no—
280C23—364no—
281C23—361no—
282Q8—31no—
283Q8—32no—
284Q8—62no—
285Q8—62no—
286Q8—61no—
287Q8C2×#61111yescharacteristic
288D4—21no—
289D4—31no—
290D4—31no—
291D4—61no—
292D4—62no—
293D4—62no—
294D4—182no—
295D4—182no—
296D4—361no—
297D4—361no—
298D4C2×(C22⋊C9)⋊C212yes—
299C2×C4—31no—
300C2×C4—31no—
301C2×C4—31no—
302C2×C4—31no—
303C2×C4—31no—
304C2×C4—34no—
305C2×C4—62no—
306C2×C4—62no—
307C2×C4—62no—
308C2×C4—61no—
309C2×C4—182no—
310C2×C4—362no—
311C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
312C8—182no—
313C8—182no—
314C2×C3—42no—
315C2×C3—61no—
316C2×C3—61no—
317C2×C3#543112yes—
318C2×C3C2×GL(2,ℤ/4)11yescharacteristic
319D3—242no—
320C22—22no—
321C22—31no—
322C22—31no—
323C22—42no—
324C22—62no—
325C22—364no—
326C22—362no—
327C22—722no—
328C22—722no—
329C22#6369411yescharacteristic
330C4—31no—
331C4—31no—
332C4—62no—
333C4—362no—
334C4#6369411yescharacteristic
335C4C22×(C22⋊C9)⋊C211yescharacteristic
336C3C2×#543111yescharacteristic
337C2—42no—
338C2—61no—
339C2—61no—
340C2—722no—
341C2#1058953312yesdirect product factor
342C2C2×#6369411yescharacteristic
subgroupG/H
centerC22#63694
commutator, cosocle#41⋊C9C23
FrattiniC3×C4C22×S4
FittingC2×C3×2−1+4D3
socleC22×C3GL(2,ℤ/4)
hypercenterC2×D4(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ #41⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4⋊C9C2semidirect
2. C2×#63692C2semidirect
3. #10589533C2direct (N × H)
4. C2×#63422C2semidirect
7. 2−1+4⋊C9C22semidirect
11. #63692C22semidirect
14. #63422C22semidirect
73. C2×2−1+4D9semidirect
141. 2−1+4C2×D9semidirect
341. C2#10589533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
C2×#636922
#105895332
C2×#634222
C2×#52453
C2×#36734