Finite Group Databasebeta

← C2×#10590565 #11865500

Subgroups — C2×#10590565 #11865500

Order 1152.

1301 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 1301 conjugacy classes of subgroups — too many to draw. Only its 228 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×#64102C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic, complemented
3C22×#3717C212yesmaximal
4C2×C3×#810C212yesmaximal, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6#10590565C218yesmaximal, direct product factor
7C2×#4818—32nomaximal
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9C22×C4×C3⋊D3—21no—
10C22×C3×Dic6C2212yes—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64102—22no—
15#64102C2214yes—
16C22×C3×C3⋊C8C2212yes—
17C2×#3724—21no—
18C2×#3724—21no—
19#63873—22no—
20#63873C2214yescomplemented
21C2×#3717—28no—
22C2×#3717C2218yes—
23C3×#810C2218yescomplemented
24#63572C2214yescomplemented
25C2×#944—32no—
26C22×#215—32no—
27C22×#204—32no—
28C2×#893—32no—
29C2×#893—61no—
30C2×C3×#103—32no—
31C2×Dic3⋊C8—32no—
32C2×#810D312yescomplemented
33#4818—316no—
34C23×C3⋊D3—21no—
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—22no—
41C2×C4⋊(C3⋊D3)D414yes—
42C2×C4⋊(C3⋊D3)C2312yes—
43C2×C4×C3⋊D3—24no—
44C2×C4×C3⋊D3—44no—
45C22×C3×Dic3—22no—
46C2×C3×Dic6—24no—
47C2×C3×Dic6—24no—
48C2×C3×Dic6—22no—
49C2×C3×Dic6C2314yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4C2312yes—
52#3752—24no—
53C4×C3⋊Dic3D412yes—
54C4×C3⋊Dic3C2312yes—
55C2×C3×C3⋊C8—24no—
56C2×C3×C3⋊C8C2314yes—
57#3724—24no—
58#3724—24no—
59#3717—216no—
60C2×#461—91noSylow
61C22×C3×Q8—32no—
62C22×D12—32no—
63C22×D12—61no—
64C22×C4×D3—62no—
65C22×C4×D3—62no—
66C22×Dic6C2×D312yes—
67C22×C3×C8—32no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4C2×D312yes—
70#944—38no—
71#944—64no—
72C2×#215—38no—
73C2×#215—68no—
74C2×(C2×D3)⋊C4—62no—
75C2×(C2×D3)⋊C4—62no—
76C2×Dic3⋊C4—62no—
77C2×Dic3⋊C4—62no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—61no—
80C22×C3⋊C8C2×D312yes—
81C2×#204—38no—
82C2×#204—68no—
83#893—38no—
84#893—64no—
85#893—64no—
86#893—64no—
87C3×#103—38no—
88Dic3⋊C8—38no—
89#810C2×D318yescomplemented
90C23×C32C2×D411yescharacteristic
91C22×C3⋊D3—24no—
92C22×C3⋊D3—22no—
93C22×C3⋊D3—42no—
94C22×C3⋊D3—42no—
95C2×C32×C4—22no—
96C2×C32×C4—42no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C32×C4#4112yes—
100C2×C32×C4C2411yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3SD1614yescomplemented
103C2×C3⋊Dic3C2×D412yes—
104C2×C3⋊Dic3C2×D412yes—
105C4⋊(C3⋊D3)—24no—
106C4⋊(C3⋊D3)—22no—
107C4⋊(C3⋊D3)C2×D414yes—
108C4×C3⋊D3—48no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—44no—
111C3×Dic6—24no—
112C3×Dic6—24no—
113C3×Dic6—44no—
114C3×C3⋊C8—24no—
115C22×SD16—92no—
116C2×C4⋊Q8—91no—
117C2×C4×D4—91no—
118#461—98no—
119C2×C4⋊C8—91no—
120C2×#103—32no—
121C23×D3—62no—
122C23×D3—62no—
123C2×C3×Q8—34no—
124C2×C3×Q8—62no—
125C2×C3×Q8—64no—
126C2×C3×Q8—64no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—62no—
131C22×C3×C4C22×D312yes—
132C22×Dic3—22no—
133C22×Dic3—32no—
134C22×Dic3—32no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C2×D12—38no—
138C2×D12—34no—
139C2×D12—62no—
140C2×D12—64no—
141C2×D12—62no—
142C2×D12—64no—
143C2×D12—64no—
144C2×D12—62no—
145C2×C4×D3—68no—
146C2×C4×D3—68no—
147C2×C4×D3—128no—
148C2×C4×D3—128no—
149C2×Dic6—24no—
150C2×Dic6—24no—
151C2×Dic6—22no—
152C2×Dic6C22×D314yes—
153C2×C3×C8—34no—
154C2×C3×C8—64no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4C22×D314yes—
159#215—616no—
160(C2×D3)⋊C4—68no—
161(C2×D3)⋊C4—68no—
162Dic3⋊C4—68no—
163Dic3⋊C4—68no—
164C4×Dic3—34no—
165C4×Dic3—34no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C2×C3⋊C8—24no—
169C2×C3⋊C8C22×D314yes—
170#204—616no—
171C22×C32#12112yes—
172C22×C32C2×SD1612yes—
173C22×C32#13712yes—
174C22×C32C22×D411yescharacteristic
175C2×C3⋊D3—24no—
176C2×C3⋊D3—42no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3—48no—
179C32×C4—42no—
180C32×C4#12112yes—
181C32×C4C22×D411yescharacteristic
182C32×C4C2×#4111yescharacteristic
183C3⋊Dic3—22no—
184C3⋊Dic3C2×SD1614yescomplemented
185C3×Dic3—44no—
186C22×Q8—32no—
187C22×D4—91no—
188C23×C4—181no—
189C2×SD16—98no—
190C2×SD16—188no—
191C22×C8—32no—
192C4⋊Q8—94no—
193C4⋊Q8—182no—
194C4×D4—94no—
195C4×D4—182no—
196C2×C4⋊C4—181no—
197C2×C4⋊C4—181no—
198C2×C4⋊C4D3211yescharacteristic
199C2×C22⋊C4—181no—
200C2×C42—91no—
201C4⋊C8—94no—
202#103—38no—
203C23×C3—21no—
204C23×C3D3×D412yes—
205C22×D3—64no—
206C22×D3—68no—
207C22×D3—68no—
208C22×D3—64no—
209C22×D3—124no—
210C22×D3—124no—
211C22×D3—124no—
212C22×D3—124no—
213C3×Q8—64no—
214C3×Q8—64no—
215C3×Q8—124no—
216C2×C3×C4—24no—
217C2×C3×C4—24no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—21no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—64no—
225C2×C3×C4—124no—
226C2×C3×C4#23514yes—
227C2×C3×C4D3×D414yes—
228C2×C3×C4D3×D412yes—
229C2×C3×C4C23×D312yes—
230C2×Dic3—24no—
231C2×Dic3—38no—
232C2×Dic3—34no—
233C2×Dic3—34no—
234C2×Dic3—44no—
235C2×Dic3—64no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—64no—
239C2×Dic3—122no—
240D12—38no—
241D12—64no—
242D12—64no—
243D12—68no—
244D12—68no—
245D12—64no—
246C4×D3—1216no—
247C4×D3—1216no—
248Dic6—24no—
249Dic6—24no—
250Dic6—44no—
251C3×C8—64no—
252C3⋊C8—24no—
253C2×C32#46114yescomplemented
254C2×C32C2×#12111yescharacteristic
255C2×C32C22×SD1611yescharacteristic
256C2×C32C2×#13711yescharacteristic
257C3⋊D3—44no—
258C24—181no—
259C2×Q8—34no—
260C2×Q8—62no—
261C2×Q8—64no—
262C2×Q8—64no—
263C2×D4—92no—
264C2×D4—94no—
265C2×D4—182no—
266C2×D4—181no—
267C22×C4—21no—
268C22×C4—62no—
269C22×C4—91no—
270C22×C4—91no—
271C22×C4—184no—
272C22×C4—364no—
273C22×C4C2×D3211yescharacteristic
274SD16—1816no—
275C2×C8—34no—
276C2×C8—64no—
277C4⋊C4—21no—
278C4⋊C4—184no—
279C4⋊C4—184no—
280C4⋊C4C2×D3212yes—
281C22⋊C4—184no—
282C42—92no—
283C42—92no—
284C22×C3—21no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3#88414yes—
289C22×C3D3×SD1614yes—
290C22×C3#91814yes—
291C22×C3C2×D3×D412yes—
292C2×D3—68no—
293C2×D3—68no—
294C2×D3—124no—
295C2×D3—124no—
296C2×D3—1216no—
297C2×D3—124no—
298C2×D3—124no—
299C2×D3—1216no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—22no—
303C3×C4—44no—
304C3×C4—44no—
305C3×C4—124no—
306C3×C4#88414yes—
307C3×C4C2×#23512yes—
308C3×C4C2×D3×D412yes—
309Dic3—38no—
310Dic3—44no—
311Dic3—64no—
312Dic3—64no—
313Dic3—122no—
314C32C2×#46111yescharacteristic, complemented, Sylow
315C23—182no—
316C23—184no—
317C23—362no—
318C23—362no—
319C23#381111yescharacteristic
320Q8—64no—
321Q8—64no—
322Q8—124no—
323D4—94no—
324D4—182no—
325D4—184no—
326C2×C4—22no—
327C2×C4—42no—
328C2×C4—64no—
329C2×C4—92no—
330C2×C4—94no—
331C2×C4—92no—
332C2×C4—124no—
333C2×C4—182no—
334C2×C4—368no—
335C2×C4#379812yes—
336C2×C4#380212yes—
337C2×C4#381111yescharacteristic
338C2×C4C22×D3211yescharacteristic
339C8—64no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—24no—
343C2×C3—21no—
344C2×C3#481818yescomplemented
345C2×C3C2×#88412yes—
346C2×C3C2×D3×SD1612yes—
347C2×C3C2×#91812yes—
348D3—128no—
349D3—128no—
350C22—184no—
351C22—362no—
352C22—362no—
353C22—368no—
354C22#6391212yes—
355C22#6393012yes—
356C22#6394512yes—
357C22C2×#381111yescharacteristic
358C4—42no—
359C4—94no—
360C4—124no—
361C4—182no—
362C4#6391212yes—
363C4C2×#379811yescharacteristic
364C4C2×#380211yescharacteristic
365C3—21no—
366C3C2×#481812yescomplemented
367C2—364no—
368C2#1059056514yesdirect product factor
369C2C2×#6391211yescharacteristic
370C2C2×#6393011yescharacteristic
371C2C2×#6394511yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#461
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63873C2semidirect
4. C2×C3×#810C2semidirect
5. C2×#63572C2semidirect
6. #10590565C2direct (N × H)
20. #63873C22semidirect
23. C3×#810C22semidirect
24. #63572C22semidirect
32. C2×#810D3semidirect
89. #810C2×D3semidirect
102. C2×C3⋊Dic3SD16semidirect
184. C3⋊Dic3C2×SD16semidirect
253. C2×C32#461semidirect
314. C32C2×#461semidirect
344. C2×C3#4818semidirect
366. C3C2×#4818semidirect
368. C2#10590565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#638732
C22×#37172
C2×C3×#8102
C2×#635722
#105905652
C2×#48183