Finite Group Databasebeta

← C2×#10590566 #11865655

Subgroups — C2×#10590566 #11865655

Order 1152.

1109 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 1109 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×#64096C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic
3C22×#3719C212yesmaximal
4C2×C3×#810C212yesmaximal
5C2×#63572C211yesmaximal, characteristic
6#10590566C218yesmaximal, direct product factor
7C2×#4795—32nomaximal
8C22×#634C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3750—21no—
12C2×C4×C3⋊Dic3—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64096—22no—
15#64096C2214yes—
16C22×C3×C3⋊C8C2212yes—
17C2×#3724—21no—
18C2×#3724—21no—
19#63873—22no—
20#63873C2214yes—
21C2×#3719—28no—
22C2×#3719C2218yes—
23C3×#810C2218yes—
24#63572C2214yes—
25C2×#944—32no—
26C22×#216—32no—
27C22×Dic12—32no—
28C2×#887—32no—
29C2×#887—61no—
30C2×C3×#103—32no—
31C2×Dic3⋊C8—32no—
32C2×#810D312yes—
33#4795—316no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×#634—21no—
40C2×#634—22no—
41C2×#634D414yes—
42C2×#634C2312yes—
43C22×C3×Dic3—22no—
44C2×C3×Dic6—24no—
45C2×C3×Dic6—24no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6C2314yes—
48C32×C4⋊C4—21no—
49C32×C4⋊C4C2312yes—
50#3750—24no—
51C4×C3⋊Dic3—24no—
52C4×C3⋊Dic3D412yes—
53C4×C3⋊Dic3C2312yes—
54C2×C3×C3⋊C8—24no—
55C2×C3×C3⋊C8C2314yes—
56#3724—24no—
57#3724—24no—
58#3719—216no—
59C2×#462—91noSylow
60C22×C3×Q8—32no—
61C22×Dic6—32no—
62C22×Dic6—61no—
63C22×Dic6C2×D312yes—
64C22×C3×C8—32no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4C2×D312yes—
67#944—38no—
68#944—64no—
69C2×#216—38no—
70C2×#216—68no—
71C2×Dic3⋊C4—62no—
72C2×Dic3⋊C4—62no—
73C2×Dic3⋊C4—62no—
74C2×Dic3⋊C4—62no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3—62no—
78C2×C4×Dic3—62no—
79C22×C3⋊C8C2×D312yes—
80C2×Dic12—38no—
81C2×Dic12—68no—
82#887—38no—
83#887—64no—
84#887—64no—
85#887—64no—
86C3×#103—38no—
87Dic3⋊C8—38no—
88#810C2×D318yes—
89C23×C32C2×D411yescharacteristic
90C2×C32×C4—22no—
91C2×C32×C4—42no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D412yes—
94C2×C32×C4#4112yes—
95C2×C32×C4C2411yescharacteristic
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3Q1614yescomplemented
100C2×C3⋊Dic3C2×D412yes—
101C2×C3⋊Dic3C2×D412yes—
102#634—24no—
103#634—22no—
104#634C2×D414yes—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—44no—
107C3×Dic6—24no—
108C3×Dic6—24no—
109C3×Dic6—44no—
110C3×C3⋊C8—24no—
111C22×Q16—92no—
112C2×C4⋊Q8—91no—
113C2×C4×Q8—91no—
114#462—98no—
115C2×C4⋊C8—91no—
116C2×#103—32no—
117C2×C3×Q8—34no—
118C2×C3×Q8—62no—
119C2×C3×Q8—64no—
120C2×C3×Q8—64no—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—21no—
124C22×C3×C4—62no—
125C22×C3×C4C22×D312yes—
126C22×Dic3—22no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C2×Dic6—24no—
134C2×Dic6—24no—
135C2×Dic6—22no—
136C2×Dic6—38no—
137C2×Dic6—34no—
138C2×Dic6—62no—
139C2×Dic6—64no—
140C2×Dic6—62no—
141C2×Dic6—64no—
142C2×Dic6—64no—
143C2×Dic6—62no—
144C2×Dic6C22×D314yes—
145C2×C3×C8—34no—
146C2×C3×C8—64no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4C22×D314yes—
151#216—616no—
152Dic3⋊C4—68no—
153Dic3⋊C4—68no—
154Dic3⋊C4—68no—
155Dic3⋊C4—68no—
156C4×Dic3—34no—
157C4×Dic3—34no—
158C4×Dic3—62no—
159C4×Dic3—62no—
160C4×Dic3—68no—
161C4×Dic3—68no—
162C2×C3⋊C8—24no—
163C2×C3⋊C8C22×D314yes—
164Dic12—616no—
165C22×C32#12112yes—
166C22×C32C2×Q1612yes—
167C22×C32#13712yes—
168C22×C32C22×D411yescharacteristic
169C32×C4—42no—
170C32×C4#12112yes—
171C32×C4C22×D411yescharacteristic
172C32×C4C2×#4111yescharacteristic
173C3⋊Dic3—24no—
174C3⋊Dic3—22no—
175C3⋊Dic3C2×Q1614yescomplemented
176C3×Dic3—44no—
177C22×Q8—32no—
178C22×Q8—91no—
179C2×Q16—98no—
180C2×Q16—188no—
181C22×C8—32no—
182C4⋊Q8—94no—
183C4⋊Q8—182no—
184C4×Q8—94no—
185C4×Q8—182no—
186C2×C4⋊C4—181no—
187C2×C4⋊C4—181no—
188C2×C4⋊C4—181no—
189C2×C4⋊C4D3211yescharacteristic
190C2×C42—91no—
191C2×C42—181no—
192C4⋊C8—94no—
193#103—38no—
194C23×C3—21no—
195C23×C3D3×D412yes—
196C3×Q8—64no—
197C3×Q8—64no—
198C3×Q8—124no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—21no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—44no—
206C2×C3×C4—44no—
207C2×C3×C4—64no—
208C2×C3×C4—124no—
209C2×C3×C4#23514yes—
210C2×C3×C4D3×D414yes—
211C2×C3×C4D3×D412yes—
212C2×C3×C4C23×D312yes—
213C2×Dic3—24no—
214C2×Dic3—38no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—44no—
218C2×Dic3—64no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—64no—
222C2×Dic3—68no—
223C2×Dic3—68no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—122no—
227Dic6—24no—
228Dic6—24no—
229Dic6—38no—
230Dic6—44no—
231Dic6—64no—
232Dic6—64no—
233Dic6—68no—
234Dic6—68no—
235Dic6—64no—
236C3×C8—64no—
237C3⋊C8—24no—
238C2×C32#46214yescomplemented
239C2×C32C2×#12111yescharacteristic
240C2×C32C22×Q1611yescharacteristic
241C2×C32C2×#13711yescharacteristic
242C2×Q8—34no—
243C2×Q8—62no—
244C2×Q8—64no—
245C2×Q8—64no—
246C2×Q8—92no—
247C2×Q8—94no—
248C2×Q8—182no—
249C2×Q8—181no—
250C22×C4—21no—
251C22×C4—62no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—181no—
255C22×C4C2×D3211yescharacteristic
256Q16—1816no—
257C2×C8—34no—
258C2×C8—64no—
259C4⋊C4—21no—
260C4⋊C4—184no—
261C4⋊C4—184no—
262C4⋊C4—184no—
263C4⋊C4C2×D3212yes—
264C42—92no—
265C42—92no—
266C42—184no—
267C22×C3—21no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3#88414yes—
272C22×C3#91514yes—
273C22×C3D3×Q1614yes—
274C22×C3C2×D3×D412yes—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—22no—
278C3×C4—44no—
279C3×C4—44no—
280C3×C4—124no—
281C3×C4#88414yes—
282C3×C4C2×#23512yes—
283C3×C4C2×D3×D412yes—
284Dic3—38no—
285Dic3—44no—
286Dic3—64no—
287Dic3—68no—
288Dic3—68no—
289Dic3—64no—
290Dic3—122no—
291C32C2×#46211yescharacteristic, complemented, Sylow
292C23#381111yescharacteristic
293Q8—64no—
294Q8—64no—
295Q8—94no—
296Q8—124no—
297Q8—182no—
298Q8—184no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—64no—
302C2×C4—92no—
303C2×C4—94no—
304C2×C4—92no—
305C2×C4—124no—
306C2×C4—182no—
307C2×C4—184no—
308C2×C4—182no—
309C2×C4#379812yes—
310C2×C4#380212yes—
311C2×C4#381111yescharacteristic
312C2×C4C22×D3211yescharacteristic
313C8—64no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—24no—
317C2×C3—21no—
318C2×C3#479518yescomplemented
319C2×C3C2×#88412yes—
320C2×C3C2×#91512yes—
321C2×C3C2×D3×Q1612yes—
322C22#6391212yes—
323C22#6393112yes—
324C22#6394412yes—
325C22C2×#381111yescharacteristic
326C4—42no—
327C4—94no—
328C4—124no—
329C4—182no—
330C4—184no—
331C4#6391212yes—
332C4C2×#379811yescharacteristic
333C4C2×#380211yescharacteristic
334C3—21no—
335C3C2×#479512yescomplemented
336C2#1059056614yesdirect product factor
337C2C2×#6391211yescharacteristic
338C2C2×#6393111yescharacteristic
339C2C2×#6394411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#462
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
6. #10590566C2direct (N × H)
99. C2×C3⋊Dic3Q16semidirect
175. C3⋊Dic3C2×Q16semidirect
238. C2×C32#462semidirect
291. C32C2×#462semidirect
318. C2×C3#4795semidirect
335. C3C2×#4795semidirect
336. C2#10590566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638732
C22×#37192
C2×C3×#8102
C2×#635722
#105905662
C2×#47953