Finite Group Databasebeta

← C2×#10591538 #11873403

Subgroups — C2×#10591538 #11873403

Order 1152.

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

normal subgroups only

This group has 993 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×#64153C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic
3C2×C3×#835C212yesmaximal
4#10591538C218yesmaximal, direct product factor
5C2×#63567C212yesmaximal
6C2×#63553C211yesmaximal, characteristic
7C2×#4792—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C22×#627—21no—
11#64153—22no—
12#64153C2214yes—
13C2×#3750—21no—
14C2×#3750—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63919—22no—
20#63919C2214yes—
21C3×#835C2218yes—
22#63567C2218yes—
23#63553C2214yes—
24C2×#944—32no—
25C2×#944—61no—
26C2×#888—32no—
27C2×C3×#103—32no—
28C2×#835D312yes—
29C2×#816—32no—
30C2×C8×Dic3—32no—
31C2×#810—32no—
32#4792—316no—
33C2×C32×Q8—21no—
34C2×C32×Q8—24no—
35C2×C32×Q8C2312yes—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×#634—24no—
42C2×#634—21no—
43C2×#634C2312yes—
44C22×C3×Dic3—22no—
45C2×#627—24no—
46C2×#627—44no—
47#3750—24no—
48#3750—24no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3C2312yes—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2314yes—
53C2×C3×C3⋊C8—24no—
54C2×C3×C3⋊C8C2314yes—
55#3724—24no—
56C2×#487—91noSylow
57C22×C3×Q8—21no—
58C22×C3×Q8C2×D312yes—
59C22×Dic6—32no—
60C22×Dic6—61no—
61C22×Dic6—62no—
62C22×C3×C8—32no—
63C2×C3×C4⋊C4—32no—
64#944—38no—
65#944—64no—
66#944—64no—
67#944—64no—
68C2×C4⋊Dic3C2×D312yes—
69C2×Dic3⋊C4—62no—
70C2×Dic3⋊C4—62no—
71C2×Dic3⋊C4—62no—
72C2×Dic3⋊C4—62no—
73C2×Dic3⋊C4—62no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—61no—
76C22×C3⋊C8C2×D312yes—
77#888—38no—
78#888—64no—
79C3×#103—38no—
80#835C2×D318yes—
81#816—38no—
82C8×Dic3—38no—
83#810—38no—
84C23×C32C2×D411yescharacteristic
85C32×Q8—24no—
86C32×Q8—42no—
87C2×C32×C4—22no—
88C2×C32×C4—42no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4#4114yes—
91C2×C32×C4C2411yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—42no—
94C2×C3⋊Dic3SD1614yes—
95C2×C3⋊Dic3Q1614yes—
96C2×C3⋊Dic3C2×D412yes—
97C2×C3⋊Dic3C2×D412yes—
98#634—24no—
99#634—42no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—44no—
102#627—48no—
103C3×C3⋊C8—24no—
104C2×C4⋊Q8—91no—
105C2×C4⋊Q8—91no—
106#487—98no—
107C2×#103—32no—
108C2×#103—92no—
109C2×C4×C8—91no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8—24no—
113C2×C3×Q8—24no—
114C2×C3×Q8—22no—
115C2×C3×Q8—44no—
116C2×C3×Q8C22×D314yes—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C22×Dic3—22no—
123C22×Dic3—32no—
124C22×Dic3—32no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C2×Dic6—34no—
130C2×Dic6—62no—
131C2×Dic6—64no—
132C2×Dic6—64no—
133C2×Dic6—68no—
134C2×Dic6—62no—
135C2×Dic6—62no—
136C2×Dic6—124no—
137C2×Dic6—128no—
138C2×C3×C8—34no—
139C2×C3×C8—64no—
140C3×C4⋊C4—34no—
141C3×C4⋊C4—62no—
142C4⋊Dic3—22no—
143C4⋊Dic3C22×D314yes—
144Dic3⋊C4—68no—
145Dic3⋊C4—68no—
146Dic3⋊C4—68no—
147Dic3⋊C4—68no—
148Dic3⋊C4—68no—
149C4×Dic3—34no—
150C4×Dic3—34no—
151C4×Dic3—62no—
152C4×Dic3—62no—
153C2×C3⋊C8—24no—
154C2×C3⋊C8C22×D314yes—
155C22×C32#12412yes—
156C22×C32C2×SD1612yes—
157C22×C32C2×Q1612yes—
158C22×C32C22×D411yescharacteristic
159C32×C4—42no—
160C32×C4#12412yes—
161C32×C4C2×#4112yes—
162C3⋊Dic3—42no—
163C3⋊Dic3C2×SD1614yes—
164C3⋊Dic3C2×Q1614yes—
165C3×Dic3—44no—
166C22×Q8—91no—
167C22×Q8—181no—
168C22×Q8D3211yescharacteristic
169C22×C8—32no—
170C4⋊Q8—94no—
171C4⋊Q8—94no—
172C4⋊Q8—182no—
173C4⋊Q8—182no—
174C2×C4⋊C4—32no—
175C2×C4⋊C4—181no—
176C2×C4⋊C4—181no—
177C2×C4⋊C4—181no—
178C2×C42—91no—
179#103—38no—
180#103—98no—
181C4×C8—94no—
182C23×C3—21no—
183C23×C3D3×D412yes—
184C3×Q8—24no—
185C3×Q8—24no—
186C3×Q8—44no—
187C3×Q8—44no—
188C3×Q8—44no—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—21no—
192C2×C3×C4—24no—
193C2×C3×C4—21no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4—64no—
197C2×C3×C4—124no—
198C2×C3×C4#23514yes—
199C2×C3×C4D3×D412yes—
200C2×C3×C4#23714yes—
201C2×C3×C4C23×D312yes—
202C2×Dic3—24no—
203C2×Dic3—38no—
204C2×Dic3—38no—
205C2×Dic3—34no—
206C2×Dic3—34no—
207C2×Dic3—44no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—124no—
215C2×Dic3—124no—
216Dic6—64no—
217Dic6—64no—
218Dic6—124no—
219Dic6—1216no—
220Dic6—124no—
221Dic6—124no—
222C3×C8—64no—
223C3⋊C8—24no—
224C2×C32#48714yescomplemented
225C2×C32C2×#12411yescharacteristic
226C2×C32C22×SD1611yescharacteristic
227C2×C32C22×Q1611yescharacteristic
228C2×Q8—21no—
229C2×Q8—24no—
230C2×Q8—92no—
231C2×Q8—184no—
232C2×Q8—181no—
233C2×Q8—184no—
234C2×Q8—364no—
235C2×Q8C2×D3212yes—
236C22×C4—21no—
237C22×C4—62no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—181no—
241C22×C4C2×D3211yescharacteristic
242C2×C8—34no—
243C2×C8—64no—
244C4⋊C4—34no—
245C4⋊C4—62no—
246C4⋊C4—184no—
247C4⋊C4—184no—
248C4⋊C4—184no—
249C42—92no—
250C42—92no—
251C22×C3—21no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3#88514yes—
256C22×C3D3×SD1614yes—
257C22×C3D3×Q1614yes—
258C22×C3C2×D3×D412yes—
259C3×C4—22no—
260C3×C4—22no—
261C3×C4—44no—
262C3×C4—44no—
263C3×C4—124no—
264C3×C4#88514yes—
265C3×C4C2×#23512yes—
266C3×C4C2×#23712yes—
267Dic3—38no—
268Dic3—38no—
269Dic3—44no—
270Dic3—64no—
271Dic3—64no—
272Dic3—124no—
273Dic3—124no—
274C32C2×#48711yescharacteristic, complemented, Sylow
275C23#381111yescharacteristic
276Q8—24no—
277Q8—42no—
278Q8—184no—
279Q8—368no—
280Q8—362no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—64no—
284C2×C4—92no—
285C2×C4—92no—
286C2×C4—94no—
287C2×C4—94no—
288C2×C4—124no—
289C2×C4—182no—
290C2×C4—362no—
291C2×C4#380414yes—
292C2×C4#381111yescharacteristic
293C2×C4C22×D3211yescharacteristic
294C8—64no—
295C2×C3—21no—
296C2×C3—24no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#479218yescomplemented
300C2×C3C2×#88512yes—
301C2×C3C2×D3×SD1612yes—
302C2×C3C2×D3×Q1612yes—
303C22#6394012yes—
304C22#6394412yes—
305C22#6395312yes—
306C22C2×#381111yescharacteristic
307C4—42no—
308C4—94no—
309C4—94no—
310C4—124no—
311C4—362no—
312C4#6395312yes—
313C4C2×#380412yes—
314C3—21no—
315C3C2×#479212yescomplemented
316C2#1059153814yesdirect product factor
317C2C2×#6394011yescharacteristic
318C2C2×#6394411yescharacteristic
319C2C2×#6395311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32C2×#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10591538C2direct (N × H)
224. C2×C32#487semidirect
274. C32C2×#487semidirect
299. C2×C3#4792semidirect
315. C3C2×#4792semidirect
316. C2#10591538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×#639192
C2×C3×#8352
#105915382
C2×#635672
C2×#635532
C2×#47923