Finite Group Databasebeta

← C2×#19137513 #25255903

Subgroups — C2×#19137513 #25255903

Order 11008.

3158 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic43C211yesmaximal, characteristic
2C22×Q8×Dic43C211yesmaximal, characteristic
3#19137513C2116yesmaximal, direct product factor
4C2×#14582797C213yesmaximal
5C2×#14582795C213yesmaximal
6C2×#14582764C213yesmaximal
7C2×C4×Dic43⋊C4C213yesmaximal
8C22×C4×Q8×C43C211yesmaximal, characteristic
9C2×Q8×Dic43—28no—
10C2×Q8×Dic43C4116yescomplemented
11C2×Q8×Dic43C2218yes—
12C2×Q8×Dic43C2218yes—
13C22×C4⋊Dic43C2213yes—
14C22×C4⋊Dic43C2213yes—
15C22×Dic43⋊C4C2213yes—
16C22×Dic43⋊C4C2213yes—
17C22×C4×Dic43C2213yes—
18C22×C4×Dic43C2213yes—
19#14582797C22124yes—
20#14582795C22124yes—
21#14582764C22124yes—
22C4×Dic43⋊C4C22124yes—
23C2×C43⋊#95C2216yes—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2213yes—
26C23×Q8×C43C2211yescharacteristic
27C2×C4×Q8×C43—28no—
28C2×C4×Q8×C43C2218yes—
29C22×C4⋊C4×C43C2213yes—
30C22×C42×C43C2213yes—
31C23×Dic43C2313yes—
32C23×Dic43C2311yescharacteristic
33C23×Dic43C2313yes—
34C23×Dic43C2311yescharacteristic
35Q8×Dic43—232no—
36Q8×Dic43C2×C4164yescomplemented
37C2×C4⋊Dic43—212no—
38C2×C4⋊Dic43C2×C4124yes—
39C2×C4⋊Dic43C23112yes—
40C2×C4⋊Dic43C23112yes—
41C2×Dic43⋊C4—212no—
42C2×Dic43⋊C4—212no—
43C2×Dic43⋊C4C23112yes—
44C2×Dic43⋊C4C23112yes—
45C2×C4×Dic43—212no—
46C2×C4×Dic43C2×C4124yes—
47C2×C4×Dic43C23112yes—
48C2×C4×Dic43C23112yes—
49C43⋊#95C23124yes—
50C43⋊#95C2314yes—
51C43⋊#95C23112yes—
52C22×Q8×C43C2×C418yes—
53C22×Q8×C43D418yes—
54C22×Q8×C43Q818yes—
55C22×Q8×C43C2314yes—
56C23×C4×C43C2313yes—
57C23×C4×C43C2311yescharacteristic
58C23×C4×C43C2313yes—
59C4×Q8×C43—232no—
60C2×C4⋊C4×C43—212no—
61C2×C4⋊C4×C43C23112yes—
62C2×C42×C43—212no—
63C2×C42×C43C23112yes—
64C24×C43C2411yescharacteristic
65C2×Q8×C43C4⋊C4164yescomplemented
66C2×Q8×C43C22×C4116yes—
67C2×Q8×C43C2×D4116yes—
68C2×Q8×C43C2×Q8116yes—
69C22×C4×C43—22no—
70C22×C4×C43—26no—
71C22×C4×C43—26no—
72C22×C4×C43—22no—
73C22×C4×C43—26no—
74C22×C4×C43C22×C4112yes—
75C22×C4×C43C2×D4112yes—
76C22×C4×C43C2×Q8112yes—
77C22×C4×C43#4114yes—
78C22×C4×C43C2416yes—
79C22×C4×C43C2412yes—
80C22×C4×C43C2416yes—
81C22×Dic43—22no—
82C22×Dic43—26no—
83C22×Dic43—26no—
84C22×Dic43—26no—
85C22×Dic43—26no—
86C22×Dic43—22no—
87C22×Dic43—22no—
88C22×Dic43—22no—
89C22×Dic43—26no—
90C22×Dic43C22×C414yes—
91C22×Dic43C22×C4112yes—
92C22×Dic43#4114yes—
93C22×Dic43C2416yes—
94C22×Dic43C2412yes—
95C22×Dic43C2416yes—
96C22×Dic43C2412yes—
97C4⋊C4×C43—224no—
98C42×C43—224no—
99C4⋊Dic43—224no—
100C4⋊Dic43C22×C4148yes—
101Dic43⋊C4—224no—
102Dic43⋊C4—224no—
103C4×Dic43—224no—
104C4×Dic43C22×C4148yes—
105C23×C43C23×C412yes—
106C23×C43C22×D412yes—
107C23×C43C22×Q812yes—
108C23×C43C2×#4112yes—
109C23×C43C2×#4112yes—
110C23×C432−1+412yes—
111C23×C432−1+412yes—
112C23×C43C2511yescharacteristic
113Q8×C43C2×C4⋊C4164yescomplemented
114C2×C4×C43—28no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—26no—
118C2×C4×C43—26no—
119C2×C4×C43—26no—
120C2×C4×C43—412no—
121C2×C4×C43C2×C4⋊C4148yes—
122C2×C4×C43C23×C4112yes—
123C2×C4×C43C22×D4112yes—
124C2×C4×C43C22×Q8112yes—
125C2×C4×C43C2×#4114yes—
126C2×Dic43—224no—
127C2×Dic43—28no—
128C2×Dic43—28no—
129C2×Dic43—22no—
130C2×Dic43—26no—
131C2×Dic43—26no—
132C2×Dic43—22no—
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—26no—
136C2×Dic43—26no—
137C2×Dic43—26no—
138C2×Dic43—412no—
139C2×Dic43C23×C414yes—
140C2×Dic43C23×C4112yes—
141C2×Dic43C2×#4114yes—
142C2×#2351—431nomaximal, Sylow
143C22×C43C22×C4⋊C414yes—
144C22×C43C4×#4114yes—
145C22×C43#51914yes—
146C22×C43#54814yes—
147C22×C43#54814yes—
148C22×C43#55714yes—
149C22×C43#55714yes—
150C22×C43C24×C411yescharacteristic
151C22×C43C23×D411yescharacteristic
152C22×C43C23×Q811yescharacteristic
153C22×C43C22×#4111yescharacteristic
154C22×C43C22×#4111yescharacteristic
155C22×C43C2×2−1+411yescharacteristic
156C22×C43C2×2−1+411yescharacteristic
157C4×C43—24no—
158C4×C43—46no—
159C4×C43C22×C4⋊C4124yes—
160Dic43—212no—
161Dic43—24no—
162Dic43—24no—
163Dic43—46no—
164C22×C4×Q8—431no—
165C22×C4×Q8—431no—
166C22×C4×Q8D4311yescharacteristic
167#2351—4316no—
168C2×#389—433no—
169C2×#389—433no—
170C2×#382—433no—
171C2×C4×C4⋊C4—433no—
172C2×C43#235118yescomplemented
173C2×C43C23×C4⋊C411yescharacteristic
174C2×C43C2×C4×#4111yescharacteristic
175C2×C43C2×#51911yescharacteristic
176C2×C43C2×#54811yescharacteristic
177C2×C43C2×#54811yescharacteristic
178C2×C43C2×#55711yescharacteristic
179C2×C43C2×#55711yescharacteristic
180C23×Q8C2×D4311yescharacteristic
181C2×C4×Q8—28no—
182C2×C4×Q8—438no—
183C2×C4×Q8—4316no—
184C2×C4×Q8—438no—
185C2×C4×Q8—868no—
186C2×C4×Q8C2×D4318yes—
187C22×C4⋊C4—433no—
188C22×C4⋊C4—433no—
189C22×C4⋊C4—433no—
190C22×C4⋊C4—433no—
191C22×C4⋊C4C2×D4313yes—
192C22×C42—433no—
193C22×C42—433no—
194C22×C42C2×D4313yes—
195#389—4324no—
196#389—4324no—
197#382—4324no—
198C4×C4⋊C4—4324no—
199C2×#95—431no—
200C2×#95—433no—
201C2×#95—436no—
202C43C2×#235111yescharacteristic, complemented, Sylow
203C22×Q8Dic8618yes—
204C22×Q8C4×D4318yes—
205C22×Q8C22⋊D4318yes—
206C22×Q8C22×D4314yes—
207C23×C4—433no—
208C23×C4—431no—
209C23×C4—431no—
210C23×C4—433no—
211C23×C4C22×D4313yes—
212C23×C4C22×D4311yescharacteristic
213C23×C4C22×D4313yes—
214C4×Q8—232no—
215C4×Q8—4364no—
216C4×Q8—8632no—
217C2×C4⋊C4—212no—
218C2×C4⋊C4—4324no—
219C2×C4⋊C4—4312no—
220C2×C4⋊C4—4312no—
221C2×C4⋊C4—4312no—
222C2×C4⋊C4—4312no—
223C2×C4⋊C4—8612no—
224C2×C4⋊C4—8612no—
225C2×C4⋊C4—8612no—
226C2×C4⋊C4C22×D43112yes—
227C2×C42—212no—
228C2×C42—4324no—
229C2×C42—4312no—
230C2×C42—4312no—
231C2×C42—8612no—
232C2×C42C22×D43112yes—
233#95—434no—
234#95—4312no—
235#95—4324no—
236C24C23×D4311yescharacteristic
237C2×Q8Dic43⋊C4164yescomplemented
238C2×Q8C2×Dic86116yes—
239C2×Q8C2×C4×D43116yes—
240C2×Q8C2×C22⋊D43116yes—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—26no—
244C22×C4—26no—
245C22×C4—26no—
246C22×C4—434no—
247C22×C4—4312no—
248C22×C4—434no—
249C22×C4—432no—
250C22×C4—436no—
251C22×C4—432no—
252C22×C4—436no—
253C22×C4—862no—
254C22×C4—866no—
255C22×C4—866no—
256C22×C4—862no—
257C22×C4—862no—
258C22×C4—862no—
259C22×C4—866no—
260C22×C4—866no—
261C22×C4—866no—
262C22×C4C2×Dic86112yes—
263C22×C4C2×C4×D43112yes—
264C22×C4#1062190214yes—
265C22×C4C2×C22⋊D43112yes—
266C22×C4C23×D4316yes—
267C22×C4C23×D4312yes—
268C22×C4C23×D4316yes—
269C4⋊C4—224no—
270C4⋊C4—4348no—
271C4⋊C4—8624no—
272C4⋊C4—8624no—
273C4⋊C4—8624no—
274C42—224no—
275C42—4348no—
276C42—8624no—
277C23C22×C4×D4312yes—
278C23C22×C22⋊D4312yes—
279C23C22×Dic8612yes—
280C23#41×D4312yes—
281C23C2×#1062190212yes—
282C23#1306337212yes—
283C23#1306337312yes—
284C23C24×D4311yescharacteristic
285Q8C2×Dic43⋊C4164yescomplemented
286C2×C4—28no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—26no—
290C2×C4—26no—
291C2×C4—26no—
292C2×C4—412no—
293C2×C4—434no—
294C2×C4—4312no—
295C2×C4—434no—
296C2×C4—868no—
297C2×C4—8624no—
298C2×C4—868no—
299C2×C4—862no—
300C2×C4—866no—
301C2×C4—866no—
302C2×C4—862no—
303C2×C4—862no—
304C2×C4—862no—
305C2×C4—866no—
306C2×C4—866no—
307C2×C4—866no—
308C2×C4—17212no—
309C2×C4C2×Dic43⋊C4148yes—
310C2×C4C22×C4×D43112yes—
311C2×C4C22×C22⋊D43112yes—
312C2×C4C22×Dic86112yes—
313C2×C4C2×#1062190214yes—
314C22C22×Dic43⋊C414yes—
315C22C4×#1062190214yes—
316C22#1458337514yes—
317C22#1458355614yes—
318C22#1458356014yes—
319C22#1458362514yes—
320C22#1458362814yes—
321C22C23×C4×D4311yescharacteristic
322C22C23×C22⋊D4311yescharacteristic
323C22C23×Dic8611yescharacteristic
324C22C2×#41×D4311yescharacteristic
325C22C22×#1062190211yescharacteristic
326C22C2×#1306337211yescharacteristic
327C22C2×#1306337311yescharacteristic
328C4—24no—
329C4—46no—
330C4—8612no—
331C4—864no—
332C4—864no—
333C4—1726no—
334C4C22×Dic43⋊C4124yes—
335C2#1913751318yesdirect product factor
336C2C23×Dic43⋊C411yescharacteristic
337C2C2×C4×#1062190211yescharacteristic
338C2C2×#1458337511yescharacteristic
339C2C2×#1458355611yescharacteristic
340C2C2×#1458356011yescharacteristic
341C2C2×#1458362511yescharacteristic
342C2C2×#1458362811yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×C4×Q8×C43C2
socle, prime radicalC24×C43C24
cosocleC23×C43C25
hypercenterC22×C4×Q8D43
hypocenterC43C2×#2351
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #19137513C2direct (N × H)
10. C2×Q8×Dic43C4semidirect
36. Q8×Dic43C2×C4semidirect
65. C2×Q8×C43C4⋊C4semidirect
113. Q8×C43C2×C4⋊C4semidirect
172. C2×C43#2351semidirect
202. C43C2×#2351semidirect
237. C2×Q8Dic43⋊C4semidirect
285. Q8C2×Dic43⋊C4semidirect
335. C2#19137513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×Dic432
#191375132
C2×#145827972
C2×#145827952
C2×#145827642
C2×C4×Dic43⋊C42
C22×C4×Q8×C432
C2×#235143