Finite Group Databasebeta

← C2×#19143193 #25960268

Subgroups — C2×#19143193 #25960268

Order 11008.

2766 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063332C211yesmaximal, characteristic
2C2×#14583382C211yesmaximal, characteristic
3#19143193C2116yesmaximal, direct product factor
4C2×#14582942C213yesmaximal, complemented
5C2×#14582939C213yesmaximal, complemented
6C2×#14582935C213yesmaximal, complemented
7C22×#13063258C213yesmaximal, complemented
8C2×C43×#520C211yesmaximal, characteristic
9C2×#13063332C4116yescomplemented
10C2×#13063332C2218yes—
11C22×#10621877C2213yes—
12C23×C43⋊C8C2213yes—
13#14583382—24no—
14#14583382C2218yes—
15C2×Q8×Dic43—21no—
16C2×D4×Dic43—23no—
17C2×#13063284C2213yes—
18C22×C4⋊Dic43C2213yes—
19#14582942C22124yescomplemented
20#14582939C22124yescomplemented
21#14582935C22124yescomplemented
22C2×#13063258C2213yes—
23C2×#13063258C2216yes—
24C2×#13063258C2211yescharacteristic
25C2×#13063258C22124yescomplemented
26C2×#13063256C2213yes—
27C2×#13063256C2213yes—
28C22×#41×C43C2211yescharacteristic
29C43×#520—24no—
30C43×#520C2218yes—
31C2×C4×Q8×C43—21no—
32C2×C4×D4×C43—23no—
33C2×#117×C43C2213yes—
34C22×C4⋊C4×C43C2213yes—
35C23×Dic43—23no—
36#13063332C2×C4164yescomplemented
37C2×#10621877C2×C4124yescomplemented
38C2×#10621877C23112yes—
39C22×C43⋊C8C2×C4124yescomplemented
40C22×C43⋊C8C2311yescharacteristic
41C22×C43⋊C8C2313yes—
42C22×C43⋊C8C23112yes—
43Q8×Dic43—28no—
44D4×Dic43—224no—
45#13063284—26no—
46#13063284C23112yes—
47C2×C4⋊Dic43—23no—
48C2×C4⋊Dic43—26no—
49C2×C4⋊Dic43C2313yes—
50C2×C4⋊Dic43C23112yes—
51C2×C4⋊Dic43C2311yescharacteristic
52C2×C22⋊Dic43—23no—
53C2×C4×Dic43—23no—
54#13063258C23112yes—
55#13063258C23124yes—
56#13063258C2314yes—
57#13063256C23112yes—
58#13063256C23112yes—
59C2×#41×C43C2×C418yes—
60C2×#41×C43D414yes—
61C2×#41×C43Q818yes—
62C2×#41×C43C2314yes—
63C22×Q8×C43D411yescharacteristic
64C22×D4×C43D413yes—
65C23×C4×C43—23no—
66C23×C4×C43C2313yes—
67C4×Q8×C43—28no—
68C4×D4×C43—224no—
69#117×C43—26no—
70#117×C43C23112yes—
71C2×C4⋊C4×C43—23no—
72C2×C4⋊C4×C43—26no—
73C2×C4⋊C4×C43C2313yes—
74C2×C4⋊C4×C43C23112yes—
75C2×C4⋊C4×C43C2311yescharacteristic
76C2×C22⋊C4×C43—23no—
77C2×C42×C43—23no—
78C24×C43C2×D413yes—
79#41×C43C4⋊C4132yes—
80#41×C43C22×C4116yes—
81#41×C43C2×Q8116yes—
82C2×Q8×C43C4⋊C418yes—
83C2×Q8×C43C2×D414yes—
84C2×D4×C43C4⋊C4124yes—
85C2×D4×C43C2×D4112yes—
86C22×C4×C43—21no—
87C22×C4×C43—23no—
88C22×C4×C43—212no—
89C22×C4×C43—86no—
90C22×C4×C43C22×C4112yes—
91C22×C4×C43C2×D413yes—
92C22×C4×C43C2×D416yes—
93C22×C4×C43C2×Q8112yes—
94C22×C4×C43C2411yescharacteristic
95C22×C4×C43C2416yes—
96C22×Dic43—21no—
97C22×Dic43—23no—
98C22×Dic43—212no—
99C22×Dic43—86no—
100C4⋊C4×C43—23no—
101C4⋊C4×C43—212no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43C2416yes—
104C4⋊C4×C43C2412yes—
105C22⋊C4×C43—212no—
106C42×C43—212no—
107C22⋊Dic43—212no—
108C4⋊Dic43—23no—
109C4⋊Dic43—212no—
110C4⋊Dic43—21no—
111C4⋊Dic43C2412yes—
112C4⋊Dic43C2416yes—
113C4×Dic43—212no—
114#10621877C22×C4148yescomplemented
115C2×C43⋊C8C22×C414yes—
116C2×C43⋊C8C22×C4112yes—
117C2×C43⋊C8C22×C4148yescomplemented
118C2×C43⋊C8C2416yes—
119C2×C43⋊C8C2412yes—
120C23×C43—26no—
121C23×C43—26no—
122C23×C43C2×C4⋊C4112yes—
123C23×C43C22×D416yes—
124C23×C43C22×D411yescharacteristic
125Q8×C43C2×C4⋊C4116yes—
126D4×C43C2×C4⋊C4148yes—
127C2×C4×C43—22no—
128C2×C4×C43—26no—
129C2×C4×C43—46no—
130C2×C4×C43—42no—
131C2×C4×C43—812no—
132C2×C4×C43C2×C4⋊C4112yes—
133C2×C4×C43C2×C4⋊C4124yes—
134C2×C4×C43C23×C412yes—
135C2×C4×C43C23×C4112yes—
136C2×C4×C43C22×D416yes—
137C2×C4×C43C22×D411yescharacteristic
138C2×C4×C43C22×Q812yes—
139C2×C4×C43C22×Q8112yes—
140C2×C4×C43C2511yescharacteristic
141C2×Dic43—22no—
142C2×Dic43—26no—
143C2×Dic43—46no—
144C2×Dic43—42no—
145C2×Dic43—812no—
146C43⋊C8C23×C414yes—
147C43⋊C8C23×C4112yes—
148C2×#2913—431nomaximal, Sylow
149C22×C43—224no—
150C22×C43—26no—
151C22×C43—26no—
152C22×C43C22×C4⋊C4112yes—
153C22×C43C22×C4⋊C412yes—
154C22×C43#57612yes—
155C22×C43#57812yes—
156C22×C43C23×D411yescharacteristic
157C4×C43—46no—
158C4×C43—42no—
159C4×C43C22×C4⋊C412yes—
160C4×C43C22×C4⋊C4112yes—
161C4×C43C24×C411yescharacteristic
162C4×C43C23×Q811yescharacteristic
163Dic43—46no—
164Dic43—42no—
165C22×#131—431no—
166C2×#520—431no—
167C2×#520D4311yescharacteristic
168#2913—4316no—
169C2×#428—433no—
170C2×#428—433no—
171C2×#427—433no—
172C22×#107—433no—
173C2×C43—212no—
174C2×C43#291314yescomplemented
175C2×C43C23×C4⋊C411yescharacteristic
176C2×C43C2×#57611yescharacteristic
177C2×C43C2×#57811yescharacteristic
178C22×#41C2×D4311yescharacteristic
179C2×#131—438no—
180C2×#131—4316no—
181C22×M16—433no—
182C23×C8—433no—
183#520—24no—
184#520—438no—
185#520—864no—
186#520C2×D4318yes—
187C2×C4×Q8—21no—
188C2×C4×Q8—861no—
189C2×C4×D4—23no—
190C2×C4×D4—863no—
191C2×#117—433no—
192C2×#117C2×D4313yes—
193C22×C4⋊C4—433no—
194C22×C4⋊C4C2×D4313yes—
195#428—4324no—
196#428—4324no—
197#427—4324no—
198C2×#107—433no—
199C2×#107—436no—
200C2×#107—4324no—
201C2×#107—431no—
202C2×#106—433no—
203C2×#106—433no—
204C43C2×#291311yescharacteristic, complemented, Sylow
205C2×#41Dic8618yes—
206C2×#41C4×D4318yes—
207C2×#41C22⋊D4314yes—
208C2×#41C22×D4314yes—
209C22×Q8C22⋊D4311yescharacteristic
210C22×D4C22⋊D4313yes—
211C23×C4—23no—
212C23×C4—863no—
213C23×C4C22×D4313yes—
214#131—4364no—
215C2×M16—4324no—
216C2×M16—4312no—
217C22×C8—4324no—
218C22×C8—431no—
219C22×C8—433no—
220C22×C8—4312no—
221C4×Q8—28no—
222C4×Q8—868no—
223C4×D4—224no—
224C4×D4—8624no—
225#117—26no—
226#117—4312no—
227#117—866no—
228#117C22×D43112yes—
229C2×C4⋊C4—23no—
230C2×C4⋊C4—26no—
231C2×C4⋊C4—433no—
232C2×C4⋊C4—4312no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—863no—
235C2×C4⋊C4—866no—
236C2×C4⋊C4C22×D4313yes—
237C2×C4⋊C4C22×D43112yes—
238C2×C4⋊C4C22×D4311yescharacteristic
239C2×C22⋊C4—23no—
240C2×C22⋊C4—863no—
241C2×C42—23no—
242C2×C42—863no—
243#107—4312no—
244#107—4324no—
245#107—434no—
246#106—4312no—
247#106—4312no—
248C24C2×C22⋊D4313yes—
249#41Dic43⋊C4132yes—
250#41C2×Dic86116yes—
251#41C2×C4×D43116yes—
252C2×Q8Dic43⋊C418yes—
253C2×Q8C2×C22⋊D4314yes—
254C2×D4Dic43⋊C4124yes—
255C2×D4C2×C22⋊D43112yes—
256C22×C4—21no—
257C22×C4—23no—
258C22×C4—212no—
259C22×C4—86no—
260C22×C4—8612no—
261C22×C4—861no—
262C22×C4—863no—
263C22×C4—3446no—
264C22×C4C2×Dic86112yes—
265C22×C4C2×C4×D43112yes—
266C22×C4C2×C22⋊D4316yes—
267C22×C4C2×C22⋊D4313yes—
268C22×C4C23×D4316yes—
269C22×C4C23×D4311yescharacteristic
270M16—4348no—
271C2×C8—434no—
272C2×C8—4312no—
273C2×C8—4348no—
274C2×C8—436no—
275C2×C8—432no—
276C4⋊C4—23no—
277C4⋊C4—212no—
278C4⋊C4—21no—
279C4⋊C4—432no—
280C4⋊C4—436no—
281C4⋊C4—863no—
282C4⋊C4—8612no—
283C4⋊C4—861no—
284C4⋊C4C23×D4312yes—
285C4⋊C4C23×D4316yes—
286C22⋊C4—212no—
287C22⋊C4—8612no—
288C42—212no—
289C42—8612no—
290C23—26no—
291C23—26no—
292C23C2×Dic43⋊C4112yes—
293C23C22×C22⋊D4316yes—
294C23C22×C22⋊D4311yescharacteristic
295Q8C2×Dic43⋊C4116yes—
296D4C2×Dic43⋊C4148yes—
297C2×C4—22no—
298C2×C4—26no—
299C2×C4—46no—
300C2×C4—42no—
301C2×C4—812no—
302C2×C4—862no—
303C2×C4—866no—
304C2×C4—34412no—
305C2×C4—1726no—
306C2×C4—1722no—
307C2×C4C2×Dic43⋊C4112yes—
308C2×C4C2×Dic43⋊C4124yes—
309C2×C4C22×C4×D4312yes—
310C2×C4C22×C4×D43112yes—
311C2×C4C22×C22⋊D4316yes—
312C2×C4C22×C22⋊D4311yescharacteristic
313C2×C4C22×Dic8612yes—
314C2×C4C22×Dic86112yes—
315C2×C4C24×D4311yescharacteristic
316C8—434no—
317C8—4312no—
318C22—224no—
319C22—26no—
320C22—26no—
321C22C22×Dic43⋊C4112yes—
322C22C22×Dic43⋊C412yes—
323C22#1458370212yes—
324C22#1458371412yes—
325C22C23×C22⋊D4311yescharacteristic
326C4—46no—
327C4—42no—
328C4—1726no—
329C4—1722no—
330C4C22×Dic43⋊C412yes—
331C4C22×Dic43⋊C4112yes—
332C4C23×C4×D4311yescharacteristic
333C4C23×Dic8611yescharacteristic
334C2—212no—
335C2#1914319314yesdirect product factor
336C2C23×Dic43⋊C411yescharacteristic
337C2C2×#1458370211yescharacteristic
338C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#520C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC2×C4×C43C25
hypercenterC2×#520D43
hypocenterC43C2×#2913
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
3. #19143193C2direct (N × H)
4. C2×#14582942C2semidirect
5. C2×#14582939C2semidirect
6. C2×#14582935C2semidirect
7. C22×#13063258C2semidirect
9. C2×#13063332C4semidirect
19. #14582942C22semidirect
20. #14582939C22semidirect
21. #14582935C22semidirect
25. C2×#13063258C22semidirect
36. #13063332C2×C4semidirect
37. C2×#10621877C2×C4semidirect
39. C22×C43⋊C8C2×C4semidirect
114. #10621877C22×C4semidirect
117. C2×C43⋊C8C22×C4semidirect
174. C2×C43#2913semidirect
204. C43C2×#2913semidirect
335. C2#19143193direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633322
C2×#145833822
#191431932
C2×#145829422
C2×#145829392
C2×#145829352
C22×#130632582
C2×C43×#5202
C2×#291343