Finite Group Databasebeta

← C2×#19143161 #25960222

Subgroups — C2×#19143161 #25960222

Order 11008.

2810 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063332C211yesmaximal, characteristic
2C2×#41×Dic43C211yesmaximal, characteristic
3#19143161C2116yesmaximal, direct product factor
4C2×#14582927C213yesmaximal, complemented
5C2×#14582925C213yesmaximal, complemented
6C2×#14582922C213yesmaximal, complemented
7C22×Dic43⋊C8C213yesmaximal, complemented
8C22×#131×C43C211yesmaximal, characteristic
9C2×#13063332—28no—
10C2×#13063332C2218yes—
11C22×#10621877C2213yes—
12C23×C43⋊C8C2213yes—
13#41×Dic43C418yes—
14#41×Dic43C2218yes—
15C2×Q8×Dic43C411yescharacteristic
16C2×Q8×Dic43C411yescharacteristic
17C2×D4×Dic43C413yes—
18C2×D4×Dic43C413yes—
19C2×#13063284C2213yes—
20C22×C4×Dic43C2213yes—
21#14582927C22124yescomplemented
22#14582925C22124yescomplemented
23#14582922C22124yescomplemented
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2213yes—
26C2×Dic43⋊C8C2213yes—
27C2×Dic43⋊C8C2213yes—
28C2×Dic43⋊C8C2216yes—
29C2×Dic43⋊C8C22124yescomplemented
30C22×#41×C43C2211yescharacteristic
31C2×#131×C43—28no—
32C2×#131×C43C2218yes—
33C22×M16×C43C2213yes—
34C23×C8×C43C2213yes—
35C23×Dic43C2×C413yes—
36C23×Dic43C2×C413yes—
37#13063332—232no—
38C2×#10621877—212no—
39C2×#10621877C23112yes—
40C22×C43⋊C8—212no—
41C22×C43⋊C8C2311yescharacteristic
42C22×C43⋊C8C2313yes—
43C22×C43⋊C8C23112yes—
44Q8×Dic43C2×C418yes—
45Q8×Dic43C2×C418yes—
46D4×Dic43C2×C4124yes—
47D4×Dic43C2×C4124yes—
48#13063284C2×C4112yes—
49#13063284C23112yes—
50C2×C4⋊Dic43C2×C413yes—
51C2×C4⋊Dic43C2×C413yes—
52C2×C22⋊Dic43C2×C416yes—
53C2×C4×Dic43C2×C413yes—
54C2×C4×Dic43C2×C413yes—
55C2×C4×Dic43C2×C4112yes—
56C2×C4×Dic43C2311yescharacteristic
57C2×C4×Dic43C2313yes—
58C2×C4×Dic43C23112yes—
59Dic43⋊C8C2314yes—
60Dic43⋊C8C23112yes—
61Dic43⋊C8C23112yes—
62Dic43⋊C8C23112yes—
63Dic43⋊C8C23124yes—
64C2×#41×C43C2×C414yes—
65C2×#41×C43D418yes—
66C2×#41×C43Q818yes—
67C2×#41×C43C2314yes—
68C22×Q8×C43C2×C411yescharacteristic
69C22×D4×C43C2×C413yes—
70C23×C4×C43C2313yes—
71#131×C43—232no—
72C2×M16×C43—212no—
73C2×M16×C43C23112yes—
74C22×C8×C43—212no—
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2313yes—
77C22×C8×C43C23112yes—
78C24×C43C22×C413yes—
79#41×C43C4⋊C4132yes—
80#41×C43C2×D4116yes—
81#41×C43C2×Q8116yes—
82C2×Q8×C43C4⋊C418yes—
83C2×Q8×C43C22×C414yes—
84C2×D4×C43C4⋊C4124yes—
85C2×D4×C43C22×C4112yes—
86C22×C4×C43C22×C413yes—
87C22×C4×C43C22×C416yes—
88C22×C4×C43C2×D4112yes—
89C22×C4×C43C2×Q8112yes—
90C22×C4×C43C2416yes—
91C22×C4×C43C2411yescharacteristic
92C22×Dic43—212no—
93C22×Dic43—46no—
94C22×Dic43C22×C411yescharacteristic
95C22×Dic43C22×C413yes—
96C22×Dic43C22×C413yes—
97C22×Dic43C22×C4112yes—
98C22×Dic43C22×C4112yes—
99C22×Dic43C22×C411yescharacteristic
100M16×C43—224no—
101C2×C8×C43—22no—
102C2×C8×C43—26no—
103C2×C8×C43—224no—
104C2×C8×C43C2412yes—
105C2×C8×C43C2416yes—
106C22⋊Dic43C22×C4124yes—
107C4⋊Dic43C22×C4112yes—
108C4⋊Dic43C22×C4112yes—
109C4×Dic43C22×C412yes—
110C4×Dic43C22×C416yes—
111C4×Dic43C22×C4112yes—
112C4×Dic43C22×C4112yes—
113C4×Dic43C2412yes—
114C4×Dic43C2416yes—
115#10621877—224no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—26no—
118C2×C43⋊C8—224no—
119C2×C43⋊C8C2412yes—
120C2×C43⋊C8C2416yes—
121C23×C43—26no—
122C23×C43—26no—
123C23×C43C2×C4⋊C4112yes—
124C23×C43C23×C416yes—
125C23×C43C23×C411yescharacteristic
126Q8×C43C2×C4⋊C4116yes—
127D4×C43C2×C4⋊C4148yes—
128C2×C4×C43C2×C4⋊C4112yes—
129C2×C4×C43C2×C4⋊C4124yes—
130C2×C4×C43C23×C411yescharacteristic
131C2×C4×C43C23×C416yes—
132C2×C4×C43C22×D412yes—
133C2×C4×C43C22×D4112yes—
134C2×C4×C43C22×Q812yes—
135C2×C4×C43C22×Q8112yes—
136C2×C4×C43C2511yescharacteristic
137C2×Dic43—26no—
138C2×Dic43—22no—
139C2×Dic43—26no—
140C2×Dic43—224no—
141C2×Dic43—412no—
142C2×Dic43#13114yescomplemented
143C2×Dic43C23×C412yes—
144C2×Dic43C23×C416yes—
145C2×Dic43C23×C416yes—
146C2×Dic43C23×C412yes—
147C8×C43—22no—
148C8×C43—26no—
149C43⋊C8—22no—
150C43⋊C8—26no—
151C2×#2906—431nomaximal, Sylow
152C22×C43—224no—
153C22×C43—26no—
154C22×C43—26no—
155C22×C43C22×C4⋊C4112yes—
156C22×C43C22×C4⋊C412yes—
157C22×C43C2×#13112yes—
158C22×C43#56812yes—
159C22×C43C24×C411yescharacteristic
160C4×C43C22×C4⋊C412yes—
161C4×C43C22×C4⋊C4112yes—
162C4×C43C23×D411yescharacteristic
163C4×C43C23×Q811yescharacteristic
164Dic43—26no—
165Dic43—22no—
166Dic43—26no—
167Dic43C2×#13114yescomplemented
168C22×#131—431no—
169C22×#131D4311yescharacteristic
170C2×C4×#41—431no—
171#2906—4316no—
172C2×#424—433no—
173C2×#424—433no—
174C2×#423—433no—
175C22×C4⋊C8—433no—
176C2×C43—212no—
177C2×C43#290614yescomplemented
178C2×C43C23×C4⋊C411yescharacteristic
179C2×C43C22×#13111yescharacteristic
180C2×C43C2×#56811yescharacteristic
181C22×#41C2×D4311yescharacteristic
182C2×#131—28no—
183C2×#131—438no—
184C2×#131—868no—
185C2×#131C2×D4318yes—
186C22×M16—433no—
187C22×M16C2×D4313yes—
188C23×C8—433no—
189C23×C8C2×D4313yes—
190C4×#41—438no—
191C4×#41—438no—
192C2×C4×Q8—431no—
193C2×C4×Q8—431no—
194C2×C4×D4—433no—
195C2×C4×D4—433no—
196C2×#117—433no—
197C22×C42—433no—
198#424—4324no—
199#424—4324no—
200#423—4324no—
201C2×C4⋊C8—431no—
202C2×C4⋊C8—433no—
203C2×C4⋊C8—433no—
204C2×C4⋊C8—433no—
205C2×C4⋊C8—4324no—
206C2×C4⋊C8—436no—
207C43C2×#290611yescharacteristic, complemented, Sylow
208C2×#41Dic8618yes—
209C2×#41C4×D4314yes—
210C2×#41C22⋊D4318yes—
211C2×#41C22×D4314yes—
212C22×Q8C4×D4311yescharacteristic
213C22×D4C4×D4313yes—
214C23×C4—433no—
215C23×C4—433no—
216C23×C4C22×D4313yes—
217#131—232no—
218#131—8632no—
219C2×M16—212no—
220C2×M16—4312no—
221C2×M16—8612no—
222C2×M16C22×D43112yes—
223C22×C8—212no—
224C22×C8—4312no—
225C22×C8—431no—
226C22×C8—433no—
227C22×C8—8612no—
228C22×C8C22×D43112yes—
229C22×C8C22×D4311yescharacteristic
230C22×C8C22×D4313yes—
231C4×Q8—438no—
232C4×Q8—438no—
233C4×D4—4324no—
234C4×D4—4324no—
235#117—4312no—
236#117—4312no—
237C2×C4⋊C4—433no—
238C2×C4⋊C4—433no—
239C2×C22⋊C4—436no—
240C2×C42—433no—
241C2×C42—433no—
242C2×C42—4312no—
243C2×C42—4312no—
244C2×C42—433no—
245C2×C42—431no—
246C4⋊C8—434no—
247C4⋊C8—4312no—
248C4⋊C8—4312no—
249C4⋊C8—4312no—
250C4⋊C8—4324no—
251C24C2×C4×D4313yes—
252#41Dic43⋊C4132yes—
253#41C2×Dic86116yes—
254#41C2×C22⋊D43116yes—
255C2×Q8Dic43⋊C418yes—
256C2×Q8C2×C4×D4314yes—
257C2×D4Dic43⋊C4124yes—
258C2×D4C2×C4×D43112yes—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—433no—
262C22×C4—433no—
263C22×C4—4312no—
264C22×C4—4312no—
265C22×C4—8612no—
266C22×C4—1726no—
267C22×C4C2×Dic86112yes—
268C22×C4C2×C4×D4313yes—
269C22×C4C2×C4×D4316yes—
270C22×C4C2×C22⋊D43112yes—
271C22×C4C23×D4316yes—
272C22×C4C23×D4311yescharacteristic
273M16—224no—
274M16—8624no—
275C2×C8—22no—
276C2×C8—26no—
277C2×C8—224no—
278C2×C8—432no—
279C2×C8—436no—
280C2×C8—862no—
281C2×C8—866no—
282C2×C8—8624no—
283C2×C8C23×D4312yes—
284C2×C8C23×D4316yes—
285C4⋊C4—4312no—
286C4⋊C4—4312no—
287C22⋊C4—4324no—
288C42—432no—
289C42—436no—
290C42—4312no—
291C42—4312no—
292C42—432no—
293C42—436no—
294C23—26no—
295C23—26no—
296C23C2×Dic43⋊C4112yes—
297C23C22×C4×D4316yes—
298C23C22×C4×D4311yescharacteristic
299Q8C2×Dic43⋊C4116yes—
300D4C2×Dic43⋊C4148yes—
301C2×C4—434no—
302C2×C4—432no—
303C2×C4—432no—
304C2×C4—436no—
305C2×C4—436no—
306C2×C4—8624no—
307C2×C4—866no—
308C2×C4—862no—
309C2×C4—866no—
310C2×C4—17212no—
311C2×C4C2×Dic43⋊C4112yes—
312C2×C4C2×Dic43⋊C4124yes—
313C2×C4C22×C4×D4311yescharacteristic
314C2×C4C22×C4×D4316yes—
315C2×C4C22×C22⋊D4312yes—
316C2×C4C22×C22⋊D43112yes—
317C2×C4C22×Dic8612yes—
318C2×C4C22×Dic86112yes—
319C2×C4C24×D4311yescharacteristic
320C8—22no—
321C8—26no—
322C8—862no—
323C8—866no—
324C22—26no—
325C22—26no—
326C22—224no—
327C22C22×Dic43⋊C4112yes—
328C22C22×Dic43⋊C412yes—
329C22#131×D4312yes—
330C22#1458366412yes—
331C22C23×C4×D4311yescharacteristic
332C4—434no—
333C4—866no—
334C4—862no—
335C4—866no—
336C4C22×Dic43⋊C412yes—
337C4C22×Dic43⋊C4112yes—
338C4C23×C22⋊D4311yescharacteristic
339C4C23×Dic8611yescharacteristic
340C2—212no—
341C2#1914316114yesdirect product factor
342C2C23×Dic43⋊C411yescharacteristic
343C2C2×#131×D4311yescharacteristic
344C2C2×#1458366411yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#131×C43C2
socleC23×C43C23×C4
prime radicalC22×#41×C43C22
cosocleC2×C4×C43C25
hypercenterC22×#131D43
hypocenterC43C2×#2906
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
3. #19143161C2direct (N × H)
4. C2×#14582927C2semidirect
5. C2×#14582925C2semidirect
6. C2×#14582922C2semidirect
7. C22×Dic43⋊C8C2semidirect
21. #14582927C22semidirect
22. #14582925C22semidirect
23. #14582922C22semidirect
29. C2×Dic43⋊C8C22semidirect
142. C2×Dic43#131semidirect
167. Dic43C2×#131semidirect
177. C2×C43#2906semidirect
207. C43C2×#2906semidirect
341. C2#19143161direct (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×#41×Dic432
#191431612
C2×#145829272
C2×#145829252
C2×#145829222
C22×Dic43⋊C82
C22×#131×C432
C2×#290643