Finite Group Databasebeta

← C2×#19143534 #25960968

Subgroups — C2×#19143534 #25960968

Order 11008.

1894 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583452C211yesmaximal, characteristic
2#19143534C2116yesmaximal, direct product factor
3C2×#14583028C214yesmaximal, complemented
4C2×#14583026C214yesmaximal, complemented
5C2×#14582925C211yesmaximal, characteristic
6C2×#14582922C211yesmaximal, characteristic
7C2×#14582857C211yesmaximal, characteristic
8C2×#14582855C211yesmaximal, characteristic
9C22×#13063235C211yesmaximal, characteristic
10C2×C43×#424C211yesmaximal, characteristic
11C22×#10621877C2211yescharacteristic
12C23×C43⋊C8C2211yescharacteristic
13#14583452C418yes—
14#14583452C2218yes—
15C2×#13063324C412yes—
16C2×#13063316C412yes—
17C2×#13063302C414yes—
18C2×C4×Dic86C2214yes—
19C2×#13063284C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21#14583028C22132yescomplemented
22#14583026C22132yescomplemented
23#14582925C2218yes—
24#14582922C2218yes—
25C2×Dic43⋊C8C2214yes—
26C2×Dic43⋊C8C2214yes—
27#14582857C2218yes—
28#14582855C2218yes—
29C2×#13063236C2212yes—
30C2×#13063235C2212yes—
31C2×#13063235C2212yes—
32C2×#13063235C2218yes—
33C2×#13063235C2212yes—
34C2×C4×C43⋊C8C2212yes—
35C2×C8×Dic43C2212yes—
36C22×M16×C43C2211yescharacteristic
37C23×C8×C43C2211yescharacteristic
38C2×#117×C43C2211yescharacteristic
39C43×#424C2218yes—
40C2×C4⋊C8×C43C2214yes—
41C22×Dic86C2×C414yes—
42C23×Dic43C2×C412yes—
43C2×#10621877—24no—
44C2×#10621877C2314yes—
45C22×C43⋊C8Q818yescomplemented
46C22×C43⋊C8C2312yes—
47C22×C43⋊C8C2311yescharacteristic
48C22×C43⋊C8C2311yescharacteristic
49C22×C43⋊C8C2314yes—
50#13063324C2×C4116yes—
51#13063316C2×C4116yes—
52#13063302C2×C4132yes—
53C4×Dic86C2×C4116yes—
54C4×Dic86C23116yes—
55#13063284C2×C414yes—
56#13063284C2314yes—
57C2×C4⋊Dic43C2×C412yes—
58C2×C4⋊Dic43C2×C414yes—
59C2×Dic43⋊C4C2×C414yes—
60C2×Dic43⋊C4C2×C414yes—
61C2×C22⋊Dic43C2×C412yes—
62C2×C4×Dic43C2×C411yescharacteristic
63C2×C4×Dic43C2×C411yescharacteristic
64C2×C4×Dic43C2×C414yes—
65C2×C4×Dic43C2312yes—
66C2×C4×Dic43C2314yes—
67C2×C4×Dic43C2312yes—
68Dic43⋊C8C23116yes—
69Dic43⋊C8C23116yes—
70#13063236C2318yes—
71#13063235C2318yes—
72#13063235C2318yes—
73#13063235C2318yes—
74C4×C43⋊C8C2318yes—
75C8×Dic43C2318yes—
76C23×C4×C43C2311yescharacteristic
77C2×M16×C43—24no—
78C2×M16×C43C2314yes—
79C22×C8×C43—24no—
80C22×C8×C43C2312yes—
81C22×C8×C43C2312yes—
82C22×C8×C43C2314yes—
83#117×C43C2×C414yes—
84#117×C43C2314yes—
85C2×C4⋊C4×C43C2×C412yes—
86C2×C22⋊C4×C43C2×C412yes—
87C2×C42×C43C2312yes—
88C4⋊C8×C43C23116yes—
89C24×C43C22×C411yescharacteristic
90C22×C4×C43C22×C414yes—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C22×C412yes—
93C22×C4×C43C2×Q814yes—
94C22×C4×C43#4114yes—
95C22×C4×C43C2412yes—
96C22×C4×C43C2411yescharacteristic
97C22×Dic43—44no—
98C22×Dic43C22×C412yes—
99C22×Dic43C22×C412yes—
100C22×Dic43C22×C414yes—
101C22×Dic43C22×C418yes—
102C2×Dic86—48no—
103C2×Dic86C22×C4116yes—
104M16×C43—28no—
105C2×C8×C43—24no—
106C2×C8×C43—28no—
107C2×C8×C43—24no—
108C2×C8×C43C2414yes—
109C2×C8×C43C2414yes—
110C4⋊C4×C43C22×C418yes—
111C22⋊C4×C43C22×C418yes—
112C42×C43C22×C414yes—
113C42×C43C2414yes—
114C22⋊Dic43C22×C418yes—
115C4⋊Dic43C22×C418yes—
116C4⋊Dic43C22×C4116yes—
117Dic43⋊C4C22×C4116yes—
118Dic43⋊C4C22×C4116yes—
119C4×Dic43C22×C414yes—
120C4×Dic43C22×C414yes—
121C4×Dic43C22×C414yes—
122C4×Dic43C22×C414yes—
123C4×Dic43C2414yes—
124C4×Dic43C2414yes—
125#10621877—28no—
126C2×C43⋊C8—24no—
127C2×C43⋊C8C2×Q814yes—
128C2×C43⋊C8C2×Q814yes—
129C2×C43⋊C8C2×Q8116yescomplemented
130C2×C43⋊C8C2414yes—
131C2×C43⋊C8C2412yes—
132C2×C43⋊C8C2412yes—
133C23×C43—24no—
134C23×C43C4×Q814yes—
135C23×C43C23×C412yes—
136C23×C43C23×C411yescharacteristic
137C2×C4×C43—28no—
138C2×C4×C43C4×Q818yes—
139C2×C4×C43C4×Q814yes—
140C2×C4×C43C23×C418yes—
141C2×C4×C43C23×C411yescharacteristic
142C2×C4×C43C23×C412yes—
143C2×C4×C43C22×Q812yes—
144C2×C4×C43C22×Q814yes—
145C2×C4×C43C2×#4112yes—
146C2×C4×C43C2×#4114yes—
147C2×C4×C43C2511yescharacteristic
148C2×Dic43—24no—
149C2×Dic43—28no—
150C2×Dic43—24no—
151C2×Dic43—48no—
152C2×Dic43C23×C414yes—
153C2×Dic43C23×C414yes—
154C2×Dic43C23×C418yes—
155Dic86—416no—
156C8×C43—24no—
157C8×C43—24no—
158C43⋊C8—24no—
159C43⋊C8C22×Q814yes—
160C43⋊C8C22×Q814yes—
161C2×#2961—431nomaximal, Sylow
162C22×C43—28no—
163C22×C43—24no—
164C22×C43C2×C4×Q814yes—
165C22×C43C2×C4×Q812yes—
166C22×C43#56814yes—
167C22×C43C24×C411yescharacteristic
168C4×C43—28no—
169C4×C43C2×C4×Q812yes—
170C4×C43C2×C4×Q814yes—
171C4×C43C23×Q811yescharacteristic
172C4×C43C22×#4111yescharacteristic
173Dic43—24no—
174Dic43—28no—
175Dic43—24no—
176C2×#533—431no—
177#2961—4316no—
178C2×#446—434no—
179C2×#446—434no—
180C2×#424—431no—
181C2×#424D4311yescharacteristic
182C2×#423—431no—
183C2×#405—431no—
184C2×#405—431no—
185C22×#97—431no—
186C2×C43—24no—
187C2×C43#296114yescomplemented
188C2×C43C22×C4×Q811yescharacteristic
189C2×C43C2×#56812yes—
190C22×M16—431no—
191C22×M16C2×D4311yescharacteristic
192C23×C8—431no—
193C23×C8C2×D4311yescharacteristic
194#533—438no—
195#533—438no—
196C2×C4⋊Q8—432no—
197C2×#125—432no—
198C2×C22⋊Q8—434no—
199C2×C4×Q8—434no—
200C2×#117—431no—
201C2×#117C2×D4311yescharacteristic
202C22×C42—431no—
203#446—4332no—
204#446—4332no—
205#424—438no—
206#424C2×D4318yes—
207#423—438no—
208C2×C4⋊C8—434no—
209C2×C4⋊C8—434no—
210C2×C4⋊C8C2×D4314yes—
211#405—438no—
212#405—438no—
213C2×#97—432no—
214C2×#97—432no—
215C2×#97—438no—
216C2×#97—432no—
217C2×#97—432no—
218C2×C4×C8—432no—
219C2×C4×C8—432no—
220C43C2×#296111yescharacteristic, complemented, Sylow
221C22×Q8—434no—
222C23×C4—432no—
223C23×C4C22×D4311yescharacteristic
224C2×M16—24no—
225C2×M16—434no—
226C2×M16—864no—
227C2×M16C22×D4314yes—
228C22×C8—24no—
229C22×C8—438no—
230C22×C8—434no—
231C22×C8—431no—
232C22×C8—431no—
233C22×C8—432no—
234C22×C8C22×D4314yes—
235C22×C8C22×D4312yes—
236C22×C8C22×D4312yes—
237C4⋊Q8—4316no—
238#125—4316no—
239C22⋊Q8—4332no—
240C4×Q8—4316no—
241C4×Q8—4316no—
242#117—434no—
243#117—434no—
244#117C4×D4314yes—
245#117C22×D4314yes—
246C2×C4⋊C4—432no—
247C2×C4⋊C4—434no—
248C2×C4⋊C4—434no—
249C2×C4⋊C4—434no—
250C2×C4⋊C4C4×D4312yes—
251C2×C22⋊C4—432no—
252C2×C22⋊C4C4×D4312yes—
253C2×C42—431no—
254C2×C42—431no—
255C2×C42—434no—
256C2×C42—434no—
257C2×C42—432no—
258C2×C42—432no—
259C2×C42C22×D4312yes—
260C4⋊C8—4316no—
261C4⋊C8—4316no—
262C4⋊C8C22×D43116yes—
263#97—438no—
264#97—438no—
265#97—438no—
266#97—438no—
267C4×C8—438no—
268C4×C8—438no—
269C24C2×C4×D4311yescharacteristic
270C2×Q8—4316no—
271C2×Q8—1728no—
272C22×C4—432no—
273C22×C4—432no—
274C22×C4—434no—
275C22×C4—438no—
276C22×C4—1724no—
277C22×C4C2×C4×D4314yes—
278C22×C4C2×C4×D4311yescharacteristic
279C22×C4C2×C4×D4312yes—
280C22×C4#1062190014yes—
281C22×C4Q8×D4314yes—
282C22×C4C23×D4312yes—
283C22×C4C23×D4311yescharacteristic
284M16—28no—
285M16—868no—
286C2×C8—24no—
287C2×C8—28no—
288C2×C8—24no—
289C2×C8—434no—
290C2×C8—434no—
291C2×C8—4316no—
292C2×C8—432no—
293C2×C8—432no—
294C2×C8—434no—
295C2×C8—864no—
296C2×C8C23×D4314yes—
297C2×C8C23×D4314yes—
298C4⋊C4—438no—
299C4⋊C4—4316no—
300C4⋊C4—4316no—
301C4⋊C4—4316no—
302C4⋊C4C2×C4×D4318yes—
303C22⋊C4—438no—
304C22⋊C4C2×C4×D4318yes—
305C42—434no—
306C42—434no—
307C42—434no—
308C42—434no—
309C42—434no—
310C42—434no—
311C42C2×C4×D4314yes—
312C42C23×D4314yes—
313C23—24no—
314C23#1306329014yes—
315C23C22×C4×D4312yes—
316C23C22×C4×D4311yescharacteristic
317Q8—17216no—
318C2×C4—28no—
319C2×C4—434no—
320C2×C4—434no—
321C2×C4—438no—
322C2×C4—864no—
323C2×C4—864no—
324C2×C4—868no—
325C2×C4—1728no—
326C2×C4#1306329018yes—
327C2×C4#1306329014yes—
328C2×C4C22×C4×D4318yes—
329C2×C4C22×C4×D4311yescharacteristic
330C2×C4C22×C4×D4312yes—
331C2×C4C2×Q8×D4314yes—
332C2×C4C2×Q8×D4312yes—
333C2×C4C2×#1062190012yes—
334C2×C4C2×#1062190014yes—
335C2×C4C24×D4311yescharacteristic
336C8—24no—
337C8—24no—
338C8—434no—
339C8—434no—
340C8—864no—
341C22—28no—
342C22—24no—
343C22C2×#1306329014yes—
344C22C2×#1306329012yes—
345C22#1458366414yes—
346C22C23×C4×D4311yescharacteristic
347C4—28no—
348C4—864no—
349C4—864no—
350C4—868no—
351C4C2×#1306329012yes—
352C4C2×#1306329014yes—
353C4C22×Q8×D4311yescharacteristic
354C4C22×#1062190011yescharacteristic
355C2—24no—
356C2#1914353414yesdirect product factor
357C2C22×#1306329011yescharacteristic
358C2C2×#1458366412yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#424C2
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
cosocleC2×C4×C43C25
hypercenterC2×#424D43
hypocenterC43C2×#2961
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. #19143534C2direct (N × H)
3. C2×#14583028C2semidirect
4. C2×#14583026C2semidirect
21. #14583028C22semidirect
22. #14583026C22semidirect
45. C22×C43⋊C8Q8semidirect
129. C2×C43⋊C8C2×Q8semidirect
187. C2×C43#2961semidirect
220. C43C2×#2961semidirect
356. C2#19143534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834522
#191435342
C2×#145830282
C2×#145830262
C2×#145829252
C2×#145829222
C2×#145828572
C2×#145828552
C22×#130632352
C2×C43×#4242
C2×#296143