Finite Group Databasebeta

← C2×#19133352 #25065597

Subgroups — C2×#19133352 #25065597

Order 11008.

854 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582921C212yesmaximal
2C2×C4×C8×D43C211yesmaximal, characteristic
3#19133352C218yesmaximal, direct product factor
4C2×#14582652C211yesmaximal, characteristic, complemented
5C2×#14582651C212yesmaximal, complemented
6C2×C43×#335C211yesmaximal, characteristic, complemented
7C22×#10621872—22no—
8C22×C8×D43C411yescharacteristic
9C22×C8×D43C411yescharacteristic
10C2×C42×D43C2211yescharacteristic
11#14582921—24no—
12#14582921C2218yes—
13C2×C4⋊(C43⋊C8)C2212yes—
14C2×Dic43⋊C8—22no—
15C2×C4×C43⋊C8C2211yescharacteristic
16C2×C8×Dic43C411yescharacteristic
17C2×C8×Dic43C411yescharacteristic
18C4×C8×D43C414yes—
19C4×C8×D43C2214yes—
20#14582652C2214yescomplemented
21#14582651C2218yescomplemented
22C2×C4⋊C8×C43C2212yes—
23C2×C4×C8×C43C2211yescharacteristic
24C43×#335C2214yescomplemented
25C22×C4×D43C2×C411yescharacteristic
26C22×C4×D43D411yescharacteristic
27C22×C4×D43Q811yescharacteristic
28C2×#10621872—28no—
29C2×#10621872—48no—
30C22×C43⋊C8—22no—
31C22×C43⋊C8C2×C411yescharacteristic
32C22×C43⋊C8C2×C411yescharacteristic
33C2×C8×D43—24no—
34C2×C8×D43—24no—
35C2×C8×D43C2×C414yes—
36C2×C8×D43C2×C414yes—
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43D411yescharacteristic
39C2×C4×Dic43Q811yescharacteristic
40C42×D43C2×C412yes—
41C42×D43D412yes—
42C42×D43Q812yes—
43C42×D43C2312yes—
44C4⋊(C43⋊C8)—22no—
45C4⋊(C43⋊C8)C2314yes—
46Dic43⋊C8—28no—
47C4×C43⋊C8C2×C412yes—
48C4×C43⋊C8C2312yes—
49C8×Dic43C2×C414yes—
50C8×Dic43C2×C414yes—
51C22×C8×C43—22no—
52C22×C8×C43C2×C411yescharacteristic
53C22×C8×C43C2×C411yescharacteristic
54C2×C42×C43C2311yescharacteristic
55C4⋊C8×C43—22no—
56C4⋊C8×C43C2314yes—
57C4×C8×C43C2×C412yes—
58C4×C8×C43C2312yes—
59C23×D43C4⋊C411yescharacteristic
60C22×C4×C43C22×C411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×Q811yescharacteristic
63C22×Dic43C4⋊C411yescharacteristic
64C22×Dic43C4⋊C411yescharacteristic
65C22×Dic43C4⋊C411yescharacteristic
66C2×C4×D43—22no—
67C2×C4×D43—22no—
68C2×C4×D43—24no—
69C2×C4×D43C4⋊C412yes—
70C2×C4×D43C4⋊C412yes—
71C2×C4×D43C4⋊C412yes—
72C2×C4×D43D814yes—
73C2×C4×D43Q1614yes—
74C2×C4×D43C22×C412yes—
75C2×C4×D43C2×D412yes—
76C2×C4×D43C2×Q812yes—
77C2×C8×C43—22no—
78C2×C8×C43—24no—
79C2×C8×C43—44no—
80C2×C8×C43M1614yescomplemented
81C2×C8×C43C22×C412yes—
82C2×C8×C43C22×C412yes—
83C42×C43C22×C411yescharacteristic
84C42×C43C2×D411yescharacteristic
85C42×C43C2×Q811yescharacteristic
86C42×C43C2411yescharacteristic
87C4×Dic43C4⋊C412yes—
88C4×Dic43C4⋊C412yes—
89C4×Dic43C4⋊C412yes—
90C4×Dic43C22×C412yes—
91C4×Dic43C2×D412yes—
92C4×Dic43C2×Q812yes—
93C2×C43⋊C8—22no—
94C2×C43⋊C8—24no—
95C2×C43⋊C8—44no—
96C2×C43⋊C8M1614yescomplemented
97C2×C43⋊C8C22×C412yes—
98C2×C43⋊C8C22×C412yes—
99#10621872—416no—
100C8×D43—28no—
101C8×D43—28no—
102C23×C43C2×C4⋊C411yescharacteristic
103C22×D43—22no—
104C22×D43—22no—
105C22×D43#10714yes—
106C22×D43C2×C4⋊C412yes—
107C2×C4×C43—22no—
108C2×C4×C43C2×C4⋊C411yescharacteristic
109C2×C4×C43C2×C4⋊C411yescharacteristic
110C2×C4×C43C2×C4⋊C411yescharacteristic
111C2×C4×C43C2×M1612yes—
112C2×C4×C43C2×M1612yes—
113C2×C4×C43C2×D812yes—
114C2×C4×C43C2×Q1612yes—
115C2×C4×C43C23×C411yescharacteristic
116C2×C4×C43C22×D411yescharacteristic
117C2×C4×C43C22×Q811yescharacteristic
118C2×Dic43—22no—
119C2×Dic43#10714yes—
120C2×Dic43#10814yes—
121C2×Dic43C2×C4⋊C412yes—
122C2×Dic43C2×C4⋊C412yes—
123C2×Dic43C2×C4⋊C412yes—
124C4×D43—22no—
125C4×D43—22no—
126C4×D43—24no—
127C4×D43—24no—
128C4×D43—24no—
129C4×D43#10718yes—
130C4×D43C2×D814yes—
131C4×D43C2×Q1614yes—
132C8×C43—22no—
133C8×C43—44no—
134C8×C43C2×M1614yescomplemented
135C43⋊C8—22no—
136C43⋊C8—44no—
137C43⋊C8C2×M1614yescomplemented
138C2×#1567—431nomaximal, Sylow
139C22×C43#42312yes—
140C22×C43C2×#10712yes—
141C22×C43C2×#10812yes—
142C22×C43C22×C4⋊C411yescharacteristic
143C2×D43—28no—
144C2×D43—22no—
145C2×D43—22no—
146C2×D43C2×#10714yes—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43#42312yes—
150C4×C43C2×#10712yes—
151C4×C43C22×M1611yescharacteristic
152C4×C43C22×M1611yescharacteristic
153C4×C43C22×D811yescharacteristic
154C4×C43C22×Q1611yescharacteristic
155Dic43—22no—
156Dic43C2×#10714yes—
157Dic43C2×#10814yes—
158C2×#423—432no—
159C22×C4×C8—431no—
160#1567—438no—
161C2×#335—432no—
162C2×#335—431no—
163C2×#335D4311yescharacteristic, complemented
164C2×C43#156714yescomplemented
165C2×C43C2×#42311yescharacteristic
166C2×C43C22×#10711yescharacteristic
167C2×C43C22×#10811yescharacteristic
168D43—24no—
169C22×M16—862no—
170C23×C8—431no—
171C23×C8—431no—
172C22×C42—431no—
173#423—438no—
174#423—864no—
175C2×C4⋊C8—432no—
176C2×C4⋊C8—862no—
177C2×C4⋊C8C2×D4312yes—
178C2×C4×C8—431no—
179C2×C4×C8—431no—
180C2×C4×C8—431no—
181C2×C4×C8—434no—
182C2×C4×C8—434no—
183C2×C4×C8C2×D4311yescharacteristic
184#335—438no—
185#335—434no—
186#335C2×D4314yescomplemented
187C43C2×#156711yescharacteristic, complemented, Sylow
188C23×C4—431no—
189C23×C4—431no—
190C23×C4—431no—
191C2×M16—868no—
192C2×M16—1728no—
193C22×C8—22no—
194C22×C8—431no—
195C22×C8—431no—
196C22×C8—434no—
197C22×C8—434no—
198C22×C8—864no—
199C22×C8—864no—
200C22×C8—862no—
201C22×C8C4×D4311yescharacteristic
202C22×C8C4×D4311yescharacteristic
203C2×C42—431no—
204C2×C42—431no—
205C2×C42—431no—
206C2×C42—432no—
207C2×C42—432no—
208C2×C42—432no—
209C2×C42—432no—
210C2×C42C22×D4311yescharacteristic
211C4⋊C8—22no—
212C4⋊C8—434no—
213C4⋊C8—868no—
214C4⋊C8—862no—
215C4⋊C8C22×D4314yes—
216C4×C8—434no—
217C4×C8—434no—
218C4×C8—432no—
219C4×C8—432no—
220C4×C8C4×D4312yes—
221C4×C8C22×D4312yes—
222C24—431no—
223C22×C4—431no—
224C22×C4—431no—
225C22×C4—432no—
226C22×C4—434no—
227C22×C4—434no—
228C22×C4—432no—
229C22×C4—431no—
230C22×C4—432no—
231C22×C4—432no—
232C22×C4—432no—
233C22×C4—432no—
234C22×C4—864no—
235C22×C4—862no—
236C22×C4—862no—
237C22×C4C2×C4×D4311yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C22×C4Q8×D4311yescharacteristic
240M16—17216no—
241C2×C8—22no—
242C2×C8—24no—
243C2×C8—44no—
244C2×C8—434no—
245C2×C8—432no—
246C2×C8—432no—
247C2×C8—868no—
248C2×C8—862no—
249C2×C8—868no—
250C2×C8—864no—
251C2×C8—1724no—
252C2×C8#1062187214yescomplemented
253C2×C8C2×C4×D4312yes—
254C2×C8C2×C4×D4312yes—
255C42—432no—
256C42—432no—
257C42—432no—
258C42—432no—
259C42—432no—
260C42—432no—
261C42C2×C4×D4311yescharacteristic
262C42D4×D4311yescharacteristic
263C42Q8×D4311yescharacteristic
264C42C23×D4311yescharacteristic
265C23—432no—
266C23—434no—
267C23—862no—
268C23—862no—
269C23C4⋊C4×D4311yescharacteristic
270C2×C4—22no—
271C2×C4—432no—
272C2×C4—432no—
273C2×C4—434no—
274C2×C4—434no—
275C2×C4—434no—
276C2×C4—434no—
277C2×C4—438no—
278C2×C4—432no—
279C2×C4—864no—
280C2×C4—864no—
281C2×C4—862no—
282C2×C4—862no—
283C2×C4—862no—
284C2×C4—864no—
285C2×C4C4⋊C4×D4311yescharacteristic
286C2×C4C4⋊C4×D4311yescharacteristic
287C2×C4C4⋊C4×D4311yescharacteristic
288C2×C4M16×D4312yes—
289C2×C4C2×#1062187212yes—
290C2×C4D8×D4312yes—
291C2×C4Q16×D4312yes—
292C2×C4C22×C4×D4311yescharacteristic
293C2×C4C2×D4×D4311yescharacteristic
294C2×C4C2×Q8×D4311yescharacteristic
295C8—22no—
296C8—44no—
297C8—434no—
298C8—862no—
299C8—1724no—
300C8C2×#1062187214yescomplemented
301C22—434no—
302C22—862no—
303C22—868no—
304C22—862no—
305C22#1458292112yes—
306C22#107×D4312yes—
307C22#108×D4312yes—
308C22C2×C4⋊C4×D4311yescharacteristic
309C4—21no—
310C4—21no—
311C4—434no—
312C4—434no—
313C4—862no—
314C4#1458292112yes—
315C4#107×D4312yes—
316C4C2×M16×D4311yescharacteristic
317C4C22×#1062187211yescharacteristic
318C4C2×D8×D4311yescharacteristic
319C4C2×Q16×D4311yescharacteristic
320C2—864no—
321C2#1913335214yesdirect product factor
322C2C2×#1458292111yescharacteristic
323C2C2×#107×D4311yescharacteristic
324C2C2×#108×D4311yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#335C2
socleC23×C43C2×C4⋊C4
prime radicalC23×D43C4⋊C4
cosocleC42×C43C24
hypercenterC2×#335D43
hypocenterC43C2×#1567
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
3. #19133352C2direct (N × H)
4. C2×#14582652C2semidirect
5. C2×#14582651C2semidirect
6. C2×C43×#335C2semidirect
20. #14582652C22semidirect
21. #14582651C22semidirect
24. C43×#335C22semidirect
80. C2×C8×C43M16semidirect
96. C2×C43⋊C8M16semidirect
134. C8×C43C2×M16semidirect
137. C43⋊C8C2×M16semidirect
163. C2×#335D43semidirect
164. C2×C43#1567semidirect
186. #335C2×D43semidirect
187. C43C2×#1567semidirect
252. C2×C8#10621872semidirect
300. C8C2×#10621872semidirect
321. C2#19133352direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145829212
C2×C4×C8×D432
#191333522
C2×#145826522
C2×#145826512
C2×C43×#3352
C2×#156743