Finite Group Databasebeta

← C2×#19137072 #25254972

Subgroups — C2×#19137072 #25254972

Order 11008.

2750 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic86C211yesmaximal, characteristic
2#19137072C2116yesmaximal, direct product factor
3C2×#14582805C212yesmaximal
4C2×#14582797C212yesmaximal
5C2×#14582783C214yesmaximal
6C2×C4×Dic43⋊C4C212yesmaximal
7C2×C4×C4⋊Dic43C211yesmaximal, characteristic
8C2×#14582745C212yesmaximal
9C2×C43×C43C211yesmaximal, characteristic
10C23×Dic86C2211yescharacteristic
11C2×C4×Dic86C4116yescomplemented
12C2×C4×Dic86C2218yes—
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2214yes—
16C22×Dic43⋊C4C2212yes—
17C22×C4×Dic43C2212yes—
18C22×C4×Dic43C2212yes—
19#14582805C22116yes—
20#14582797C22116yes—
21#14582783C22132yes—
22C4×Dic43⋊C4C22116yes—
23C4×C4⋊Dic43C2218yes—
24#14582745C22116yes—
25C2×C43⋊#95C2214yes—
26C2×C43⋊#95C2214yes—
27C2×C43⋊#95C2214yes—
28C2×C43⋊#95C2212yes—
29C22×C42×C43C2212yes—
30C22×C42×C43C2211yescharacteristic
31C22×C42×C43C2212yes—
32C22×C42×C43C2211yescharacteristic
33C22×C42×C43C2211yescharacteristic
34C43×C43C2218yes—
35C22×Dic86—28no—
36C22×Dic86C2×C418yes—
37C22×Dic86C2314yes—
38C23×Dic43C2314yes—
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C4×Dic86C2×C4164yescomplemented
42C2×C4⋊Dic43—28no—
43C2×C4⋊Dic43C2×C418yes—
44C2×C4⋊Dic43C2318yes—
45C2×C4⋊Dic43C2314yes—
46C2×Dic43⋊C4—216no—
47C2×Dic43⋊C4C2×C4116yes—
48C2×Dic43⋊C4C23116yes—
49C2×Dic43⋊C4C2318yes—
50C2×C4×Dic43—28no—
51C2×C4×Dic43C2×C4116yes—
52C2×C4×Dic43C2318yes—
53C2×C4×Dic43C2318yes—
54C43⋊#95C23116yes—
55C43⋊#95C23116yes—
56C43⋊#95C23116yes—
57C43⋊#95C2318yes—
58C23×C4×C43C2311yescharacteristic
59C23×C4×C43C2312yes—
60C23×C4×C43C2312yes—
61C23×C4×C43C2311yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C2×C42×C43—28no—
64C2×C42×C43—28no—
65C2×C42×C43—24no—
66C2×C42×C43C2×C418yes—
67C2×C42×C43Q818yescomplemented
68C2×C42×C43C2318yes—
69C2×C42×C43C2314yes—
70C2×C42×C43C2318yes—
71C2×C42×C43C2314yes—
72C2×C42×C43C2314yes—
73C24×C43C2411yescharacteristic
74C22×C4×C43—24no—
75C22×C4×C43—24no—
76C22×C4×C43—24no—
77C22×C4×C43—24no—
78C22×C4×C43—24no—
79C22×C4×C43C22×C414yes—
80C22×C4×C43C22×C414yes—
81C22×C4×C43C22×C414yes—
82C22×C4×C43C2×Q818yes—
83C22×C4×C43C2×Q814yes—
84C22×C4×C43#4118yes—
85C22×C4×C43#4118yes—
86C22×C4×C43#4114yes—
87C22×C4×C43C2412yes—
88C22×C4×C43C2414yes—
89C22×C4×C43C2414yes—
90C22×C4×C43C2412yes—
91C22×C4×C43C2412yes—
92C22×Dic43—28no—
93C22×Dic43—28no—
94C22×Dic43—28no—
95C22×Dic43—28no—
96C22×Dic43—28no—
97C22×Dic43C22×C418yes—
98C22×Dic43C22×C418yes—
99C22×Dic43C2418yes—
100C22×Dic43C2414yes—
101C22×Dic43C2414yes—
102C2×Dic86—232no—
103C2×Dic86—216no—
104C2×Dic86C22×C4116yes—
105C42×C43—216no—
106C42×C43—216no—
107C42×C43—28no—
108C42×C43C22×C4116yes—
109C42×C43C2×Q8116yescomplemented
110C4⋊Dic43—216no—
111C4⋊Dic43C22×C4116yes—
112Dic43⋊C4—232no—
113Dic43⋊C4C22×C4132yes—
114C4×Dic43—216no—
115C4×Dic43C22×C4132yes—
116C23×C43C23×C412yes—
117C23×C43C22×Q812yes—
118C23×C43C2×#4114yes—
119C23×C43C2×#4112yes—
120C23×C43C2×#4114yes—
121C23×C43C2511yescharacteristic
122C2×C4×C43—28no—
123C2×C4×C43—216no—
124C2×C4×C43—216no—
125C2×C4×C43—24no—
126C2×C4×C43—24no—
127C2×C4×C43—24no—
128C2×C4×C43—24no—
129C2×C4×C43—24no—
130C2×C4×C43#117116yes—
131C2×C4×C43C4×Q8116yes—
132C2×C4×C43C23×C414yes—
133C2×C4×C43C23×C414yes—
134C2×C4×C43C23×C414yes—
135C2×C4×C43C22×Q818yes—
136C2×C4×C43C22×Q814yes—
137C2×C4×C43C2×#4118yes—
138C2×C4×C43C2×#4118yes—
139C2×C4×C43C2×#4114yes—
140C2×Dic43—216no—
141C2×Dic43—216no—
142C2×Dic43—28no—
143C2×Dic43—28no—
144C2×Dic43—28no—
145C2×Dic43—28no—
146C2×Dic43—28no—
147C2×Dic43—416no—
148C2×Dic43C23×C418yes—
149C2×Dic43C23×C418yes—
150Dic86—232no—
151C2×#2295—431nomaximal, Sylow
152C22×C43C2×#11714yes—
153C22×C43C2×C4×Q814yes—
154C22×C43C4×#4114yes—
155C22×C43#52918yes—
156C22×C43#53318yes—
157C22×C43C24×C411yescharacteristic
158C22×C43C23×Q811yescharacteristic
159C22×C43C22×#4112yes—
160C22×C43C22×#4111yescharacteristic
161C22×C43C22×#4112yes—
162C4×C43—24no—
163C4×C43—28no—
164C4×C43—28no—
165C4×C43C2×#11718yes—
166C4×C43C2×C4×Q818yes—
167Dic43—28no—
168Dic43—28no—
169Dic43—48no—
170C22×C4×Q8—431no—
171#2295—4316no—
172C2×#391—432no—
173C2×#389—432no—
174C2×#387—434no—
175C2×C4×C4⋊C4—431no—
176C2×C4×C4⋊C4—432no—
177C2×#376—432no—
178C2×C43D4311yescharacteristic
179C2×C43#229518yescomplemented
180C2×C43C22×#11711yescharacteristic
181C2×C43C22×C4×Q811yescharacteristic
182C2×C43C2×C4×#4111yescharacteristic
183C2×C43C2×#52912yes—
184C2×C43C2×#53312yes—
185C23×Q8—431no—
186C2×C4×Q8—438no—
187C2×C4×Q8—4316no—
188C22×C4⋊C4—432no—
189C22×C4⋊C4—431no—
190C22×C4⋊C4—434no—
191C22×C4⋊C4—432no—
192C22×C42—432no—
193C22×C42—432no—
194C22×C42C2×D4312yes—
195C22×C42C2×D4312yes—
196C22×C42C2×D4311yescharacteristic
197C22×C42C2×D4311yescharacteristic
198C22×C42C2×D4311yescharacteristic
199#391—4316no—
200#389—4316no—
201#387—4332no—
202C4×C4⋊C4—438no—
203C4×C4⋊C4—4316no—
204#376—4316no—
205C2×#95—434no—
206C2×#95—434no—
207C2×#95—432no—
208C2×#95—434no—
209C43C2×D4318yes—
210C43C2×#229511yescharacteristic, complemented, Sylow
211C22×Q8—438no—
212C22×Q8—434no—
213C22×Q8—868no—
214C23×C4—432no—
215C23×C4—432no—
216C23×C4—434no—
217C23×C4C22×D4312yes—
218C23×C4C22×D4311yescharacteristic
219C23×C4C22×D4312yes—
220C23×C4C22×D4311yescharacteristic
221C23×C4C22×D4311yescharacteristic
222C4×Q8—4364no—
223C2×C4⋊C4—4316no—
224C2×C4⋊C4—438no—
225C2×C4⋊C4—438no—
226C2×C4⋊C4—434no—
227C2×C4⋊C4—4316no—
228C2×C4⋊C4—438no—
229C2×C4⋊C4—8616no—
230C2×C4⋊C4—868no—
231C2×C42—28no—
232C2×C42—28no—
233C2×C42—24no—
234C2×C42—4316no—
235C2×C42—438no—
236C2×C42—438no—
237C2×C42—868no—
238C2×C42Dic8618yescomplemented
239C2×C42C4×D4318yes—
240C2×C42C22×D4314yes—
241C2×C42C22×D4318yes—
242C2×C42C22×D4318yes—
243C2×C42C22×D4314yes—
244C2×C42C22×D4314yes—
245#95—4316no—
246#95—4316no—
247#95—438no—
248#95—4316no—
249C24C23×D4311yescharacteristic
250C2×Q8—4316no—
251C2×Q8—8632no—
252C2×Q8—8616no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—438no—
259C22×C4—438no—
260C22×C4—434no—
261C22×C4—434no—
262C22×C4—438no—
263C22×C4—868no—
264C22×C4—868no—
265C22×C4—868no—
266C22×C4—868no—
267C22×C4—868no—
268C22×C4C2×Dic8618yes—
269C22×C4C2×Dic8614yes—
270C22×C4C2×C4×D4314yes—
271C22×C4C2×C4×D4314yes—
272C22×C4C2×C4×D4314yes—
273C22×C4#1062189818yes—
274C22×C4#1062189818yes—
275C22×C4#1062189814yes—
276C22×C4C23×D4312yes—
277C22×C4C23×D4314yes—
278C22×C4C23×D4314yes—
279C22×C4C23×D4312yes—
280C22×C4C23×D4312yes—
281C4⋊C4—4332no—
282C4⋊C4—4316no—
283C4⋊C4—8632no—
284C4⋊C4—8616no—
285C42—216no—
286C42—216no—
287C42—28no—
288C42—4332no—
289C42—8616no—
290C42C2×Dic86116yescomplemented
291C42C2×C4×D43116yes—
292C23C22×C4×D4312yes—
293C23C22×Dic8612yes—
294C23C2×#1062189814yes—
295C23C2×#1062189812yes—
296C23C2×#1062189814yes—
297C23C24×D4311yescharacteristic
298Q8—8632no—
299C2×C4—28no—
300C2×C4—216no—
301C2×C4—216no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—438no—
308C2×C4—438no—
309C2×C4—8616no—
310C2×C4—8616no—
311C2×C4—868no—
312C2×C4—868no—
313C2×C4—868no—
314C2×C4—868no—
315C2×C4—868no—
316C2×C4—17216no—
317C2×C4#13063282116yes—
318C2×C4C4×Dic86116yes—
319C2×C4C22×C4×D4314yes—
320C2×C4C22×C4×D4314yes—
321C2×C4C22×C4×D4314yes—
322C2×C4C22×Dic8618yes—
323C2×C4C22×Dic8614yes—
324C2×C4C2×#1062189818yes—
325C2×C4C2×#1062189818yes—
326C2×C4C2×#1062189814yes—
327C22C2×#1306328214yes—
328C22C2×C4×Dic8614yes—
329C22C4×#1062189814yes—
330C22#1458343318yes—
331C22#1458345618yes—
332C22C23×C4×D4311yescharacteristic
333C22C23×Dic8611yescharacteristic
334C22C22×#1062189811yescharacteristic
335C22C22×#1062189812yes—
336C22C22×#1062189812yes—
337C4—28no—
338C4—28no—
339C4—24no—
340C4—868no—
341C4—868no—
342C4—1728no—
343C4C2×#1306328218yes—
344C4C2×C4×Dic8618yes—
345C2#1913707218yesdirect product factor
346C2C22×#1306328211yescharacteristic
347C2C22×C4×Dic8611yescharacteristic
348C2C2×C4×#1062189811yescharacteristic
349C2C2×#1458343312yes—
350C2C2×#1458345612yes—
subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×C43C2
socle, prime radicalC24×C43C24
cosocleC23×C43C25
hypercenterC2×C43D43
hypocenterC43C2×#2295
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
2. #19137072C2direct (N × H)
11. C2×C4×Dic86C4semidirect
41. C4×Dic86C2×C4semidirect
67. C2×C42×C43Q8semidirect
109. C42×C43C2×Q8semidirect
179. C2×C43#2295semidirect
210. C43C2×#2295semidirect
238. C2×C42Dic86semidirect
290. C42C2×Dic86semidirect
345. C2#19137072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic862
#191370722
C2×#145828052
C2×#145827972
C2×#145827832
C2×C4×Dic43⋊C42
C2×C4×C4⋊Dic432
C2×#145827452
C2×C43×C432
C2×#229543