Finite Group Databasebeta

← C2×#14561469 #18071994

Subgroups — C2×#14561469 #18071994

Order 4864.

830 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C19⋊C8)C211yesmaximal, characteristic
2C22×C4×C19⋊C8C211yesmaximal, characteristic
3#14561469C214yesmaximal, direct product factor
4C22×C19×C4⋊C8C211yesmaximal, characteristic
5C23×C19⋊C8—21no—
6C23×C19⋊C8C412yes—
7C2×C4⋊(C19⋊C8)—21no—
8C2×C4⋊(C19⋊C8)—22no—
9C2×C4⋊(C19⋊C8)C414yes—
10C2×C4⋊(C19⋊C8)C2212yes—
11C2×C4×C19⋊C8—22no—
12C2×C4×C19⋊C8—22no—
13C2×C4×C19⋊C8C412yes—
14C2×C4×C19⋊C8C2212yes—
15C23×C8×C19—21no—
16C22×C42×C19C2211yescharacteristic
17C2×C19×C4⋊C8—21no—
18C2×C19×C4⋊C8—22no—
19C2×C19×C4⋊C8C414yes—
20C2×C19×C4⋊C8C2212yes—
21C23×C4×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19Q811yescharacteristic
24C22×C8×C19—24no—
25C22×C8×C19—22no—
26C22×C8×C19—42no—
27C22×C8×C19—42no—
28C2×C42×C19C2×C411yescharacteristic
29C2×C42×C19C2×C412yes—
30C2×C42×C19C2×C412yes—
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D412yes—
33C2×C42×C19D412yes—
34C2×C42×C19Q811yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C22×C19⋊C8—24no—
37C22×C19⋊C8—24no—
38C22×C19⋊C8—24no—
39C22×C19⋊C8—22no—
40C22×C19⋊C8—42no—
41C22×C19⋊C8—42no—
42C22×C19⋊C8C818yescomplemented
43C22×C19⋊C8C2×C414yes—
44C19×C4⋊C8—24no—
45C19×C4⋊C8—22no—
46C19×C4⋊C8C2×C414yes—
47C4⋊(C19⋊C8)—24no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)C2×C414yes—
50C4×C19⋊C8—24no—
51C4×C19⋊C8—22no—
52C4×C19⋊C8—22no—
53C24×C19C4⋊C411yescharacteristic
54C22×C4×C19—24no—
55C22×C4×C19C4212yes—
56C22×C4×C19C22⋊C412yes—
57C22×C4×C19C22⋊C412yes—
58C22×C4×C19C22⋊C412yes—
59C22×C4×C19C4⋊C411yescharacteristic
60C22×C4×C19C4⋊C412yes—
61C22×C4×C19C4⋊C411yescharacteristic
62C22×C4×C19C4⋊C411yescharacteristic
63C22×C4×C19C4⋊C412yes—
64C22×C4×C19C2×C814yes—
65C22×C4×C19M1614yes—
66C22×C4×C19D812yes—
67C22×C4×C19SD1612yes—
68C22×C4×C19SD1612yes—
69C22×C4×C19Q1612yes—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×Q811yescharacteristic
73C2×C8×C19—24no—
74C2×C8×C19—48no—
75C2×C8×C19—42no—
76C2×C8×C19—42no—
77C42×C19C4212yes—
78C42×C19C22⋊C412yes—
79C42×C19C22⋊C412yes—
80C42×C19C22⋊C412yes—
81C42×C19C4⋊C412yes—
82C42×C19C4⋊C412yes—
83C42×C19C22×C411yescharacteristic
84C42×C19C22×C411yescharacteristic
85C42×C19C2×D411yescharacteristic
86C42×C19C2×D411yescharacteristic
87C2×C19⋊C8—216no—
88C2×C19⋊C8—24no—
89C2×C19⋊C8—24no—
90C2×C19⋊C8—24no—
91C2×C19⋊C8—48no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8C2×C818yescomplemented
95C2×#1277—191nomaximal, Sylow
96C23×C19#9512yes—
97C23×C19C4⋊C814yes—
98C23×C19#10612yes—
99C23×C19#10712yes—
100C23×C19#10814yes—
101C23×C19C2×C4⋊C411yescharacteristic
102C2×C4×C19—24no—
103C2×C4×C19—24no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19#9512yes—
107C2×C4×C19#9512yes—
108C2×C4×C19#9512yes—
109C2×C4×C19C4×C814yes—
110C2×C4×C19#9714yes—
111C2×C4×C19C22⋊C818yes—
112C2×C4×C19#10214yes—
113C2×C4×C19#10214yes—
114C2×C4×C19#10314yes—
115C2×C4×C19#10314yes—
116C2×C4×C19C4⋊C814yes—
117C2×C4×C19#10612yes—
118C2×C4×C19#10712yes—
119C2×C4×C19C2×C4211yescharacteristic
120C2×C4×C19C2×C22⋊C411yescharacteristic
121C2×C4×C19C2×C22⋊C411yescharacteristic
122C2×C4×C19C2×C22⋊C411yescharacteristic
123C2×C4×C19C2×C4⋊C411yescharacteristic
124C2×C4×C19C2×C4⋊C411yescharacteristic
125C2×C4×C19C22×C812yes—
126C2×C4×C19C2×M1612yes—
127C2×C4×C19C2×D811yescharacteristic
128C2×C4×C19C2×SD1611yescharacteristic
129C2×C4×C19C2×SD1611yescharacteristic
130C2×C4×C19C2×Q1611yescharacteristic
131C8×C19—44no—
132C19⋊C8—28no—
133C19⋊C8—44no—
134C22×C4⋊C8—191no—
135C22×C4⋊C8D1911yescharacteristic
136C22×C4×C8—191no—
137#1277—194no—
138C22×C19#33418yes—
139C22×C19#33518yes—
140C22×C19#33614yes—
141C22×C19#34014yes—
142C22×C19#34114yes—
143C22×C19C2×#9511yescharacteristic
144C22×C19C2×C4⋊C812yes—
145C22×C19C2×#10611yescharacteristic
146C22×C19C2×#10711yescharacteristic
147C22×C19C2×#10812yes—
148C4×C19—22no—
149C4×C19—21no—
150C4×C19—21no—
151C4×C19#33614yes—
152C4×C19#34014yes—
153C4×C19C2×C4×C811yescharacteristic
154C4×C19C2×#9711yescharacteristic
155C4×C19C2×C22⋊C812yes—
156C4×C19C2×#10211yescharacteristic
157C4×C19C2×#10211yescharacteristic
158C4×C19C2×#10311yescharacteristic
159C4×C19C2×#10311yescharacteristic
160C23×C8—21no—
161C23×C8—192no—
162C23×C8—381no—
163C22×C42C2×D1911yescharacteristic
164C2×C4⋊C8—21no—
165C2×C4⋊C8—22no—
166C2×C4⋊C8—194no—
167C2×C4⋊C8—192no—
168C2×C4⋊C8—382no—
169C2×C4⋊C8—381no—
170C2×C4⋊C8Dic1914yes—
171C2×C4⋊C8C2×D1912yes—
172C2×C4×C8—192no—
173C2×C4×C8—192no—
174C2×C4×C8—382no—
175C2×C4×C8—382no—
176C2×C19#127718yescomplemented
177C2×C19C2×#33412yes—
178C2×C19C2×#33512yes—
179C2×C19C2×#33611yescharacteristic
180C2×C19C2×#34011yescharacteristic
181C2×C19C2×#34111yescharacteristic
182C23×C4Dic3811yescharacteristic
183C23×C4C4×D1911yescharacteristic
184C23×C4C22⋊D1911yescharacteristic
185C22×C8—24no—
186C22×C8—22no—
187C22×C8—42no—
188C22×C8—42no—
189C22×C8—198no—
190C22×C8—194no—
191C22×C8—384no—
192C22×C8—384no—
193C22×C8—384no—
194C22×C8—382no—
195C22×C8—762no—
196C22×C8—762no—
197C2×C42Dic3811yescharacteristic
198C2×C42C4×D1911yescharacteristic
199C2×C42C4×D1912yes—
200C2×C42D7612yes—
201C2×C42C2×Dic1912yes—
202C2×C42C22⋊D1912yes—
203C2×C42C22⋊D1911yescharacteristic
204C2×C42C22×D1911yescharacteristic
205C4⋊C8—24no—
206C4⋊C8—22no—
207C4⋊C8—194no—
208C4⋊C8—384no—
209C4⋊C8—382no—
210C4⋊C8C2×Dic1914yes—
211C4×C8—384no—
212C4×C8—382no—
213C4×C8—382no—
214C19C2×#127711yescharacteristic, complemented, Sylow
215C24Dic19⋊C411yescharacteristic
216C22×C4—24no—
217C22×C4C8×D1914yes—
218C22×C4#6451514yes—
219C22×C4C4×Dic1912yes—
220C22×C4Dic19⋊C411yescharacteristic
221C22×C4Dic19⋊C412yes—
222C22×C4Dic19⋊C411yescharacteristic
223C22×C4Dic19⋊C411yescharacteristic
224C22×C4C4⋊Dic1912yes—
225C22×C4(C2×D19)⋊C412yes—
226C22×C4(C2×D19)⋊C412yes—
227C22×C4#6452512yes—
228C22×C4#6452612yes—
229C22×C4#6452712yes—
230C22×C4#6452812yes—
231C22×C4C22⋊Dic1912yes—
232C22×C4C2×Dic3811yescharacteristic
233C22×C4C2×C4×D1911yescharacteristic
234C22×C4C2×C22⋊D1911yescharacteristic
235C2×C8—24no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—48no—
239C2×C8—198no—
240C2×C8—3816no—
241C2×C8—384no—
242C2×C8—384no—
243C2×C8—384no—
244C2×C8—762no—
245C2×C8—762no—
246C2×C8—768no—
247C42C4×Dic1912yes—
248C42Dic19⋊C412yes—
249C42C4⋊Dic1912yes—
250C42(C2×D19)⋊C412yes—
251C42(C2×D19)⋊C412yes—
252C42C22⋊Dic1912yes—
253C42C2×C4×D1911yescharacteristic
254C42C2×D7611yescharacteristic
255C42C22×Dic1911yescharacteristic
256C42C2×C22⋊D1911yescharacteristic
257C23#1059726412yes—
258C23#1059726512yes—
259C23Dic19⋊C814yes—
260C23#1059727914yes—
261C23C19⋊#9512yes—
262C23C2×Dic19⋊C411yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4#1059726412yes—
268C2×C4#1059726512yes—
269C2×C4#1059726614yes—
270C2×C4#1059726714yes—
271C2×C4C8×Dic1914yes—
272C2×C4Dic19⋊C814yes—
273C2×C4#1059727214yes—
274C2×C4(C2×D19)⋊C818yes—
275C2×C4C19⋊#9512yes—
276C2×C4C19⋊#9512yes—
277C2×C4C19⋊#9512yes—
278C2×C4#1059728914yes—
279C2×C4#1059729214yes—
280C2×C4C2×C8×D1912yes—
281C2×C4C2×#6451512yes—
282C2×C4C2×C4×Dic1911yescharacteristic
283C2×C4C2×Dic19⋊C411yescharacteristic
284C2×C4C2×C4⋊Dic1911yescharacteristic
285C2×C4C2×(C2×D19)⋊C411yescharacteristic
286C2×C4C2×(C2×D19)⋊C411yescharacteristic
287C2×C4C2×#6452511yescharacteristic
288C2×C4C2×#6452611yescharacteristic
289C2×C4C2×#6452711yescharacteristic
290C2×C4C2×#6452811yescharacteristic
291C2×C4C2×C22⋊Dic1911yescharacteristic
292C8—44no—
293C8—388no—
294C8—764no—
295C22#1192629418yes—
296C22#1192629618yes—
297C22#1192629814yes—
298C22#1192630614yes—
299C22#1192630814yes—
300C22C2×C19⋊#9511yescharacteristic
301C22C2×Dic19⋊C812yes—
302C22C2×#1059726511yescharacteristic
303C22C2×#1059726411yescharacteristic
304C22C2×#1059727912yes—
305C4—22no—
306C4—21no—
307C4—21no—
308C4#1192629814yes—
309C4#1192630614yes—
310C4C2×C8×Dic1911yescharacteristic
311C4C2×#1059727211yescharacteristic
312C4C2×(C2×D19)⋊C812yes—
313C4C2×#1059726611yescharacteristic
314C4C2×#1059728911yescharacteristic
315C4C2×#1059726711yescharacteristic
316C4C2×#1059729211yescharacteristic
317C2#1456146918yesdirect product factor
318C2C2×#1192629412yes—
319C2C2×#1192629612yes—
320C2C2×#1192629811yescharacteristic
321C2C2×#1192630611yescharacteristic
322C2C2×#1192630811yescharacteristic
subgroupG/H
centerC23×C4C22⋊D19
commutatorC4×C19C2×C4×C8
FrattiniC2×C42C22×D19
FittingC22×C19×C4⋊C8C2
socle, prime radicalC24×C19C4⋊C4
cosocleC2×C42×C19C23
hypercenterC22×C4⋊C8D19
hypocenterC19C2×#1277
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #14561469C2direct (N × H)
42. C22×C19⋊C8C8semidirect
94. C2×C19⋊C8C2×C8semidirect
176. C2×C19#1277semidirect
214. C19C2×#1277semidirect
317. C2#14561469direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C19⋊C8)2
C22×C4×C19⋊C82
#145614692
C22×C19×C4⋊C82
C2×#127719