Finite Group Databasebeta

← C8×#10597289 #18073301

Subgroups — C8×#10597289 #18073301

Order 4864.

606 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×C4⋊Dic19C211yesmaximal, characteristic, complemented
2C4×#10597289C211yesmaximal, characteristic
3C2×D4⋊(C19⋊C8)C211yesmaximal, characteristic
4C2×C8×C19⋊C8C211yesmaximal, characteristic, complemented
5#14561474C211yesmaximal, characteristic, complemented
6#14561469C211yesmaximal, characteristic, complemented
7C2×C8×D4×C19C211yesmaximal, characteristic
8C2×C4⋊(C19⋊C8)C2211yescharacteristic
9C2×#10597289C412yes—
10C2×C4×C19⋊C8C2211yescharacteristic
11C2×C4×C19⋊C8C2211yescharacteristic
12C2×C8×Dic19—21no—
13C4×C4⋊Dic19C2211yescharacteristic
14#11926306C412yes—
15#11926298—21no—
16D4⋊(C19⋊C8)C414yescomplemented
17C8×C19⋊C8—22no—
18C23×C8×C19—21no—
19C2×C4×D4×C19C2211yescharacteristic
20C8×D4×C19—22no—
21C8×D4×C19C414yescomplemented
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C19×C22⋊C8—21no—
24C2×C4×C8×C19C2211yescharacteristic
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19—21no—
27C22×C8×C19—21no—
28C22×C8×C19—24no—
29C22×C8×C19—42no—
30C22×C8×C19—42no—
31C22×C8×C19D411yescharacteristic
32C22×C8×C19D411yescharacteristic
33C4×D4×C19—21no—
34C4×D4×C19—21no—
35C4×D4×C19C2×C412yes—
36C4×D4×C19C2×C412yes—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C42×C19C2311yescharacteristic
40C2×C4⋊Dic19C2×C412yes—
41C2×C4×Dic19—21no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8—21no—
44C22×C19⋊C8C2×C412yes—
45C19×C4⋊C8—21no—
46C19×C4⋊C8C2×C412yes—
47C19×C22⋊C8—24no—
48C4×C8×C19C2×C412yes—
49C4×C8×C19D412yes—
50#10597289C818yesdirect product factor
51C19⋊#95—21no—
52C8×Dic19—42no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)C2×C412yes—
55C4×C19⋊C8—21no—
56C4×C19⋊C8—21no—
57C4×C19⋊C8—21no—
58C4×C19⋊C8C2×C412yes—
59C24×C19—21no—
60C2×D4×C19—21no—
61C2×D4×C19—22no—
62C2×D4×C19C4212yes—
63C2×D4×C19C2×C814yes—
64C22×C4×C19—21no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—41no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
70C22×C4×C19—41no—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19#4111yescharacteristic
74C22×Dic19—22no—
75C2×C8×C19—21no—
76C2×C8×C19—21no—
77C2×C8×C19—22no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C2×C8×C19—48no—
81C2×C8×C19C22⋊C412yes—
82C2×C8×C19C22⋊C412yes—
83C2×C8×C19D812yes—
84C2×C8×C19SD1612yes—
85C4⋊C4×C19—21no—
86C4⋊C4×C19C4212yes—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C42×C19C22×C411yescharacteristic
90C42×C19C22×C411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19#4111yescharacteristic
93C4⋊Dic19—22no—
94C4⋊Dic19C2×C814yescomplemented
95C4×Dic19—41no—
96C4×Dic19—41no—
97C2×C19⋊C8—24no—
98C2×C19⋊C8—22no—
99C2×C19⋊C8—22no—
100C2×C19⋊C8—22no—
101C2×C19⋊C8—22no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8C2×C814yescomplemented
105C8×#102—191nomaximal, Sylow
106C23×C19—22no—
107C23×C19—24no—
108C23×C19—41no—
109C23×C19—41no—
110C23×C19—42no—
111C23×C19C4×D411yescharacteristic
112D4×C19—22no—
113D4×C19—24no—
114D4×C19C4×C814yescomplemented
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19C2×C4211yescharacteristic
124C2×C4×C19C2×C22⋊C411yescharacteristic
125C2×C4×C19#11711yescharacteristic
126C2×C4×C19C4×D411yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19C22×C812yes—
130C2×C4×C19#13112yes—
131C2×C4×C19C2×D811yescharacteristic
132C2×C4×C19C2×SD1611yescharacteristic
133C2×C4×C19#13511yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×Dic19—24no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C8×C19—22no—
139C8×C19—42no—
140C8×C19#10214yescomplemented
141C19⋊C8—24no—
142C19⋊C8—24no—
143C19⋊C8—42no—
144C2×C8×D4D1911yescharacteristic
145C8×C4⋊C4—191no—
146C4×#102—191no—
147C2×D4⋊C8—191no—
148C2×C82—191no—
149#1279—191no—
150#1277—191no—
151C22×C19—24no—
152C22×C19—44no—
153C22×C19—44no—
154C22×C19—42no—
155C22×C19—42no—
156C22×C19C4×C22⋊C411yescharacteristic
157C22×C19C8×D412yes—
158C22×C19C4×D811yescharacteristic
159C22×C19C4×SD1611yescharacteristic
160C22×C19#44312yes—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—42no—
164C4×C19C2×C4×C811yescharacteristic
165C4×C19#40511yescharacteristic
166C4×C19C2×#10211yescharacteristic
167C4×C19#41611yescharacteristic
168C4×C19C8×D412yes—
169C4×C19C4×D811yescharacteristic
170C4×C19C4×SD1611yescharacteristic
171Dic19—44no—
172C23×C8—21no—
173C2×C4×D4C2×D1911yescharacteristic
174C8×D4—22no—
175C8×D4Dic1914yescomplemented
176C2×C4⋊C8—191no—
177C2×C4⋊C8C2×D1911yescharacteristic
178C2×#102—192no—
179C2×C22⋊C8—21no—
180C2×C4×C8—191no—
181C2×C4×C8—191no—
182C2×C4×C8—381no—
183C2×C4×C8C2×D1911yescharacteristic
184C4×C4⋊C4—191no—
185#340—192no—
186#336—381no—
187D4⋊C8—194no—
188C82—382no—
189C2×C19—44no—
190C2×C19C8×D812yes—
191C2×C19C8×SD1612yes—
192C2×C19C8×C22⋊C411yescharacteristic
193C2×C19C4×#10211yescharacteristic
194C2×C19#176411yescharacteristic
195C22×D4C4×D1911yescharacteristic
196C23×C4—21no—
197C22×C8—21no—
198C22×C8—24no—
199C22×C8—42no—
200C22×C8—42no—
201C22×C8—192no—
202C22×C8—381no—
203C22×C8—381no—
204C22×C8C22⋊D1911yescharacteristic
205C22×C8C22⋊D1911yescharacteristic
206C4×D4—21no—
207C4×D4—21no—
208C4×D4C4×D1912yes—
209C4×D4C2×Dic1912yes—
210C2×C4⋊C4—192no—
211C2×C4⋊C4C4×D1911yescharacteristic
212C2×C22⋊C4—21no—
213C2×C42—381no—
214C2×C42C22×D1911yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—192no—
217C4⋊C8—381no—
218C4⋊C8C2×Dic1912yes—
219#102—198no—
220C22⋊C8—24no—
221C4×C8—192no—
222C4×C8—381no—
223C4×C8—381no—
224C4×C8—381no—
225C4×C8—762no—
226C4×C8C2×Dic1912yes—
227C4×C8C22⋊D1912yes—
228#95—381no—
229C19C8×#10211yescharacteristic, complemented, Sylow
230C24—21no—
231C2×D4—22no—
232C2×D4—21no—
233C2×D4C8×D1914yes—
234C2×D4C4×Dic1912yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—382no—
243C22×C4C2×C4×D1911yescharacteristic
244C22×C4#6454111yescharacteristic
245C22×C4C2×C22⋊D1911yescharacteristic
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—48no—
252C2×C8—194no—
253C2×C8—384no—
254C2×C8—382no—
255C2×C8—382no—
256C2×C8—382no—
257C2×C8—382no—
258C2×C8—761no—
259C2×C8—761no—
260C2×C8#6452512yes—
261C2×C8#6452612yes—
262C2×C8C22⋊Dic1912yes—
263C2×C8C22⋊Dic1912yes—
264C4⋊C4—21no—
265C4⋊C4—194no—
266C4⋊C4—382no—
267C4⋊C4C4×Dic1912yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42—761no—
271C42—761no—
272C42C2×C4×D1911yescharacteristic
273C42#6454111yescharacteristic
274C42C22×Dic1911yescharacteristic
275C42C2×C22⋊D1911yescharacteristic
276C23—24no—
277C23—22no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23C4×C22⋊D1911yescharacteristic
282D4—24no—
283D4—22no—
284D4C8×Dic1914yescomplemented
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—384no—
294C2×C4—762no—
295C2×C4—762no—
296C2×C4C2×C8×D1912yes—
297C2×C4#1059734712yes—
298C2×C4C2×C4×Dic1911yescharacteristic
299C2×C4#1059737211yescharacteristic
300C2×C4C4×C22⋊D1911yescharacteristic
301C2×C4C4×C22⋊D1911yescharacteristic
302C2×C4C4×C22⋊D1911yescharacteristic
303C2×C4C2×#6452511yescharacteristic
304C2×C4C2×#6452611yescharacteristic
305C2×C4#1059739611yescharacteristic
306C2×C4#1059739611yescharacteristic
307C2×C4C2×C22⋊Dic1911yescharacteristic
308C8—22no—
309C8—42no—
310C8—384no—
311C8—384no—
312C8—762no—
313C8#1059728914yesdirect product factor
314C22—24no—
315C22—42no—
316C22—44no—
317C22—44no—
318C22—42no—
319C22C4×C22⋊Dic1911yescharacteristic
320C22C8×C22⋊D1912yes—
321C22C4×#6452511yescharacteristic
322C22C4×#6452611yescharacteristic
323C22#1192665912yes—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—764no—
328C4C2×C8×Dic1911yescharacteristic
329C4#1192649911yescharacteristic
330C4C2×#1059728911yescharacteristic
331C4#1192654011yescharacteristic
332C4C8×C22⋊D1912yes—
333C4C4×#6452511yescharacteristic
334C4C4×#6452611yescharacteristic
335C2—44no—
336C2C8×#6452512yes—
337C2C8×#6452612yes—
338C2C8×C22⋊Dic1911yescharacteristic
339C2C4×#1059728911yescharacteristic
340C2#1456347011yescharacteristic
subgroupG/H
centerC22×C8C22⋊D19
commutatorC4×C19C2×C4×C8
FrattiniC2×C42C22×D19
FittingC2×C8×D4×C19C2
socleC23×C19C4×D4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenterC2×C8×D4D19
hypocenterC19C8×#102
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C8×C4⋊Dic19C2semidirect
4. C2×C8×C19⋊C8C2semidirect
5. #14561474C2semidirect
6. #14561469C2semidirect
16. D4⋊(C19⋊C8)C4semidirect
21. C8×D4×C19C4semidirect
50. #10597289C8direct (N × H)
94. C4⋊Dic19C2×C8semidirect
104. C2×C19⋊C8C2×C8semidirect
114. D4×C19C4×C8semidirect
140. C8×C19#102semidirect
175. C8×D4Dic19semidirect
229. C19C8×#102semidirect
284. D4C8×Dic19semidirect
313. C8#10597289direct (N × H)

Maximal subgroups

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

subgroupindex
C8×C4⋊Dic192
C4×#105972892
C2×D4⋊(C19⋊C8)2
C2×C8×C19⋊C82
#145614742
#145614692
C2×C8×D4×C192
C8×#10219