Finite Group Databasebeta

← #18075627

Subgroups — #18075627

Order 4864.

434 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926671C211yesmaximal, characteristic
2#14563791C211yesmaximal, characteristic
3#14563641C211yesmaximal, characteristic
4#14563637C211yesmaximal, characteristic
5C2×#11926296C211yesmaximal, characteristic
6#14561519C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9#11926671—22no—
10#11926671C414yescomplemented
11C2×#10597265—21no—
12C2×#10597265—21no—
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14C2×Dic19⋊C8—21no—
15C2×#10597273—21no—
16C2×#10597267—21no—
17C2×#10597272—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926414C2211yescharacteristic
20#11926307—21no—
21#11926306—21no—
22#11926296—22no—
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C19×#384C2211yescharacteristic
26C22×Dic38D411yescharacteristic
27C22×C8×C19—21no—
28C22×C8×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19D411yescharacteristic
37C2×Dic19⋊C4—21no—
38C2×C4×Dic19—21no—
39C22×C19⋊C8—21no—
40C22×C19⋊C8D411yescharacteristic
41C22×C19⋊C8D411yescharacteristic
42C4×Dic38—21no—
43C4×Dic38—21no—
44C4×Dic38C2×C412yes—
45C4×Dic38Q812yes—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8—21no—
49C19×C4⋊C8C2×C412yes—
50#10597273—42no—
51#10597272—24no—
52Dic19⋊C8—24no—
53#10597267—42no—
54#10597265—42no—
55#10597265—42no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4×C19⋊C8C2×C412yes—
59C4×C19⋊C8D412yes—
60C22×C4×C19—41no—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19#4111yescharacteristic
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—41no—
67C2×Dic38—21no—
68C2×Dic38—21no—
69C2×Dic38—21no—
70C2×Dic38—21no—
71C2×Dic38—21no—
72C2×Dic38C4⋊C412yes—
73C2×C8×C19—22no—
74C2×C8×C19—41no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C2×C8×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—81no—
84C42×C19C22×C411yescharacteristic
85C42×C19C2×D411yescharacteristic
86C42×C19C2×Q811yescharacteristic
87C42×C19#4111yescharacteristic
88C4⋊Dic19—21no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—81no—
94C4⋊Dic19C4⋊C412yes—
95Dic19⋊C4—22no—
96Dic19⋊C4—22no—
97C4×Dic19—22no—
98C4×Dic19—22no—
99C2×C19⋊C8—21no—
100C2×C19⋊C8—21no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8C22⋊C412yes—
105C2×C19⋊C8C22⋊C412yes—
106C2×C19⋊C8SD1612yes—
107C2×C19⋊C8Q1612yes—
108#8651—191nomaximal, Sylow
109C23×C19#12111yescharacteristic
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—81no—
113C2×C4×C19—81no—
114C2×C4×C19—81no—
115C2×C4×C19C2×C22⋊C411yescharacteristic
116C2×C4×C19C2×C4⋊C411yescharacteristic
117C2×C4×C19#11711yescharacteristic
118C2×C4×C19#12111yescharacteristic
119C2×C4×C19C22⋊Q811yescharacteristic
120C2×C4×C19C22⋊Q811yescharacteristic
121C2×C4×C19C2×SD1611yescharacteristic
122C2×C4×C19C2×Q1611yescharacteristic
123C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C19#13711yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×C4×C19#13711yescharacteristic
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—81no—
136C2×Dic19—81no—
137C2×Dic19—81no—
138Dic38—22no—
139Dic38—22no—
140Dic38—41no—
141Dic38—41no—
142C8×C19—42no—
143C8×C19—81no—
144C19⋊C8—22no—
145C19⋊C8—81no—
146C19⋊C8#10314yescomplemented
147C2×#446—191no—
148#1844—191no—
149#1803—191no—
150#1803—191no—
151C2×#335—191no—
152#1296—191no—
153#1296D1911yescharacteristic
154C22×C19#38011yescharacteristic
155C22×C19#46011yescharacteristic
156C22×C19#46211yescharacteristic
157C22×C19#46811yescharacteristic
158C22×C19#46811yescharacteristic
159C22×C19#47111yescharacteristic
160C22×C19#47111yescharacteristic
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—161no—
164C4×C19C2×#10311yescharacteristic
165C4×C19#41711yescharacteristic
166C4×C19#42811yescharacteristic
167C4×C19#42811yescharacteristic
168C4×C19#46911yescharacteristic
169C4×C19#47011yescharacteristic
170C4×C19#47511yescharacteristic
171C4×C19#47711yescharacteristic
172Dic19—42no—
173Dic19—42no—
174Dic19—161no—
175C2×C4×Q8—191no—
176#446—194no—
177#446—382no—
178C2×#106—381no—
179C2×#106—381no—
180C2×C4⋊C8—191no—
181C2×C4⋊C8—381no—
182C2×C4⋊C8C2×D1911yescharacteristic
183C2×C4⋊C8C2×D1911yescharacteristic
184C2×#103—381no—
185C2×#103—381no—
186C2×#97—381no—
187C2×C4×C8—191no—
188#384—191no—
189#384C2×D1911yescharacteristic
190#340—381no—
191#340—381no—
192#335—382no—
193C2×C19#168611yescharacteristic
194C2×C19#168611yescharacteristic
195C2×C19#169211yescharacteristic
196C2×C19#169211yescharacteristic
197C2×C19#180311yescharacteristic
198C2×C19#180911yescharacteristic
199C2×C19#181511yescharacteristic
200C22×Q8—191no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—191no—
204C22×C8—191no—
205C22×C8—381no—
206C4×Q8—192no—
207C4×Q8—192no—
208C4×Q8—381no—
209C4×Q8—381no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—381no—
215C2×C4⋊C4—381no—
216C2×C4⋊C4—381no—
217C2×C4⋊C4—381no—
218C2×C42—381no—
219C2×C42C22×D1911yescharacteristic
220#106—762no—
221#106—762no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—384no—
226C4⋊C8—381no—
227C4⋊C8—381no—
228C4⋊C8C4×D1912yes—
229#103—762no—
230#103—762no—
231#97—384no—
232C4×C8—192no—
233C4×C8—192no—
234C19#865111yescharacteristic, complemented, Sylow
235C2×Q8—192no—
236C2×Q8—381no—
237C2×Q8—381no—
238C2×Q8—381no—
239C2×Q8—381no—
240C2×Q8—381no—
241C22×C4—41no—
242C22×C4—381no—
243C22×C4—381no—
244C22×C4—761no—
245C22×C4#6454111yescharacteristic
246C22×C4D4×D1911yescharacteristic
247C22×C4D4×D1911yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—192no—
255C2×C8—192no—
256C2×C8—192no—
257C2×C8—192no—
258C2×C8—381no—
259C2×C8—381no—
260C2×C8—761no—
261C2×C8—761no—
262C2×C8—761no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—81no—
268C4⋊C4—192no—
269C4⋊C4—382no—
270C4⋊C4—381no—
271C4⋊C4—382no—
272C4⋊C4—761no—
273C4⋊C4—761no—
274C4⋊C4—761no—
275C4⋊C4—761no—
276C4⋊C4—1521no—
277C42—382no—
278C42—382no—
279C42C2×C4×D1911yescharacteristic
280C42#6454111yescharacteristic
281C42D4×D1911yescharacteristic
282C42Q8×D1911yescharacteristic
283C23#1059733011yescharacteristic
284Q8—382no—
285Q8—382no—
286Q8—761no—
287Q8—761no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—382no—
294C2×C4—382no—
295C2×C4—761no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—761no—
299C2×C4—1521no—
300C2×C4—1521no—
301C2×C4—1521no—
302C2×C4#1059731811yescharacteristic
303C2×C4C22⋊C4×D1911yescharacteristic
304C2×C4#1059733011yescharacteristic
305C2×C4C4⋊C4×D1911yescharacteristic
306C2×C4#1059734211yescharacteristic
307C2×C4#1059734211yescharacteristic
308C2×C4#1059735711yescharacteristic
309C2×C4#1059735711yescharacteristic
310C2×C4SD16×D1911yescharacteristic
311C2×C4#1059736011yescharacteristic
312C2×C4#1059736111yescharacteristic
313C2×C4#1059736111yescharacteristic
314C2×C4Q16×D1911yescharacteristic
315C2×C4#1059736411yescharacteristic
316C8—42no—
317C8—81no—
318C8—194no—
319C8—382no—
320C8—1521no—
321C22#1192640311yescharacteristic
322C22#1192674311yescharacteristic
323C22#1192675311yescharacteristic
324C22#1192678911yescharacteristic
325C22#1192679311yescharacteristic
326C22#1192680611yescharacteristic
327C22#1192681011yescharacteristic
328C4—21no—
329C4—21no—
330C4—161no—
331C4—3041no—
332C4—762no—
333C4—762no—
334C4#103×D1911yescharacteristic
335C4#1192654211yescharacteristic
336C4#1192658311yescharacteristic
337C4#1192658511yescharacteristic
338C4#1192679611yescharacteristic
339C4#1192680111yescharacteristic
340C4#1192682811yescharacteristic
341C4#1192683811yescharacteristic
342C2#1456310611yescharacteristic
343C2#1456311011yescharacteristic
344C2#1456314011yescharacteristic
345C2#1456314411yescharacteristic
346C2#1456363911yescharacteristic
347C2#1456366711yescharacteristic
348C2#1456369311yescharacteristic
subgroupG/H
centerC23#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#1296D19
hypocenterC19#8651
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
10. #11926671C4semidirect
146. C19⋊C8#103semidirect
234. C19#8651semidirect

Maximal subgroups

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

subgroupindex
C2×#119266712
#145637912
#145636412
#145636372
C2×#119262962
#145615192
C19×#12962
#865119