Finite Group Databasebeta

← #18075401

Subgroups — #18075401

Order 4864.

462 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
1C2×#11926498C211yesmaximal, characteristic
2#14562383C211yesmaximal, characteristic, complemented
3#14561947C212yesmaximal
4#14561465C212yesmaximal, complemented
5C19×#1564C211yesmaximal, characteristic, complemented
6C22×#64515C411yescharacteristic
7C22×C8×D19C411yescharacteristic
8C2×#10597318C2211yescharacteristic
9#11926597C2212yes—
10#11926498—21no—
11#11926498—21no—
12#11926498—21no—
13#11926498—21no—
14C2×#10597260C2211yescharacteristic
15C2×#10597272C411yescharacteristic
16C2×C8×Dic19C411yescharacteristic
17#11926297—21no—
18#11926295—21no—
19#11926269—22no—
20#11926267—22no—
21C19×#431C2212yes—
22C2×C4×C8×C19C2211yescharacteristic
23C19×#335—21no—
24C19×#334—21no—
25C22×C4×D19C2×C411yescharacteristic
26C22×C8×C19C2×C411yescharacteristic
27C22×C8×C19C2×C411yescharacteristic
28C2×C42×C19C2311yescharacteristic
29C2×(C2×D19)⋊C4D411yescharacteristic
30C2×(C2×D19)⋊C4Q811yescharacteristic
31C2×Dic19⋊C4D411yescharacteristic
32C2×Dic19⋊C4Q811yescharacteristic
33C2×C4×Dic19C2×C411yescharacteristic
34C22×C19⋊C8C2×C411yescharacteristic
35C22×C19⋊C8C2×C411yescharacteristic
36C2×#64515—21no—
37C2×#64515—21no—
38C2×#64515—22no—
39C2×#64515C814yescomplemented
40C2×C8×D19—22no—
41C2×C8×D19—21no—
42C2×C8×D19—21no—
43C2×C8×D19—22no—
44#10597318—21no—
45#10597318—21no—
46#10597318—21no—
47#10597318—21no—
48C19×C4⋊C8—22no—
49C19×C22⋊C8—22no—
50C4×C8×C19—22no—
51C4×C8×C19D411yescharacteristic
52C4×C8×C19D411yescharacteristic
53C4×C8×C19D411yescharacteristic
54C4×C8×C19D411yescharacteristic
55C22⋊(C19⋊C8)—22no—
56#10597272—21no—
57#10597272—21no—
58C8×Dic19—21no—
59C8×Dic19—21no—
60C4⋊(C19⋊C8)—22no—
61#10597260—21no—
62#10597260—21no—
63C4×C19⋊C8—22no—
64C23×D19C4⋊C411yescharacteristic
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×Q811yescharacteristic
68C22×Dic19C4⋊C411yescharacteristic
69C22×Dic19C4⋊C411yescharacteristic
70C22×Dic19C4⋊C411yescharacteristic
71C2×C4×D19—21no—
72C2×C4×D19—21no—
73C2×C4×D19—21no—
74C2×C4×D19—21no—
75C2×C4×D19C2×C812yes—
76C2×C4×D19M1612yes—
77C2×C8×C19—21no—
78C2×C8×C19—21no—
79C2×C8×C19—42no—
80C2×C8×C19C22⋊C411yescharacteristic
81C2×C8×C19C22⋊C411yescharacteristic
82C2×C8×C19C22⋊C411yescharacteristic
83C2×C8×C19C22⋊C411yescharacteristic
84C2×C8×C19C2×C812yes—
85C2×C8×C19M1612yes—
86C42×C19C2×D411yescharacteristic
87C42×C19C2×D411yescharacteristic
88C42×C19#4111yescharacteristic
89C42×C19#4111yescharacteristic
90(C2×D19)⋊C4—21no—
91(C2×D19)⋊C4—21no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94Dic19⋊C4—21no—
95Dic19⋊C4—21no—
96Dic19⋊C4—21no—
97Dic19⋊C4—21no—
98C4×Dic19—21no—
99C4×Dic19—21no—
100C2×C19⋊C8—21no—
101C2×C19⋊C8—21no—
102C2×C19⋊C8—21no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—42no—
105C2×C19⋊C8C2×C812yes—
106C2×C19⋊C8M1612yes—
107#64515—24no—
108#64515—24no—
109C8×D19—24no—
110C8×D19—24no—
111#8602—191nomaximal, Sylow
112C23×C19C2×C4⋊C411yescharacteristic
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—41no—
116C22×D19—41no—
117C22×D19C4⋊C812yes—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19C2×C22⋊C411yescharacteristic
121C2×C4×C19#11711yescharacteristic
122C2×C4×C19#12111yescharacteristic
123C2×C4×C19#12111yescharacteristic
124C2×C4×C19C22⋊Q811yescharacteristic
125C2×C4×C19C22⋊Q811yescharacteristic
126C2×C4×C19C22×C811yescharacteristic
127C2×C4×C19C2×M1611yescharacteristic
128C2×C4×C19C2×M1611yescharacteristic
129C2×C4×C19C2×M1611yescharacteristic
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19C4⋊C812yes—
137C4×D19—22no—
138C4×D19—22no—
139C4×D19—22no—
140C4×D19—22no—
141C8×C19—21no—
142C8×C19—21no—
143C8×C19—82no—
144C8×C19C22⋊C812yes—
145C8×C19C22⋊C812yes—
146C19⋊C8—22no—
147C19⋊C8—22no—
148C19⋊C8—82no—
149C2×#405—191no—
150#1564—191no—
151#1564D1911yescharacteristic, complemented
152#1458—192no—
153#1275—192no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19#38011yescharacteristic
157C22×C19C2×C4⋊C811yescharacteristic
158C22×C19#42311yescharacteristic
159C2×D19—22no—
160C2×D19—42no—
161C2×D19—41no—
162C2×D19—41no—
163C2×D19—42no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19C2×C22⋊C811yescharacteristic
169C4×C19#40711yescharacteristic
170C4×C19#43111yescharacteristic
171C4×C19#43211yescharacteristic
172Dic19—22no—
173Dic19—41no—
174Dic19—41no—
175C22×M16—191no—
176C23×C8—191no—
177C2×#117—191no—
178#431—192no—
179#431C2×D1912yes—
180#405—381no—
181#405—381no—
182#405—381no—
183#405—381no—
184C2×#97—191no—
185C2×#97—191no—
186C2×C4×C8—191no—
187C2×C4×C8C2×D1911yescharacteristic
188#335—21no—
189#335—381no—
190#334—21no—
191#334—381no—
192#324—382no—
193#323—382no—
194C2×C19—21no—
195C2×C19—21no—
196C2×C19#179711yescharacteristic
197C2×C19#181211yescharacteristic
198C2×C19#181311yescharacteristic
199D19—42no—
200C23×C4—191no—
201C2×M16—194no—
202C2×M16—382no—
203C2×M16—381no—
204C2×M16—381no—
205C22×C8—191no—
206C22×C8—191no—
207C22×C8—382no—
208C22×C8—382no—
209C22×C8—381no—
210C22×C8—381no—
211C22×C8C4×D1911yescharacteristic
212C22×C8C4×D1911yescharacteristic
213#117—381no—
214#117—381no—
215#117—381no—
216#117—381no—
217C2×C4⋊C4—191no—
218C2×C4⋊C4—191no—
219C2×C22⋊C4—191no—
220C2×C22⋊C4—191no—
221C2×C42—191no—
222C2×C42C22×D1911yescharacteristic
223C4⋊C8—22no—
224C4⋊C8—382no—
225C22⋊C8—22no—
226C22⋊C8—382no—
227#97—381no—
228#97—381no—
229#97—381no—
230#97—381no—
231C4×C8—22no—
232C4×C8—381no—
233C4×C8—381no—
234C4×C8—382no—
235C4×C8D7611yescharacteristic
236C4×C8D7611yescharacteristic
237C4×C8C22⋊D1911yescharacteristic
238C4×C8C22⋊D1911yescharacteristic
239C19#860211yescharacteristic, complemented, Sylow
240C24—191no—
241C22×C4—191no—
242C22×C4—192no—
243C22×C4—192no—
244C22×C4—191no—
245C22×C4—191no—
246C22×C4—381no—
247C22×C4—381no—
248C22×C4—381no—
249C22×C4—381no—
250C22×C4C2×C4×D1911yescharacteristic
251C22×C4D4×D1911yescharacteristic
252C22×C4Q8×D1911yescharacteristic
253M16—384no—
254M16—384no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—192no—
259C2×C8—192no—
260C2×C8—384no—
261C2×C8—384no—
262C2×C8—381no—
263C2×C8—381no—
264C2×C8—381no—
265C2×C8—381no—
266C2×C8—762no—
267C2×C8C8×D1912yes—
268C2×C8#6451512yes—
269C2×C8(C2×D19)⋊C411yescharacteristic
270C2×C8(C2×D19)⋊C411yescharacteristic
271C2×C8(C2×D19)⋊C411yescharacteristic
272C2×C8(C2×D19)⋊C411yescharacteristic
273C4⋊C4—381no—
274C4⋊C4—381no—
275C4⋊C4—381no—
276C4⋊C4—381no—
277C22⋊C4—381no—
278C22⋊C4—381no—
279C22⋊C4—381no—
280C22⋊C4—381no—
281C42—381no—
282C42—381no—
283C42C2×D7611yescharacteristic
284C42#6454311yescharacteristic
285C42#6454511yescharacteristic
286C42C2×C22⋊D1911yescharacteristic
287C23—192no—
288C23—381no—
289C23—381no—
290C23—761no—
291C23—761no—
292C23C4⋊C4×D1911yescharacteristic
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—192no—
296C2×C4—381no—
297C2×C4—381no—
298C2×C4—382no—
299C2×C4—382no—
300C2×C4—382no—
301C2×C4—382no—
302C2×C4—381no—
303C2×C4—381no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4#1059733811yescharacteristic
307C2×C4#1059734111yescharacteristic
308C2×C4#1059734311yescharacteristic
309C2×C4C2×C8×D1911yescharacteristic
310C2×C4C2×#6451511yescharacteristic
311C2×C4M16×D1911yescharacteristic
312C2×C4M16×D1911yescharacteristic
313C2×C4C2×(C2×D19)⋊C411yescharacteristic
314C2×C4#1059738411yescharacteristic
315C2×C4#1059739211yescharacteristic
316C8—21no—
317C8—21no—
318C8—82no—
319C8—382no—
320C8—382no—
321C8—1522no—
322C8(C2×D19)⋊C812yes—
323C8(C2×D19)⋊C812yes—
324C22—21no—
325C22—21no—
326C22—382no—
327C22—762no—
328C22—762no—
329C22—761no—
330C22—761no—
331C22#1192640111yescharacteristic
332C22C4⋊C8×D1911yescharacteristic
333C22#1192656611yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—382no—
339C4—761no—
340C4—761no—
341C4C2×(C2×D19)⋊C811yescharacteristic
342C4#1192650711yescharacteristic
343C4#1192659611yescharacteristic
344C4#1192660011yescharacteristic
345C2—21no—
346C2—21no—
347C2—762no—
348C2#1456361211yescharacteristic
349C2#1456367811yescharacteristic
350C2#1456368211yescharacteristic
subgroupG/H
centerC2×C4#10597338
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC19×#1564C2
socleC22×C19#380
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1564D19
hypocenterC19#8602
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. #14562383C2semidirect
4. #14561465C2semidirect
5. C19×#1564C2semidirect
39. C2×#64515C8semidirect
151. #1564D19semidirect
239. C19#8602semidirect

Maximal subgroups

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

subgroupindex
C2×#119264982
#145623832
#145619472
#145614652
C19×#15642
#860219