Finite Group Databasebeta

← #18075373

Subgroups — #18075373

Order 4864.

598 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
1C2×C4×C8×D19C211yesmaximal, characteristic
2#14563612C212yesmaximal
3C2×#11926294C212yesmaximal, complemented
4#14561470C211yesmaximal, characteristic, complemented
5C19×#1277C211yesmaximal, characteristic, complemented
6C22×C8×D19C411yescharacteristic
7C22×C8×D19C411yescharacteristic
8C2×C42×D19C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2212yes—
10C2×(C2×D19)⋊C8—22no—
11C2×C4×C19⋊C8C2211yescharacteristic
12C2×C8×Dic19C411yescharacteristic
13C2×C8×Dic19C411yescharacteristic
14C4×C8×D19—24no—
15#11926298—22no—
16#11926294—24no—
17C2×C19×C4⋊C8C2212yes—
18C2×C4×C8×C19C2211yescharacteristic
19C22×C4×D19C2×C411yescharacteristic
20C22×C4×D19D411yescharacteristic
21C22×C4×D19Q811yescharacteristic
22C22×C8×C19—22no—
23C22×C8×C19C2×C411yescharacteristic
24C22×C8×C19C2×C411yescharacteristic
25C2×C42×C19C2311yescharacteristic
26C2×C4×Dic19C2×C411yescharacteristic
27C2×C4×Dic19D411yescharacteristic
28C2×C4×Dic19Q811yescharacteristic
29C22×C19⋊C8—22no—
30C22×C19⋊C8C2×C411yescharacteristic
31C22×C19⋊C8C2×C411yescharacteristic
32C2×C8×D19—22no—
33C2×C8×D19—22no—
34C2×C8×D19—22no—
35C2×C8×D19—22no—
36C2×C8×D19—22no—
37C2×C8×D19C814yescomplemented
38C42×D19—22no—
39C42×D19—22no—
40C19×C4⋊C8—22no—
41C19×C4⋊C8—22no—
42C4×C8×C19—22no—
43(C2×D19)⋊C8—44no—
44C8×Dic19—22no—
45C8×Dic19—22no—
46C4⋊(C19⋊C8)—22no—
47C4⋊(C19⋊C8)—22no—
48C4×C19⋊C8D414yes—
49C23×D19C4⋊C411yescharacteristic
50C22×C4×C19C22×C411yescharacteristic
51C22×C4×C19C2×D411yescharacteristic
52C22×C4×C19C2×Q811yescharacteristic
53C22×Dic19C4⋊C411yescharacteristic
54C22×Dic19C4⋊C411yescharacteristic
55C22×Dic19C4⋊C411yescharacteristic
56C2×C4×D19—22no—
57C2×C4×D19—21no—
58C2×C4×D19—21no—
59C2×C4×D19—22no—
60C2×C4×D19—22no—
61C2×C4×D19—21no—
62C2×C4×D19—21no—
63C2×C4×D19—21no—
64C2×C4×D19—21no—
65C2×C4×D19—22no—
66C2×C4×D19C2×C812yes—
67C2×C4×D19M1612yes—
68C2×C4×D19SD1614yes—
69C2×C8×C19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—21no—
72C2×C8×C19—21no—
73C2×C8×C19—42no—
74C2×C8×C19—42no—
75C2×C8×C19—42no—
76C2×C8×C19C2×C812yes—
77C2×C8×C19M1612yes—
78C42×C19C2×D412yes—
79C42×C19#4112yes—
80C4×Dic19—21no—
81C4×Dic19—21no—
82C4×Dic19—22no—
83C4×Dic19—22no—
84C2×C19⋊C8—21no—
85C2×C19⋊C8—21no—
86C2×C19⋊C8—42no—
87C2×C19⋊C8—42no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8C22⋊C412yes—
90C2×C19⋊C8C22⋊C412yes—
91C2×C19⋊C8C2×C812yes—
92C2×C19⋊C8M1612yes—
93C8×D19—28no—
94C8×D19—28no—
95#8595—191nomaximal, Sylow
96C23×C19C2×C4⋊C411yescharacteristic
97C22×D19—21no—
98C22×D19—21no—
99C22×D19—21no—
100C22×D19—21no—
101C22×D19C4⋊C812yes—
102C22×D19#10612yes—
103C22×D19#10812yes—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19C2×C22⋊C411yescharacteristic
107C2×C4×C19#11711yescharacteristic
108C2×C4×C19#12112yes—
109C2×C4×C19C22⋊Q812yes—
110C2×C4×C19C22×C811yescharacteristic
111C2×C4×C19C2×M1611yescharacteristic
112C2×C4×C19C2×M1611yescharacteristic
113C2×C4×C19C2×M1611yescharacteristic
114C2×C4×C19C2×SD1612yes—
115C2×C4×C19#13511yescharacteristic
116C2×C4×C19#13511yescharacteristic
117C2×Dic19—21no—
118C2×Dic19—21no—
119C2×Dic19—21no—
120C2×Dic19—21no—
121C2×Dic19—21no—
122C2×Dic19—21no—
123C2×Dic19C4⋊C812yes—
124C2×Dic19#10612yes—
125C2×Dic19#10812yes—
126C4×D19—28no—
127C4×D19—22no—
128C4×D19—22no—
129C4×D19—22no—
130C4×D19—22no—
131C4×D19—24no—
132C4×D19—24no—
133C8×C19—22no—
134C8×C19—22no—
135C8×C19—82no—
136C19⋊C8—22no—
137C19⋊C8—82no—
138C19⋊C8C22⋊C814yescomplemented
139C22×C4×C8—191no—
140#1797—192no—
141C2×#334—192no—
142#1277—191no—
143#1277D1911yescharacteristic, complemented
144C22×C19#38011yescharacteristic
145C22×C19C2×C4⋊C811yescharacteristic
146C22×C19#42311yescharacteristic
147C22×C19C2×#10611yescharacteristic
148C22×C19#42711yescharacteristic
149C22×C19C2×#10811yescharacteristic
150C22×C19C2×#10811yescharacteristic
151C2×D19—22no—
152C2×D19—22no—
153C2×D19—22no—
154C2×D19—22no—
155C2×D19—22no—
156C2×D19—22no—
157C2×D19#33414yescomplemented
158C4×C19—22no—
159C4×C19C2×C22⋊C811yescharacteristic
160C4×C19#40711yescharacteristic
161C4×C19#43111yescharacteristic
162C4×C19#43211yescharacteristic
163C4×C19#46512yes—
164C4×C19#46512yes—
165Dic19—22no—
166Dic19—22no—
167Dic19—22no—
168C23×C8—191no—
169C23×C8—191no—
170C22×C42—191no—
171C2×C4⋊C8—192no—
172C2×C4⋊C8C2×D1912yes—
173C2×C22⋊C8—382no—
174C2×C4×C8—191no—
175C2×C4×C8—191no—
176C2×C4×C8—191no—
177C2×C4×C8—384no—
178C2×C4×C8C2×D1911yescharacteristic
179#336—382no—
180#334—384no—
181C2×C19C2×#33411yescharacteristic
182C2×C19#156411yescharacteristic
183C2×C19#156611yescharacteristic
184C2×C19#156811yescharacteristic
185C2×C19#179711yescharacteristic
186C2×C19#180711yescharacteristic
187C2×C19#181011yescharacteristic
188D19—24no—
189C23×C4—191no—
190C23×C4—191no—
191C23×C4—191no—
192C22×C8—22no—
193C22×C8—191no—
194C22×C8—191no—
195C22×C8—194no—
196C22×C8—382no—
197C22×C8—382no—
198C22×C8—382no—
199C22×C8—382no—
200C22×C8—382no—
201C22×C8—382no—
202C22×C8C4×D1911yescharacteristic
203C22×C8C4×D1911yescharacteristic
204C2×C42—191no—
205C2×C42—191no—
206C2×C42—191no—
207C2×C42—382no—
208C2×C42—382no—
209C2×C42C22×D1911yescharacteristic
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—382no—
213C4⋊C8—382no—
214C22⋊C8—764no—
215C4×C8—22no—
216C4×C8—194no—
217C4×C8—382no—
218C4×C8—382no—
219C19#859511yescharacteristic, complemented, Sylow
220C24—191no—
221C22×C4—191no—
222C22×C4—191no—
223C22×C4—191no—
224C22×C4—192no—
225C22×C4—192no—
226C22×C4—194no—
227C22×C4—382no—
228C22×C4—382no—
229C22×C4—381no—
230C22×C4—381no—
231C22×C4—382no—
232C22×C4—382no—
233C22×C4—381no—
234C22×C4—381no—
235C22×C4—381no—
236C22×C4—381no—
237C22×C4C2×C4×D1911yescharacteristic
238C22×C4D4×D1911yescharacteristic
239C22×C4Q8×D1911yescharacteristic
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—192no—
248C2×C8—192no—
249C2×C8—192no—
250C2×C8—192no—
251C2×C8—388no—
252C2×C8—388no—
253C2×C8—381no—
254C2×C8—381no—
255C2×C8—762no—
256C2×C8—762no—
257C2×C8—762no—
258C2×C8C8×D1912yes—
259C2×C8#6451512yes—
260C42—381no—
261C42—381no—
262C42—382no—
263C42—382no—
264C42#6454112yes—
265C42D4×D1912yes—
266C23—192no—
267C23—192no—
268C23—192no—
269C23—381no—
270C23—381no—
271C23—381no—
272C23—381no—
273C23C4⋊C4×D1911yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—192no—
277C2×C4—192no—
278C2×C4—192no—
279C2×C4—388no—
280C2×C4—381no—
281C2×C4—381no—
282C2×C4—381no—
283C2×C4—381no—
284C2×C4—381no—
285C2×C4—381no—
286C2×C4—382no—
287C2×C4—382no—
288C2×C4—382no—
289C2×C4—382no—
290C2×C4—384no—
291C2×C4—384no—
292C2×C4#1059731811yescharacteristic
293C2×C4C22⋊C4×D1911yescharacteristic
294C2×C4#1059733012yes—
295C2×C4#1059734212yes—
296C2×C4C2×C8×D1911yescharacteristic
297C2×C4C2×#6451511yescharacteristic
298C2×C4M16×D1911yescharacteristic
299C2×C4M16×D1911yescharacteristic
300C2×C4#1059735811yescharacteristic
301C2×C4SD16×D1912yes—
302C2×C4#1059736511yescharacteristic
303C8—22no—
304C8—22no—
305C8—82no—
306C8—194no—
307C8—382no—
308C8—1522no—
309C22—194no—
310C22—382no—
311C22—382no—
312C22—382no—
313C22—382no—
314C22—382no—
315C22—382no—
316C22#1192640311yescharacteristic
317C22C4⋊C8×D1911yescharacteristic
318C22#1192656611yescharacteristic
319C22#106×D1911yescharacteristic
320C22#1192658111yescharacteristic
321C22#108×D1911yescharacteristic
322C22#108×D1911yescharacteristic
323C4—22no—
324C4—382no—
325C4—382no—
326C4—382no—
327C4C22⋊C8×D1911yescharacteristic
328C4#1192650611yescharacteristic
329C4#1192659511yescharacteristic
330C4#1192659911yescharacteristic
331C4#1192677212yes—
332C4#1192677612yes—
333C2—384no—
334C2D19×#33411yescharacteristic
335C2#1456238211yescharacteristic
336C2#1456238911yescharacteristic
337C2#1456239711yescharacteristic
338C2#1456361411yescharacteristic
339C2#1456365911yescharacteristic
340C2#1456367211yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC19×#1277C2
socleC23×C19C2×C4⋊C4
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1277D19
hypocenterC19#8595
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
3. C2×#11926294C2semidirect
4. #14561470C2semidirect
5. C19×#1277C2semidirect
37. C2×C8×D19C8semidirect
138. C19⋊C8C22⋊C8semidirect
143. #1277D19semidirect
157. C2×D19#334semidirect
219. C19#8595semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C8×D192
#145636122
C2×#119262942
#145614702
C19×#12772
#859519