Finite Group Databasebeta

← #18081127

Subgroups — #18081127

Order 4864.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563751C211yesmaximal, characteristic
2C4⋊C8×Dic19C211yesmaximal, characteristic
3C4×Dic19⋊C8C211yesmaximal, characteristic
4C2×#11926296C211yesmaximal, characteristic
5#14561470C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C2×C19×#334C211yesmaximal, characteristic
8C2×C4⋊(C19⋊C8)C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×Dic19⋊C8C411yescharacteristic
11C2×Dic19⋊C8C411yescharacteristic
12C2×C4×C19⋊C8C2211yescharacteristic
13C2×C8×Dic19—21no—
14C42×Dic19C2211yescharacteristic
15#11926298—21no—
16#11926298—21no—
17#11926298—21no—
18#11926298C411yescharacteristic
19#11926298C411yescharacteristic
20#11926296—22no—
21C2×C19×C4⋊C8C2211yescharacteristic
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C19C2211yescharacteristic
24C19×#334—22no—
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C22×C8×C19C2×C411yescharacteristic
28C22×C8×C19C2×C411yescharacteristic
29C2×C42×C19C2311yescharacteristic
30C2×C4×Dic19C2×C411yescharacteristic
31C2×C4×Dic19C2×C411yescharacteristic
32C2×C4×Dic19D411yescharacteristic
33C2×C4×Dic19D411yescharacteristic
34C2×C4×Dic19Q811yescharacteristic
35C2×C4×Dic19Q811yescharacteristic
36C22×C19⋊C8—21no—
37C22×C19⋊C8—21no—
38C22×C19⋊C8C2×C411yescharacteristic
39C22×C19⋊C8C2×C411yescharacteristic
40C19×C4⋊C8—21no—
41C19×C4⋊C8—21no—
42C19×C4⋊C8—21no—
43C19×C4⋊C8D412yes—
44C4×C8×C19—21no—
45C4×C8×C19—21no—
46Dic19⋊C8—22no—
47Dic19⋊C8C814yescomplemented
48C8×Dic19—42no—
49C4⋊(C19⋊C8)—21no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)Q812yes—
53C4×C19⋊C8—21no—
54C4×C19⋊C8—21no—
55C22×C4×C19C22×C411yescharacteristic
56C22×C4×C19C2×D411yescharacteristic
57C22×C4×C19C2×Q811yescharacteristic
58C22×Dic19C4⋊C411yescharacteristic
59C22×Dic19C4⋊C411yescharacteristic
60C22×Dic19C4⋊C411yescharacteristic
61C22×Dic19C4⋊C411yescharacteristic
62C2×C8×C19—21no—
63C2×C8×C19—21no—
64C2×C8×C19—21no—
65C2×C8×C19—22no—
66C2×C8×C19—21no—
67C2×C8×C19—21no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C2×C8×C19C2×C812yes—
74C42×C19C2×D411yescharacteristic
75C42×C19C2×Q811yescharacteristic
76C42×C19#4111yescharacteristic
77C42×C19#4111yescharacteristic
78C4×Dic19—21no—
79C4×Dic19—21no—
80C4×Dic19—21no—
81C4×Dic19—21no—
82C4×Dic19—21no—
83C4×Dic19—21no—
84C4×Dic19—22no—
85C4×Dic19—41no—
86C4×Dic19C2×C812yes—
87C4×Dic19M1612yes—
88C2×C19⋊C8—21no—
89C2×C19⋊C8—21no—
90C2×C19⋊C8—21no—
91C2×C19⋊C8—22no—
92C2×C19⋊C8—21no—
93C2×C19⋊C8—21no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8C2×C812yes—
100#9603—191nomaximal, Sylow
101C23×C19C2×C4⋊C411yescharacteristic
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19C4×D411yescharacteristic
105C2×C4×C19C4×Q811yescharacteristic
106C2×C4×C19#12111yescharacteristic
107C2×C4×C19C22⋊Q811yescharacteristic
108C2×C4×C19#12511yescharacteristic
109C2×C4×C19C4⋊Q811yescharacteristic
110C2×C4×C19C22×C811yescharacteristic
111C2×C4×C19C2×M1611yescharacteristic
112C2×C4×C19#13111yescharacteristic
113C2×C4×C19#13111yescharacteristic
114C2×C4×C19#13511yescharacteristic
115C2×C4×C19#13511yescharacteristic
116C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C19#13711yescharacteristic
118C2×Dic19—21no—
119C2×Dic19—21no—
120C2×Dic19—21no—
121C2×Dic19—21no—
122C2×Dic19—21no—
123C2×Dic19—21no—
124C2×Dic19—21no—
125C2×Dic19—21no—
126C2×Dic19—21no—
127C2×Dic19C4⋊C812yes—
128C2×Dic19C4⋊C812yes—
129C2×Dic19#10812yes—
130C8×C19—22no—
131C8×C19—41no—
132C8×C19—42no—
133C8×C19—81no—
134C19⋊C8—22no—
135C19⋊C8—41no—
136C19⋊C8—42no—
137C19⋊C8—81no—
138#1831—191no—
139C4×C4⋊C8—191no—
140C4×C4⋊C8—191no—
141C2×#335—191no—
142C2×#334D1911yescharacteristic
143#1277—191no—
144#1277—191no—
145C22×C19#38911yescharacteristic
146C22×C19C2×C4⋊C811yescharacteristic
147C22×C19#42411yescharacteristic
148C22×C19#42711yescharacteristic
149C22×C19#42811yescharacteristic
150C22×C19C2×#10811yescharacteristic
151C22×C19#43011yescharacteristic
152C4×C19—21no—
153C4×C19—21no—
154C4×C19C8×D411yescharacteristic
155C4×C19#43611yescharacteristic
156C4×C19C8×Q811yescharacteristic
157C4×C19#44611yescharacteristic
158C4×C19#46311yescharacteristic
159C4×C19#46411yescharacteristic
160C4×C19#47811yescharacteristic
161C4×C19#47911yescharacteristic
162Dic19—22no—
163Dic19—22no—
164Dic19—22no—
165Dic19—41no—
166C2×C4⋊C8—191no—
167C2×C4⋊C8—191no—
168C2×C4⋊C8—191no—
169C2×C4⋊C8—191no—
170C2×C4⋊C8C2×D1911yescharacteristic
171C2×C4⋊C8C2×D1911yescharacteristic
172C2×C4×C8—191no—
173C2×C4×C8—381no—
174C2×C4×C8C2×D1911yescharacteristic
175C43—191no—
176#336—191no—
177#336—191no—
178#336—381no—
179#336—381no—
180#336—381no—
181#335—382no—
182#334—22no—
183C2×C19#156411yescharacteristic
184C2×C19#156511yescharacteristic
185C2×C19#157211yescharacteristic
186C2×C19#157311yescharacteristic
187C2×C19#193911yescharacteristic
188C2×C19#194911yescharacteristic
189C2×C19#195011yescharacteristic
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—191no—
193C22×C8—191no—
194C22×C8—381no—
195C22×C8—381no—
196C22×C8C4×D1911yescharacteristic
197C22×C8C4×D1911yescharacteristic
198C2×C42—191no—
199C2×C42—191no—
200C2×C42—191no—
201C2×C42—191no—
202C2×C42—191no—
203C2×C42—191no—
204C2×C42C22×D1911yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—194no—
209C4⋊C8—192no—
210C4⋊C8—382no—
211C4⋊C8—381no—
212C4⋊C8—381no—
213C4⋊C8—381no—
214C4⋊C8C22⋊D1912yes—
215C4×C8—21no—
216C4×C8—21no—
217C4×C8—381no—
218C4×C8—381no—
219C4×C8—762no—
220C19#960311yescharacteristic, complemented, Sylow
221C22×C4—191no—
222C22×C4—191no—
223C22×C4—191no—
224C22×C4—191no—
225C22×C4C2×C4×D1911yescharacteristic
226C22×C4D4×D1911yescharacteristic
227C22×C4Q8×D1911yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—22no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—192no—
240C2×C8—381no—
241C2×C8—381no—
242C2×C8—382no—
243C2×C8—381no—
244C2×C8—381no—
245C2×C8—381no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C2×C8—761no—
251C2×C8C8×D1912yes—
252C42—192no—
253C42—192no—
254C42—382no—
255C42—381no—
256C42—381no—
257C42—381no—
258C42—381no—
259C42—381no—
260C42—381no—
261C42—761no—
262C42#6454111yescharacteristic
263C42#6454311yescharacteristic
264C42Q8×D1911yescharacteristic
265C42C2×C22⋊D1911yescharacteristic
266C23C4⋊C4×D1911yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—192no—
270C2×C4—192no—
271C2×C4—192no—
272C2×C4—381no—
273C2×C4—381no—
274C2×C4—381no—
275C2×C4—381no—
276C2×C4—381no—
277C2×C4—381no—
278C2×C4—381no—
279C2×C4—381no—
280C2×C4—381no—
281C2×C4#1059733311yescharacteristic
282C2×C4#1059733511yescharacteristic
283C2×C4#1059734211yescharacteristic
284C2×C4C2×C8×D1911yescharacteristic
285C2×C4#1059734711yescharacteristic
286C2×C4M16×D1911yescharacteristic
287C2×C4#1059735311yescharacteristic
288C2×C4#1059736011yescharacteristic
289C2×C4#1059736111yescharacteristic
290C2×C4#1059736211yescharacteristic
291C2×C4#1059736211yescharacteristic
292C2×C4C4×C22⋊D1911yescharacteristic
293C2×C4#1059738511yescharacteristic
294C2×C4#1059739011yescharacteristic
295C8—22no—
296C8—41no—
297C8—42no—
298C8—81no—
299C8—382no—
300C8—762no—
301C8—761no—
302C8—1521no—
303C22#1192643911yescharacteristic
304C22C4⋊C8×D1911yescharacteristic
305C22#1192656911yescharacteristic
306C22#1192657911yescharacteristic
307C22#1192658311yescharacteristic
308C22#108×D1911yescharacteristic
309C22#1192659111yescharacteristic
310C4—21no—
311C4—21no—
312C4—382no—
313C4—382no—
314C4—382no—
315C4—761no—
316C4C8×C22⋊D1911yescharacteristic
317C4#1192662011yescharacteristic
318C4#1192666811yescharacteristic
319C4#1192667311yescharacteristic
320C4#1192676111yescharacteristic
321C4#1192676411yescharacteristic
322C4#1192684311yescharacteristic
323C4#1192685411yescharacteristic
324C2#1456238011yescharacteristic
325C2#1456238411yescharacteristic
326C2#1456241211yescharacteristic
327C2#1456241711yescharacteristic
328C2#1456435011yescharacteristic
329C2#1456440411yescharacteristic
330C2#1456440711yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC2×C19×#334C2
socle, prime radicalC23×C19C2×C4⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#334D19
hypocenterC19#9603
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
47. Dic19⋊C8C8semidirect
220. C19#9603semidirect

Maximal subgroups

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

subgroupindex
#145637512
C4⋊C8×Dic192
C4×Dic19⋊C82
C2×#119262962
#145614702
#145614692
C2×C19×#3342
#960319