Finite Group Databasebeta

← #18080772

Subgroups — #18080772

Order 4864.

378 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10597290C211yesmaximal, characteristic
2#14562385C211yesmaximal, characteristic, complemented
3#14562026C211yesmaximal, characteristic
4C8×#64520C211yesmaximal, characteristic, complemented
5#14561485C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C2×C19×D4⋊C8C211yesmaximal, characteristic
8#11926597C2211yescharacteristic
9#11926597C2211yescharacteristic
10C2×#10597290C411yescharacteristic
11C2×#10597290C411yescharacteristic
12C4×#64520C2211yescharacteristic
13C4×#64520C2211yescharacteristic
14#11926313C411yescharacteristic
15#11926313C411yescharacteristic
16#11926296—21no—
17#11926294—21no—
18D4⋊(C19⋊C8)—21no—
19D4⋊(C19⋊C8)—21no—
20#11926266—21no—
21C8×C19⋊C8—21no—
22C2×C4×D4×C19C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C19C2211yescharacteristic
25C19×D4⋊C8—21no—
26C19×D4⋊C8—21no—
27C22×D4×C19C2×C411yescharacteristic
28C23×C4×C19—21no—
29C22×C8×C19—21no—
30C22×C8×C19—21no—
31C4×D4×C19—21no—
32C4×D4×C19—21no—
33C4×D4×C19—21no—
34C4×D4×C19—21no—
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C22⋊C4×C19—21no—
37C2×C42×C19C2311yescharacteristic
38C2×#64520C2×C411yescharacteristic
39C2×#64520C2×C411yescharacteristic
40C2×#64520C2×C411yescharacteristic
41C2×#64520C2×C411yescharacteristic
42C19×C4⋊C8—21no—
43C19×C4⋊C8—21no—
44C4×C8×C19—21no—
45C4×C8×C19D411yescharacteristic
46C4×C8×C19D411yescharacteristic
47#10597290—22no—
48#10597290C814yescomplemented
49C22⋊(C19⋊C8)—21no—
50C22⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)D411yescharacteristic
53C4⋊(C19⋊C8)D411yescharacteristic
54#10597260—21no—
55#10597260—21no—
56C4×C19⋊C8—21no—
57C4×C19⋊C8—21no—
58C4×C19⋊C8—21no—
59C4×C19⋊C8—21no—
60C24×C19—21no—
61C2×D4×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19—21no—
66C2×D4×C19C2×C812yes—
67C22×C4×C19—21no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
70C22×C4×C19—81no—
71C22×C4×C19—81no—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19#4111yescharacteristic
74C22×C4×C19#4111yescharacteristic
75C2×C8×C19—21no—
76C2×C8×C19—21no—
77C2×C8×C19—42no—
78C2×C8×C19—41no—
79C2×C8×C19—81no—
80C4⋊C4×C19—21no—
81C4⋊C4×C19—21no—
82C22⋊C4×C19—41no—
83C22⋊C4×C19—41no—
84C42×C19C2×D411yescharacteristic
85C42×C19C2×D411yescharacteristic
86C42×C19#4111yescharacteristic
87C42×C19#4111yescharacteristic
88#64520—21no—
89#64520—21no—
90#64520—21no—
91#64520—21no—
92#64520—21no—
93#64520C2×C812yes—
94#64520C2×C812yes—
95#64520M1612yes—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—21no—
99C2×C19⋊C8—21no—
100C2×C19⋊C8—21no—
101C2×C19⋊C8—21no—
102C2×C19⋊C8—41no—
103#9550—191nomaximal, Sylow
104C23×C19—22no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19—81no—
108C23×C19—81no—
109C23×C19#11711yescharacteristic
110D4×C19—22no—
111D4×C19—22no—
112D4×C19—41no—
113D4×C19—41no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—82no—
119C2×C4×C19—81no—
120C2×C4×C19—81no—
121C2×C4×C19—81no—
122C2×C4×C19C4×D411yescharacteristic
123C2×C4×C19C4×D411yescharacteristic
124C2×C4×C19#12111yescharacteristic
125C2×C4×C19#12311yescharacteristic
126C2×C4×C19#12411yescharacteristic
127C2×C4×C19#12611yescharacteristic
128C2×C4×C19C22×C811yescharacteristic
129C2×C4×C19C2×M1611yescharacteristic
130C2×C4×C19#13111yescharacteristic
131C2×C4×C19#13111yescharacteristic
132C8×C19—22no—
133C8×C19—41no—
134C8×C19—81no—
135C19⋊C8—22no—
136C19⋊C8—22no—
137C19⋊C8—22no—
138C19⋊C8—41no—
139C19⋊C8—41no—
140C19⋊C8—41no—
141C19⋊C8—81no—
142C4×#100—191no—
143#1565—191no—
144#1478—191no—
145C2×D4⋊C8D1911yescharacteristic
146C8×M16—191no—
147#1283—191no—
148#1278—191no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—42no—
152C22×C19—82no—
153C22×C19—82no—
154C22×C19—81no—
155C22×C19—81no—
156C22×C19#38811yescharacteristic
157C22×C19#43111yescharacteristic
158C22×C19#43311yescharacteristic
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—81no—
163C4×C19C8×D411yescharacteristic
164C4×C19C8×D411yescharacteristic
165C4×C19#43511yescharacteristic
166C4×C19#43611yescharacteristic
167C4×C19#47111yescharacteristic
168C4×C19#47211yescharacteristic
169C2×C4×D4C2×D1911yescharacteristic
170#431—191no—
171#431—191no—
172C2×C4⋊C8C2×D1911yescharacteristic
173C2×#100—191no—
174C2×#100—191no—
175C4×M16—191no—
176C4×M16—191no—
177C2×C4×C8C2×D1911yescharacteristic
178#343—191no—
179#343—191no—
180#335—381no—
181#334—381no—
182D4⋊C8—21no—
183D4⋊C8—21no—
184D4⋊C8—381no—
185D4⋊C8—381no—
186#322—381no—
187C82—381no—
188C2×C19—21no—
189C2×C19—21no—
190C2×C19—82no—
191C2×C19#192311yescharacteristic
192C2×C19#193111yescharacteristic
193C2×C19#193211yescharacteristic
194C22×D4C4×D1911yescharacteristic
195C23×C4—21no—
196C2×M16—191no—
197C2×M16—191no—
198C2×M16—191no—
199C2×M16—191no—
200C22×C8—21no—
201C22×C8—21no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C2×C4⋊C4C4×D1911yescharacteristic
207C2×C22⋊C4—21no—
208C2×C42C22×D1911yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—191no—
212C4⋊C8—191no—
213C4⋊C8—381no—
214#100—194no—
215#100—382no—
216C22⋊C8—381no—
217C22⋊C8—381no—
218#97—381no—
219#97—381no—
220C4×C8—21no—
221C4×C8—381no—
222C4×C8—381no—
223C4×C8—381no—
224C4×C8—381no—
225C4×C8C22⋊D1911yescharacteristic
226C4×C8C22⋊D1911yescharacteristic
227C19#955011yescharacteristic, complemented, Sylow
228C24—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C8×D1912yes—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4C2×C4×D1911yescharacteristic
241C22×C4#6454311yescharacteristic
242C22×C4#6454311yescharacteristic
243M16—192no—
244M16—192no—
245M16—192no—
246M16—381no—
247M16—381no—
248M16—381no—
249M16—381no—
250M16—381no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—42no—
254C2×C8—41no—
255C2×C8—81no—
256C2×C8—381no—
257C2×C8—381no—
258C2×C8—381no—
259C2×C8—381no—
260C2×C8—381no—
261C2×C8—381no—
262C2×C8—761no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C42#6454111yescharacteristic
268C42D4×D1911yescharacteristic
269C42#6454311yescharacteristic
270C42C2×C22⋊D1911yescharacteristic
271C23—22no—
272C23—41no—
273C23—41no—
274C23—81no—
275C23—81no—
276C23#1059732311yescharacteristic
277D4—22no—
278D4—22no—
279D4—41no—
280D4—41no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4#1059732511yescharacteristic
290C2×C4(C22⋊D19)⋊C411yescharacteristic
291C2×C4#1059733111yescharacteristic
292C2×C4C2×C8×D1911yescharacteristic
293C2×C4#1059734711yescharacteristic
294C2×C4M16×D1911yescharacteristic
295C2×C4#1059735311yescharacteristic
296C2×C4C4×C22⋊D1911yescharacteristic
297C2×C4#1059738111yescharacteristic
298C2×C4#1059738411yescharacteristic
299C8—22no—
300C8—41no—
301C8—81no—
302C8—382no—
303C8—382no—
304C8—382no—
305C8—761no—
306C8—761no—
307C8—761no—
308C8—1521no—
309C22—21no—
310C22—21no—
311C22—42no—
312C22—82no—
313C22—82no—
314C22—81no—
315C22—81no—
316C22#1192643211yescharacteristic
317C22#1192659411yescharacteristic
318C22#1192660211yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—81no—
323C4(C22⋊D19)⋊C811yescharacteristic
324C4C8×C22⋊D1911yescharacteristic
325C4#1192661311yescharacteristic
326C4#1192661911yescharacteristic
327C4#1192680411yescharacteristic
328C4#1192681111yescharacteristic
329C2—21no—
330C2—21no—
331C2—82no—
332C2#1456423811yescharacteristic
333C2#1456429411yescharacteristic
334C2#1456430111yescharacteristic
subgroupG/H
centerC2×C4#10597384
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC2×C19×D4⋊C8C2
socleC22×C19#388
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenterC2×D4⋊C8D19
hypocenterC19#9550
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14562385C2semidirect
4. C8×#64520C2semidirect
5. #14561485C2semidirect
6. #14561472C2semidirect
48. #10597290C8semidirect
227. C19#9550semidirect

Maximal subgroups

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

subgroupindex
C4×#105972902
#145623852
#145620262
C8×#645202
#145614852
#145614722
C2×C19×D4⋊C82
#955019