Finite Group Databasebeta

← #18076554

Subgroups — #18076554

Order 4864.

458 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563933C211yesmaximal, characteristic
2#14563839C212yesmaximal, complemented
3#14561953C211yesmaximal, characteristic
4#14561522C212yesmaximal, complemented
5C19×#2975C211yesmaximal, characteristic
6C22×#64520C2211yescharacteristic
7C2×#10597279—22no—
8C2×C22⋊(C19⋊C8)—21no—
9C2×C22⋊(C19⋊C8)C2211yescharacteristic
10C2×C22⋊(C19⋊C8)C2212yes—
11#11926308—22no—
12#11926299—21no—
13#11926270C412yes—
14#11926268C412yes—
15C2×C4×D4×C19C2211yescharacteristic
16C19×#436—22no—
17C19×#436—22no—
18C19×#431—21no—
19C19×#407—21no—
20C19×#407C2212yes—
21C22×D4×C19Q811yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C2×M16×C19—21no—
25C2×M16×C19—21no—
26C2×M16×C19D412yes—
27C2×M16×C19D412yes—
28C4×D4×C19—22no—
29C4×D4×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19Q811yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×#64520—22no—
35C2×#64520—42no—
36C22×C19⋊C8—21no—
37C22×C19⋊C8—22no—
38C22×C19⋊C8—21no—
39C19×C4⋊C8—21no—
40C19×C4⋊C8—21no—
41C19×C22⋊C8—22no—
42C19×C22⋊C8—22no—
43C19×C22⋊C8—22no—
44C4×C8×C19—22no—
45C22⋊(C19⋊C8)—22no—
46C22⋊(C19⋊C8)—22no—
47C22⋊(C19⋊C8)—42no—
48C22⋊(C19⋊C8)C2×C414yes—
49#10597279—44no—
50C24×C19C4⋊C411yescharacteristic
51C24×C19C2×Q811yescharacteristic
52C2×D4×C19—22no—
53C2×D4×C19—22no—
54C2×D4×C19—41no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—41no—
58C22×C4×C19—41no—
59C22×C4×C19—41no—
60C22×C4×C19—41no—
61C22×C4×C19C4⋊C411yescharacteristic
62C22×C4×C19C4⋊C411yescharacteristic
63C22×C4×C19C4⋊C411yescharacteristic
64C22×C4×C19C22×C411yescharacteristic
65C22×C4×C19C2×D412yes—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19#4112yes—
68M16×C19—42no—
69M16×C19—42no—
70M16×C19—81no—
71M16×C19—81no—
72C2×C8×C19—22no—
73C2×C8×C19—22no—
74C4⋊C4×C19—22no—
75C22⋊C4×C19—22no—
76C22⋊C4×C19—22no—
77C42×C19—21no—
78C42×C19—21no—
79#64520—24no—
80#64520—42no—
81C2×C19⋊C8—22no—
82C2×C19⋊C8—24no—
83C2×C19⋊C8—42no—
84C2×C19⋊C8—42no—
85C2×C19⋊C8—41no—
86C2×C19⋊C8—41no—
87C2×C19⋊C8—41no—
88C2×C19⋊C8—41no—
89C2×C19⋊C8—41no—
90#8860—191nomaximal, Sylow
91C23×C19—21no—
92C23×C19—21no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—41no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19C2×C4⋊C411yescharacteristic
101C23×C19C22⋊Q812yes—
102D4×C19—44no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—41no—
112C2×C4×C19—42no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19—81no—
118C2×C4×C19#10812yescomplemented
119C2×C4×C19C4×D412yes—
120C2×C4×C19#12011yescharacteristic
121C2×C4×C19#12311yescharacteristic
122C8×C19—42no—
123C8×C19—42no—
124C19⋊C8—44no—
125C19⋊C8—42no—
126C19⋊C8—81no—
127#2975D1911yescharacteristic
128#1870—191no—
129#1855—192no—
130#1459—191no—
131#1298—192no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—22no—
135C22×C19—22no—
136C22×C19—22no—
137C22×C19—42no—
138C22×C19—41no—
139C22×C19—41no—
140C22×C19—41no—
141C22×C19—81no—
142C22×C19—81no—
143C22×C19—81no—
144C22×C19#38511yescharacteristic
145C22×C19C2×#10811yescharacteristic
146C22×C19#43011yescharacteristic
147C4×C19—22no—
148C4×C19—22no—
149C4×C19—21no—
150C4×C19—41no—
151C4×C19—41no—
152C4×C19B(4,𝔽2)11yescharacteristic
153C4×C19#45811yescharacteristic
154C22×M16—191no—
155C2×C4×D4C2×D1911yescharacteristic
156#436—22no—
157#436—22no—
158#431—21no—
159C2×#108—382no—
160#407—21no—
161#407C2×D1912yes—
162C2×C22⋊C8—192no—
163C2×C22⋊C8—191no—
164C2×C22⋊C8—381no—
165#341—382no—
166#336—381no—
167#324—192no—
168#323—192no—
169C2×C19—21no—
170C2×C19—21no—
171C2×C19—42no—
172C2×C19—81no—
173C2×C19#185511yescharacteristic
174C2×C19#185811yescharacteristic
175C2×C19#186711yescharacteristic
176C22×D4Dic3811yescharacteristic
177C23×C4C22⋊D1911yescharacteristic
178C23×C4C22×D1911yescharacteristic
179C2×M16—21no—
180C2×M16—21no—
181C2×M16—382no—
182C2×M16—762no—
183C2×M16C22⋊D1912yes—
184C2×M16C22⋊D1912yes—
185C22×C8—381no—
186C22×C8—382no—
187C22×C8—381no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4C4×D1911yescharacteristic
191C2×C22⋊C4Dic3811yescharacteristic
192C2×C22⋊C4C4×D1911yescharacteristic
193C2×C42C22⋊D1911yescharacteristic
194#108—764no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—194no—
201C22⋊C8—382no—
202C22⋊C8—382no—
203C22⋊C8—762no—
204C4×C8—22no—
205C19#886011yescharacteristic, complemented, Sylow
206C24Dic19⋊C411yescharacteristic
207C24C2×Dic3811yescharacteristic
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4Dic19⋊C411yescharacteristic
218C22×C4Dic19⋊C411yescharacteristic
219C22×C4Dic19⋊C411yescharacteristic
220C22×C4C2×C4×D1911yescharacteristic
221C22×C4#6454112yes—
222C22×C4C2×C22⋊D1912yes—
223C22×C4C2×C22⋊D1911yescharacteristic
224M16—42no—
225M16—42no—
226M16—81no—
227M16—81no—
228M16—384no—
229M16—762no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—382no—
233C2×C8—384no—
234C2×C8—762no—
235C2×C8—762no—
236C2×C8—761no—
237C2×C8—761no—
238C2×C8—761no—
239C2×C8—761no—
240C2×C8—761no—
241C4⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—22no—
244C42—21no—
245C42—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23C2×Dic19⋊C411yescharacteristic
256C23#1059737012yes—
257D4—44no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4#1059727912yescomplemented
274C2×C4C4×C22⋊D1912yes—
275C2×C4#1059737511yescharacteristic
276C2×C4#1059739911yescharacteristic
277C8—42no—
278C8—42no—
279C8—764no—
280C8—762no—
281C8—1521no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22#1192641711yescharacteristic
295C22C2×#1059727911yescharacteristic
296C22#1192659211yescharacteristic
297C4—22no—
298C4—22no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4#1192673111yescharacteristic
303C4#1192673411yescharacteristic
304C2—21no—
305C2—21no—
306C2—42no—
307C2—81no—
308C2#1456384011yescharacteristic
309C2#1456385511yescharacteristic
310C2#1456391611yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2975C2
socleC22×C19#385
prime radicalC22×D4×C19Q8
cosocleC23×C4×C19C23
hypercenter#2975D19
hypocenterC19#8860
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #14563839C2semidirect
4. #14561522C2semidirect
118. C2×C4×C19#108semidirect
205. C19#8860semidirect
273. C2×C4#10597279semidirect

Maximal subgroups

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

subgroupindex
#145639332
#145638392
#145619532
#145615222
C19×#29752
#886019