Finite Group Databasebeta

← #18071202

Subgroups — #18071202

Order 4864.

400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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#14572002C211yesmaximal, characteristic
2#14563778C211yesmaximal, characteristic, complemented
3#14561459C212yesmaximal, complemented
4#14561455C212yesmaximal
5C19×#1839C211yesmaximal, characteristic, complemented
6C2×#10597322—21no—
7#11926446C411yescharacteristic
8#11926446C411yescharacteristic
9#11926446C2211yescharacteristic
10#11926442C411yescharacteristic
11#11926442C411yescharacteristic
12#11926442C2211yescharacteristic
13#11926435—21no—
14#11926435—21no—
15#11926435—21no—
16#11926299—21no—
17#11926299—21no—
18#11926299C2212yes—
19C43×C19C2211yescharacteristic
20C19×#336—21no—
21C19×#336—21no—
22C19×#336C2212yes—
23C22×D76C2×C411yescharacteristic
24C22×C8×C19—22no—
25C2×C42×C19C2×C411yescharacteristic
26C2×C42×C19C2×C411yescharacteristic
27C2×C42×C19D411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×(C2×D19)⋊C4—21no—
33C2×(C2×D19)⋊C4—21no—
34C2×(C2×D19)⋊C4—21no—
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C22×C19⋊C8—22no—
45#10597322—44no—
46C19⋊#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C23×D19—21no—
50C22×C4×C19C22⋊C411yescharacteristic
51C22×C4×C19C22⋊C411yescharacteristic
52C22×C4×C19C22⋊C411yescharacteristic
53C22×C4×C19C22⋊C411yescharacteristic
54C22×C4×C19C22×C411yescharacteristic
55C22×C4×C19C2×D411yescharacteristic
56C22×C4×C19C2×D411yescharacteristic
57C22×Dic19—21no—
58C22×Dic19—21no—
59C22×Dic19—21no—
60C2×D76—22no—
61C2×D76—41no—
62C2×D76—41no—
63C2×C8×C19—42no—
64C2×C8×C19—42no—
65C2×C8×C19—42no—
66C42×C19—22no—
67C42×C19—22no—
68C42×C19—22no—
69C42×C19—41no—
70C42×C19—41no—
71C42×C19—41no—
72C42×C19—41no—
73(C2×D19)⋊C4—42no—
74(C2×D19)⋊C4—42no—
75(C2×D19)⋊C4—42no—
76(C2×D19)⋊C4—42no—
77(C2×D19)⋊C4—42no—
78(C2×D19)⋊C4—42no—
79C4⋊Dic19—22no—
80C4⋊Dic19—41no—
81C4⋊Dic19—41no—
82Dic19⋊C4—42no—
83Dic19⋊C4—42no—
84Dic19⋊C4—42no—
85C2×C19⋊C8—42no—
86C2×C19⋊C8—42no—
87C2×C19⋊C8—42no—
88#7726—191nomaximal, Sylow
89C23×C19C2×C22⋊C411yescharacteristic
90C22×D19—41no—
91C22×D19—41no—
92C22×D19—41no—
93C22×D19—41no—
94C22×D19—41no—
95C22×D19—41no—
96C22×D19—41no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19#13112yes—
116C2×C4×C19#13512yes—
117C2×C4×C19AGL(1,ℤ/8)12yes—
118C2×Dic19—41no—
119C2×Dic19—41no—
120C2×Dic19—41no—
121C2×Dic19—41no—
122C2×Dic19—41no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127D76—82no—
128C8×C19—82no—
129C19⋊C8—82no—
130#2860—191no—
131#1839—191no—
132#1839D1911yescharacteristic, complemented
133#1271—192no—
134#1270—192no—
135C22×C19#40811yescharacteristic
136C22×C19#41011yescharacteristic
137C22×C19#41311yescharacteristic
138C22×C19#41611yescharacteristic
139C22×C19#41811yescharacteristic
140C22×C19#42111yescharacteristic
141C22×C19#42111yescharacteristic
142C2×D19—81no—
143C2×D19—81no—
144C2×D19—81no—
145C2×D19—81no—
146C2×D19—81no—
147C2×D19—81no—
148C2×D19—81no—
149C4×C19—22no—
150C4×C19—22no—
151C4×C19—22no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19—41no—
155C4×C19—41no—
156Dic19—81no—
157Dic19—81no—
158Dic19—81no—
159C2×#126—381no—
160#390—191no—
161#390—191no—
162#390—191no—
163#389—191no—
164#389—191no—
165#389—191no—
166#388—381no—
167#388—381no—
168#388—381no—
169C43C2×D1911yescharacteristic
170#336—21no—
171#336—21no—
172#336—192no—
173#336—381no—
174#336—381no—
175#336C2×D1912yes—
176C2×C19#147311yescharacteristic
177C2×C19#148211yescharacteristic
178C2×C19#149611yescharacteristic
179C2×C19#151411yescharacteristic
180C2×C19#152111yescharacteristic
181C2×C19#153511yescharacteristic
182C2×C19#155311yescharacteristic
183D19—161no—
184C22×D4—191no—
185C22×C8—22no—
186C22×C8—382no—
187#126—764no—
188C2×C4⋊C4—191no—
189C2×C4⋊C4—191no—
190C2×C4⋊C4—191no—
191C2×C4⋊C4—381no—
192C2×C4⋊C4—381no—
193C2×C4⋊C4—381no—
194C2×C22⋊C4—381no—
195C2×C22⋊C4—381no—
196C2×C22⋊C4—381no—
197C2×C22⋊C4—381no—
198C2×C22⋊C4—381no—
199C2×C22⋊C4—381no—
200C2×C42C4×D1911yescharacteristic
201C2×C42C4×D1911yescharacteristic
202C2×C42D7611yescharacteristic
203C2×C42D7611yescharacteristic
204C2×C42C22⋊D1911yescharacteristic
205C2×C42C22⋊D1911yescharacteristic
206C2×C42C22×D1911yescharacteristic
207#95—381no—
208#95—381no—
209#95—381no—
210C19#772611yescharacteristic, complemented, Sylow
211C24—381no—
212C2×D4—382no—
213C2×D4—761no—
214C2×D4—761no—
215C22×C4—381no—
216C22×C4—381no—
217C22×C4—381no—
218C22×C4(C2×D19)⋊C411yescharacteristic
219C22×C4(C2×D19)⋊C411yescharacteristic
220C22×C4(C2×D19)⋊C411yescharacteristic
221C22×C4(C2×D19)⋊C411yescharacteristic
222C22×C4C2×C4×D1911yescharacteristic
223C22×C4C2×D7611yescharacteristic
224C22×C4C2×C22⋊D1911yescharacteristic
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—762no—
229C2×C8—762no—
230C2×C8—762no—
231C4⋊C4—382no—
232C4⋊C4—761no—
233C4⋊C4—761no—
234C4⋊C4—762no—
235C4⋊C4—762no—
236C4⋊C4—762no—
237C22⋊C4—762no—
238C22⋊C4—762no—
239C22⋊C4—762no—
240C22⋊C4—762no—
241C22⋊C4—762no—
242C22⋊C4—762no—
243C42—22no—
244C42—22no—
245C42—22no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—41no—
250C23—761no—
251C23—761no—
252C23—761no—
253C23—761no—
254C23—761no—
255C23—761no—
256C23—761no—
257C23C2×(C2×D19)⋊C411yescharacteristic
258D4—1522no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—761no—
278C2×C4—761no—
279C2×C4—761no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4#1059735012yes—
287C2×C4#1059735312yes—
288C2×C4#1059739512yes—
289C8—82no—
290C8—1522no—
291C22—1521no—
292C22—1521no—
293C22—1521no—
294C22—1521no—
295C22—1521no—
296C22—1521no—
297C22—1521no—
298C22#1192651211yescharacteristic
299C22#1192651711yescharacteristic
300C22#1192652611yescharacteristic
301C22#1192654111yescharacteristic
302C22#1192654811yescharacteristic
303C22#1192656011yescharacteristic
304C22#1192656211yescharacteristic
305C4—22no—
306C4—22no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—1521no—
313C4—1521no—
314C4—1521no—
315C2—3041no—
316C2#1456200511yescharacteristic
317C2#1456204411yescharacteristic
318C2#1456210311yescharacteristic
319C2#1456218111yescharacteristic
320C2#1456221311yescharacteristic
321C2#1456226411yescharacteristic
322C2#1456233811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1839C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1839D19
hypocenterC19#7726
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
2. #14563778C2semidirect
3. #14561459C2semidirect
5. C19×#1839C2semidirect
132. #1839D19semidirect
210. C19#7726semidirect

Maximal subgroups

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

subgroupindex
#145720022
#145637782
#145614592
#145614552
C19×#18392
#772619