Finite Group Databasebeta

← #18071201

Subgroups — #18071201

Order 4864.

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

normal subgroups only

This group has 400 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#14563778C211yesmaximal, characteristic, complemented
2#14563778C211yesmaximal, characteristic, complemented
3#14561458C212yesmaximal, complemented
4#14561456C212yesmaximal
5C19×#2860C211yesmaximal, characteristic
6#11926299—21no—
7#11926299—21no—
8#11926299—21no—
9#11926299—21no—
10#11926299C2212yes—
11#11926299C2212yes—
12C2×C19×#126—21no—
13C19×#390C411yescharacteristic
14C19×#390C411yescharacteristic
15C19×#390C2211yescharacteristic
16C19×#389C411yescharacteristic
17C19×#389C411yescharacteristic
18C19×#389C2211yescharacteristic
19C19×#388—21no—
20C19×#388—21no—
21C19×#388—21no—
22C43×C19C2211yescharacteristic
23C22×D4×C19C2×C411yescharacteristic
24C19×#126—44no—
25C2×C4⋊C4×C19—21no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19—21no—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19C2×C411yescharacteristic
38C2×C42×C19C2×C411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C42×C19C2311yescharacteristic
44C22×C19⋊C8—22no—
45C22×C19⋊C8—22no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C24×C19—21no—
50C2×D4×C19—22no—
51C2×D4×C19—41no—
52C2×D4×C19—41no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19C22⋊C411yescharacteristic
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22×C411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C4⋊C4×C19—22no—
64C4⋊C4×C19—41no—
65C4⋊C4×C19—41no—
66C4⋊C4×C19—42no—
67C4⋊C4×C19—42no—
68C4⋊C4×C19—42no—
69C22⋊C4×C19—42no—
70C22⋊C4×C19—42no—
71C22⋊C4×C19—42no—
72C22⋊C4×C19—42no—
73C22⋊C4×C19—42no—
74C22⋊C4×C19—42no—
75C42×C19—22no—
76C42×C19—22no—
77C42×C19—22no—
78C42×C19—41no—
79C42×C19—41no—
80C42×C19—41no—
81C42×C19—41no—
82C2×C19⋊C8—42no—
83C2×C19⋊C8—42no—
84C2×C19⋊C8—42no—
85C2×C19⋊C8—42no—
86C2×C19⋊C8—42no—
87C2×C19⋊C8—42no—
88#7726—191nomaximal, Sylow
89C23×C19—41no—
90C23×C19—41no—
91C23×C19—41no—
92C23×C19—41no—
93C23×C19—41no—
94C23×C19—41no—
95C23×C19—41no—
96C23×C19C2×C22⋊C411yescharacteristic
97D4×C19—82no—
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—21no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19#13112yes—
126C2×C4×C19#13512yes—
127C2×C4×C19AGL(1,ℤ/8)12yes—
128C19⋊C8—82no—
129C19⋊C8—82no—
130#2860D1911yescharacteristic
131#1839—191no—
132#1839—191no—
133#1271—192no—
134#1270—192no—
135C22×C19—81no—
136C22×C19—81no—
137C22×C19—81no—
138C22×C19—81no—
139C22×C19—81no—
140C22×C19—81no—
141C22×C19—81no—
142C22×C19#40811yescharacteristic
143C22×C19#41011yescharacteristic
144C22×C19#41311yescharacteristic
145C22×C19#41611yescharacteristic
146C22×C19#41811yescharacteristic
147C22×C19#42111yescharacteristic
148C22×C19#42111yescharacteristic
149C4×C19—22no—
150C4×C19—22no—
151C4×C19—22no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19—41no—
155C4×C19—41no—
156C4×C19—81no—
157C4×C19—81no—
158C4×C19—81no—
159C2×#126—21no—
160#390Dic1911yescharacteristic
161#390Dic1911yescharacteristic
162#390C2×D1911yescharacteristic
163#389Dic1911yescharacteristic
164#389Dic1911yescharacteristic
165#389C2×D1911yescharacteristic
166#388—21no—
167#388—21no—
168#388—21no—
169C43C2×D1911yescharacteristic
170#336—192no—
171#336—192no—
172#336—381no—
173#336—381no—
174#336—381no—
175#336—381no—
176C2×C19—161no—
177C2×C19#147311yescharacteristic
178C2×C19#148211yescharacteristic
179C2×C19#149611yescharacteristic
180C2×C19#151411yescharacteristic
181C2×C19#152111yescharacteristic
182C2×C19#153511yescharacteristic
183C2×C19#155311yescharacteristic
184C22×D4C2×Dic1911yescharacteristic
185C22×C8—382no—
186C22×C8—382no—
187#126—44no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×Dic1911yescharacteristic
192C2×C4⋊C4C2×Dic1911yescharacteristic
193C2×C4⋊C4C2×Dic1911yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C42C2×Dic1911yescharacteristic
201C2×C42C2×Dic1911yescharacteristic
202C2×C42C22⋊D1911yescharacteristic
203C2×C42C22⋊D1911yescharacteristic
204C2×C42C22⋊D1911yescharacteristic
205C2×C42C22⋊D1911yescharacteristic
206C2×C42C22×D1911yescharacteristic
207#95—21no—
208#95—21no—
209#95—21no—
210C19#772611yescharacteristic, complemented, Sylow
211C24—21no—
212C2×D4—22no—
213C2×D4—41no—
214C2×D4—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4C22⋊Dic1911yescharacteristic
219C22×C4C22⋊Dic1911yescharacteristic
220C22×C4C22⋊Dic1911yescharacteristic
221C22×C4C22⋊Dic1911yescharacteristic
222C22×C4C22×Dic1911yescharacteristic
223C22×C4C2×C22⋊D1911yescharacteristic
224C22×C4C2×C22⋊D1911yescharacteristic
225C2×C8—762no—
226C2×C8—762no—
227C2×C8—762no—
228C2×C8—762no—
229C2×C8—762no—
230C2×C8—762no—
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C42—22no—
244C42—22no—
245C42—22no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23C2×C22⋊Dic1911yescharacteristic
258D4—82no—
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—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4#1059737812yes—
287C2×C4#1059739412yes—
288C2×C4#1059739612yes—
289C8—1522no—
290C8—1522no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#1192651111yescharacteristic
299C22#1192651811yescharacteristic
300C22#1192652811yescharacteristic
301C22#1192654011yescharacteristic
302C22#1192654911yescharacteristic
303C22#1192656111yescharacteristic
304C22#1192656111yescharacteristic
305C4—22no—
306C4—22no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C2—161no—
316C2#1456200411yescharacteristic
317C2#1456204311yescharacteristic
318C2#1456210411yescharacteristic
319C2#1456218211yescharacteristic
320C2#1456221211yescharacteristic
321C2#1456226611yescharacteristic
322C2#1456234011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2860C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2860D19
hypocenterC19#7726
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. #14563778C2semidirect
2. #14563778C2semidirect
3. #14561458C2semidirect
210. C19#7726semidirect

Maximal subgroups

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

subgroupindex
#145637782
#145614582
#145614562
C19×#28602
#772619