Finite Group Databasebeta

← #18071210

Subgroups — #18071210

Order 4864.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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#14571987C211yesmaximal, characteristic
2#14563615C211yesmaximal, characteristic
3#14561457C214yesmaximal, complemented
4C19×#1817C211yesmaximal, characteristic
5C2×#10597315C411yescharacteristic
6C2×#10597370—21no—
7C2×C4⋊(C19⋊C8)—21no—
8C2×C22⋊(C19⋊C8)—21no—
9#11926450—21no—
10#11926442—21no—
11#11926442C2212yes—
12#11926414C411yescharacteristic
13#11926404—21no—
14#11926404C412yes—
15#11926299C2212yes—
16C22×C42×C19C2211yescharacteristic
17C2×C19×C22⋊C8—21no—
18C19×#336—21no—
19C19×#336C2212yes—
20C23×C4×C19C2×C411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C22×Dic38—21no—
24C22×C8×C19—22no—
25C2×C42×C19—42no—
26C2×C42×C19C2×C411yescharacteristic
27C2×C42×C19D411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19C2311yescharacteristic
30C2×C22⋊Dic19—22no—
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19C2×C412yes—
35C2×C4⋊Dic19C2×C412yes—
36#10597370—42no—
37#10597370—42no—
38C2×Dic19⋊C4—22no—
39C22×C19⋊C8—22no—
40#10597315—42no—
41C19×C22⋊C8—42no—
42C19⋊#95—22no—
43C19⋊#95—22no—
44C22⋊(C19⋊C8)—42no—
45C4⋊(C19⋊C8)—42no—
46C24×C19C22⋊C411yescharacteristic
47C22×C4×C19—22no—
48C22×C4×C19—22no—
49C22×C4×C19—22no—
50C22×C4×C19—22no—
51C22×C4×C19—41no—
52C22×C4×C19—41no—
53C22×C4×C19—41no—
54C22×C4×C19—41no—
55C22×C4×C19C22⋊C411yescharacteristic
56C22×C4×C19C22⋊C411yescharacteristic
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19D812yes—
59C22×C4×C19SD1612yes—
60C22×C4×C19C22×C411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×Dic19—22no—
64C22×Dic19—22no—
65C2×Dic38—42no—
66C2×Dic38—42no—
67C2×Dic38—42no—
68C2×C8×C19—42no—
69C2×C8×C19—42no—
70C2×C8×C19—42no—
71C42×C19—22no—
72C42×C19—22no—
73C42×C19—41no—
74C42×C19—41no—
75C22⋊Dic19—44no—
76C4⋊Dic19—24no—
77C4⋊Dic19—42no—
78C4⋊Dic19—42no—
79C4⋊Dic19—42no—
80C4⋊Dic19—42no—
81Dic19⋊C4—42no—
82Dic19⋊C4—42no—
83C2×C19⋊C8—42no—
84C2×C19⋊C8—42no—
85C2×C19⋊C8—42no—
86#7728—191nomaximal, Sylow
87C23×C19—21no—
88C23×C19—21no—
89C23×C19—21no—
90C23×C19—21no—
91C23×C19—21no—
92C23×C19—21no—
93C23×C19#10212yes—
94C23×C19C2×C22⋊C411yescharacteristic
95C2×C4×C19—21no—
96C2×C4×C19—21no—
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—42no—
108C2×C4×C19—42no—
109C2×C4×C19—44no—
110C2×C4×C19—44no—
111C2×C4×C19#9912yes—
112C2×C4×C19#10112yes—
113C2×C4×C19#10212yes—
114C2×C4×C19#13112yes—
115C2×C4×C19C2×D811yescharacteristic
116C2×C4×C19C2×SD1611yescharacteristic
117C2×C4×C19#13712yes—
118C2×Dic19—42no—
119C2×Dic19—42no—
120C2×Dic19—42no—
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124Dic38—84no—
125C8×C19—82no—
126C19⋊C8—82no—
127#2857—191no—
128#1817D1911yescharacteristic
129#1797—191no—
130#1271—194no—
131C22×C19—22no—
132C22×C19—22no—
133C22×C19—22no—
134C22×C19—41no—
135C22×C19—41no—
136C22×C19—41no—
137C22×C19—41no—
138C22×C19#40811yescharacteristic
139C22×C19C2×#9911yescharacteristic
140C22×C19C2×#10111yescharacteristic
141C22×C19C2×#10211yescharacteristic
142C22×C19#41911yescharacteristic
143C22×C19#42111yescharacteristic
144C22×C19#42111yescharacteristic
145C4×C19—22no—
146C4×C19—22no—
147C4×C19—22no—
148C4×C19—22no—
149C4×C19—21no—
150C4×C19—22no—
151C4×C19—21no—
152Dic19—82no—
153Dic19—82no—
154C2×C4⋊Q8—191no—
155C2×C22⋊Q8—381no—
156C22×C42C2×D1911yescharacteristic
157C2×C4⋊C8—381no—
158C2×C22⋊C8—21no—
159C2×C22⋊C8—381no—
160#391—381no—
161#389—192no—
162#389—381no—
163#384—191no—
164#380—192no—
165#380—381no—
166#336—21no—
167#336—192no—
168#336C2×D1912yes—
169C2×C19—42no—
170C2×C19#147211yescharacteristic
171C2×C19#148011yescharacteristic
172C2×C19#149711yescharacteristic
173C2×C19#151111yescharacteristic
174C2×C19#151911yescharacteristic
175C2×C19#153711yescharacteristic
176C2×C19#154611yescharacteristic
177C22×Q8—381no—
178C23×C4C4×D1911yescharacteristic
179C23×C4D7611yescharacteristic
180C23×C4C22⋊D1911yescharacteristic
181C22×C8—22no—
182C22×C8—382no—
183C4⋊Q8—762no—
184C22⋊Q8—762no—
185C22⋊Q8—762no—
186C2×C4⋊C4—192no—
187C2×C4⋊C4—192no—
188C2×C4⋊C4—381no—
189C2×C4⋊C4—381no—
190C2×C4⋊C4—381no—
191C2×C4⋊C4—382no—
192C2×C22⋊C4—382no—
193C2×C42—42no—
194C2×C42C4×D1911yescharacteristic
195C2×C42D7611yescharacteristic
196C2×C42C22⋊D1911yescharacteristic
197C2×C42C22×D1911yescharacteristic
198C4⋊C8—762no—
199C22⋊C8—42no—
200C22⋊C8—762no—
201#95—382no—
202#95—382no—
203C19#772811yescharacteristic, complemented, Sylow
204C24(C2×D19)⋊C411yescharacteristic
205C2×Q8—762no—
206C2×Q8—762no—
207C2×Q8—762no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—382no—
217C22×C4—382no—
218C22×C4#6451612yes—
219C22×C4D15212yes—
220C22×C4(C2×D19)⋊C411yescharacteristic
221C22×C4(C2×D19)⋊C411yescharacteristic
222C22×C4(C2×D19)⋊C411yescharacteristic
223C22×C4C2×C4×D1911yescharacteristic
224C22×C4C2×D7611yescharacteristic
225C22×C4C2×C22⋊D1911yescharacteristic
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—762no—
230C2×C8—762no—
231C2×C8—762no—
232C4⋊C4—384no—
233C4⋊C4—762no—
234C4⋊C4—762no—
235C4⋊C4—762no—
236C4⋊C4—762no—
237C4⋊C4—762no—
238C4⋊C4—762no—
239C22⋊C4—764no—
240C42—22no—
241C42—22no—
242C42—41no—
243C42—41no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#1059727812yes—
251C23C2×(C2×D19)⋊C411yescharacteristic
252Q8—1524no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—762no—
270C2×C4—762no—
271C2×C4—762no—
272C2×C4—762no—
273C2×C4—762no—
274C2×C4—762no—
275C2×C4#1059726312yes—
276C2×C4#1059727812yes—
277C2×C4#1059728112yes—
278C2×C4C2×#6451611yescharacteristic
279C2×C4C2×D15211yescharacteristic
280C2×C4#1059735312yes—
281C2×C4#1059739712yes—
282C8—82no—
283C8—1522no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22#1192651211yescharacteristic
292C22C2×#1059726311yescharacteristic
293C22C2×#1059728111yescharacteristic
294C22C2×#1059727811yescharacteristic
295C22#1192655211yescharacteristic
296C22#1192656011yescharacteristic
297C22#1192656211yescharacteristic
298C4—22no—
299C4—22no—
300C4—21no—
301C4—22no—
302C4—21no—
303C4—22no—
304C4—22no—
305C4—1522no—
306C4—1522no—
307C2—42no—
308C2#1456200011yescharacteristic
309C2#1456203511yescharacteristic
310C2#1456210711yescharacteristic
311C2#1456216711yescharacteristic
312C2#1456220411yescharacteristic
313C2#1456227211yescharacteristic
314C2#1456230611yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1817D19
hypocenterC19#7728
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #14561457C2semidirect
203. C19#7728semidirect

Maximal subgroups

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

subgroupindex
#145719872
#145636152
#145614572
C19×#18172
#772819