Finite Group Databasebeta

← #18077598

Subgroups — #18077598

Order 4864.

660 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#11926474C211yesmaximal, characteristic
2#14563719C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic
4#14561513C212yesmaximal
5C19×#2316C211yesmaximal, characteristic
6C22×C4⋊Dic19C2211yescharacteristic
7C22×Dic19⋊C4—21no—
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926474—22no—
10#11926474C414yescomplemented
11C2×C19⋊#95—21no—
12C2×C19⋊#95C2211yescharacteristic
13#11926306—24no—
14#11926270—22no—
15C2×C19×#117—21no—
16C22×C4⋊C4×C19C2211yescharacteristic
17C19×#389—24no—
18C19×#380—21no—
19C19×#380C2212yes—
20C23×C4×C19D411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19C2311yescharacteristic
23C23×Dic19—21no—
24C23×Dic19—21no—
25C19×#117—42no—
26C19×#117—42no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19C2×C412yes—
32C2×C4⋊C4×C19D412yes—
33C2×C4⋊C4×C19D414yes—
34C2×C22⋊C4×C19—22no—
35C2×C42×C19—22no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19C2×C412yes—
40C2×Dic19⋊C4—24no—
41C2×Dic19⋊C4—42no—
42C2×Dic19⋊C4—42no—
43C22×C19⋊C8—22no—
44C19×#95—22no—
45C19×#95—22no—
46C19⋊#95—24no—
47C19⋊#95—21no—
48C19⋊#95C2×C412yes—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C24×C19C2×D411yescharacteristic
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—24no—
59C22×C4×C19—42no—
60C22×C4×C19—42no—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19D812yes—
64C22×C4×C19SD1612yes—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19#4112yes—
69C22×Dic19—24no—
70C22×Dic19—22no—
71C22×Dic19—22no—
72C22×Dic19—42no—
73C22×Dic19—41no—
74C22×Dic19—41no—
75C22×Dic19—41no—
76C22×Dic19—41no—
77C22×Dic19—41no—
78C22×Dic19—41no—
79C22×Dic19—41no—
80C22×Dic19—41no—
81C4⋊C4×C19—24no—
82C4⋊C4×C19—24no—
83C4⋊C4×C19—44no—
84C4⋊C4×C19—44no—
85C4⋊C4×C19—82no—
86C22⋊C4×C19—42no—
87C22⋊C4×C19—42no—
88C42×C19—44no—
89C4⋊Dic19—24no—
90C4⋊Dic19—42no—
91Dic19⋊C4—48no—
92C2×C19⋊C8—44no—
93C2×C19⋊C8—42no—
94#9027—191nomaximal, Sylow
95C23×C19—22no—
96C23×C19—22no—
97C23×C19C2×C22⋊C411yescharacteristic
98C23×C19#12011yescharacteristic
99C23×C19#12311yescharacteristic
100C23×C19C2×D811yescharacteristic
101C23×C19C2×SD1611yescharacteristic
102C23×C19AGL(1,ℤ/8)11yescharacteristic
103C23×C19#13711yescharacteristic
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—24no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—44no—
118C2×C4×C19—44no—
119C2×C4×C19—44no—
120C2×C4×C19—81no—
121C2×C4×C19#10214yes—
122C2×C4×C19C4×D412yes—
123C2×C4×C19#12112yes—
124C2×Dic19—24no—
125C2×Dic19—44no—
126C2×Dic19—44no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—42no—
132C2×Dic19—81no—
133C2×Dic19—81no—
134C2×Dic19—81no—
135C2×Dic19—81no—
136C19⋊C8—82no—
137C2×#398—191no—
138#2316D1911yescharacteristic
139#1823—192no—
140C2×#324—191no—
141#1294—192no—
142C22×C19—22no—
143C22×C19—22no—
144C22×C19—22no—
145C22×C19—22no—
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19#38611yescharacteristic
151C22×C19C2×#10211yescharacteristic
152C22×C19#41711yescharacteristic
153C22×C19#44711yescharacteristic
154C22×C19#44811yescharacteristic
155C22×C19#45612yes—
156C22×C19#45812yes—
157C22×C19#48011yescharacteristic
158C22×C19#48111yescharacteristic
159C4×C19—24no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—42no—
163C4×C19—84no—
164Dic19—44no—
165Dic19—82no—
166C2×#117—21no—
167C22×C4⋊C4—191no—
168C22×C4⋊C4—381no—
169C22×C4⋊C4C2×D1911yescharacteristic
170C2×C22⋊C8—192no—
171#398—194no—
172#398—382no—
173#389—24no—
174#380—21no—
175#380C2×D1912yes—
176C2×#95—191no—
177C2×#95—381no—
178#340—384no—
179#324—382no—
180C2×C19—21no—
181C2×C19—21no—
182C2×C19—21no—
183C2×C19—21no—
184C2×C19#161012yes—
185C2×C19#161112yes—
186C2×C19#187411yescharacteristic
187C2×C19#188611yescharacteristic
188C2×C19#189011yescharacteristic
189C23×C4—381no—
190C23×C4—381no—
191C23×C4C22⋊D1911yescharacteristic
192C23×C4C22⋊D1911yescharacteristic
193C23×C4C22×D1911yescharacteristic
194C22×C8—382no—
195#117—42no—
196#117—42no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—192no—
202C2×C4⋊C4—382no—
203C2×C4⋊C4—382no—
204C2×C4⋊C4—384no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—762no—
207C2×C4⋊C4—762no—
208C2×C4⋊C4C4×D1912yes—
209C2×C4⋊C4D7612yes—
210C2×C4⋊C4C22⋊D1914yes—
211C2×C22⋊C4—22no—
212C2×C42—22no—
213C22⋊C8—382no—
214C22⋊C8—382no—
215#95—22no—
216#95—22no—
217#95—192no—
218#95—384no—
219#95—381no—
220C19#902711yescharacteristic, complemented, Sylow
221C24C2×C22⋊D1911yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—384no—
232C22×C4—382no—
233C22×C4—382no—
234C22×C4—762no—
235C22×C4—761no—
236C22×C4—761no—
237C22×C4—761no—
238C22×C4—761no—
239C22×C4—761no—
240C22×C4—761no—
241C22×C4—761no—
242C22×C4—761no—
243C22×C4(C2×D19)⋊C412yes—
244C22×C4(C2×D19)⋊C412yes—
245C22×C4#6452512yes—
246C22×C4#6452712yes—
247C22×C4C2×C4×D1911yescharacteristic
248C22×C4C2×D7611yescharacteristic
249C22×C4#6454112yes—
250C22×C4C2×C22⋊D1912yes—
251C2×C8—764no—
252C2×C8—762no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—44no—
256C4⋊C4—44no—
257C4⋊C4—82no—
258C4⋊C4—384no—
259C4⋊C4—762no—
260C4⋊C4—768no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—44no—
264C23—22no—
265C23—22no—
266C23C2×(C2×D19)⋊C411yescharacteristic
267C23#1059737511yescharacteristic
268C23C2×#6452511yescharacteristic
269C23#1059737811yescharacteristic
270C23C2×#6452711yescharacteristic
271C23#1059738811yescharacteristic
272C23#1059739911yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—81no—
290C2×C4—384no—
291C2×C4—764no—
292C2×C4—764no—
293C2×C4—762no—
294C2×C4—762no—
295C2×C4—762no—
296C2×C4—762no—
297C2×C4—762no—
298C2×C4—1521no—
299C2×C4—1521no—
300C2×C4—1521no—
301C2×C4—1521no—
302C2×C4#1059726614yes—
303C2×C4C4×C22⋊D1912yes—
304C2×C4#1059737612yes—
305C8—1522no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22#1192642311yescharacteristic
315C22C2×#1059726611yescharacteristic
316C22#1192654311yescharacteristic
317C22#1192667811yescharacteristic
318C22#1192668311yescharacteristic
319C22#1192672712yes—
320C22#1192673412yes—
321C22#1192685711yescharacteristic
322C22#1192686211yescharacteristic
323C4—24no—
324C4—22no—
325C4—22no—
326C4—42no—
327C4—84no—
328C4—764no—
329C4—1522no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#1456263812yes—
335C2#1456264312yes—
336C2#1456395211yescharacteristic
337C2#1456402811yescharacteristic
338C2#1456404811yescharacteristic
subgroupG/H
centerC23#10597399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2316C2
socleC23×C19#120
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2316D19
hypocenterC19#9027
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
10. #11926474C4semidirect
220. C19#9027semidirect

Maximal subgroups

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

subgroupindex
C2×#119264742
#145637192
C2×#119262702
#145615132
C19×#23162
#902719