Finite Group Databasebeta

← #18074985

Subgroups — #18074985

Order 4864.

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

normal subgroups only

This group has 736 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
1#14564605C212yesmaximal, complemented
2#14564452C211yesmaximal, characteristic
3C2×#11926286C212yesmaximal, complemented
4C2×#11926284C211yesmaximal, characteristic
5C2×C19×#563C211yesmaximal, characteristic
6C2×#10597292—21no—
7C2×#10597289—21no—
8C2×#10597260C2211yescharacteristic
9C2×#10597260C2212yes—
10#11926414C2211yescharacteristic
11#11926306—22no—
12#11926306—22no—
13#11926286—24no—
14#11926284—22no—
15C19×#563—24no—
16C19×#563—22no—
17C19×#563C414yescomplemented
18C2×C19×C4⋊Q8—21no—
19C2×C19×#126—22no—
20C2×C19×#125C2212yes—
21C2×C19×#124C2211yescharacteristic
22C2×C19×#123—21no—
23C2×C19×C22⋊Q8—22no—
24C22×Q8×C19—21no—
25C22×Q8×C19D411yescharacteristic
26C22×D4×C19D411yescharacteristic
27C23×C4×C19—21no—
28C19×C4⋊Q8—24no—
29C19×C4⋊Q8—24no—
30C19×#126—28no—
31C19×#126—28no—
32C19×#125—22no—
33C19×#125—22no—
34C19×#125C2×C414yes—
35C19×#125D414yes—
36C19×#124—22no—
37C19×#124C2×C412yes—
38C19×#124D412yes—
39C19×#123—24no—
40C19×#123—24no—
41C19×C22⋊Q8—28no—
42C19×C22⋊Q8—28no—
43C2×C4⋊C4×C19—22no—
44C2×C4⋊C4×C19—22no—
45C2×C4⋊C4×C19—22no—
46C2×C4⋊C4×C19D412yes—
47C2×C4⋊C4×C19D412yes—
48C2×C22⋊C4×C19—22no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—22no—
51C2×C42×C19—21no—
52C2×C42×C19C2311yescharacteristic
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—22no—
55C22×C19⋊C8—21no—
56C22×C19⋊C8—22no—
57#10597292—42no—
58#10597289—42no—
59#10597260—22no—
60#10597260—22no—
61#10597260—22no—
62C24×C19—21no—
63C2×Q8×C19—24no—
64C2×Q8×C19—21no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—81no—
68C2×Q8×C19—81no—
69C2×Q8×C19C22⋊C412yes—
70C2×D4×C19—21no—
71C2×D4×C19—41no—
72C2×D4×C19—41no—
73C2×D4×C19C22⋊C412yes—
74C22×C4×C19—22no—
75C22×C4×C19—21no—
76C22×C4×C19—22no—
77C22×C4×C19—24no—
78C22×C4×C19—81no—
79C22×C4×C19—81no—
80C22×C4×C19C2×D412yes—
81C22×C4×C19C2×D411yescharacteristic
82C22×Dic19—41no—
83C4⋊C4×C19—28no—
84C4⋊C4×C19—24no—
85C4⋊C4×C19—24no—
86C4⋊C4×C19—24no—
87C4⋊C4×C19—24no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19C22⋊C414yes—
91C4⋊C4×C19C22⋊C414yes—
92C22⋊C4×C19—28no—
93C22⋊C4×C19—24no—
94C22⋊C4×C19—24no—
95C22⋊C4×C19—24no—
96C42×C19—24no—
97C42×C19C22×C411yescharacteristic
98C42×C19C2×D412yes—
99C42×C19C2×D411yescharacteristic
100C4⋊Dic19—41no—
101C4⋊Dic19—41no—
102C4⋊Dic19—44no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8—24no—
105C2×C19⋊C8—42no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—42no—
108C2×C19⋊C8—41no—
109#8507—191nomaximal, Sylow
110C23×C19—22no—
111C23×C19—41no—
112C23×C19—42no—
113C23×C19—41no—
114C23×C19—42no—
115C23×C19#12011yescharacteristic
116Q8×C19—42no—
117Q8×C19—81no—
118Q8×C19—84no—
119D4×C19—42no—
120D4×C19—81no—
121C2×C4×C19—21no—
122C2×C4×C19—22no—
123C2×C4×C19—21no—
124C2×C4×C19—22no—
125C2×C4×C19—24no—
126C2×C4×C19—22no—
127C2×C4×C19—24no—
128C2×C4×C19—42no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—84no—
135C2×C4×C19C2×C22⋊C412yes—
136C2×C4×C19C2×C22⋊C411yescharacteristic
137C2×C4×C19#12012yes—
138C2×C4×C19#12011yescharacteristic
139C2×Dic19—81no—
140C2×Dic19—82no—
141C19⋊C8—42no—
142C19⋊C8—44no—
143C2×#563D1911yescharacteristic
144#1992—192no—
145#1959—191no—
146C2×#330—192no—
147C2×#329—191no—
148C22×C19—42no—
149C22×C19—44no—
150C22×C19—81no—
151C22×C19—81no—
152C22×C19—82no—
153C22×C19#37911yescharacteristic
154C22×C19#45311yescharacteristic
155C22×C19#45412yes—
156C22×C19#45511yescharacteristic
157C22×C19#45612yes—
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—44no—
163C4×C19—42no—
164C4×C19—44no—
165Dic19—161no—
166#563—24no—
167#563—22no—
168#563Dic1914yescomplemented
169C2×C4⋊Q8—21no—
170C2×#126—22no—
171C2×#125C2×D1912yes—
172C2×#124C2×D1911yescharacteristic
173C2×#123—21no—
174C2×C22⋊Q8—22no—
175C2×#103—381no—
176C2×#102—381no—
177C2×#97—191no—
178C2×#97—192no—
179#384—191no—
180#340—382no—
181#340—382no—
182#330—384no—
183#329—382no—
184C2×C19—82no—
185C2×C19#165711yescharacteristic
186C2×C19#166011yescharacteristic
187C2×C19#166412yes—
188C2×C19#179211yescharacteristic
189C2×C19#179312yes—
190C22×Q8—21no—
191C22×Q8C22⋊D1911yescharacteristic
192C22×D4C22⋊D1911yescharacteristic
193C23×C4—21no—
194C22×C8—382no—
195C22×C8—381no—
196C4⋊Q8—24no—
197C4⋊Q8—24no—
198#126—28no—
199#126—28no—
200#125—22no—
201#125—22no—
202#125C2×Dic1914yes—
203#125C22⋊D1914yes—
204#124—22no—
205#124C2×Dic1912yes—
206#124C22⋊D1912yes—
207#123—24no—
208#123—24no—
209C22⋊Q8—28no—
210C22⋊Q8—28no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—382no—
215C2×C4⋊C4—381no—
216C2×C4⋊C4C22⋊D1912yes—
217C2×C4⋊C4C22⋊D1912yes—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—22no—
221C2×C42—21no—
222C2×C42C22×D1911yescharacteristic
223#103—762no—
224#102—762no—
225#97—382no—
226#97—382no—
227#97—382no—
228C19#850711yescharacteristic, complemented, Sylow
229C24—21no—
230C2×Q8—24no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—81no—
235C2×Q8—81no—
236C2×Q8C22⋊Dic1912yes—
237C2×D4—21no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4C22⋊Dic1912yes—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—24no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—761no—
248C22×C4C2×C22⋊D1912yes—
249C22×C4C2×C22⋊D1911yescharacteristic
250C2×C8—382no—
251C2×C8—384no—
252C2×C8—762no—
253C2×C8—761no—
254C2×C8—762no—
255C2×C8—761no—
256C4⋊C4—28no—
257C4⋊C4—24no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—764no—
266C4⋊C4C22⋊Dic1914yes—
267C4⋊C4C22⋊Dic1914yes—
268C22⋊C4—28no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C42—24no—
273C42C22×Dic1911yescharacteristic
274C42C2×C22⋊D1912yes—
275C42C2×C22⋊D1911yescharacteristic
276C23—22no—
277C23—41no—
278C23—42no—
279C23—41no—
280C23—42no—
281C23#1059739911yescharacteristic
282Q8—42no—
283Q8—81no—
284Q8—84no—
285D4—42no—
286D4—81no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—84no—
301C2×C4—1521no—
302C2×C4—1522no—
303C2×C4C2×C22⋊Dic1912yes—
304C2×C4C2×C22⋊Dic1911yescharacteristic
305C2×C4#1059739912yes—
306C2×C4#1059739911yescharacteristic
307C8—762no—
308C8—764no—
309C22—42no—
310C22—44no—
311C22—81no—
312C22—81no—
313C22—82no—
314C22#1192640011yescharacteristic
315C22#1192671211yescharacteristic
316C22#1192671712yes—
317C22#1192672211yescharacteristic
318C22#1192672712yes—
319C4—21no—
320C4—21no—
321C4—22no—
322C4—22no—
323C4—44no—
324C4—42no—
325C4—44no—
326C4—3041no—
327C2—82no—
328C2#1456293311yescharacteristic
329C2#1456294611yescharacteristic
330C2#1456296912yes—
331C2#1456358911yescharacteristic
332C2#1456359412yes—
subgroupG/H
centerC23#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#563C2
socleC23×C19#120
prime radicalC22×D4×C19D4
cosocleC2×C42×C19C23
hypercenterC2×#563D19
hypocenterC19#8507
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. #14564605C2semidirect
3. C2×#11926286C2semidirect
17. C19×#563C4semidirect
168. #563Dic19semidirect
228. C19#8507semidirect

Maximal subgroups

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

subgroupindex
#145646052
#145644522
C2×#119262862
C2×#119262842
C2×C19×#5632
#850719