Finite Group Databasebeta

← #18080183

Subgroups — #18080183

Order 4864.

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

normal subgroups only

This group has 474 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#14568084C211yesmaximal, characteristic
2#14563712C211yesmaximal, characteristic
3#14562169C212yesmaximal
4#14561489C212yesmaximal
5C19×#2921C211yesmaximal, characteristic
6C2×#10597370C2211yescharacteristic
7#11926472—21no—
8#11926472—21no—
9#11926449C411yescharacteristic, complemented
10#11926449C411yescharacteristic, complemented
11#11926428—21no—
12#11926428—21no—
13#11926413C411yescharacteristic, complemented
14#11926409C411yescharacteristic, complemented
15#11926407C2212yes—
16C4×C22⋊Dic19C2211yescharacteristic
17#11926311—21no—
18#11926311—21no—
19#11926282—24no—
20C2×C19×#117C2211yescharacteristic
21C19×#433—24no—
22C19×#423—21no—
23C19×#407C2212yes—
24C4×M16×C19—21no—
25C23×C4×C19C2311yescharacteristic
26C22×Dic38C2×C411yescharacteristic
27C2×M16×C19—22no—
28C19×#117—22no—
29C19×#117—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19D411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C42×C19D411yescharacteristic
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—22no—
39C2×C4⋊Dic19C2×C411yescharacteristic
40#10597370—22no—
41#10597370—22no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×C4×Dic19C2×C411yescharacteristic
46C2×C4×Dic19C2×C411yescharacteristic
47C19×C4⋊C8—24no—
48C19×C22⋊C8—22no—
49C19×C22⋊C8D414yes—
50C19×#97—22no—
51C4×C8×C19—22no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—22no—
60C19⋊#95—22no—
61C24×C19C2×D411yescharacteristic
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D412yes—
71C22×C4×C19#4112yes—
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—42no—
77C2×Dic38—22no—
78C2×Dic38—41no—
79C2×Dic38—41no—
80M16×C19—42no—
81M16×C19—42no—
82C2×C8×C19—24no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C22⋊C4×C19—22no—
86C22⋊C4×C19—22no—
87C42×C19—21no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C22⋊Dic19—42no—
92C22⋊Dic19—42no—
93C22⋊Dic19—42no—
94C22⋊Dic19—42no—
95C4⋊Dic19—22no—
96Dic19⋊C4—42no—
97Dic19⋊C4—42no—
98Dic19⋊C4—41no—
99Dic19⋊C4—41no—
100C4×Dic19—41no—
101C4×Dic19—41no—
102#9444—191nomaximal, Sylow
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19C2×C22⋊C411yescharacteristic
108C23×C19#12112yes—
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—21no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19C4×D412yes—
124C2×C4×C19#12011yescharacteristic
125C2×C4×C19#12311yescharacteristic
126C2×Dic19—22no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—82no—
139C2×Dic19—82no—
140C2×Dic19—82no—
141Dic38—82no—
142C8×C19—44no—
143#2921D1911yescharacteristic
144#2499—191no—
145#1820—191no—
146#1511—192no—
147#1284—192no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—22no—
151C22×C19—22no—
152C22×C19—22no—
153C22×C19—81no—
154C22×C19—81no—
155C22×C19#38611yescharacteristic
156C22×C19#41011yescharacteristic
157C22×C19#41011yescharacteristic
158C4×C19—21no—
159C4×C19—22no—
160C4×C19—21no—
161C4×C19—41no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19—41no—
165Dic19—42no—
166Dic19—81no—
167Dic19—81no—
168Dic19—81no—
169Dic19—162no—
170C2×C22⋊Q8—191no—
171C2×#117C2×D1911yescharacteristic
172#433—24no—
173#423—21no—
174#407C2×D1912yes—
175C4×M16—21no—
176#397—381no—
177#397—381no—
178#391—191no—
179#391—191no—
180#387—381no—
181#387—381no—
182#384—191no—
183#382—191no—
184#381—192no—
185C4×C22⋊C4—191no—
186#342—381no—
187#342—381no—
188#328—384no—
189C2×C19—21no—
190C2×C19—21no—
191C2×C19—42no—
192C2×C19#188411yescharacteristic
193C2×C19#189911yescharacteristic
194C2×C19#190911yescharacteristic
195C22×Q8—191no—
196C23×C4C22×D1911yescharacteristic
197C2×M16—22no—
198C22⋊Q8—382no—
199C22⋊Q8—382no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—191no—
203C2×C4⋊C4—381no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4C4×D1911yescharacteristic
207C2×C4⋊C4C4×D1911yescharacteristic
208C2×C22⋊C4—381no—
209C2×C22⋊C4—381no—
210C2×C22⋊C4—382no—
211C2×C22⋊C4D7611yescharacteristic
212C2×C22⋊C4D7611yescharacteristic
213C2×C42—191no—
214C2×C42—191no—
215C2×C42C22⋊D1911yescharacteristic
216C2×C42C22⋊D1911yescharacteristic
217C4⋊C8—24no—
218C22⋊C8—22no—
219C22⋊C8C22⋊D1914yes—
220#97—22no—
221C4×C8—22no—
222#95—381no—
223#95—381no—
224#95—381no—
225#95—381no—
226#95—381no—
227#95—381no—
228#95—381no—
229#95—382no—
230#95—382no—
231C19#944411yescharacteristic, complemented, Sylow
232C24C2×D7611yescharacteristic
233C2×Q8—382no—
234C2×Q8—761no—
235C2×Q8—761no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—381no—
239C22×C4—381no—
240C22×C4—381no—
241C22×C4—381no—
242C22×C4—762no—
243C22×C4(C2×D19)⋊C411yescharacteristic
244C22×C4(C2×D19)⋊C411yescharacteristic
245C22×C4(C2×D19)⋊C411yescharacteristic
246C22×C4(C2×D19)⋊C411yescharacteristic
247C22×C4C2×C4×D1911yescharacteristic
248C22×C4#6454112yes—
249C22×C4C2×C22⋊D1911yescharacteristic
250C22×C4C2×C22⋊D1912yes—
251M16—42no—
252M16—42no—
253C2×C8—24no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—382no—
257C4⋊C4—762no—
258C4⋊C4—762no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—762no—
264C22⋊C4—762no—
265C22⋊C4—762no—
266C22⋊C4—762no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—761no—
272C42—761no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23C2×(C2×D19)⋊C411yescharacteristic
278C23#1059737612yes—
279Q8—1522no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—382no—
295C2×C4—761no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—1522no—
307C2×C4—1522no—
308C2×C4—1522no—
309C2×C4C4×C22⋊D1912yes—
310C2×C4#1059737511yescharacteristic
311C2×C4#1059739911yescharacteristic
312C8—44no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22#1192642311yescharacteristic
321C22#1192651711yescharacteristic
322C22#1192651711yescharacteristic
323C4—21no—
324C4—22no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3042no—
331C4—762no—
332C4—1521no—
333C4—1521no—
334C4—1521no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1456401811yescharacteristic
339C2#1456409311yescharacteristic
340C2#1456415711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2921C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2921D19
hypocenterC19#9444
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2921

Complements

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

NH ≅ G/Ntype
9. #11926449C4semidirect
10. #11926449C4semidirect
13. #11926413C4semidirect
14. #11926409C4semidirect
231. C19#9444semidirect

Maximal subgroups

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

subgroupindex
#145680842
#145637122
#145621692
#145614892
C19×#29212
#944419