Finite Group Databasebeta

← #18080418

Subgroups — #18080418

Order 4864.

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

normal subgroups only

This group has 544 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#14569212C211yesmaximal, characteristic
2#14562083C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561500C212yesmaximal, complemented
5C19×#2873C211yesmaximal, characteristic
6C2×C4×Dic38C2211yescharacteristic
7#11926601C2212yes—
8#11926474C411yescharacteristic
9#11926469C411yescharacteristic
10#11926464C411yescharacteristic
11#11926456C411yescharacteristic
12#11926432—21no—
13#11926428—21no—
14#11926425—21no—
15#11926417—21no—
16#11926412C2211yescharacteristic
17#11926276—24no—
18#11926270—21no—
19#11926268—21no—
20C22×M16×C19—21no—
21C2×C19×#117C2211yescharacteristic
22C19×#405—24no—
23C4×M16×C19—21no—
24C4×M16×C19C2212yes—
25C23×C4×C19D411yescharacteristic
26C22×Dic38C2×C411yescharacteristic
27C2×M16×C19—22no—
28C2×M16×C19—24no—
29C2×M16×C19—24no—
30C2×M16×C19—22no—
31C22×C8×C19—22no—
32C19×#117—22no—
33C19×#117—22no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C42×C19D411yescharacteristic
39C2×C42×C19C2311yescharacteristic
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×Dic19⋊C4—21no—
46C2×C4×Dic19—21no—
47C4×Dic38—22no—
48C4×Dic38—22no—
49C19×#97—22no—
50C19×#97—22no—
51C4×C8×C19—22no—
52C4×C8×C19D414yes—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95C2×C411yescharacteristic
60C19⋊#95C2×C411yescharacteristic
61C22⋊(C19⋊C8)—22no—
62C4⋊(C19⋊C8)—22no—
63#10597260—22no—
64C24×C19C22⋊C411yescharacteristic
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—21no—
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—21no—
79C2×Dic38—22no—
80C2×Dic38—42no—
81M16×C19—28no—
82M16×C19—24no—
83M16×C19—24no—
84C2×C8×C19—28no—
85C2×C8×C19—24no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19C2×D412yes—
93C42×C19#4112yes—
94C22⋊Dic19—42no—
95C22⋊Dic19—42no—
96C4⋊Dic19—22no—
97Dic19⋊C4—42no—
98Dic19⋊C4—42no—
99Dic19⋊C4—41no—
100Dic19⋊C4—41no—
101C4×Dic19—42no—
102C2×C19⋊C8—42no—
103#9491—191nomaximal, Sylow
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—41no—
107C23×C19—41no—
108C23×C19#10412yes—
109C23×C19C2×C22⋊C411yescharacteristic
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—24no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19#10412yes—
124C2×C4×C19C4×D412yes—
125C2×C4×C19#12011yescharacteristic
126C2×C4×C19#12112yes—
127C2×C4×C19#12311yescharacteristic
128C2×Dic19—22no—
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—41no—
139C2×Dic19—41no—
140Dic38—24no—
141Dic38—42no—
142C8×C19—28no—
143C19⋊C8—82no—
144#2873D1911yescharacteristic
145#2599—191no—
146#1491—192no—
147#1464—191no—
148#1288—192no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—22no—
152C22×C19—42no—
153C22×C19—41no—
154C22×C19—41no—
155C22×C19—81no—
156C22×C19#38611yescharacteristic
157C22×C19C2×#10411yescharacteristic
158C22×C19C2×#10411yescharacteristic
159C4×C19—22no—
160C4×C19—21no—
161C4×C19—22no—
162C4×C19—21no—
163C4×C19—22no—
164C4×C19—41no—
165C4×C19—41no—
166Dic19—42no—
167Dic19—81no—
168Dic19—81no—
169Dic19—81no—
170C22×M16—21no—
171C2×C4×Q8—191no—
172C2×#117C2×D1911yescharacteristic
173#432—192no—
174#405—24no—
175C4×M16—21no—
176C4×M16C2×D1912yes—
177#398—191no—
178#397—191no—
179#395—191no—
180#393—191no—
181#388—381no—
182#387—381no—
183#387—381no—
184#385—381no—
185#383—191no—
186Q8⋊C8—384no—
187#324—381no—
188#323—381no—
189C2×C19—21no—
190C2×C19—21no—
191C2×C19—42no—
192C2×C19#189111yescharacteristic
193C2×C19#189611yescharacteristic
194C2×C19#190911yescharacteristic
195C22×Q8—191no—
196C23×C4C22⋊D1911yescharacteristic
197C2×M16—24no—
198C2×M16—24no—
199C2×M16—22no—
200C2×M16—22no—
201C22×C8—22no—
202C4×Q8—382no—
203C4×Q8—382no—
204#117—22no—
205#117—22no—
206C2×C4⋊C4—191no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4C4×D1911yescharacteristic
211C2×C4⋊C4D7611yescharacteristic
212C2×C22⋊C4—381no—
213C2×C22⋊C4—381no—
214C2×C22⋊C4C4×D1911yescharacteristic
215C2×C22⋊C4D7611yescharacteristic
216C2×C42—381no—
217C2×C42C22⋊D1911yescharacteristic
218C2×C42C22×D1911yescharacteristic
219C4⋊C8—382no—
220C22⋊C8—382no—
221#97—22no—
222#97—22no—
223#97—382no—
224C4×C8—22no—
225C4×C8C22⋊D1914yes—
226#95—191no—
227#95—191no—
228#95—381no—
229#95—381no—
230#95—381no—
231#95—381no—
232#95—381no—
233#95—381no—
234C19#949111yescharacteristic, complemented, Sylow
235C24(C2×D19)⋊C411yescharacteristic
236C2×Q8—382no—
237C2×Q8—762no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—381no—
243C22×C4—381no—
244C22×C4—381no—
245C22×C4—381no—
246C22×C4(C2×D19)⋊C411yescharacteristic
247C22×C4(C2×D19)⋊C411yescharacteristic
248C22×C4(C2×D19)⋊C411yescharacteristic
249C22×C4C2×C4×D1911yescharacteristic
250C22×C4C2×D7611yescharacteristic
251C22×C4C2×C22⋊D1911yescharacteristic
252M16—28no—
253M16—24no—
254M16—24no—
255C2×C8—28no—
256C2×C8—24no—
257C2×C8—762no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—382no—
261C4⋊C4—762no—
262C4⋊C4—761no—
263C4⋊C4—762no—
264C4⋊C4—761no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—762no—
268C22⋊C4—762no—
269C42—21no—
270C42—21no—
271C42—762no—
272C42#6454112yes—
273C42C2×C22⋊D1912yes—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#1059726212yes—
279C23C2×(C2×D19)⋊C411yescharacteristic
280Q8—384no—
281Q8—762no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—382no—
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—761no—
307C2×C4#1059726212yes—
308C2×C4C4×C22⋊D1912yes—
309C2×C4#1059737511yescharacteristic
310C2×C4#1059737612yes—
311C2×C4#1059739911yescharacteristic
312C8—28no—
313C8—1522no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1192642311yescharacteristic
322C22C2×#1059726211yescharacteristic
323C22C2×#1059726211yescharacteristic
324C4—22no—
325C4—22no—
326C4—21no—
327C4—22no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—762no—
332C4—1521no—
333C4—1521no—
334C4—1521no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1456405311yescharacteristic
339C2#1456407811yescharacteristic
340C2#1456415711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2873C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2873D19
hypocenterC19#9491
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. #14562083C2semidirect
4. #14561500C2semidirect
234. C19#9491semidirect

Maximal subgroups

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

subgroupindex
#145692122
#145620832
#145619692
#145615002
C19×#28732
#949119