Finite Group Databasebeta

← #18078560

Subgroups — #18078560

Order 4864.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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#14572199C211yesmaximal, characteristic
2#14569401C211yesmaximal, characteristic
3#14562306C212yesmaximal, complemented
4#14561494C212yesmaximal, complemented
5C19×#1458C211yesmaximal, characteristic
6C22×#64520—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597370—21no—
9#11926571—24no—
10#11926568—21no—
11#11926568C2212yes—
12#11926474—21no—
13#11926474C412yes—
14#11926469—21no—
15#11926469C412yes—
16#11926450—21no—
17#11926410C2211yescharacteristic
18#11926289—24no—
19C2×C19×#117C2211yescharacteristic
20C19×#431C2212yes—
21C19×#324—21no—
22C19×#323—21no—
23C23×C4×C19D411yescharacteristic
24C22×Dic38—21no—
25C19×#117—22no—
26C19×#117—22no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C22⋊C4×C19C2×C411yescharacteristic
30C2×C22⋊C4×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×C22⋊Dic19—22no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19C2×C412yes—
37#10597370—42no—
38#10597370—42no—
39C2×Dic19⋊C4—22no—
40C2×#64520—22no—
41C2×#64520—22no—
42C2×#64520—42no—
43C2×#64520—42no—
44C22×C19⋊C8—22no—
45#10597315—22no—
46#10597315—22no—
47C19×C4⋊C8—22no—
48C19×C22⋊C8—22no—
49C4×C8×C19—22no—
50C19⋊#95—22no—
51C19⋊#95—22no—
52C19⋊#95—21no—
53C19⋊#95C2×C412yes—
54C4⋊(C19⋊C8)—24no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)D414yes—
57C24×C19C22⋊C411yescharacteristic
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19D812yes—
66C22×C4×C19SD1612yes—
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×Dic19—22no—
71C22×Dic19—22no—
72C2×Dic38—41no—
73C2×Dic38—41no—
74C2×Dic38—41no—
75C2×Dic38—41no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C2×C8×C19—42no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—22no—
81C22⋊C4×C19—22no—
82C22⋊C4×C19—22no—
83C42×C19—21no—
84C42×C19—21no—
85C42×C19C2×D412yes—
86C42×C19#4112yes—
87C22⋊Dic19—44no—
88C4⋊Dic19—24no—
89C4⋊Dic19—42no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92Dic19⋊C4—44no—
93#64520—44no—
94#64520—42no—
95#64520—42no—
96C2×C19⋊C8—24no—
97C2×C19⋊C8—44no—
98#9195—191nomaximal, Sylow
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19#10212yes—
104C23×C19C2×C22⋊C411yescharacteristic
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19#10212yes—
118C2×C4×C19C4×D412yes—
119C2×C4×C19#12011yescharacteristic
120C2×C4×C19#12112yes—
121C2×C4×C19#12311yescharacteristic
122C2×C4×C19C2×D811yescharacteristic
123C2×C4×C19C2×SD1611yescharacteristic
124C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—42no—
132Dic38—81no—
133Dic38—81no—
134Dic38—81no—
135Dic38—81no—
136C8×C19—82no—
137C19⋊C8—44no—
138#2905—191no—
139#2621—191no—
140#1546—192no—
141#1458D1911yescharacteristic
142#1286—192no—
143C22×C19—21no—
144C22×C19—21no—
145C22×C19—22no—
146C22×C19—42no—
147C22×C19—41no—
148C22×C19—41no—
149C22×C19—81no—
150C22×C19#38611yescharacteristic
151C22×C19C2×#10211yescharacteristic
152C22×C19#41711yescharacteristic
153C4×C19—22no—
154C4×C19—22no—
155C4×C19—22no—
156C4×C19—41no—
157C4×C19—41no—
158C4×C19#44711yescharacteristic
159C4×C19#44811yescharacteristic
160C4×C19#48011yescharacteristic
161C4×C19#48111yescharacteristic
162Dic19—82no—
163Dic19—82no—
164C22×M16—381no—
165C2×C4⋊Q8—191no—
166C2×C22⋊Q8—381no—
167C2×#117C2×D1911yescharacteristic
168#431C2×D1912yes—
169#424—384no—
170#423—192no—
171#423—381no—
172#398—192no—
173#398—381no—
174#397—192no—
175#397—381no—
176#391—381no—
177#382—191no—
178#332—384no—
179#324—21no—
180#323—21no—
181C2×C19—21no—
182C2×C19—21no—
183C2×C19—42no—
184C2×C19#187411yescharacteristic
185C2×C19#190911yescharacteristic
186C2×C19#191511yescharacteristic
187C22×Q8—381no—
188C23×C4D7611yescharacteristic
189C2×M16—382no—
190C2×M16—382no—
191C2×M16—762no—
192C2×M16—762no—
193C22×C8—382no—
194C4⋊Q8—382no—
195C4⋊Q8—382no—
196C22⋊Q8—762no—
197C22⋊Q8—762no—
198#117—22no—
199#117—22no—
200C2×C4⋊C4—192no—
201C2×C4⋊C4—382no—
202C2×C4⋊C4—381no—
203C2×C4⋊C4—381no—
204C2×C4⋊C4C4×D1911yescharacteristic
205C2×C4⋊C4C22⋊D1911yescharacteristic
206C2×C22⋊C4—382no—
207C2×C22⋊C4C4×D1911yescharacteristic
208C2×C22⋊C4C22⋊D1911yescharacteristic
209C2×C42D7611yescharacteristic
210C2×C42C22×D1911yescharacteristic
211C4⋊C8—22no—
212C4⋊C8—194no—
213C4⋊C8—384no—
214C4⋊C8—382no—
215C22⋊C8—22no—
216C4×C8—22no—
217#95—192no—
218#95—382no—
219#95—382no—
220#95—381no—
221C19#919511yescharacteristic, complemented, Sylow
222C24(C2×D19)⋊C411yescharacteristic
223C2×Q8—761no—
224C2×Q8—761no—
225C2×Q8—761no—
226C2×Q8—761no—
227C2×Q8—761no—
228C2×Q8—761no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—382no—
234C22×C4—382no—
235C22×C4#6451612yes—
236C22×C4D15212yes—
237C22×C4(C2×D19)⋊C411yescharacteristic
238C22×C4(C2×D19)⋊C411yescharacteristic
239C22×C4(C2×D19)⋊C411yescharacteristic
240C22×C4C2×C4×D1911yescharacteristic
241C22×C4C2×D7611yescharacteristic
242C22×C4C2×C22⋊D1911yescharacteristic
243M16—764no—
244M16—762no—
245M16—762no—
246C2×C8—42no—
247C2×C8—384no—
248C2×C8—764no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—384no—
252C4⋊C4—762no—
253C4⋊C4—764no—
254C4⋊C4—761no—
255C4⋊C4—761no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—764no—
259C42—21no—
260C42—21no—
261C42D4×D1912yes—
262C42#6454312yes—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23#1059727812yes—
268C23C2×(C2×D19)⋊C411yescharacteristic
269Q8—1521no—
270Q8—1521no—
271Q8—1521no—
272Q8—1521no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—762no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4—762no—
290C2×C4—762no—
291C2×C4#1059727812yes—
292C2×C4(C22⋊D19)⋊C412yes—
293C2×C4#1059732811yescharacteristic
294C2×C4#1059733211yescharacteristic
295C2×C4C2×#6451611yescharacteristic
296C2×C4C2×D15211yescharacteristic
297C2×C4#1059735411yescharacteristic
298C2×C4#1059735511yescharacteristic
299C2×C4#1059738512yes—
300C8—82no—
301C8—764no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—81no—
309C22#1192642111yescharacteristic
310C22C2×#1059727811yescharacteristic
311C22#1192654611yescharacteristic
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—1522no—
318C4—1522no—
319C4#1192668011yescharacteristic
320C4#1192668511yescharacteristic
321C4#1192685811yescharacteristic
322C4#1192686311yescharacteristic
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1456395011yescharacteristic
327C2#1456415511yescharacteristic
328C2#1456418511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1458C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1458D19
hypocenterC19#9195
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #14562306C2semidirect
4. #14561494C2semidirect
221. C19#9195semidirect

Maximal subgroups

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

subgroupindex
#145721992
#145694012
#145623062
#145614942
C19×#14582
#919519