Finite Group Databasebeta

← #18079258

Subgroups — #18079258

Order 4864.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#14574788C211yesmaximal, characteristic
2#14566383C211yesmaximal, characteristic
3#14564616C211yesmaximal, characteristic
4#14562319C211yesmaximal, characteristic
5#14562200C211yesmaximal, characteristic
6#14561494C211yesmaximal, characteristic
7C19×#1274C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10#11926949C412yescomplemented
11#11926895C412yescomplemented
12#11926880—22no—
13#11926840—22no—
14#11926568C2211yescharacteristic
15#11926448—22no—
16#11926442—21no—
17#11926427—22no—
18#11926410C2211yescharacteristic
19C4×C4⋊Dic19—21no—
20#11926304—21no—
21#11926304—21no—
22#11926291—22no—
23#11926282—22no—
24C19×#431C2211yescharacteristic
25C19×#431C2211yescharacteristic
26C19×#376C2211yescharacteristic
27C22×Dic38—21no—
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19C2311yescharacteristic
31#10597372—21no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19D412yes—
35#10597370—21no—
36#10597370—21no—
37C2×Dic19⋊C4—22no—
38C2×C4×Dic19—22no—
39C2×#64520—21no—
40#10597316—21no—
41#10597315—21no—
42#10597315—21no—
43#10597315C2×C411yescharacteristic
44#10597315C2×C411yescharacteristic
45#10597315C2×C412yes—
46#10597315D412yes—
47C4×Dic38—21no—
48C4×Dic38—21no—
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51C19×C22⋊C8—21no—
52C19×C22⋊C8—21no—
53C4×C8×C19—21no—
54C4×C8×C19C2×C412yes—
55C19×#95—21no—
56C19×#95—21no—
57C19⋊#95—22no—
58C19⋊#95—22no—
59C19⋊#95—21no—
60C19⋊#95D412yes—
61#10597275—24no—
62#10597273—24no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×Dic19—22no—
71C22×Dic19—22no—
72C2×Dic38—21no—
73C2×Dic38—22no—
74C2×Dic38—22no—
75C2×Dic38—21no—
76C2×Dic38—82no—
77C2×C8×C19—22no—
78C2×C8×C19—41no—
79C42×C19—21no—
80C42×C19—21no—
81C42×C19—21no—
82C42×C19Q1612yes—
83C42×C19C22×C411yescharacteristic
84C42×C19C2×D411yescharacteristic
85C42×C19#4111yescharacteristic
86C42×C19#4111yescharacteristic
87C22⋊Dic19—41no—
88C4⋊Dic19—22no—
89C4⋊Dic19—22no—
90C4⋊Dic19—22no—
91C4⋊Dic19—21no—
92C4⋊Dic19—21no—
93C4⋊Dic19—21no—
94C4⋊Dic19—21no—
95C4⋊Dic19—41no—
96C4⋊Dic19—41no—
97C4⋊Dic19C22⋊C414yes—
98Dic19⋊C4—41no—
99Dic19⋊C4—41no—
100Dic19⋊C4—82no—
101C4×Dic19—41no—
102C4×Dic19—82no—
103#64520—41no—
104#64520—41no—
105C2×C19⋊C8—41no—
106#9298—191nomaximal, Sylow
107C23×C19#12011yescharacteristic
108C2×C4×C19—22no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19C2×C22⋊C411yescharacteristic
117C2×C4×C19C4×D411yescharacteristic
118C2×C4×C19C4×D411yescharacteristic
119C2×C4×C19#12111yescharacteristic
120C2×C4×C19#12111yescharacteristic
121C2×C4×C19#12311yescharacteristic
122C2×C4×C19C2×Q1611yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19#13711yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×Dic19—24no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—42no—
134Dic38—42no—
135Dic38—82no—
136Dic38—82no—
137Dic38—81no—
138C8×C19—42no—
139C8×C19—81no—
140C19⋊C8—81no—
141#3230—191no—
142#2331—191no—
143#1995—191no—
144#1549—191no—
145#1518—191no—
146#1286—191no—
147#1274D1911yescharacteristic
148C22×C19—21no—
149C22×C19—21no—
150C22×C19#38611yescharacteristic
151C22×C19#45111yescharacteristic
152C22×C19#45211yescharacteristic
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—42no—
158C4×C19—81no—
159C4×C19C4×Q1611yescharacteristic
160C4×C19#44111yescharacteristic
161C4×C19#46211yescharacteristic
162C4×C19#46411yescharacteristic
163Dic19—44no—
164Dic19—82no—
165Dic19—81no—
166Dic19—81no—
167#533—191no—
168C2×C4⋊Q8—191no—
169#500—192no—
170#487—192no—
171#484—382no—
172#477—382no—
173#431C2×D1911yescharacteristic
174#431C2×D1911yescharacteristic
175#423—191no—
176#391—382no—
177#389—381no—
178#387—382no—
179#382—191no—
180C4×C4⋊C4—381no—
181#376C2×D1911yescharacteristic
182#339—381no—
183#339—381no—
184#332—382no—
185#328—382no—
186C2×C19—21no—
187C2×C19—21no—
188C2×C19#187811yescharacteristic
189C2×C19#190411yescharacteristic
190C2×C19#191211yescharacteristic
191C22×Q8—381no—
192C2×M16—381no—
193C4⋊Q8—192no—
194C4⋊Q8—191no—
195C4⋊Q8—191no—
196C4⋊Q8—192no—
197C4⋊Q8—381no—
198C4⋊Q8—381no—
199#125—381no—
200C22⋊Q8—381no—
201C22⋊Q8—381no—
202C4×Q8—381no—
203C4×Q8—381no—
204#117—381no—
205C2×C4⋊C4—192no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—382no—
209C2×C42—382no—
210C2×C42D7611yescharacteristic
211C2×C42D7611yescharacteristic
212C2×C42C22×D1911yescharacteristic
213#107—384no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—381no—
217C4⋊C8—381no—
218#103—384no—
219C22⋊C8—21no—
220C22⋊C8—21no—
221C4×C8—21no—
222C4×C8C4×D1912yes—
223#95—21no—
224#95—21no—
225#95—192no—
226#95—382no—
227#95—382no—
228#95—381no—
229C19#929811yescharacteristic, complemented, Sylow
230C2×Q8—382no—
231C2×Q8—382no—
232C2×Q8—381no—
233C2×Q8—381no—
234C2×Q8—1522no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—382no—
238C22×C4—382no—
239C22×C4C2×D7611yescharacteristic
240C22×C4D4×D1911yescharacteristic
241C22×C4D4×D1911yescharacteristic
242M16—761no—
243M16—761no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—761no—
247C4⋊C4—194no—
248C4⋊C4—382no—
249C4⋊C4—382no—
250C4⋊C4—382no—
251C4⋊C4—381no—
252C4⋊C4—381no—
253C4⋊C4—381no—
254C4⋊C4—381no—
255C4⋊C4—761no—
256C4⋊C4—761no—
257C4⋊C4—761no—
258C4⋊C4—761no—
259C4⋊C4—1522no—
260C22⋊C4—761no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—761no—
265C42—1522no—
266C42Dic7612yes—
267C42C2×C4×D1911yescharacteristic
268C42#6454111yescharacteristic
269C42D4×D1911yescharacteristic
270C42#6454511yescharacteristic
271C23#1059732811yescharacteristic
272Q8—762no—
273Q8—1522no—
274Q8—1522no—
275Q8—1521no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—384no—
285C2×C4—762no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4—761no—
290C2×C4—761no—
291C2×C4—762no—
292C2×C4C4×D7611yescharacteristic
293C2×C4C22⋊C4×D1911yescharacteristic
294C2×C4#1059733011yescharacteristic
295C2×C4#1059733911yescharacteristic
296C2×C4#1059734011yescharacteristic
297C2×C4#1059734111yescharacteristic
298C2×C4#1059735011yescharacteristic
299C2×C4C2×Dic7611yescharacteristic
300C2×C4#1059735511yescharacteristic
301C2×C4#1059735511yescharacteristic
302C8—42no—
303C8—81no—
304C8—1521no—
305C22—21no—
306C22—21no—
307C22#1192642211yescharacteristic
308C22#1192670211yescharacteristic
309C22#1192670811yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—81no—
316C4—764no—
317C4—1522no—
318C4—1521no—
319C4—1521no—
320C4C4×Dic7611yescharacteristic
321C4#1192665211yescharacteristic
322C4#1192675511yescharacteristic
323C4#1192676711yescharacteristic
324C2—21no—
325C2—21no—
326C2#1456397511yescharacteristic
327C2#1456412311yescharacteristic
328C2#1456417111yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1274C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#1274D19
hypocenterC19#9298
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
10. #11926949C4semidirect
11. #11926895C4semidirect
229. C19#9298semidirect

Maximal subgroups

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

subgroupindex
#145747882
#145663832
#145646162
#145623192
#145622002
#145614942
C19×#12742
#929819