Finite Group Databasebeta

← #18074318

Subgroups — #18074318

Order 4864.

782 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#11927254C211yesmaximal, characteristic
2#14562321C212yesmaximal, complemented
3#14562059C212yesmaximal
4#14561959C211yesmaximal, characteristic, complemented
5C19×#1801C211yesmaximal, characteristic, complemented
6#11927254—24no—
7#11927254—24no—
8C2×#10597315C2211yescharacteristic
9C2×#10597316C412yes—
10C2×#10597342—22no—
11C2×#10597392—21no—
12C2×C4×D76C412yes—
13C2×C4×D76C2211yescharacteristic
14C2×C4⋊C4×D19—21no—
15#11926597C2212yes—
16#11926289—24no—
17#11926271—24no—
18#11926270—22no—
19C2×C4×Q8×C19C2211yescharacteristic
20C19×#423C2212yes—
21C2×C19×#101—21no—
22C19×#343—21no—
23C22×Q8×C19D411yescharacteristic
24C22×D76C2×C411yescharacteristic
25C22×C4×D19—21no—
26C22×C4×D19—22no—
27C22×Dic38—21no—
28C2×M16×C19—22no—
29C4×Q8×C19—22no—
30C4×Q8×C19—22no—
31C2×C4⋊C4×C19D412yes—
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C42×C19C2×C412yes—
34C2×C42×C19C2311yescharacteristic
35#10597392—28no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C412yes—
41C2×Dic19⋊C4—22no—
42C2×Dic19⋊C4—22no—
43#10597342—216no—
44C4⋊C4×D19—28no—
45C4×D76—24no—
46C4×D76—22no—
47C4×D76—24no—
48C4×D76D414yes—
49#10597316—24no—
50#10597316—24no—
51#10597315—22no—
52#10597315D414yes—
53C19×C4⋊C8—22no—
54C19×C4⋊C8—22no—
55C19×#101—42no—
56C22⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58C4×C19⋊C8—22no—
59C23×D19—21no—
60C2×Q8×C19—22no—
61C2×Q8×C19—22no—
62C2×Q8×C19—21no—
63C2×Q8×C19—21no—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19C22⋊C412yes—
66C22×C4×C19C22×C411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×Dic19—22no—
70C22×Dic19—21no—
71C2×D76—21no—
72C2×D76—24no—
73C2×D76C22⋊C412yes—
74C2×C4×D19—24no—
75C2×C4×D19—28no—
76C2×C4×D19—42no—
77C2×C4×D19—41no—
78C2×C4×D19—41no—
79C2×C4×D19—84no—
80C2×Dic38—24no—
81C2×Dic38—82no—
82M16×C19—42no—
83M16×C19—42no—
84C2×C8×C19—42no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—24no—
87C42×C19—22no—
88C42×C19—22no—
89C42×C19C2×D412yes—
90C42×C19C2×D412yes—
91(C2×D19)⋊C4—28no—
92(C2×D19)⋊C4—24no—
93C4⋊Dic19—22no—
94C4⋊Dic19—21no—
95C4⋊Dic19—24no—
96C4⋊Dic19C22⋊C414yes—
97C4⋊Dic19C22⋊C412yes—
98Dic19⋊C4—28no—
99Dic19⋊C4—28no—
100C2×C19⋊C8—42no—
101#8398—191nomaximal, Sylow
102C23×C19C2×C22⋊C411yescharacteristic
103C22×D19—24no—
104C22×D19—22no—
105C22×D19—42no—
106C22×D19—41no—
107C22×D19—41no—
108Q8×C19—42no—
109Q8×C19—42no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19C2×C22⋊C411yescharacteristic
118C2×C4×C19C2×C22⋊C411yescharacteristic
119C2×C4×C19#12012yes—
120C2×C4×C19#12012yes—
121C2×C4×C19#13512yes—
122C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×Dic19—22no—
125C2×Dic19—24no—
126C2×Dic19—44no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129D76—24no—
130D76—22no—
131D76#10114yescomplemented
132C4×D19—44no—
133C4×D19—44no—
134C4×D19—88no—
135Dic38—84no—
136C8×C19—82no—
137C19⋊C8—82no—
138C2×#554—191no—
139#1801D1911yescharacteristic, complemented
140#1549—192no—
141#1486—192no—
142#1461—191no—
143C22×C19—21no—
144C22×C19—21no—
145C22×C19#37911yescharacteristic
146C22×C19#41611yescharacteristic
147C22×C19#41711yescharacteristic
148C2×D19—24no—
149C2×D19—44no—
150C2×D19—44no—
151C2×D19—42no—
152C2×D19—42no—
153C4×C19—22no—
154C4×C19—21no—
155C4×C19—42no—
156C4×C19—42no—
157C4×C19C2×#10112yes—
158C4×C19#44912yes—
159C4×C19#45212yes—
160Dic19—44no—
161Dic19—42no—
162#554—384no—
163#554—384no—
164C2×C4⋊Q8—191no—
165C2×#125—192no—
166C2×C22⋊Q8—381no—
167C2×C22⋊Q8—382no—
168C2×C4×Q8C2×D1911yescharacteristic
169C2×C4×D4—192no—
170C2×C4×D4—191no—
171C22×C4⋊C4—381no—
172#431—192no—
173#423C2×D1912yes—
174C2×#101—21no—
175#343—21no—
176#332—384no—
177D4⋊C8—384no—
178#324—382no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19#178411yescharacteristic
182C2×C19#178811yescharacteristic
183C2×C19#179511yescharacteristic
184D19—44no—
185C22×Q8—381no—
186C22×Q8C22⋊D1911yescharacteristic
187C22×D4—191no—
188C23×C4—381no—
189C23×C4—382no—
190C2×M16—22no—
191C4⋊Q8—194no—
192C4⋊Q8—382no—
193#125—384no—
194#125—384no—
195C22⋊Q8—3816no—
196C22⋊Q8—388no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×D4—194no—
200C4×D4—384no—
201C4×D4—384no—
202C4×D4—382no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—192no—
205C2×C4⋊C4—388no—
206C2×C4⋊C4—382no—
207C2×C4⋊C4—382no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4D7612yes—
210C2×C4⋊C4C22⋊D1911yescharacteristic
211C2×C22⋊C4—382no—
212C2×C22⋊C4—381no—
213C2×C42C4×D1912yes—
214C2×C42C22×D1911yescharacteristic
215C4⋊C8—22no—
216C4⋊C8—22no—
217C4⋊C8—382no—
218#101—42no—
219C22⋊C8—382no—
220C4×C8—382no—
221C19#839811yescharacteristic, complemented, Sylow
222C24—381no—
223C2×Q8—21no—
224C2×Q8—22no—
225C2×Q8—21no—
226C2×Q8—22no—
227C2×Q8—384no—
228C2×Q8—1522no—
229C2×D4—192no—
230C2×D4—384no—
231C2×D4—381no—
232C22×C4—388no—
233C22×C4—381no—
234C22×C4—382no—
235C22×C4—384no—
236C22×C4—761no—
237C22×C4—761no—
238C22×C4—762no—
239C22×C4—1524no—
240C22×C4(C2×D19)⋊C412yes—
241C22×C4(C2×D19)⋊C412yes—
242C22×C4C2×C4×D1911yescharacteristic
243C22×C4C2×D7611yescharacteristic
244C22×C4C2×C22⋊D1911yescharacteristic
245M16—42no—
246M16—42no—
247C2×C8—42no—
248C2×C8—762no—
249C4⋊C4—22no—
250C4⋊C4—24no—
251C4⋊C4—192no—
252C4⋊C4—194no—
253C4⋊C4—388no—
254C4⋊C4—388no—
255C4⋊C4—384no—
256C4⋊C4—381no—
257C4⋊C4—382no—
258C22⋊C4—388no—
259C22⋊C4—384no—
260C42—22no—
261C42—22no—
262C42D4×D1912yes—
263C42D4×D1912yes—
264C23—384no—
265C23—382no—
266C23—762no—
267C23—761no—
268C23—761no—
269C23C2×(C2×D19)⋊C411yescharacteristic
270Q8—42no—
271Q8—42no—
272Q8—1524no—
273D4—194no—
274D4—384no—
275D4—382no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—382no—
284C2×C4—384no—
285C2×C4—764no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—764no—
289C2×C4—764no—
290C2×C4—1528no—
291C2×C4C22⋊C4×D1911yescharacteristic
292C2×C4C22⋊C4×D1911yescharacteristic
293C2×C4#1059732812yes—
294C2×C4#1059737811yescharacteristic
295C2×C4#1059738312yes—
296C2×C4#1059738811yescharacteristic
297C2×C4#1059739612yes—
298C8—82no—
299C8—1522no—
300C22—21no—
301C22—21no—
302C22—384no—
303C22—764no—
304C22—764no—
305C22—762no—
306C22—762no—
307C22#1192639911yescharacteristic
308C22#1192653811yescharacteristic
309C22#1192654311yescharacteristic
310C4—22no—
311C4—21no—
312C4—42no—
313C4—42no—
314C4—764no—
315C4—762no—
316C4#101×D1912yes—
317C4#1192668712yes—
318C4#1192670412yes—
319C2—21no—
320C2—21no—
321C2—764no—
322C2#1456355711yescharacteristic
323C2#1456357311yescharacteristic
324C2#1456360611yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1801C2
socleC22×C19#379
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1801D19
hypocenterC19#8398
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #14562321C2semidirect
4. #14561959C2semidirect
5. C19×#1801C2semidirect
131. D76#101semidirect
139. #1801D19semidirect
221. C19#8398semidirect

Maximal subgroups

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

subgroupindex
C2×#119272542
#145623212
#145620592
#145619592
C19×#18012
#839819