Finite Group Databasebeta

← #18080486

Subgroups — #18080486

Order 4864.

684 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 103 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#14572664C211yesmaximal, characteristic
2#14567000C211yesmaximal, characteristic
3#14563558C212yesmaximal, complemented
4#14561542C212yesmaximal, complemented
5C19×#1465C211yesmaximal, characteristic
6C23×Dic38C2211yescharacteristic
7C2×#10597370—21no—
8#11926616—24no—
9#11926601—21no—
10C2×#10597281—24no—
11#11926508C2212yes—
12C2×C22⋊(C19⋊C8)—21no—
13#11926464—21no—
14#11926456—21no—
15#11926450—21no—
16#11926424C412yes—
17#11926416C412yes—
18#11926404C2211yescharacteristic
19C2×C4×D4×C19C2211yescharacteristic
20C19×#407C2212yes—
21C19×#324—21no—
22C19×#323—21no—
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19C2×C412yes—
27C22×Dic38—21no—
28C22×Dic38—22no—
29C22×Dic38—21no—
30C22×Dic38—22no—
31C22×Dic38—44no—
32C2×M16×C19—22no—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C42×C19D411yescharacteristic
39C2×C22⋊Dic19—22no—
40C2×C22⋊Dic19C2×C412yes—
41C2×C4⋊Dic19—21no—
42#10597370—44no—
43C2×Dic19⋊C4—22no—
44C2×#64520D414yes—
45C22×C19⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95—21no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54#10597281—48no—
55C4⋊(C19⋊C8)—22no—
56#10597260—22no—
57C24×C19C22⋊C411yescharacteristic
58C24×C19C22×C411yescharacteristic
59C2×D4×C19—22no—
60C2×D4×C19—22no—
61C2×D4×C19—41no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—42no—
65C22×C4×C19—42no—
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D412yes—
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19#4112yes—
73C22×Dic19—22no—
74C22×Dic19—24no—
75C22×Dic19—22no—
76C22×Dic19—44no—
77C2×Dic38—28no—
78C2×Dic38—24no—
79C2×Dic38—44no—
80C2×Dic38—48no—
81C2×Dic38—44no—
82C2×Dic38—42no—
83C2×Dic38—41no—
84C2×Dic38—42no—
85C2×Dic38—41no—
86M16×C19—44no—
87C2×C8×C19—42no—
88C4⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—22no—
91C42×C19—21no—
92C42×C19—21no—
93C22⋊Dic19—44no—
94C22⋊Dic19—42no—
95C4⋊Dic19—42no—
96Dic19⋊C4—44no—
97#64520—44no—
98C2×C19⋊C8—24no—
99C2×C19⋊C8—82no—
100#9505—191nomaximal, Sylow
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19—41no—
108C23×C19—41no—
109C23×C19#10112yescomplemented
110C23×C19C2×C22⋊C411yescharacteristic
111C23×C19C4×D412yes—
112D4×C19—44no—
113C2×C4×C19—24no—
114C2×C4×C19—22no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—81no—
126C2×C4×C19#12011yescharacteristic
127C2×C4×C19#12112yes—
128C2×C4×C19#12311yescharacteristic
129C2×Dic19—24no—
130C2×Dic19—28no—
131C2×Dic19—42no—
132C2×Dic19—44no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137Dic38—48no—
138Dic38—44no—
139Dic38—44no—
140C8×C19—82no—
141C19⋊C8—44no—
142#2973—191no—
143#2409—191no—
144#1784—192no—
145#1465D1911yescharacteristic
146#1305—192no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—22no—
150C22×C19—22no—
151C22×C19—22no—
152C22×C19—22no—
153C22×C19—42no—
154C22×C19—42no—
155C22×C19—42no—
156C22×C19—41no—
157C22×C19—41no—
158C22×C19—81no—
159C22×C19#38611yescharacteristic
160C22×C19C2×#10111yescharacteristic
161C22×C19#41311yescharacteristic
162C4×C19—22no—
163C4×C19—21no—
164C4×C19—41no—
165C4×C19—41no—
166C4×C19—41no—
167C4×C19B(4,𝔽2)12yes—
168Dic19—44no—
169Dic19—82no—
170C23×Q8—191no—
171C2×C22⋊Q8—381no—
172C2×C4×D4C2×D1911yescharacteristic
173#435—384no—
174#432—381no—
175C2×#101—384no—
176#407—192no—
177#407C2×D1912yes—
178C2×C22⋊C8—381no—
179#395—381no—
180#393—381no—
181#391—381no—
182#386—192no—
183#385—192no—
184#380—191no—
185#324—21no—
186#323—21no—
187C2×C19—21no—
188C2×C19—21no—
189C2×C19—42no—
190C2×C19—42no—
191C2×C19#188911yescharacteristic
192C2×C19#190111yescharacteristic
193C2×C19#191511yescharacteristic
194C22×Q8—381no—
195C22×Q8—382no—
196C22×Q8—382no—
197C22×Q8—381no—
198C22×Q8—764no—
199C22×D4C4×D1911yescharacteristic
200C23×C4—192no—
201C23×C4D7611yescharacteristic
202C23×C4C22×D1911yescharacteristic
203C2×M16—22no—
204C2×M16—194no—
205C22×C8—382no—
206C22⋊Q8—764no—
207C4×D4—22no—
208C4×D4—22no—
209C2×C4⋊C4—382no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4C22⋊D1911yescharacteristic
212C2×C22⋊C4—192no—
213C2×C22⋊C4—382no—
214C2×C22⋊C4C4×D1911yescharacteristic
215C2×C22⋊C4C22⋊D1911yescharacteristic
216C2×C42D7611yescharacteristic
217C4⋊C8—382no—
218#101—768no—
219C22⋊C8—22no—
220C22⋊C8—22no—
221C22⋊C8—382no—
222C22⋊C8—382no—
223C22⋊C8—382no—
224#97—382no—
225#95—382no—
226#95—382no—
227#95—381no—
228C19#950511yescharacteristic, complemented, Sylow
229C24(C2×D19)⋊C411yescharacteristic
230C24C2×C4×D1911yescharacteristic
231C2×Q8—388no—
232C2×Q8—384no—
233C2×Q8—762no—
234C2×Q8—764no—
235C2×Q8—768no—
236C2×Q8—764no—
237C2×Q8—762no—
238C2×Q8—761no—
239C2×Q8—761no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—384no—
248C22×C4—382no—
249C22×C4—382no—
250C22×C4—764no—
251C22×C4(C2×D19)⋊C411yescharacteristic
252C22×C4(C2×D19)⋊C411yescharacteristic
253C22×C4(C2×D19)⋊C411yescharacteristic
254C22×C4C2×D7611yescharacteristic
255C22×C4D4×D1912yes—
256C22×C4#6454312yes—
257C22×C4C2×C22⋊D1911yescharacteristic
258M16—44no—
259M16—764no—
260C2×C8—42no—
261C2×C8—384no—
262C2×C8—1522no—
263C4⋊C4—22no—
264C4⋊C4—762no—
265C4⋊C4—764no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—764no—
269C22⋊C4—762no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#1059728112yescomplemented
281C23(C22⋊D19)⋊C412yes—
282C23C2×(C2×D19)⋊C411yescharacteristic
283Q8—768no—
284Q8—764no—
285Q8—764no—
286D4—44no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—384no—
301C2×C4—388no—
302C2×C4—762no—
303C2×C4—764no—
304C2×C4—762no—
305C2×C4—762no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4#1059732811yescharacteristic
309C2×C4#1059733211yescharacteristic
310C2×C4#1059738512yes—
311C8—82no—
312C8—764no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22#1192642111yescharacteristic
326C22C2×#1059728111yescharacteristic
327C22#1192652611yescharacteristic
328C4—22no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—764no—
334C4—1522no—
335C4#1192673212yes—
336C2—21no—
337C2—21no—
338C2—42no—
339C2—42no—
340C2#1456404111yescharacteristic
341C2#1456410111yescharacteristic
342C2#1456418511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1465C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#1465D19
hypocenterC19#9505
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #14563558C2semidirect
4. #14561542C2semidirect
109. C23×C19#101semidirect
228. C19#9505semidirect
280. C23#10597281semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145670002
#145635582
#145615422
C19×#14652
#950519