Finite Group Databasebeta

← #18085285

Subgroups — #18085285

Order 4864.

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

normal subgroups only

This group has 576 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#14574776C211yesmaximal, characteristic
2#14572031C211yesmaximal, characteristic
3#14564613C211yesmaximal, characteristic
4#14562307C211yesmaximal, characteristic
5#14562306C211yesmaximal, characteristic
6#14561467C211yesmaximal, characteristic
7C19×#3229C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597390—22no—
10#11926940—21no—
11#11926894—21no—
12#11926872—22no—
13#11926829—22no—
14#11926597C2211yescharacteristic
15#11926568C2211yescharacteristic
16#11926413—22no—
17#11926413—22no—
18C42×Dic19C2211yescharacteristic
19#11926303—22no—
20#11926290—22no—
21#11926289—22no—
22C19×#533C2211yescharacteristic
23C2×C19×C4⋊Q8C2211yescharacteristic
24C19×#498—21no—
25C19×#487—21no—
26C19×#483—22no—
27C19×#475—22no—
28C19×#431C2211yescharacteristic
29C22×Q8×C19—21no—
30C22×Dic38—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8D411yescharacteristic
36C19×C4⋊Q8D411yescharacteristic
37C19×#125—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C4×Q8×C19—21no—
41C4×Q8×C19—21no—
42C19×#117—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D412yes—
45C2×C42×C19C2311yescharacteristic
46#10597390—44no—
47#10597390—44no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19D412yes—
50C2×Dic19⋊C4—28no—
51C2×C4×Dic19—21no—
52C2×C4×Dic19—21no—
53C2×C4×Dic19D412yes—
54C2×#64520—21no—
55#10597315—21no—
56#10597315—21no—
57#10597315—21no—
58#10597315—21no—
59C19×#106—24no—
60C19×C4⋊C8D412yes—
61C19×#103—24no—
62C19×C22⋊C8—21no—
63C4×C8×C19—21no—
64#10597292—24no—
65C22⋊(C19⋊C8)—21no—
66#10597265—24no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)D412yes—
70C4×C19⋊C8—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—41no—
74C2×Q8×C19—41no—
75C2×Q8×C19—42no—
76C2×Q8×C19—42no—
77C22×C4×C19—22no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×Dic19—22no—
82C22×Dic19—22no—
83C2×Dic38—41no—
84C2×Dic38—41no—
85C2×Dic38—42no—
86C2×Dic38—42no—
87C2×C8×C19—22no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C22⋊C4×C19—41no—
99C42×C19—41no—
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19#4111yescharacteristic
104C4⋊Dic19—22no—
105C4⋊Dic19—22no—
106C4⋊Dic19—41no—
107C4⋊Dic19—41no—
108Dic19⋊C4—416no—
109C4×Dic19—24no—
110C4×Dic19—24no—
111C4×Dic19—22no—
112C4×Dic19SD1614yes—
113#64520—42no—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—41no—
116#10299—191nomaximal, Sylow
117C23×C19#12011yescharacteristic
118Q8×C19—42no—
119Q8×C19—42no—
120Q8×C19—82no—
121Q8×C19—81no—
122Q8×C19—81no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—42no—
128C2×C4×C19—44no—
129C2×C4×C19#12011yescharacteristic
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12711yescharacteristic
135C2×C4×C19C2×SD1612yes—
136C2×C4×C19AGL(1,ℤ/8)12yes—
137C2×Dic19—24no—
138C2×Dic19—24no—
139C2×Dic19—24no—
140C2×Dic19—42no—
141C2×Dic19—44no—
142Dic38—82no—
143Dic38—81no—
144Dic38—81no—
145C8×C19—42no—
146C19⋊C8—42no—
147C19⋊C8—81no—
148#3229—191no—
149#3229D1911yescharacteristic
150#2868—191no—
151#1994—191no—
152#1546—191no—
153#1546—191no—
154#1276—191no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19#39211yescharacteristic
158C22×C19#45012yes—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—81no—
162C4×C19—81no—
163C4×C19—82no—
164C4×C19#45612yes—
165C4×C19#45612yes—
166C4×C19#46012yes—
167C4×C19#49211yescharacteristic
168C4×C19#49611yescharacteristic
169Dic19—28no—
170Dic19—82no—
171#533C2×D1911yescharacteristic
172C2×C4⋊Q8—191no—
173C2×C4⋊Q8—382no—
174C2×C4⋊Q8C2×D1911yescharacteristic
175#498—21no—
176#498—381no—
177#487—21no—
178#487—381no—
179#483—22no—
180#483—382no—
181#475—22no—
182#475—382no—
183#431—191no—
184#431C2×D1911yescharacteristic
185#423—191no—
186#384—382no—
187#384—382no—
188C43—191no—
189#339—382no—
190#332—382no—
191#332—382no—
192C2×C19—22no—
193C2×C19#200511yescharacteristic
194C2×C19#200511yescharacteristic
195C2×C19#201411yescharacteristic
196C22×Q8—21no—
197C22×Q8—381no—
198C2×M16—381no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—381no—
204C4⋊Q8—381no—
205C4⋊Q8—381no—
206C4⋊Q8—381no—
207C4⋊Q8—764no—
208C4⋊Q8—764no—
209C4⋊Q8C22⋊D1911yescharacteristic
210C4⋊Q8C22⋊D1911yescharacteristic
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216#117—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—192no—
219C2×C4⋊C4—388no—
220C2×C4⋊C4—381no—
221C2×C4⋊C4C22⋊D1912yes—
222C2×C42—192no—
223C2×C42—381no—
224C2×C42—381no—
225C2×C42C22×D1911yescharacteristic
226#106—24no—
227#106—384no—
228C4⋊C8—192no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4⋊C8C22⋊D1912yes—
232#103—24no—
233#103—384no—
234C22⋊C8—21no—
235C22⋊C8—381no—
236C4×C8—21no—
237C4×C8—381no—
238C19#1029911yescharacteristic, complemented, Sylow
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—761no—
246C2×Q8—761no—
247C2×Q8—762no—
248C2×Q8—762no—
249C22×C4—22no—
250C22×C4—382no—
251C22×C4—382no—
252C22×C4D4×D1911yescharacteristic
253C22×C4D4×D1911yescharacteristic
254C22×C4C2×C22⋊D1911yescharacteristic
255M16—762no—
256C2×C8—22no—
257C2×C8—382no—
258C2×C8—761no—
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—382no—
270C4⋊C4—382no—
271C4⋊C4—7616no—
272C4⋊C4—761no—
273C4⋊C4—761no—
274C22⋊C4—41no—
275C42—41no—
276C42—194no—
277C42—384no—
278C42—384no—
279C42—382no—
280C42D4×D1911yescharacteristic
281C42#6454311yescharacteristic
282C42C2×C22⋊D1911yescharacteristic
283C42C2×C22⋊D1911yescharacteristic
284C23#1059738311yescharacteristic
285Q8—42no—
286Q8—42no—
287Q8—81no—
288Q8—81no—
289Q8—82no—
290Q8—1521no—
291Q8—1521no—
292Q8—1522no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—44no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—384no—
300C2×C4—384no—
301C2×C4—384no—
302C2×C4—764no—
303C2×C4—762no—
304C2×C4SD16×D1912yes—
305C2×C4#1059736012yes—
306C2×C4#1059738311yescharacteristic
307C2×C4#1059738411yescharacteristic
308C2×C4#1059738511yescharacteristic
309C2×C4#1059738511yescharacteristic
310C2×C4#1059738611yescharacteristic
311C2×C4#1059739911yescharacteristic
312C8—42no—
313C8—762no—
314C8—1521no—
315C22—21no—
316C22—21no—
317C22#1192645211yescharacteristic
318C22#1192669312yes—
319C4—21no—
320C4—21no—
321C4—81no—
322C4—81no—
323C4—82no—
324C4—388no—
325C4—1522no—
326C4#1192672512yes—
327C4#1192672712yes—
328C4#1192674212yes—
329C4#1192691511yescharacteristic
330C4#1192693011yescharacteristic
331C2—22no—
332C2#1456466811yescharacteristic
333C2#1456466911yescharacteristic
334C2#1456472111yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3229C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#3229D19
hypocenterC19#10299
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
238. C19#10299semidirect

Maximal subgroups

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

subgroupindex
#145747762
#145720312
#145646132
#145623072
#145623062
#145614672
C19×#32292
#1029919