Finite Group Databasebeta

← #18084095

Subgroups — #18084095

Order 4864.

454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 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#14575026C211yesmaximal, characteristic
2#14574779C211yesmaximal, characteristic
3#14564625C211yesmaximal, characteristic
4#14562229C211yesmaximal, characteristic
5#14562056C211yesmaximal, characteristic
6#14561525C211yesmaximal, characteristic
7C19×#3165C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926940—21no—
10#11926896—21no—
11#11926874—22no—
12#11926829—21no—
13#11926826—22no—
14#11926826—21no—
15#11926800—22no—
16#11926754—21no—
17#11926751—21no—
18#11926597C2211yescharacteristic
19#11926568C2211yescharacteristic
20C4×#64520C2211yescharacteristic
21#11926313—22no—
22#11926285—22no—
23Q8⋊(C19⋊C8)—22no—
24C19×#533C2211yescharacteristic
25C2×C19×C4⋊Q8C2211yescharacteristic
26C19×#501—22no—
27C19×#500—21no—
28C19×#498—21no—
29C19×#428—22no—
30C4×M16×C19C2211yescharacteristic
31C22×Q8×C19—21no—
32C2×M16×C19—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8D411yescharacteristic
38C19×C4⋊Q8D411yescharacteristic
39C19×#125—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C4×Q8×C19—21no—
43C4×Q8×C19—21no—
44C19×#117—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19D412yes—
47C2×C42×C19C2311yescharacteristic
48C2×#64528—22no—
49#10597372—21no—
50#10597370—21no—
51#10597370—21no—
52C2×#64520—21no—
53C2×#64520D412yes—
54#10597316—21no—
55#10597315D411yescharacteristic
56#10597315D411yescharacteristic
57C4×Dic38—21no—
58C4×Dic38—21no—
59C19×#107—24no—
60C19×#106—24no—
61C19×#97D412yes—
62C4×C8×C19—21no—
63#10597292—22no—
64C22⋊(C19⋊C8)—21no—
65#10597267—22no—
66#10597267—24no—
67#10597265—22no—
68#10597265—24no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)D412yes—
72#10597260—21no—
73C4×C19⋊C8—21no—
74C4×C19⋊C8—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—41no—
78C2×Q8×C19—41no—
79C2×Q8×C19—82no—
80C22×C4×C19—22no—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C2×Dic38—21no—
85C2×Dic38—21no—
86M16×C19—24no—
87C2×C8×C19—22no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
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×C19C2×D411yescharacteristic
104C22⋊Dic19—41no—
105#64528—82no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108C4⋊Dic19—21no—
109C4⋊Dic19—21no—
110Dic19⋊C4—41no—
111Dic19⋊C4—41no—
112C4×Dic19—41no—
113#64520—22no—
114#64520—41no—
115#64520—42no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8—22no—
118C2×C19⋊C8—41no—
119#10119—191nomaximal, Sylow
120C23×C19#12111yescharacteristic
121Q8×C19—41no—
122Q8×C19—41no—
123Q8×C19—42no—
124Q8×C19—82no—
125Q8×C19—82no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—42no—
133C2×C4×C19—82no—
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12011yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12111yescharacteristic
139C2×C4×C19#12711yescharacteristic
140C2×Dic19—41no—
141C2×Dic19—41no—
142Dic38—41no—
143Dic38—41no—
144Dic38—42no—
145C8×C19—24no—
146C19⋊C8—42no—
147C19⋊C8—42no—
148C19⋊C8—42no—
149#3255—191no—
150#3229—191no—
151#3165D1911yescharacteristic
152#1997—191no—
153#1526—191no—
154#1485—191no—
155#1299—191no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19#39211yescharacteristic
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—81no—
164C4×C19—82no—
165C4×C19—81no—
166C4×C19#45511yescharacteristic
167C4×C19#45611yescharacteristic
168C4×C19#45612yes—
169C4×C19#47112yes—
170Dic19—81no—
171Dic19—81no—
172#533—191no—
173#533C2×D1911yescharacteristic
174C2×C4⋊Q8C2×D1911yescharacteristic
175#501—22no—
176#500—21no—
177#498—21no—
178#498—381no—
179#487—381no—
180#483—382no—
181#475—382no—
182#475—381no—
183#475—381no—
184#470—382no—
185#462—381no—
186#462—381no—
187#431—191no—
188#428—22no—
189#423—191no—
190C4×M16—191no—
191C4×M16C2×D1911yescharacteristic
192#343—382no—
193#330—382no—
194Q8⋊C8—382no—
195C2×C19—41no—
196C2×C19#200511yescharacteristic
197C2×C19#200711yescharacteristic
198C2×C19#201911yescharacteristic
199C22×Q8—21no—
200C2×Q16—382no—
201C2×M16—21no—
202C2×M16—192no—
203C2×M16—381no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—191no—
209C4⋊Q8—191no—
210C4⋊Q8C22⋊D1911yescharacteristic
211C4⋊Q8C22⋊D1911yescharacteristic
212#125—21no—
213#125—381no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—381no—
217C22⋊Q8—381no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—381no—
221C4×Q8—381no—
222#117—21no—
223#117—381no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C22⋊D1912yes—
226C2×C42C22×D1911yescharacteristic
227#107—24no—
228#106—24no—
229#106—382no—
230#106—384no—
231C4⋊C8—192no—
232C4⋊C8—381no—
233C4⋊C8—381no—
234#103—382no—
235#103—384no—
236#103—382no—
237C22⋊C8—381no—
238#97—381no—
239#97C22⋊D1912yes—
240C4×C8—21no—
241C4×C8—381no—
242C4×C8—381no—
243C19#1011911yescharacteristic, complemented, Sylow
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—82no—
249C2×Q8—381no—
250C2×Q8—381no—
251C22×C4—22no—
252C22×C4D4×D1911yescharacteristic
253C22×C4#6454311yescharacteristic
254C22×C4C2×C22⋊D1911yescharacteristic
255Q16—1522no—
256M16—24no—
257M16—382no—
258M16—761no—
259M16—762no—
260C2×C8—22no—
261C2×C8—382no—
262C2×C8—382no—
263C2×C8—761no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—381no—
275C4⋊C4—381no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C22⋊C4—41no—
281C22⋊C4—761no—
282C42—41no—
283C42—761no—
284C42D4×D1911yescharacteristic
285C42D4×D1911yescharacteristic
286C42C2×C22⋊D1911yescharacteristic
287C42C2×C22⋊D1911yescharacteristic
288C23#1059738511yescharacteristic
289Q8—42no—
290Q8—41no—
291Q8—41no—
292Q8—82no—
293Q8—82no—
294Q8—761no—
295Q8—761no—
296Q8—762no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4#1059738311yescharacteristic
308C2×C4#1059738311yescharacteristic
309C2×C4#1059738411yescharacteristic
310C2×C4#1059738511yescharacteristic
311C2×C4#1059738611yescharacteristic
312C2×C4#1059739911yescharacteristic
313C8—24no—
314C8—762no—
315C8—762no—
316C8—762no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#1192645211yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—82no—
326C4—81no—
327C4—1521no—
328C4—1521no—
329C4#1192672011yescharacteristic
330C4#1192672511yescharacteristic
331C4#1192672612yes—
332C4#1192680512yes—
333C2—41no—
334C2#1456467111yescharacteristic
335C2#1456468011yescharacteristic
336C2#1456474911yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3165C2
socleC22×C19#392
prime radicalC23×C19#121
hypercenter#3165D19
hypocenterC19#10119
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
243. C19#10119semidirect

Maximal subgroups

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

subgroupindex
#145750262
#145747792
#145646252
#145622292
#145620562
#145615252
C19×#31652
#1011919