Finite Group Databasebeta

← #18084096

Subgroups — #18084096

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#14574776C211yesmaximal, characteristic
2#14574182C211yesmaximal, characteristic
3#14564623C211yesmaximal, characteristic
4#14562230C211yesmaximal, characteristic
5#14562056C211yesmaximal, characteristic
6#14561524C211yesmaximal, characteristic
7C19×#3255C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926954—22no—
10#11926947—21no—
11#11926940—21no—
12#11926940—21no—
13#11926894—21no—
14#11926872—22no—
15#11926829—22no—
16#11926597C2211yescharacteristic
17#11926587—22no—
18C4×#64520C2211yescharacteristic
19C4×#64520C2211yescharacteristic
20#11926312—22no—
21#11926286—22no—
22Q8⋊(C19⋊C8)—22no—
23C19×#533C2211yescharacteristic
24C19×#533C2211yescharacteristic
25C19×#475—21no—
26C19×#475—21no—
27C19×#470—22no—
28C19×#462—21no—
29C19×#462—21no—
30C19×#423C2211yescharacteristic
31C22×Dic38—21no—
32C2×Q16×C19—22no—
33C2×M16×C19D412yes—
34C19×C4⋊Q8D411yescharacteristic
35C19×C4⋊Q8D411yescharacteristic
36C19×C4⋊Q8D411yescharacteristic
37C19×C4⋊Q8D411yescharacteristic
38C19×#125—21no—
39C19×#125—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C19×C22⋊Q8—21no—
43C19×C22⋊Q8—21no—
44C4×Q8×C19—21no—
45C4×Q8×C19—21no—
46C4×Q8×C19—21no—
47C4×Q8×C19—21no—
48C19×#117—21no—
49C19×#117—21no—
50C2×C42×C19C2311yescharacteristic
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19D412yes—
53C2×#64520—21no—
54C2×#64520—21no—
55#10597315—21no—
56#10597315—21no—
57#10597315—21no—
58#10597315—21no—
59C19×#106—22no—
60C19×C4⋊C8—21no—
61C19×C4⋊C8—21no—
62C19×#103—22no—
63C19×#103—22no—
64#10597292—24no—
65C22⋊(C19⋊C8)—21no—
66#10597265—24no—
67#10597265—24no—
68#10597264—24no—
69C4⋊(C19⋊C8)D412yes—
70#10597260—21no—
71#10597260D412yes—
72C4×C19⋊C8—21no—
73C4×C19⋊C8—21no—
74C4×C19⋊C8—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—21no—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C22×Dic19—22no—
83C2×Dic38—41no—
84C2×Dic38—41no—
85C2×Dic38—82no—
86Q16×C19—82no—
87M16×C19—42no—
88C2×C8×C19—22no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C22⋊C4×C19—41no—
102C22⋊C4×C19—41no—
103C42×C19—41no—
104C42×C19—41no—
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19C2×D411yescharacteristic
109C4⋊Dic19—22no—
110C4⋊Dic19—22no—
111C4⋊Dic19—41no—
112C4⋊Dic19—41no—
113#64520—24no—
114#64520—22no—
115#64520—41no—
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—41no—
125Q8×C19—41no—
126Q8×C19—42no—
127C2×C4×C19—21no—
128C2×C4×C19—22no—
129C2×C4×C19—21no—
130C2×C4×C19—22no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12011yescharacteristic
137C2×C4×C19#12011yescharacteristic
138C2×C4×C19#12111yescharacteristic
139C2×C4×C19#12111yescharacteristic
140C2×C4×C19#12711yescharacteristic
141C2×Dic19—42no—
142C2×Dic19—82no—
143Dic38—82no—
144Dic38—82no—
145C8×C19—42no—
146C19⋊C8—24no—
147C19⋊C8—42no—
148C19⋊C8—42no—
149#3255D1911yescharacteristic
150#3229—191no—
151#3165—191no—
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—81no—
165C4×C19—81no—
166C4×C19—81no—
167C4×C19#45511yescharacteristic
168C4×C19#45612yes—
169C4×C19#45611yescharacteristic
170C4×C19#47112yes—
171Dic19—82no—
172#533C2×D1911yescharacteristic
173#533C2×D1911yescharacteristic
174C2×C4⋊Q8—191no—
175#501—382no—
176#500—381no—
177#498—381no—
178#498—381no—
179#487—381no—
180#483—382no—
181#475—21no—
182#475—21no—
183#475—382no—
184#470—22no—
185#462—21no—
186#462—21no—
187#431—191no—
188#428—382no—
189#423C2×D1911yescharacteristic
190C4×M16—191no—
191C4×M16—191no—
192#343—382no—
193#330—382no—
194Q8⋊C8—382no—
195C2×C19—41no—
196C2×C19#200511yescharacteristic
197C2×C19#200711yescharacteristic
198C2×C19#201911yescharacteristic
199C22×Q8—381no—
200C2×Q16—22no—
201C2×M16—381no—
202C2×M16—381no—
203C2×M16C22⋊D1912yes—
204C4⋊Q8—381no—
205C4⋊Q8—381no—
206C4⋊Q8—381no—
207C4⋊Q8—381no—
208C4⋊Q8C22⋊D1911yescharacteristic
209C4⋊Q8C22⋊D1911yescharacteristic
210C4⋊Q8C22⋊D1911yescharacteristic
211C4⋊Q8C22⋊D1911yescharacteristic
212#125—21no—
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223#117—21no—
224C2×C4⋊C4—192no—
225C2×C4⋊C4—381no—
226C2×C42C22×D1911yescharacteristic
227#107—384no—
228#106—22no—
229#106—384no—
230#106—384no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—192no—
234#103—22no—
235#103—22no—
236#103—384no—
237C22⋊C8—381no—
238#97—192no—
239#97—381no—
240C4×C8—381no—
241C4×C8—381no—
242C4×C8—381no—
243C19#1011911yescharacteristic, complemented, Sylow
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—761no—
249C2×Q8—761no—
250C2×Q8—1522no—
251C22×C4—382no—
252C22×C4D4×D1911yescharacteristic
253C22×C4#6454311yescharacteristic
254C22×C4C2×C22⋊D1911yescharacteristic
255Q16—82no—
256M16—42no—
257M16—384no—
258M16—382no—
259M16—761no—
260C2×C8—22no—
261C2×C8—382no—
262C2×C8—382no—
263C2×C8—761no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—382no—
277C4⋊C4—382no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42D4×D1911yescharacteristic
285C42D4×D1911yescharacteristic
286C42C2×C22⋊D1911yescharacteristic
287C42C2×C22⋊D1911yescharacteristic
288C23#1059738411yescharacteristic
289Q8—42no—
290Q8—41no—
291Q8—41no—
292Q8—42no—
293Q8—41no—
294Q8—41no—
295Q8—1522no—
296Q8—1522no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—762no—
306C2×C4—1522no—
307C2×C4#1059738311yescharacteristic
308C2×C4#1059738311yescharacteristic
309C2×C4#1059738511yescharacteristic
310C2×C4#1059738511yescharacteristic
311C2×C4#1059738611yescharacteristic
312C2×C4#1059739911yescharacteristic
313C8—42no—
314C8—384no—
315C8—762no—
316C8—762no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#1192645211yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—1522no—
329C4#1192672211yescharacteristic
330C4#1192672512yes—
331C4#1192672711yescharacteristic
332C4#1192680912yes—
333C2—41no—
334C2#1456466811yescharacteristic
335C2#1456468211yescharacteristic
336C2#1456474611yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3255C2
socleC22×C19#392
prime radicalC23×C19#121
hypercenter#3255D19
hypocenterC19#10119
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

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
#145747762
#145741822
#145646232
#145622302
#145620562
#145615242
C19×#32552
#1011919