Finite Group Databasebeta

← #18083461

Subgroups — #18083461

Order 4864.

470 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 81 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#14574188C211yesmaximal, characteristic
2#14569511C211yesmaximal, characteristic
3#14562261C211yesmaximal, characteristic
4#14562186C211yesmaximal, characteristic
5#14562082C211yesmaximal, characteristic
6#14561501C211yesmaximal, characteristic
7C19×#3113C211yesmaximal, characteristic
8C2×#10597316C2211yescharacteristic
9#11926950—21no—
10#11926950—21no—
11#11926943—22no—
12#11926601C2211yescharacteristic
13#11926587—21no—
14#11926587—21no—
15C4×#64520C2211yescharacteristic
16#11926483—21no—
17#11926482—21no—
18#11926474—21no—
19#11926463—21no—
20#11926428—22no—
21#11926412C2211yescharacteristic
22#11926285—22no—
23#11926281—22no—
24Q8⋊(C19⋊C8)—22no—
25C19×#533C2211yescharacteristic
26C2×C4×Q8×C19C2211yescharacteristic
27C19×#483—21no—
28C19×#475—21no—
29C19×#462—21no—
30C19×#451—21no—
31C19×#441—22no—
32C19×#432C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C2×Q16×C19—22no—
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—
42C4×Q8×C19—21no—
43C4×Q8×C19—21no—
44C4×Q8×C19—21no—
45C4×Q8×C19—21no—
46C19×#117—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C42×C19—21no—
50C2×C42×C19C2311yescharacteristic
51C2×C4⋊Dic19D411yescharacteristic
52C2×C4⋊Dic19D411yescharacteristic
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4—21no—
55C2×Dic19⋊C4—21no—
56C2×#64520—21no—
57#10597316—21no—
58#10597316—21no—
59#10597316—21no—
60#10597316—21no—
61C19×#106—22no—
62C19×C4⋊C8—21no—
63C19×#103—22no—
64C19×#103—22no—
65C19×C22⋊C8—21no—
66C19×#97D412yes—
67C19⋊#95—22no—
68C19⋊#95—22no—
69C19⋊#95—22no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95D412yes—
73C22⋊(C19⋊C8)—21no—
74#10597265—22no—
75#10597265—22no—
76#10597264—22no—
77#10597264—22no—
78C4⋊(C19⋊C8)—21no—
79#10597260—21no—
80#10597260—21no—
81C4×C19⋊C8D412yes—
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—42no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×Dic19—22no—
93C22×Dic19—21no—
94C22×Dic19—21no—
95Q16×C19—44no—
96C2×C8×C19—22no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C42×C19—41no—
109C42×C19—41no—
110C42×C19—41no—
111C42×C19C2×D411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19#4111yescharacteristic
115C4⋊Dic19—21no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119Dic19⋊C4—44no—
120Dic19⋊C4—41no—
121Dic19⋊C4—41no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124#64520—24no—
125C2×C19⋊C8—22no—
126C2×C19⋊C8—41no—
127#10025—191nomaximal, Sylow
128C23×C19#12011yescharacteristic
129Q8×C19—22no—
130Q8×C19—22no—
131Q8×C19—41no—
132Q8×C19—41no—
133Q8×C19—42no—
134Q8×C19—81no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—42no—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12111yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12711yescharacteristic
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—42no—
158C8×C19—42no—
159C19⋊C8—24no—
160C19⋊C8—81no—
161#3166—191no—
162#3113D1911yescharacteristic
163#2634—191no—
164#1534—191no—
165#1515—191no—
166#1491—191no—
167#1288—191no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19#39211yescharacteristic
171C22×C19#45612yes—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—42no—
179C4×C19—81no—
180C4×C19—81no—
181C4×C19—81no—
182Dic19—82no—
183Dic19—81no—
184Dic19—81no—
185#533C2×D1911yescharacteristic
186C2×#125—191no—
187C2×C4×Q8C2×D1911yescharacteristic
188#501—381no—
189#501—381no—
190#499—382no—
191#483—21no—
192#475—21no—
193#462—21no—
194#451—21no—
195#441—22no—
196#432—191no—
197#432C2×D1911yescharacteristic
198#428—381no—
199#428—381no—
200C4×M16—191no—
201#400—381no—
202#400—381no—
203#398—381no—
204#395—381no—
205#387—382no—
206#383—191no—
207#330—382no—
208#328—382no—
209Q8⋊C8—382no—
210C2×C19—22no—
211C2×C19#200511yescharacteristic
212C2×C19#200911yescharacteristic
213C2×C19#201011yescharacteristic
214C22×Q8C22⋊D1911yescharacteristic
215C2×Q16—22no—
216C2×M16—381no—
217C4⋊Q8C22⋊D1911yescharacteristic
218C4⋊Q8C22⋊D1911yescharacteristic
219#125—21no—
220#125—381no—
221#125—381no—
222#125—381no—
223#125—381no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232#117—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—191no—
235C2×C4⋊C4—191no—
236C2×C4⋊C4—382no—
237C2×C4⋊C4—381no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4C22⋊D1911yescharacteristic
240C2×C42—21no—
241C2×C42C22×D1911yescharacteristic
242#107—382no—
243#107—382no—
244#106—22no—
245#106—382no—
246#106—382no—
247C4⋊C8—21no—
248C4⋊C8—381no—
249#103—22no—
250#103—22no—
251C22⋊C8—21no—
252C22⋊C8—381no—
253#97—381no—
254#97—381no—
255#97C22⋊D1912yes—
256C4×C8—192no—
257#95—192no—
258#95—382no—
259#95—382no—
260#95—382no—
261#95—381no—
262#95—381no—
263C19#1002511yescharacteristic, complemented, Sylow
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—42no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—382no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4D4×D1911yescharacteristic
275C22×C4D4×D1911yescharacteristic
276C22×C4C2×C22⋊D1911yescharacteristic
277Q16—44no—
278M16—384no—
279C2×C8—22no—
280C2×C8—382no—
281C2×C8—761no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4—764no—
297C4⋊C4—761no—
298C4⋊C4—761no—
299C4⋊C4—761no—
300C4⋊C4—761no—
301C22⋊C4—41no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42D4×D1911yescharacteristic
306C42#6454311yescharacteristic
307C42C2×C22⋊D1911yescharacteristic
308C42C2×C22⋊D1911yescharacteristic
309C23#1059738311yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—762no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—762no—
333C2×C4#1059738311yescharacteristic
334C2×C4#1059738411yescharacteristic
335C2×C4#1059738511yescharacteristic
336C2×C4#1059738511yescharacteristic
337C2×C4#1059738611yescharacteristic
338C2×C4#1059739911yescharacteristic
339C8—42no—
340C8—384no—
341C8—1521no—
342C22—21no—
343C22—21no—
344C22#1192645211yescharacteristic
345C22#1192672512yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—1522no—
357C4—1521no—
358C4—1521no—
359C2—22no—
360C2#1456466811yescharacteristic
361C2#1456469311yescharacteristic
362C2#1456470011yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3113C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#3113D19
hypocenterC19#10025
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
263. C19#10025semidirect

Maximal subgroups

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

subgroupindex
#145741882
#145695112
#145622612
#145621862
#145620822
#145615012
C19×#31132
#1002519