Finite Group Databasebeta

← #18083464

Subgroups — #18083464

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#14574184C211yesmaximal, characteristic
2#14573765C211yesmaximal, characteristic
3#14562262C211yesmaximal, characteristic
4#14562185C211yesmaximal, characteristic
5#14562082C211yesmaximal, characteristic
6#14561499C211yesmaximal, characteristic
7C19×#2634C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926954—21no—
10#11926954—21no—
11#11926943—22no—
12#11926874—21no—
13#11926829—21no—
14#11926754—21no—
15#11926700—21no—
16#11926649—22no—
17#11926601C2211yescharacteristic
18#11926601C2211yescharacteristic
19#11926584—21no—
20#11926584—21no—
21C4×#64520C2211yescharacteristic
22#11926286—22no—
23#11926280—22no—
24Q8⋊(C19⋊C8)—22no—
25C2×C19×#125C2211yescharacteristic
26C2×C4×Q8×C19C2211yescharacteristic
27C19×#400—21no—
28C19×#400—21no—
29C19×#398—21no—
30C19×#395—21no—
31C19×#387—22no—
32C19×#383C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C19×#125—21no—
35C19×#125—21no—
36C19×#125—21no—
37C19×#125—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C4×Q8×C19—21no—
42C2×C4⋊C4×C19—22no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19D411yescharacteristic
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C42×C19—21no—
50C2×C42×C19C2311yescharacteristic
51C2×#64528—22no—
52#10597372—21no—
53#10597370—21no—
54#10597370—21no—
55C2×#64520—21no—
56#10597316—21no—
57#10597315D411yescharacteristic
58#10597315D411yescharacteristic
59C4×Dic38—21no—
60C4×Dic38—21no—
61C19×#95—22no—
62C19×#95—22no—
63C19×#95—22no—
64C19×#95—21no—
65C19×#95—21no—
66C19×#95D412yes—
67#10597292—22no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70#10597267—22no—
71#10597265—22no—
72#10597265—22no—
73#10597265—22no—
74#10597264—22no—
75#10597264—22no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78#10597260—21no—
79#10597260—21no—
80#10597260D412yes—
81C4×C19⋊C8D412yes—
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—42no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—22no—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C2×Dic38—21no—
94C2×Dic38—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—44no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C42×C19—41no—
109C42×C19—41no—
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19#4111yescharacteristic
114C22⋊Dic19—41no—
115#64528—44no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120Dic19⋊C4—41no—
121Dic19⋊C4—41no—
122C4×Dic19—41no—
123#64520—24no—
124C2×C19⋊C8—22no—
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—
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12011yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12111yescharacteristic
153C2×C4×C19#12711yescharacteristic
154C2×Dic19—41no—
155C2×Dic19—41no—
156Dic38—42no—
157Dic38—81no—
158C19⋊C8—24no—
159C19⋊C8—42no—
160C19⋊C8—81no—
161#3166—191no—
162#3113—191no—
163#2634D1911yescharacteristic
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—82no—
180C4×C19—81no—
181C4×C19—81no—
182C4×C19—81no—
183Dic19—81no—
184Dic19—81no—
185#533—191no—
186C2×#125C2×D1911yescharacteristic
187C2×C4×Q8C2×D1911yescharacteristic
188#501—381no—
189#501—381no—
190#499—382no—
191#483—381no—
192#475—381no—
193#462—381no—
194#451—381no—
195#441—382no—
196#432—191no—
197#432—191no—
198#428—381no—
199#428—381no—
200C4×M16—191no—
201#400—21no—
202#400—21no—
203#398—21no—
204#395—21no—
205#387—22no—
206#383C2×D1911yescharacteristic
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—382no—
216C2×M16—381no—
217C4⋊Q8—191no—
218C4⋊Q8—191no—
219#125—21no—
220#125—21no—
221#125—21no—
222#125—21no—
223#125—381no—
224C22⋊Q8—381no—
225C22⋊Q8—381no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—381no—
231C4×Q8—381no—
232#117—381no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C22⋊D1911yescharacteristic
238C2×C4⋊C4C22⋊D1911yescharacteristic
239C2×C4⋊C4C22⋊D1911yescharacteristic
240C2×C42—21no—
241C2×C42C22×D1911yescharacteristic
242#107—382no—
243#107—382no—
244#106—382no—
245#106—382no—
246#106—382no—
247C4⋊C8—381no—
248C4⋊C8—381no—
249#103—382no—
250#103—382no—
251C22⋊C8—381no—
252C22⋊C8—381no—
253#97—192no—
254#97—381no—
255#97—381no—
256C4×C8—192no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—21no—
261#95—21no—
262#95C22⋊D1912yes—
263C19#1002511yescharacteristic, complemented, Sylow
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—42no—
267C2×Q8—381no—
268C2×Q8—381no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4C2×C22⋊D1911yescharacteristic
275C22×C4C2×C22⋊D1911yescharacteristic
276C22×C4C2×C22⋊D1911yescharacteristic
277Q16—764no—
278M16—384no—
279C2×C8—382no—
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—44no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—381no—
296C4⋊C4—381no—
297C4⋊C4—381no—
298C4⋊C4—381no—
299C4⋊C4—761no—
300C4⋊C4—761no—
301C22⋊C4—761no—
302C42—41no—
303C42—41no—
304C42—761no—
305C42D4×D1911yescharacteristic
306C42D4×D1911yescharacteristic
307C42D4×D1911yescharacteristic
308C42#6454311yescharacteristic
309C23#1059739911yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—762no—
315Q8—1521no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4#1059738311yescharacteristic
334C2×C4#1059738311yescharacteristic
335C2×C4#1059738411yescharacteristic
336C2×C4#1059738511yescharacteristic
337C2×C4#1059738511yescharacteristic
338C2×C4#1059738611yescharacteristic
339C8—384no—
340C8—762no—
341C8—1521no—
342C22—21no—
343C22—21no—
344C22#1192645211yescharacteristic
345C22#1192672712yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—82no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—1521no—
358C4—1521no—
359C2—22no—
360C2#1456466911yescharacteristic
361C2#1456469511yescharacteristic
362C2#1456470011yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2634C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#2634D19
hypocenterC19#10025
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2634

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
#145741842
#145737652
#145622622
#145621852
#145620822
#145614992
C19×#26342
#1002519