Finite Group Databasebeta

← #18074932

Subgroups — #18074932

Order 4864.

692 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 131 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#14564456C211yesmaximal, characteristic, complemented
2#14562361C211yesmaximal, characteristic, complemented
3#14562255C212yesmaximal, complemented
4#14562173C212yesmaximal, complemented
5C19×#3544C211yesmaximal, characteristic
6#11926601C2212yes—
7C2×#10597292—22no—
8C2×#10597260C2211yescharacteristic
9#11926410C2211yescharacteristic
10#11926293—22no—
11#11926286—22no—
12#11926284—22no—
13#11926281—22no—
14#11926278—22no—
15C19×#563—22no—
16Q82×C19C411yescharacteristic, complemented
17C19×#555C411yescharacteristic, complemented
18C19×#554C412yescomplemented
19C19×#552—22no—
20C19×#547—22no—
21C19×#544—22no—
22C19×#542—22no—
23C19×#536—22no—
24C2×C19×C4⋊Q8C2211yescharacteristic
25C19×#529C2212yes—
26C2×#41×C19—22no—
27C22×Q8×C19D412yes—
28C19×C4⋊Q8—22no—
29C19×C4⋊Q8—22no—
30C19×C4⋊Q8—22no—
31C19×C4⋊Q8—22no—
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×C4⋊Q8D412yes—
35C19×#126—24no—
36C19×#126—22no—
37C19×#125—24no—
38C19×#125—22no—
39C19×#125D412yes—
40C19×#124—22no—
41C19×#124—22no—
42C19×#124D412yes—
43C19×#123—24no—
44C19×#123—24no—
45C19×#123—22no—
46C19×C22⋊Q8—24no—
47C19×C22⋊Q8—24no—
48C19×C22⋊Q8—24no—
49C19×C22⋊Q8—22no—
50C19×C22⋊Q8D412yes—
51C19×#121—22no—
52C19×#121D412yes—
53C4×Q8×C19—22no—
54C4×Q8×C19C2×C412yes—
55C4×D4×C19—22no—
56C4×D4×C19—22no—
57C4×D4×C19C2×C412yes—
58C19×#117—22no—
59C19×#117—22no—
60C19×#117—22no—
61C2×C4⋊C4×C19—22no—
62C2×C4⋊C4×C19—22no—
63C2×C42×C19C2311yescharacteristic
64C2×C4⋊Dic19—21no—
65C22×C19⋊C8—21no—
66#10597292—44no—
67C19⋊#95—22no—
68C22⋊(C19⋊C8)—22no—
69C4⋊(C19⋊C8)—22no—
70#10597260—22no—
71#10597260—22no—
72#41×C19—82no—
73#41×C19—82no—
74C2×Q8×C19—22no—
75C2×Q8×C19—22no—
76C2×Q8×C19—42no—
77C2×Q8×C19—42no—
78C2×Q8×C19C22⋊C412yes—
79C2×Q8×C19C22⋊C412yes—
80C2×Q8×C19C22⋊C412yes—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19C22⋊C412yes—
84C22×C4×C19—22no—
85C22×C4×C19—24no—
86C22×C4×C19—22no—
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D412yes—
89C22×Dic19—41no—
90C4⋊C4×C19—24no—
91C4⋊C4×C19—24no—
92C4⋊C4×C19—24no—
93C4⋊C4×C19—22no—
94C4⋊C4×C19—22no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—24no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19C22⋊C412yes—
101C4⋊C4×C19C22⋊C412yes—
102C22⋊C4×C19—24no—
103C22⋊C4×C19—24no—
104C22⋊C4×C19—22no—
105C22⋊C4×C19—22no—
106C22⋊C4×C19—22no—
107C22⋊C4×C19—22no—
108C22⋊C4×C19—22no—
109C42×C19—22no—
110C42×C19—22no—
111C42×C19—22no—
112C42×C19C22×C411yescharacteristic
113C42×C19C2×D412yes—
114C42×C19C2×D411yescharacteristic
115C4⋊Dic19—42no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—42no—
120#8498—191nomaximal, Sylow
121C23×C19—22no—
122C23×C19#12011yescharacteristic
123Q8×C19—42no—
124Q8×C19—42no—
125Q8×C19—42no—
126Q8×C19—82no—
127Q8×C19—82no—
128D4×C19—42no—
129D4×C19—42no—
130D4×C19—42no—
131D4×C19—82no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—22no—
139C2×C4×C19—42no—
140C2×C4×C19—44no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—84no—
144C2×C4×C19C2×C22⋊C412yes—
145C2×C4×C19C2×C22⋊C411yescharacteristic
146C2×C4×C19#12012yes—
147C2×C4×C19#12011yescharacteristic
148C2×Dic19—82no—
149C2×Dic19—81no—
150C19⋊C8—42no—
151C19⋊C8—82no—
152#3544D1911yescharacteristic
153#1960—191no—
154#1558—191no—
155#1532—192no—
156#1512—192no—
157C22×C19—22no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19—42no—
161C22×C19#37911yescharacteristic
162C22×C19#45311yescharacteristic
163C22×C19#45511yescharacteristic
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—22no—
167C4×C19—22no—
168C4×C19—42no—
169C4×C19—42no—
170C4×C19—42no—
171C4×C19—42no—
172C4×C19—42no—
173Dic19—161no—
174#563—22no—
175Q82Dic1911yescharacteristic, complemented
176#555Dic1911yescharacteristic, complemented
177#554Dic1912yescomplemented
178#552—22no—
179#547—22no—
180#544—22no—
181#542—22no—
182#536—22no—
183C2×C4⋊Q8C2×D1911yescharacteristic
184#529C2×D1912yes—
185#432—192no—
186C2×#103—382no—
187C2×#97—191no—
188#382—191no—
189#333—382no—
190#330—382no—
191#329—382no—
192#328—382no—
193#327—382no—
194C2×C19—21no—
195C2×C19—21no—
196C2×C19—82no—
197C2×C19#179211yescharacteristic
198C2×C19#179612yes—
199C2×#41—22no—
200C22×Q8C22⋊D1912yes—
201C22×C8—381no—
202C4⋊Q8—22no—
203C4⋊Q8—22no—
204C4⋊Q8—22no—
205C4⋊Q8—22no—
206C4⋊Q8C2×Dic1911yescharacteristic
207C4⋊Q8C2×Dic1911yescharacteristic
208C4⋊Q8C22⋊D1912yes—
209#126—24no—
210#126—22no—
211#125—24no—
212#125—22no—
213#125C22⋊D1912yes—
214#124—22no—
215#124—22no—
216#124C22⋊D1912yes—
217#123—24no—
218#123—24no—
219#123—22no—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222C22⋊Q8—24no—
223C22⋊Q8—22no—
224C22⋊Q8C22⋊D1912yes—
225#121—22no—
226#121C22⋊D1912yes—
227C4×Q8—22no—
228C4×Q8C2×Dic1912yes—
229C4×D4—22no—
230C4×D4—22no—
231C4×D4C2×Dic1912yes—
232#117—22no—
233#117—22no—
234#117—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—381no—
238C2×C42C22×D1911yescharacteristic
239C4⋊C8—382no—
240#103—764no—
241C22⋊C8—382no—
242#97—382no—
243#97—382no—
244#95—382no—
245C19#849811yescharacteristic, complemented, Sylow
246#41—82no—
247#41—82no—
248C2×Q8—22no—
249C2×Q8—22no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8C22⋊Dic1912yes—
253C2×Q8C22⋊Dic1912yes—
254C2×Q8C22⋊Dic1912yes—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4C22⋊Dic1912yes—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—761no—
262C22×C4C2×C22⋊D1911yescharacteristic
263C22×C4C2×C22⋊D1912yes—
264C2×C8—382no—
265C2×C8—761no—
266C2×C8—761no—
267C2×C8—762no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—762no—
279C4⋊C4C22⋊Dic1912yes—
280C4⋊C4C22⋊Dic1912yes—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42C22×Dic1911yescharacteristic
292C42C2×C22⋊D1912yes—
293C42C2×C22⋊D1911yescharacteristic
294C23—22no—
295C23#1059739911yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—42no—
299Q8—82no—
300Q8—82no—
301D4—42no—
302D4—42no—
303D4—42no—
304D4—82no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—84no—
317C2×C4—1522no—
318C2×C4—1521no—
319C2×C4C2×C22⋊Dic1912yes—
320C2×C4C2×C22⋊Dic1911yescharacteristic
321C2×C4#1059739912yes—
322C2×C4#1059739911yescharacteristic
323C8—762no—
324C8—1522no—
325C22—22no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22#1192640011yescharacteristic
330C22#1192671211yescharacteristic
331C22#1192672211yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—42no—
337C4—42no—
338C4—42no—
339C4—42no—
340C4—42no—
341C4—3041no—
342C2—21no—
343C2—21no—
344C2—82no—
345C2#1456358911yescharacteristic
346C2#1456361012yes—
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3544C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3544D19
hypocenterC19#8498
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3544

Complements

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

NH ≅ G/Ntype
1. #14564456C2semidirect
2. #14562361C2semidirect
3. #14562255C2semidirect
4. #14562173C2semidirect
16. Q82×C19C4semidirect
17. C19×#555C4semidirect
18. C19×#554C4semidirect
175. Q82Dic19semidirect
176. #555Dic19semidirect
177. #554Dic19semidirect
245. C19#8498semidirect

Maximal subgroups

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

subgroupindex
#145644562
#145623612
#145622552
#145621732
C19×#35442
#849819