Finite Group Databasebeta

← #18076818

Subgroups — #18076818

Order 4864.

388 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563806C211yesmaximal, characteristic, complemented
2#14562423C211yesmaximal, characteristic, complemented
3#14562074C211yesmaximal, characteristic
4#14562017C211yesmaximal, characteristic
5#14561524C211yesmaximal, characteristic, complemented
6#14561471C211yesmaximal, characteristic, complemented
7C19×#2991C211yesmaximal, characteristic
8#11926597C2211yescharacteristic
9C2×#10597279—22no—
10#11926568C2211yescharacteristic
11C4×#64520C2211yescharacteristic
12C2×C4×C19⋊C8C2211yescharacteristic
13#11926296—21no—
14#11926294—21no—
15Q8⋊(C19⋊C8)—21no—
16Q8⋊(C19⋊C8)C411yescharacteristic
17Q8⋊(C19⋊C8)C411yescharacteristic
18D4⋊(C19⋊C8)—21no—
19D4⋊(C19⋊C8)C411yescharacteristic
20D4⋊(C19⋊C8)C411yescharacteristic
21C4×#41×C19C2211yescharacteristic
22C8×Q8×C19—21no—
23C19×#436—22no—
24C19×#436—21no—
25C19×#431—21no—
26C19×#431C2211yescharacteristic
27C19×#423—21no—
28C19×#423C2211yescharacteristic
29C2×#41×C19Q811yescharacteristic
30C2×M16×C19—22no—
31C2×M16×C19D412yes—
32C4×Q8×C19C2×C411yescharacteristic
33C4×Q8×C19D411yescharacteristic
34C4×D4×C19—21no—
35C4×D4×C19—21no—
36C4×D4×C19C2×C411yescharacteristic
37C4×D4×C19D411yescharacteristic
38C19×#117—21no—
39C19×#117Q811yescharacteristic
40C2×C42×C19—21no—
41C2×C42×C19C2311yescharacteristic
42C2×#64520—21no—
43C2×#64520—21no—
44C22×C19⋊C8—21no—
45C19×C4⋊C8—22no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8D411yescharacteristic
49C19×C4⋊C8D411yescharacteristic
50C19×C22⋊C8—22no—
51C19×C22⋊C8—21no—
52C4×C8×C19—22no—
53C4×C8×C19—21no—
54C22⋊(C19⋊C8)—21no—
55#10597279—44no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)C2×C411yescharacteristic
59C4⋊(C19⋊C8)C2×C411yescharacteristic
60#10597260—21no—
61C4×C19⋊C8—21no—
62C4×C19⋊C8—21no—
63C4×C19⋊C8—21no—
64C4×C19⋊C8C2×C411yescharacteristic
65C4×C19⋊C8C2×C411yescharacteristic
66#41×C19—22no—
67#41×C19—41no—
68C2×Q8×C19C4⋊C411yescharacteristic
69C2×D4×C19—21no—
70C2×D4×C19C4⋊C411yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×Q811yescharacteristic
76C22×C4×C19#4111yescharacteristic
77M16×C19—42no—
78M16×C19—82no—
79C2×C8×C19—21no—
80C2×C8×C19—22no—
81C2×C8×C19—21no—
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19C4⋊C411yescharacteristic
85C4⋊C4×C19C4⋊C411yescharacteristic
86C22⋊C4×C19—21no—
87C22⋊C4×C19—21no—
88C22⋊C4×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19C22×C411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19C2×D411yescharacteristic
95C42×C19#4111yescharacteristic
96#64520—22no—
97#64520—41no—
98#64520—42no—
99C2×C19⋊C8—22no—
100C2×C19⋊C8—22no—
101C2×C19⋊C8—21no—
102C2×C19⋊C8—21no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—41no—
107#8899—191nomaximal, Sylow
108C23×C19—21no—
109C23×C19C22⋊Q811yescharacteristic
110Q8×C19—21no—
111Q8×C19#10812yescomplemented
112D4×C19—21no—
113D4×C19—21no—
114D4×C19—42no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—42no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19C2×C4⋊C411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19C22⋊Q811yescharacteristic
134C2×C4×C19#12311yescharacteristic
135C8×C19—42no—
136C8×C19—41no—
137C8×C19—41no—
138C19⋊C8—22no—
139C19⋊C8—22no—
140C19⋊C8—42no—
141C19⋊C8—41no—
142C19⋊C8—41no—
143C19⋊C8—81no—
144#2991D1911yescharacteristic
145#1848—191no—
146#1574—191no—
147#1489—191no—
148#1476—191no—
149#1299—191no—
150#1278—191no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—21no—
154C22×C19—41no—
155C22×C19—41no—
156C22×C19—41no—
157C22×C19#38511yescharacteristic
158C4×C19—21no—
159C4×C19—22no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19C2×#10811yescharacteristic
165C4×C19#43011yescharacteristic
166C4×C19#44311yescharacteristic
167C4×C19#44411yescharacteristic
168C4×C19#45311yescharacteristic
169C4×C19#45611yescharacteristic
170C4×#41C2×D1911yescharacteristic
171C8×Q8—21no—
172#436—22no—
173#436—21no—
174#431—21no—
175#431—191no—
176#431C2×D1911yescharacteristic
177C2×#108—382no—
178#423—21no—
179#423—191no—
180#423C2×D1911yescharacteristic
181C4×M16—191no—
182C2×C4×C8—191no—
183#335—381no—
184#334—381no—
185Q8⋊C8—191no—
186Q8⋊C8—191no—
187Q8⋊C8—381no—
188D4⋊C8—191no—
189D4⋊C8—191no—
190D4⋊C8—381no—
191C2×C19—41no—
192C2×C19—81no—
193C2×C19#185511yescharacteristic
194C2×C19#185911yescharacteristic
195C2×C19#186611yescharacteristic
196C2×#41Dic3811yescharacteristic
197C2×M16—22no—
198C2×M16—381no—
199C2×M16—381no—
200C2×M16C22⋊D1912yes—
201C22×C8—381no—
202C4×Q8C4×D1911yescharacteristic
203C4×Q8C22⋊D1911yescharacteristic
204C4×D4—21no—
205C4×D4—21no—
206C4×D4C4×D1911yescharacteristic
207C4×D4C22⋊D1911yescharacteristic
208#117—21no—
209#117Dic3811yescharacteristic
210C2×C42—21no—
211C2×C42C22×D1911yescharacteristic
212#108—764no—
213C4⋊C8—22no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—191no—
217C4⋊C8—191no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220C4⋊C8C22⋊D1911yescharacteristic
221C4⋊C8C22⋊D1911yescharacteristic
222C22⋊C8—22no—
223C22⋊C8—21no—
224C22⋊C8—381no—
225#97—381no—
226C4×C8—22no—
227C4×C8—21no—
228C4×C8—191no—
229C4×C8—191no—
230C4×C8—381no—
231C4×C8—381no—
232C4×C8—381no—
233C19#889911yescharacteristic, complemented, Sylow
234#41—22no—
235#41—41no—
236C2×Q8Dic19⋊C411yescharacteristic
237C2×D4—21no—
238C2×D4Dic19⋊C411yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic3811yescharacteristic
243C22×C4#6454111yescharacteristic
244C22×C4C2×C22⋊D1911yescharacteristic
245M16—42no—
246M16—82no—
247M16—382no—
248M16—761no—
249M16—762no—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—21no—
253C2×C8—382no—
254C2×C8—382no—
255C2×C8—381no—
256C2×C8—381no—
257C2×C8—381no—
258C2×C8—381no—
259C2×C8—761no—
260C2×C8—761no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4Dic19⋊C411yescharacteristic
264C4⋊C4Dic19⋊C411yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42C2×C4×D1911yescharacteristic
272C42#6454111yescharacteristic
273C42C2×C22⋊D1911yescharacteristic
274C42C2×C22⋊D1911yescharacteristic
275C23—21no—
276C23#1059737011yescharacteristic
277Q8—21no—
278Q8#1059727912yescomplemented
279D4—21no—
280D4—21no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4C2×Dic19⋊C411yescharacteristic
297C2×C4#1059737011yescharacteristic
298C2×C4C4×C22⋊D1911yescharacteristic
299C2×C4C4×C22⋊D1911yescharacteristic
300C2×C4#1059737511yescharacteristic
301C2×C4#1059739911yescharacteristic
302C8—42no—
303C8—41no—
304C8—41no—
305C8—382no—
306C8—382no—
307C8—762no—
308C8—761no—
309C8—761no—
310C8—1521no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1192641711yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4C2×#1059727911yescharacteristic
325C4#1192659211yescharacteristic
326C4#1192665911yescharacteristic
327C4#1192666411yescharacteristic
328C4#1192671211yescharacteristic
329C4#1192672711yescharacteristic
330C2—41no—
331C2—81no—
332C2#1456384011yescharacteristic
333C2#1456386111yescharacteristic
334C2#1456391011yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2991C2
socleC22×C19#385
prime radicalC2×#41×C19Q8
cosocleC2×C42×C19C23
hypercenter#2991D19
hypocenterC19#8899
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2991

Complements

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

NH ≅ G/Ntype
1. #14563806C2semidirect
2. #14562423C2semidirect
5. #14561524C2semidirect
6. #14561471C2semidirect
111. Q8×C19#108semidirect
233. C19#8899semidirect
278. Q8#10597279semidirect

Maximal subgroups

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

subgroupindex
#145638062
#145624232
#145620742
#145620172
#145615242
#145614712
C19×#29912
#889919