Finite Group Databasebeta

← #18080762

Subgroups — #18080762

Order 4864.

392 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564571C211yesmaximal, characteristic
2#14563502C211yesmaximal, characteristic
3C4×#10597273C211yesmaximal, characteristic
4C2×#11926297C211yesmaximal, characteristic
5C2×#11926276C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic
7C19×#1273C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×#10597273C411yescharacteristic
12C2×#10597273C411yescharacteristic
13C2×#10597272—21no—
14C4×C4⋊Dic19C2211yescharacteristic
15#11926307C411yescharacteristic
16#11926307C411yescharacteristic
17#11926298—21no—
18#11926298—21no—
19#11926298—21no—
20#11926297—22no—
21#11926276—22no—
22C2×C4×C8×C19C2211yescharacteristic
23C2×C4×C8×C19C2211yescharacteristic
24C2×C4×C8×C19C2211yescharacteristic
25C22×Dic38C2×C411yescharacteristic
26C22×C8×C19—21no—
27C22×C8×C19C2×C411yescharacteristic
28C22×C8×C19C2×C411yescharacteristic
29C22×C8×C19D411yescharacteristic
30C22×C8×C19D411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19C2×C411yescharacteristic
33C2×C4⋊Dic19C2×C411yescharacteristic
34C2×C4⋊Dic19C2×C411yescharacteristic
35C2×Dic19⋊C4—21no—
36C2×C4×Dic19—21no—
37C2×C4×Dic19—21no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8—21no—
40C4×Dic38—21no—
41C4×Dic38—21no—
42C4×Dic38—21no—
43C4×Dic38—21no—
44C4×C8×C19—21no—
45C4×C8×C19—21no—
46C4×C8×C19—21no—
47C4×C8×C19—21no—
48C4×C8×C19—21no—
49C4×C8×C19—21no—
50C19⋊#95—21no—
51#10597273—22no—
52#10597273—22no—
53#10597272—42no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)D412yes—
58C22×C4×C19C22×C411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19#4111yescharacteristic
61C22×Dic19—21no—
62C22×Dic19—21no—
63C22×Dic19—21no—
64C22×Dic19—21no—
65C2×Dic38—21no—
66C2×Dic38—21no—
67C2×Dic38—21no—
68C2×Dic38—21no—
69C2×Dic38—21no—
70C2×Dic38M1612yes—
71C2×C8×C19—21no—
72C2×C8×C19—21no—
73C2×C8×C19—21no—
74C2×C8×C19—21no—
75C2×C8×C19—22no—
76C2×C8×C19—21no—
77C2×C8×C19—21no—
78C2×C8×C19—21no—
79C2×C8×C19—21no—
80C2×C8×C19—21no—
81C2×C8×C19—21no—
82C2×C8×C19—41no—
83C2×C8×C19—41no—
84C2×C8×C19M1612yes—
85C2×C8×C19Q1612yes—
86C42×C19C2×D411yescharacteristic
87C42×C19#4111yescharacteristic
88C42×C19#4111yescharacteristic
89C42×C19#4111yescharacteristic
90C4⋊Dic19—21no—
91C4⋊Dic19—21no—
92C4⋊Dic19—21no—
93C4⋊Dic19—21no—
94C4⋊Dic19—21no—
95C4⋊Dic19—21no—
96Dic19⋊C4—41no—
97Dic19⋊C4—41no—
98C4×Dic19—41no—
99C4×Dic19—41no—
100C4×Dic19—41no—
101C4×Dic19—41no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108#9548—191nomaximal, Sylow
109C23×C19C4×D411yescharacteristic
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19#11711yescharacteristic
113C2×C4×C19C4×D411yescharacteristic
114C2×C4×C19#12111yescharacteristic
115C2×C4×C19#12311yescharacteristic
116C2×C4×C19#12411yescharacteristic
117C2×C4×C19#12611yescharacteristic
118C2×C4×C19C2×M1611yescharacteristic
119C2×C4×C19C2×M1611yescharacteristic
120C2×C4×C19#13111yescharacteristic
121C2×C4×C19#13111yescharacteristic
122C2×C4×C19C2×Q1611yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×Dic19—22no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138Dic38—22no—
139Dic38—22no—
140Dic38—41no—
141Dic38—41no—
142C8×C19—22no—
143C8×C19—22no—
144C8×C19—42no—
145C8×C19—41no—
146C8×C19—41no—
147C19⋊C8—42no—
148C19⋊C8—81no—
149#1984—191no—
150#1770—191no—
151C4×#103—191no—
152C2×#335—191no—
153C2×Q8⋊C8—191no—
154#1279—191no—
155#1273D1911yescharacteristic
156C22×C19#38811yescharacteristic
157C22×C19#43511yescharacteristic
158C22×C19#43611yescharacteristic
159C22×C19C4×Q1611yescharacteristic
160C22×C19#44011yescharacteristic
161C22×C19#44311yescharacteristic
162C22×C19#44411yescharacteristic
163C4×C19—21no—
164C4×C19—21no—
165C4×C19#43211yescharacteristic
166C4×C19#43311yescharacteristic
167C4×C19#43511yescharacteristic
168C4×C19#43511yescharacteristic
169C4×C19#46211yescharacteristic
170C4×C19#46311yescharacteristic
171C4×C19#48411yescharacteristic
172C4×C19#48511yescharacteristic
173Dic19—42no—
174Dic19—81no—
175Dic19—81no—
176Dic19—81no—
177C2×C4×Q8—191no—
178C2×C4⋊C8—191no—
179C2×C4⋊C8—191no—
180C2×#103—191no—
181C2×#103—191no—
182C2×#97—381no—
183C2×C4×C8C2×D1911yescharacteristic
184C2×C4×C8C2×D1911yescharacteristic
185C2×C4×C8C2×D1911yescharacteristic
186C4×C4⋊C4—191no—
187#340—191no—
188#340—191no—
189#336—381no—
190#336—381no—
191#336—381no—
192#335—382no—
193Q8⋊C8—382no—
194C2×C19#158411yescharacteristic
195C2×C19#158811yescharacteristic
196C2×C19#159111yescharacteristic
197C2×C19#159211yescharacteristic
198C2×C19#192411yescharacteristic
199C2×C19#192811yescharacteristic
200C2×C19#192911yescharacteristic
201C22×Q8—191no—
202C22×C8—21no—
203C22×C8—381no—
204C22×C8—381no—
205C22×C8C4×D1911yescharacteristic
206C22×C8C4×D1911yescharacteristic
207C22×C8D7611yescharacteristic
208C22×C8D7611yescharacteristic
209C4×Q8—381no—
210C4×Q8—381no—
211C4×Q8—381no—
212C4×Q8—381no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—381no—
217C2×C42—381no—
218C2×C42—381no—
219C2×C42C22×D1911yescharacteristic
220C4⋊C8—192no—
221C4⋊C8—381no—
222C4⋊C8—381no—
223C4⋊C8—381no—
224#103—382no—
225#103—382no—
226#97—762no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233#95—381no—
234C19#954811yescharacteristic, complemented, Sylow
235C2×Q8—192no—
236C2×Q8—381no—
237C2×Q8—381no—
238C2×Q8—381no—
239C2×Q8—381no—
240C2×Q8—381no—
241C22×C4—381no—
242C22×C4—381no—
243C22×C4—381no—
244C22×C4—381no—
245C22×C4C2×C4×D1911yescharacteristic
246C22×C4C2×D7611yescharacteristic
247C22×C4#6454111yescharacteristic
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—22no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—382no—
262C2×C8—761no—
263C2×C8—761no—
264C2×C8—761no—
265C2×C8—761no—
266C2×C8—761no—
267C2×C8#6451512yes—
268C2×C8Dic7612yes—
269C4⋊C4—381no—
270C4⋊C4—381no—
271C4⋊C4—381no—
272C4⋊C4—381no—
273C4⋊C4—381no—
274C4⋊C4—381no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C42—761no—
278C42—761no—
279C42—761no—
280C42—761no—
281C42D4×D1911yescharacteristic
282C42#6454311yescharacteristic
283C42#6454311yescharacteristic
284C42#6454511yescharacteristic
285C23C4×D7611yescharacteristic
286Q8—382no—
287Q8—382no—
288Q8—761no—
289Q8—761no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—382no—
293C2×C4—761no—
294C2×C4—761no—
295C2×C4—761no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4(C22⋊D19)⋊C411yescharacteristic
305C2×C4#1059733111yescharacteristic
306C2×C4#1059733211yescharacteristic
307C2×C4#1059733811yescharacteristic
308C2×C4#1059734111yescharacteristic
309C2×C4#1059734411yescharacteristic
310C2×C4C2×#6451511yescharacteristic
311C2×C4#1059734711yescharacteristic
312C2×C4#1059735011yescharacteristic
313C2×C4C2×Dic7611yescharacteristic
314C2×C4M16×D1911yescharacteristic
315C2×C4#1059735311yescharacteristic
316C2×C4#1059735411yescharacteristic
317C2×C4#1059735511yescharacteristic
318C8—22no—
319C8—22no—
320C8—42no—
321C8—41no—
322C8—41no—
323C8—762no—
324C8—1521no—
325C22#1192643611yescharacteristic
326C22#1192661711yescharacteristic
327C22#1192662311yescharacteristic
328C22C4×Dic7611yescharacteristic
329C22#1192664611yescharacteristic
330C22#1192666211yescharacteristic
331C22#1192666711yescharacteristic
332C4—21no—
333C4—21no—
334C4—762no—
335C4—1521no—
336C4—1521no—
337C4—1521no—
338C4#1192660011yescharacteristic
339C4#1192660411yescharacteristic
340C4#1192661211yescharacteristic
341C4#1192661811yescharacteristic
342C4#1192675511yescharacteristic
343C4#1192676011yescharacteristic
344C4#1192688011yescharacteristic
345C4#1192688611yescharacteristic
346C2#1456248711yescharacteristic
347C2#1456251511yescharacteristic
348C2#1456253311yescharacteristic
349C2#1456253911yescharacteristic
350C2#1456424911yescharacteristic
351C2#1456427711yescharacteristic
352C2#1456428411yescharacteristic
subgroupG/H
centerC22×C4C2×D76
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1273C2
socle, prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenter#1273D19
hypocenterC19#9548
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1273

Complements

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

NH ≅ G/Ntype
234. C19#9548semidirect

Maximal subgroups

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

subgroupindex
#145645712
#145635022
C4×#105972732
C2×#119262972
C2×#119262762
#145614752
C19×#12732
#954819