Finite Group Databasebeta

← #18086976

Subgroups — #18086976

Order 4864.

494 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568661C211yesmaximal, characteristic
2#14564391C211yesmaximal, characteristic
3#14563794C211yesmaximal, characteristic
4#14561519C211yesmaximal, characteristic
5#14561476C211yesmaximal, characteristic
6#14561474C211yesmaximal, characteristic
7C19×#1947C211yesmaximal, characteristic
8C2×#10597315—21no—
9C2×#10597334—21no—
10C2×#10597264—21no—
11C2×#10597264—22no—
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13C2×C4×C19⋊C8C2211yescharacteristic
14#11926465—22no—
15#11926443—21no—
16#11926442—21no—
17#11926414C2211yescharacteristic
18C4×C4⋊Dic19C2211yescharacteristic
19#11926306—21no—
20C2×C19×#107—21no—
21C2×C19×C4⋊C8C2211yescharacteristic
22C19×#384C2211yescharacteristic
23C4×C4⋊C4×C19C2211yescharacteristic
24C19×#340—21no—
25C22×Dic38—22no—
26C22×C8×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C42×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19—22no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4⋊Dic19D412yes—
40C2×Dic19⋊C4—22no—
41C2×C4×Dic19—21no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8—21no—
44#10597334—42no—
45#10597334—42no—
46#10597315—42no—
47#10597315—42no—
48C19×#107—42no—
49C19×C4⋊C8—21no—
50C19×C4⋊C8Q812yescomplemented
51C19×#95—21no—
52C19⋊#95—22no—
53C19⋊#95—21no—
54#10597264—44no—
55#10597264—42no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)Q812yescomplemented
58C4×C19⋊C8—21no—
59C4×C19⋊C8Q812yescomplemented
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—41no—
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×Dic19—21no—
67C22×Dic19—21no—
68C22×Dic19—22no—
69C2×Dic38—44no—
70C2×Dic38—44no—
71C2×Dic38—82no—
72C2×C8×C19—22no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C4⋊C4×C19—21no—
76C4⋊C4×C19—21no—
77C4⋊C4×C19—42no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19D812yes—
83C4⋊C4×C19Q1612yes—
84C42×C19—41no—
85C42×C19—41no—
86C42×C19C2×Q811yescharacteristic
87C42×C19C2×Q811yescharacteristic
88C42×C19C2×Q811yescharacteristic
89C42×C19#4111yescharacteristic
90C4⋊Dic19—21no—
91C4⋊Dic19—21no—
92C4⋊Dic19—44no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95C4⋊Dic19—41no—
96C4⋊Dic19—41no—
97C4⋊Dic19—42no—
98C4⋊Dic19D812yes—
99C4⋊Dic19Q1612yes—
100Dic19⋊C4—44no—
101C4×Dic19—41no—
102C4×Dic19—41no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—22no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109#10573—191nomaximal, Sylow
110C23×C19#12011yescharacteristic
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—81no—
120C2×C4×C19—81no—
121C2×C4×C19—81no—
122C2×C4×C19C22⋊Q811yescharacteristic
123C2×C4×C19C22⋊Q811yescharacteristic
124C2×C4×C19C22⋊Q811yescharacteristic
125C2×C4×C19C4⋊Q811yescharacteristic
126C2×C4×C19C4⋊Q811yescharacteristic
127C2×C4×C19C4⋊Q811yescharacteristic
128C2×C4×C19C2×D811yescharacteristic
129C2×C4×C19C2×D811yescharacteristic
130C2×C4×C19C2×Q1611yescharacteristic
131C2×C4×C19C2×Q1611yescharacteristic
132C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×C4×C19#13711yescharacteristic
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—42no—
145Dic38—88no—
146C8×C19—42no—
147C19⋊C8—24no—
148C19⋊C8—42no—
149#2551—191no—
150#1947—191no—
151#1947D1911yescharacteristic
152#1845—191no—
153#1296—191no—
154#1279—191no—
155#1279—191no—
156C22×C19#39511yescharacteristic
157C22×C19#44711yescharacteristic
158C22×C19#44711yescharacteristic
159C22×C19#45111yescharacteristic
160C22×C19#45111yescharacteristic
161C22×C19#45311yescharacteristic
162C22×C19#45611yescharacteristic
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—42no—
166C4×C19—42no—
167C4×C19—161no—
168C4×C19#47411yescharacteristic
169C4×C19#47411yescharacteristic
170C4×C19#47711yescharacteristic
171C4×C19#47711yescharacteristic
172C4×C19#50011yescharacteristic
173C4×C19#50011yescharacteristic
174C4×C19#50111yescharacteristic
175C4×C19#50111yescharacteristic
176Dic19—42no—
177Dic19—42no—
178Dic19—82no—
179C2×C4⋊Q8—381no—
180C2×C4⋊Q8—381no—
181C2×#107—21no—
182C2×#107—382no—
183C2×#107—381no—
184C2×C4⋊C8—191no—
185C2×C4⋊C8C2×D1911yescharacteristic
186C2×C4×C8—191no—
187#395—382no—
188#389—381no—
189#389—381no—
190#384—191no—
191#384C2×D1911yescharacteristic
192C4×C4⋊C4—191no—
193C4×C4⋊C4C2×D1911yescharacteristic
194#340—21no—
195#340—381no—
196C2×C19#161911yescharacteristic
197C2×C19#163311yescharacteristic
198C2×C19#164911yescharacteristic
199C2×C19#164911yescharacteristic
200C2×C19#205711yescharacteristic
201C2×C19#205711yescharacteristic
202C2×C19#206011yescharacteristic
203C22×Q8—382no—
204C22×C8—21no—
205C22×C8—381no—
206C22×C8—381no—
207C4⋊Q8—762no—
208C4⋊Q8—762no—
209C4⋊Q8—762no—
210C4⋊Q8—762no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—192no—
217C2×C4⋊C4—382no—
218C2×C4⋊C4—382no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4—381no—
221C2×C4⋊C4C22⋊D1911yescharacteristic
222C2×C4⋊C4C22⋊D1911yescharacteristic
223C2×C42—21no—
224C2×C42—381no—
225C2×C42C22×D1911yescharacteristic
226#107—42no—
227#107—762no—
228#107—764no—
229C4⋊C8—21no—
230C4⋊C8—192no—
231C4⋊C8—381no—
232C4⋊C8Dic3812yescomplemented
233C4×C8—192no—
234C4×C8—381no—
235#95—21no—
236#95—382no—
237#95—381no—
238C19#1057311yescharacteristic, complemented, Sylow
239C2×Q8—764no—
240C2×Q8—764no—
241C2×Q8—1522no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—381no—
246C22×C4—381no—
247C22×C4—382no—
248C22×C4D4×D1911yescharacteristic
249C22×C4D4×D1911yescharacteristic
250C22×C4C2×C22⋊D1911yescharacteristic
251C2×C8—22no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—382no—
255C2×C8—382no—
256C2×C8—382no—
257C2×C8—382no—
258C2×C8—761no—
259C2×C8—761no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—192no—
268C4⋊C4—192no—
269C4⋊C4—381no—
270C4⋊C4—381no—
271C4⋊C4—762no—
272C4⋊C4—764no—
273C4⋊C4—764no—
274C4⋊C4—761no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C4⋊C4—761no—
278C4⋊C4#6452512yes—
279C4⋊C4#6452812yes—
280C42—41no—
281C42—41no—
282C42—761no—
283C42—761no—
284C42C2×Dic3811yescharacteristic
285C42#6454111yescharacteristic
286C42Q8×D1911yescharacteristic
287C42Q8×D1911yescharacteristic
288C23#1059738311yescharacteristic
289Q8—1528no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—382no—
302C2×C4—382no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—762no—
310C2×C4#1059733411yescharacteristic
311C2×C4#1059733411yescharacteristic
312C2×C4#1059734211yescharacteristic
313C2×C4#1059734211yescharacteristic
314C2×C4D8×D1911yescharacteristic
315C2×C4#1059735711yescharacteristic
316C2×C4Q16×D1911yescharacteristic
317C2×C4#1059736411yescharacteristic
318C2×C4#1059737011yescharacteristic
319C2×C4C2×#6452511yescharacteristic
320C2×C4C2×#6452811yescharacteristic
321C2×C4#1059739011yescharacteristic
322C2×C4#1059739511yescharacteristic
323C2×C4#1059739711yescharacteristic
324C8—42no—
325C8—384no—
326C8—762no—
327C22#1192646411yescharacteristic
328C22#1192667611yescharacteristic
329C22#1192667711yescharacteristic
330C22#1192669811yescharacteristic
331C22#1192669911yescharacteristic
332C22#1192671011yescharacteristic
333C22#1192672511yescharacteristic
334C4—21no—
335C4—21no—
336C4—42no—
337C4—42no—
338C4—161no—
339C4—762no—
340C4—762no—
341C4—1522no—
342C4#1192682311yescharacteristic
343C4#1192682411yescharacteristic
344C4#1192683811yescharacteristic
345C4#1192683911yescharacteristic
346C4#1192694711yescharacteristic
347C4#1192694811yescharacteristic
348C4#1192695211yescharacteristic
349C4#1192695411yescharacteristic
350C2#1456268811yescharacteristic
351C2#1456277411yescharacteristic
352C2#1456288211yescharacteristic
353C2#1456288311yescharacteristic
354C2#1456496111yescharacteristic
355C2#1456496311yescharacteristic
356C2#1456497811yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1947C2
socle, prime radicalC23×C19#120
hypercenter#1947D19
hypocenterC19#10573
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
50. C19×C4⋊C8Q8semidirect
57. C4⋊(C19⋊C8)Q8semidirect
59. C4×C19⋊C8Q8semidirect
232. C4⋊C8Dic38semidirect
238. C19#10573semidirect

Maximal subgroups

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

subgroupindex
#145686612
#145643912
#145637942
#145615192
#145614762
#145614742
C19×#19472
#1057319