Finite Group Databasebeta

← #18088152

Subgroups — #18088152

Order 4864.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926299C211yesmaximal, characteristic
2C2×#11926298C212yesmaximal
3C2×#11926298C212yesmaximal
4C4×C19⋊#95C211yesmaximal, characteristic
5C22×C4×C8×C19C211yesmaximal, characteristic
6C23×C19⋊C8C2212yes—
7C22×C4×Dic19C2212yes—
8C2×C19⋊#95C412yes—
9C2×C19⋊#95C412yes—
10#11926299C414yescomplemented
11#11926298—24no—
12#11926298—24no—
13C23×C8×C19C2211yescharacteristic
14C23×C8×C19C2211yescharacteristic
15C22×C42×C19C2211yescharacteristic
16C2×C4×C8×C19—24no—
17C2×C4×C8×C19C414yescomplemented
18C23×C4×C19C2×C411yescharacteristic
19C23×C4×C19C2×C411yescharacteristic
20C23×C4×C19C2311yescharacteristic
21C23×Dic19C2×C414yes—
22C22×C8×C19—22no—
23C22×C8×C19—22no—
24C22×C8×C19—22no—
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C22×C8×C19C2×C412yes—
28C22×C8×C19C2×C412yes—
29C22×C8×C19D414yes—
30C22×C8×C19D412yes—
31C22×C8×C19Q812yes—
32C2×C42×C19—22no—
33C2×C42×C19—22no—
34C2×C42×C19C2×C412yes—
35C2×C42×C19C2×C412yes—
36C2×C4×Dic19—22no—
37C2×C4×Dic19—22no—
38C2×C4×Dic19—22no—
39C2×C4×Dic19—22no—
40C2×C4×Dic19—22no—
41C2×C4×Dic19—22no—
42C22×C19⋊C8—22no—
43C22×C19⋊C8—22no—
44C22×C19⋊C8—22no—
45C22×C19⋊C8—22no—
46C22×C19⋊C8—22no—
47C22×C19⋊C8—22no—
48C22×C19⋊C8C2×C414yes—
49C4×C8×C19—28no—
50C19⋊#95—24no—
51C19⋊#95C818yescomplemented
52C24×C19C22×C411yescharacteristic
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19C4212yes—
58C22×C4×C19C4212yes—
59C22×C4×C19C2×C814yes—
60C22×C4×C19M1614yes—
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×Q811yescharacteristic
66C22×C4×C19#4112yes—
67C22×C4×C19#4112yes—
68C22×C4×C19#4111yescharacteristic
69C22×C4×C19#4112yes—
70C22×C4×C19#4111yescharacteristic
71C22×Dic19—24no—
72C22×Dic19—24no—
73C22×Dic19—24no—
74C22×Dic19—24no—
75C22×Dic19—24no—
76C22×Dic19—24no—
77C22×Dic19C2×C818yes—
78C2×C8×C19—22no—
79C2×C8×C19—22no—
80C2×C8×C19—22no—
81C2×C8×C19—22no—
82C2×C8×C19—24no—
83C2×C8×C19—24no—
84C2×C8×C19—24no—
85C2×C8×C19—24no—
86C2×C8×C19C22⋊C414yes—
87C2×C8×C19C4⋊C414yes—
88C42×C19—22no—
89C42×C19—22no—
90C42×C19—24no—
91C4×Dic19—42no—
92C4×Dic19—42no—
93C4×Dic19—42no—
94C4×Dic19—42no—
95C2×C19⋊C8—24no—
96C2×C19⋊C8—24no—
97C2×C19⋊C8—24no—
98C2×C19⋊C8—42no—
99C2×C19⋊C8—42no—
100C2×C19⋊C8—42no—
101C2×C19⋊C8—42no—
102#10797—191nomaximal, Sylow
103C23×C19C2×C4211yescharacteristic
104C23×C19#11712yes—
105C23×C19C4×D411yescharacteristic
106C23×C19C4×D412yes—
107C23×C19C4×Q811yescharacteristic
108C23×C19C22×C812yes—
109C23×C19C2×M1612yes—
110C23×C19#13112yes—
111C23×C19#13112yes—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—28no—
117C2×C4×C19—28no—
118C2×C4×C19C4×C814yes—
119C2×C4×C19#9714yes—
120C2×C4×C19C2×C22⋊C411yescharacteristic
121C2×C4×C19C2×C4⋊C411yescharacteristic
122C2×C4×C19#11712yes—
123C2×C4×C19#11711yescharacteristic
124C2×C4×C19#11711yescharacteristic
125C2×C4×C19#11711yescharacteristic
126C2×C4×C19#11711yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19C4×D412yes—
129C2×C4×C19C4×Q811yescharacteristic
130C2×C4×C19#12112yes—
131C2×C4×C19C22⋊Q812yes—
132C2×C4×C19#12312yes—
133C2×C4×C19#12312yes—
134C2×C4×C19#12412yes—
135C2×C4×C19#12512yes—
136C2×C4×C19#12612yes—
137C2×C4×C19#12612yes—
138C2×Dic19—28no—
139C2×Dic19—28no—
140C2×Dic19—28no—
141C2×Dic19—44no—
142C2×Dic19—44no—
143C2×Dic19—44no—
144C2×Dic19—44no—
145C8×C19—24no—
146C8×C19—24no—
147C19⋊C8—44no—
148C22×C4×C8D1911yescharacteristic
149C2×#336—191no—
150C2×#336—192no—
151C2×#336—192no—
152C4×#95—191no—
153C22×C19#37611yescharacteristic
154C22×C19C4×C22⋊C411yescharacteristic
155C22×C19C4×C4⋊C411yescharacteristic
156C22×C19#38712yes—
157C22×C19#38812yes—
158C22×C19C2×C4×C811yescharacteristic
159C22×C19C2×#9711yescharacteristic
160C22×C19#40511yescharacteristic
161C22×C19#40511yescharacteristic
162C22×C19#43114yes—
163C22×C19#43314yes—
164C22×C19C8×D414yes—
165C22×C19C8×D412yes—
166C22×C19#43514yes—
167C22×C19#43612yes—
168C22×C19C8×Q812yes—
169C22×C19#44612yes—
170C4×C19—24no—
171C4×C19—24no—
172C4×C19#38011yescharacteristic
173C4×C19#38111yescharacteristic
174C4×C19#38211yescharacteristic
175C4×C19#38311yescharacteristic
176C4×C19#38712yes—
177C4×C19#38812yes—
178Dic19—48no—
179C23×C8—192no—
180C23×C8C2×D1911yescharacteristic
181C23×C8C2×D1911yescharacteristic
182C22×C42—192no—
183C22×C42C2×D1911yescharacteristic
184C2×C4×C8—24no—
185C2×C4×C8Dic1914yescomplemented
186C2×#95—192no—
187C2×#95—192no—
188#336—194no—
189#336—384no—
190#336—384no—
191C2×C19#143411yescharacteristic
192C2×C19#174411yescharacteristic
193C2×C19#174611yescharacteristic
194C2×C19C8×C22⋊C411yescharacteristic
195C2×C19#175211yescharacteristic
196C2×C19C8×C4⋊C411yescharacteristic
197C2×C19#177011yescharacteristic
198C2×C19#191614yes—
199C2×C19#192314yes—
200C23×C4—194no—
201C23×C4C4×D1911yescharacteristic
202C23×C4C4×D1911yescharacteristic
203C23×C4C22×D1911yescharacteristic
204C22×C8—22no—
205C22×C8—21no—
206C22×C8—22no—
207C22×C8—21no—
208C22×C8—22no—
209C22×C8—194no—
210C22×C8—382no—
211C22×C8—382no—
212C22×C8—382no—
213C22×C8—382no—
214C22×C8—382no—
215C22×C8—382no—
216C22×C8Dic3812yes—
217C22×C8D7612yes—
218C22×C8C2×Dic1912yes—
219C22×C8C2×Dic1912yes—
220C22×C8C22⋊D1914yes—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—382no—
224C2×C42—382no—
225C2×C42—382no—
226C2×C42—382no—
227C2×C42—382no—
228C2×C42—382no—
229C2×C42C4×D1912yes—
230C2×C42C2×Dic1912yes—
231C4×C8—28no—
232#95—198no—
233#95—384no—
234C19#1079711yescharacteristic, complemented, Sylow
235C24C2×C4×D1911yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—198no—
241C22×C4—384no—
242C22×C4—384no—
243C22×C4—384no—
244C22×C4—384no—
245C22×C4—384no—
246C22×C4—384no—
247C22×C4C8×D1914yes—
248C22×C4#6451514yes—
249C22×C4C4×Dic1912yes—
250C22×C4C4×Dic1912yes—
251C22×C4C2×Dic3811yescharacteristic
252C22×C4C2×C4×D1911yescharacteristic
253C22×C4C2×D7611yescharacteristic
254C22×C4#6454112yes—
255C22×C4#6454111yescharacteristic
256C22×C4#6454112yes—
257C22×C4#6454112yes—
258C22×C4#6454111yescharacteristic
259C22×C4C22×Dic1911yescharacteristic
260C22×C4C2×C22⋊D1912yes—
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—24no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—384no—
270C2×C8—384no—
271C2×C8—384no—
272C2×C8—762no—
273C2×C8—762no—
274C2×C8—762no—
275C2×C8—762no—
276C2×C8C4⋊Dic1914yes—
277C2×C8C22⋊Dic1914yes—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—762no—
282C42—762no—
283C42—762no—
284C42—762no—
285C23C4×Dic3811yescharacteristic
286C23#1059731812yes—
287C23C4×D7611yescharacteristic
288C23C2×C8×D1912yes—
289C23C2×#6451512yes—
290C23#1059734712yes—
291C23#1059734712yes—
292C23C2×C4×Dic1911yescharacteristic
293C23C4×C22⋊D1912yes—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—388no—
301C2×C4—388no—
302C2×C4—388no—
303C2×C4—764no—
304C2×C4—764no—
305C2×C4—764no—
306C2×C4—764no—
307C2×C4C8×Dic1914yes—
308C2×C4#1059727214yes—
309C2×C4C4×Dic3811yescharacteristic
310C2×C4#1059731612yes—
311C2×C4#1059731812yes—
312C2×C4C4×D7611yescharacteristic
313C2×C4#1059732112yes—
314C2×C4#1059732212yes—
315C2×C4#1059732212yes—
316C2×C4#1059737012yes—
317C2×C4C2×C4⋊Dic1911yescharacteristic
318C2×C4#1059737211yescharacteristic
319C2×C4#1059737211yescharacteristic
320C2×C4#1059737211yescharacteristic
321C2×C4#1059737211yescharacteristic
322C2×C4C4×C22⋊D1912yes—
323C2×C4#1059737512yes—
324C2×C4#1059737512yes—
325C2×C4#1059737612yes—
326C2×C4C2×C22⋊Dic1911yescharacteristic
327C8—24no—
328C8—24no—
329C8—764no—
330C22#1192639011yescharacteristic
331C22C4×C22⋊Dic1911yescharacteristic
332C22C4×C4⋊Dic1911yescharacteristic
333C22#1192642812yes—
334C22#1192643512yes—
335C22C2×C8×Dic1911yescharacteristic
336C22C2×#1059727211yescharacteristic
337C22#1192649911yescharacteristic
338C22#1192649911yescharacteristic
339C22#1192659514yes—
340C22#1192660314yes—
341C22C8×C22⋊D1914yes—
342C22C8×D7612yes—
343C22#1192661514yes—
344C22#1192662312yes—
345C22C8×Dic3812yes—
346C22#1192667412yes—
347C4—24no—
348C4—24no—
349C4—768no—
350C4#1192640411yescharacteristic
351C4#1192640711yescharacteristic
352C4#1192641011yescharacteristic
353C4#1192641211yescharacteristic
354C4#1192642812yes—
355C4#1192643512yes—
356C2#1456186211yescharacteristic
357C2#1456338011yescharacteristic
358C2#1456338611yescharacteristic
359C2C8×C22⋊Dic1911yescharacteristic
360C2#1456341111yescharacteristic
361C2C8×C4⋊Dic1911yescharacteristic
362C2#1456350211yescharacteristic
363C2#1456419214yes—
364C2#1456424114yes—
subgroupG/H
center, FrattiniC23×C4C22×D19
commutatorC22×C19C2×C4×C8
FittingC22×C4×C8×C19C2
socle, prime radicalC24×C19C22×C4
cosocleC23×C4×C19C23
hypercenterC22×C4×C8D19
hypocenterC19#10797
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

Complements

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

NH ≅ G/Ntype
10. #11926299C4semidirect
17. C2×C4×C8×C19C4semidirect
51. C19⋊#95C8semidirect
185. C2×C4×C8Dic19semidirect
234. C19#10797semidirect

Maximal subgroups

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

subgroupindex
C2×#119262992
C2×#119262982
C4×C19⋊#952
C22×C4×C8×C192
#1079719