Finite Group Databasebeta

← #18088153

Subgroups — #18088153

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
1C22×C4×C19⋊C8C211yesmaximal, characteristic
2C2×#11926299C212yesmaximal
3C2×#11926299C212yesmaximal
4C2×#11926299C211yesmaximal, characteristic
5C4×C19×#95C211yesmaximal, characteristic
6C23×C19⋊C8C2212yes—
7C23×C19⋊C8C2211yescharacteristic
8C23×C19⋊C8C2211yescharacteristic
9C2×C4×C19⋊C8—24no—
10C2×C4×C19⋊C8C414yescomplemented
11#11926299—24no—
12#11926299—24no—
13#11926299C414yescomplemented
14C22×C42×C19C2212yes—
15C22×C42×C19C2211yescharacteristic
16C2×C19×#95C412yes—
17C2×C19×#95C412yes—
18C23×C4×C19C2×C414yes—
19C23×C4×C19C2×C411yescharacteristic
20C23×C4×C19C2×C411yescharacteristic
21C23×C4×C19C2311yescharacteristic
22C2×C42×C19—22no—
23C2×C42×C19—22no—
24C2×C42×C19—22no—
25C2×C42×C19—22no—
26C2×C42×C19—22no—
27C2×C42×C19—22no—
28C2×C42×C19—22no—
29C2×C42×C19—22no—
30C2×C42×C19C2×C412yes—
31C2×C42×C19C2×C412yes—
32C22×C19⋊C8—22no—
33C22×C19⋊C8—22no—
34C22×C19⋊C8—22no—
35C22×C19⋊C8—21no—
36C22×C19⋊C8—21no—
37C22×C19⋊C8—22no—
38C22×C19⋊C8—22no—
39C22×C19⋊C8—22no—
40C22×C19⋊C8—22no—
41C22×C19⋊C8—22no—
42C22×C19⋊C8—22no—
43C22×C19⋊C8C2×C414yes—
44C22×C19⋊C8C2×C412yes—
45C22×C19⋊C8C2×C412yes—
46C22×C19⋊C8D414yes—
47C22×C19⋊C8D412yes—
48C22×C19⋊C8Q812yes—
49C19×#95—24no—
50C19×#95C818yescomplemented
51C4×C19⋊C8—28no—
52C24×C19C22×C411yescharacteristic
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—24no—
58C22×C4×C19—24no—
59C22×C4×C19—24no—
60C22×C4×C19—24no—
61C22×C4×C19—24no—
62C22×C4×C19—24no—
63C22×C4×C19C4212yes—
64C22×C4×C19C4212yes—
65C22×C4×C19C2×C818yes—
66C22×C4×C19C2×C814yes—
67C22×C4×C19M1614yes—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C22×C411yescharacteristic
70C22×C4×C19C2×D412yes—
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×Q811yescharacteristic
73C22×C4×C19#4112yes—
74C22×C4×C19#4112yes—
75C22×C4×C19#4112yes—
76C22×C4×C19#4111yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C42×C19—22no—
79C42×C19—22no—
80C42×C19—24no—
81C42×C19—42no—
82C42×C19—42no—
83C42×C19—42no—
84C42×C19—42no—
85C2×C19⋊C8—22no—
86C2×C19⋊C8—22no—
87C2×C19⋊C8—22no—
88C2×C19⋊C8—22no—
89C2×C19⋊C8—24no—
90C2×C19⋊C8—24no—
91C2×C19⋊C8—24no—
92C2×C19⋊C8—24no—
93C2×C19⋊C8—24no—
94C2×C19⋊C8—24no—
95C2×C19⋊C8—24no—
96C2×C19⋊C8—42no—
97C2×C19⋊C8—42no—
98C2×C19⋊C8—42no—
99C2×C19⋊C8—42no—
100C2×C19⋊C8C22⋊C414yes—
101C2×C19⋊C8C4⋊C414yes—
102#10797—191nomaximal, Sylow
103C23×C19C2×C4211yescharacteristic
104C23×C19#11712yes—
105C23×C19C4×D412yes—
106C23×C19C4×D411yescharacteristic
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×C19—28no—
119C2×C4×C19—28no—
120C2×C4×C19—28no—
121C2×C4×C19—44no—
122C2×C4×C19—44no—
123C2×C4×C19—44no—
124C2×C4×C19—44no—
125C2×C4×C19C4×C814yes—
126C2×C4×C19#9714yes—
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C2×C4⋊C411yescharacteristic
129C2×C4×C19#11711yescharacteristic
130C2×C4×C19#11711yescharacteristic
131C2×C4×C19#11712yes—
132C2×C4×C19#11711yescharacteristic
133C2×C4×C19#11711yescharacteristic
134C2×C4×C19C4×D412yes—
135C2×C4×C19C4×D411yescharacteristic
136C2×C4×C19C4×Q811yescharacteristic
137C2×C4×C19#12112yes—
138C2×C4×C19C22⋊Q812yes—
139C2×C4×C19#12312yes—
140C2×C4×C19#12312yes—
141C2×C4×C19#12412yes—
142C2×C4×C19#12512yes—
143C2×C4×C19#12612yes—
144C2×C4×C19#12612yes—
145C19⋊C8—24no—
146C19⋊C8—24no—
147C19⋊C8—44no—
148C22×C4×C8—191no—
149C2×#336—191no—
150C2×#336—192no—
151C2×#336—192no—
152C4×#95D1911yescharacteristic
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—48no—
173C4×C19#38011yescharacteristic
174C4×C19#38111yescharacteristic
175C4×C19#38211yescharacteristic
176C4×C19#38311yescharacteristic
177C4×C19#38712yes—
178C4×C19#38812yes—
179C23×C8—191no—
180C23×C8—191no—
181C23×C8—192no—
182C22×C42C2×D1912yes—
183C22×C42C2×D1911yescharacteristic
184C2×C4×C8—194no—
185C2×C4×C8—384no—
186C2×#95Dic1912yes—
187C2×#95Dic1912yes—
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×C4C2×Dic1914yes—
201C23×C4C2×Dic1911yescharacteristic
202C23×C4C2×Dic1911yescharacteristic
203C23×C4C22×D1911yescharacteristic
204C22×C8—192no—
205C22×C8—192no—
206C22×C8—192no—
207C22×C8—194no—
208C22×C8—192no—
209C22×C8—194no—
210C22×C8—382no—
211C22×C8—382no—
212C22×C8—382no—
213C22×C8—381no—
214C22×C8—381no—
215C22×C8—382no—
216C22×C8—382no—
217C22×C8—382no—
218C22×C8—382no—
219C22×C8—382no—
220C22×C8—382no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42C4×D1912yes—
230C2×C42C4×D1912yes—
231C4×C8—388no—
232#95—24no—
233#95C19⋊C818yescomplemented
234C19#1079711yescharacteristic, complemented, Sylow
235C24C22×Dic1911yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4C2×C19⋊C818yes—
247C22×C4C2×C19⋊C814yes—
248C22×C4#6452014yes—
249C22×C4C4×Dic1912yes—
250C22×C4C4×Dic1912yes—
251C22×C4C2×C4×D1911yescharacteristic
252C22×C4C2×C4×D1911yescharacteristic
253C22×C4#6454112yes—
254C22×C4#6454112yes—
255C22×C4D4×D1912yes—
256C22×C4D4×D1911yescharacteristic
257C22×C4#6454312yes—
258C22×C4#6454311yescharacteristic
259C22×C4Q8×D1911yescharacteristic
260C22×C4#6454511yescharacteristic
261C2×C8—194no—
262C2×C8—194no—
263C2×C8—382no—
264C2×C8—382no—
265C2×C8—382no—
266C2×C8—384no—
267C2×C8—384no—
268C2×C8—382no—
269C2×C8—384no—
270C2×C8—384no—
271C2×C8—384no—
272C2×C8—384no—
273C2×C8—384no—
274C2×C8—762no—
275C2×C8—762no—
276C2×C8—762no—
277C2×C8—762no—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42—42no—
285C23C22×C19⋊C812yes—
286C23C2×#6452012yes—
287C23C2×C4×Dic1911yescharacteristic
288C23#1059737212yes—
289C23D4×Dic1912yes—
290C23D4×Dic1911yescharacteristic
291C23Q8×Dic1911yescharacteristic
292C23#1059739412yes—
293C23#1059739412yes—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4C4×C19⋊C814yes—
308C2×C4#1059726014yes—
309C2×C4#1059731811yescharacteristic
310C2×C4#1059731811yescharacteristic
311C2×C4#1059731812yes—
312C2×C4#1059732311yescharacteristic
313C2×C4#1059732512yes—
314C2×C4C22⋊C4×D1911yescharacteristic
315C2×C4(C22⋊D19)⋊C412yes—
316C2×C4#1059732912yes—
317C2×C4#1059733012yes—
318C2×C4#1059733112yes—
319C2×C4#1059733311yescharacteristic
320C2×C4#1059733512yes—
321C2×C4C4⋊C4×D1911yescharacteristic
322C2×C4#1059733811yescharacteristic
323C2×C4#1059733911yescharacteristic
324C2×C4#1059734012yes—
325C2×C4#1059734212yes—
326C2×C4#1059734412yes—
327C8—384no—
328C8—384no—
329C8—764no—
330C22#1192639011yescharacteristic
331C22C22⋊C4×Dic1911yescharacteristic
332C22C4⋊C4×Dic1911yescharacteristic
333C22#1192643012yes—
334C22#1192643712yes—
335C22C2×C4×C19⋊C811yescharacteristic
336C22C2×#1059726011yescharacteristic
337C22#1192650011yescharacteristic
338C22#1192650011yescharacteristic
339C22#1192659714yes—
340C22#1192660514yes—
341C22D4×C19⋊C814yes—
342C22D4×C19⋊C812yes—
343C22#1192661614yes—
344C22#1192662212yes—
345C22Q8×C19⋊C812yes—
346C22#1192667512yes—
347C4—24no—
348C4—24no—
349C4—48no—
350C4#1192640311yescharacteristic
351C4#1192640611yescharacteristic
352C4#1192640811yescharacteristic
353C4#1192641111yescharacteristic
354C4#1192642612yes—
355C4#1192643312yes—
356C2#1456186011yescharacteristic
357C2#1456338111yescharacteristic
358C2#1456338711yescharacteristic
359C2C22⋊C4×C19⋊C811yescharacteristic
360C2#1456341311yescharacteristic
361C2C4⋊C4×C19⋊C811yescharacteristic
362C2#1456350411yescharacteristic
363C2#1456419414yes—
364C2#1456424314yes—
subgroupG/H
center, FrattiniC23×C4C22×D19
commutatorC22×C19C2×C4×C8
FittingC4×C19×#95C2
socle, prime radicalC24×C19C22×C4
cosocleC23×C4×C19C23
hypercenterC4×#95D19
hypocenterC19#10797
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
10. C2×C4×C19⋊C8C4semidirect
13. #11926299C4semidirect
50. C19×#95C8semidirect
233. #95C19⋊C8semidirect
234. C19#10797semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C19⋊C82
C2×#119262992
C4×C19×#952
#1079719