Finite Group Databasebeta

← #18090979

Subgroups — #18090979

Order 4864.

734 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926313C211yesmaximal, characteristic
2#14563356C212yesmaximal
3C2×#11926303C212yesmaximal
4#14561864C211yesmaximal, characteristic
5C19×#2316C211yesmaximal, characteristic
6C22×#64520C2212yes—
7C22×C4⋊Dic19C2211yescharacteristic
8C22×C4×Dic19C2211yescharacteristic
9C2×C19⋊#95—22no—
10#11926313C414yescomplemented
11#11926306—22no—
12#11926306—22no—
13#11926303—24no—
14C2×C19×#117C2212yes—
15C22×C4⋊C4×C19C2211yescharacteristic
16C19×#389—22no—
17C19×#389—22no—
18C19×#380—22no—
19C23×C4×C19D412yes—
20C23×C4×C19C2311yescharacteristic
21C23×Dic19—21no—
22C23×Dic19—21no—
23C19×#117—22no—
24C19×#117—22no—
25C19×#117—22no—
26C19×#117—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19C2×C412yes—
32C2×C4⋊C4×C19D412yes—
33C2×C4⋊C4×C19D412yes—
34C2×C4⋊C4×C19Q812yes—
35C2×C22⋊C4×C19—22no—
36C2×C42×C19—22no—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19—22no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19Q812yes—
41C2×C4×Dic19—22no—
42C2×C4×Dic19—22no—
43C2×C4×Dic19—21no—
44C2×C4×Dic19D412yes—
45C2×#64520—22no—
46C2×#64520—22no—
47C2×#64520—22no—
48C2×#64520—22no—
49C2×#64520—22no—
50C2×#64520C2×C414yes—
51C22×C19⋊C8—22no—
52C19×#95—24no—
53C19⋊#95—44no—
54C24×C19C2×D411yescharacteristic
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—42no—
60C22×C4×C19—42no—
61C22×C4×C19C4⋊C414yes—
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×Q811yescharacteristic
66C22×C4×C19C2×Q811yescharacteristic
67C22×C4×C19#4112yes—
68C22×C4×C19#4112yes—
69C22×C4×C19#4111yescharacteristic
70C22×C4×C19#4112yes—
71C22×C4×C19#4111yescharacteristic
72C22×Dic19—22no—
73C22×Dic19—22no—
74C22×Dic19—22no—
75C22×Dic19—22no—
76C22×Dic19—41no—
77C22×Dic19—41no—
78C22×Dic19—41no—
79C22×Dic19—41no—
80C22×Dic19—42no—
81C22×Dic19—42no—
82C22×Dic19—41no—
83C22×Dic19—41no—
84C4⋊C4×C19—24no—
85C4⋊C4×C19—24no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—82no—
91C4⋊C4×C19—82no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—42no—
94C42×C19—42no—
95C42×C19—42no—
96C4⋊Dic19—24no—
97C4⋊Dic19—42no—
98C4×Dic19—24no—
99C4×Dic19—42no—
100#64520—24no—
101#64520—24no—
102#64520—42no—
103#64520—42no—
104C2×C19⋊C8—24no—
105C2×C19⋊C8—42no—
106C2×C19⋊C8—42no—
107#11296—191nomaximal, Sylow
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19C2×C4⋊C411yescharacteristic
113C23×C19#12011yescharacteristic
114C23×C19#12111yescharacteristic
115C23×C19C22⋊Q811yescharacteristic
116C23×C19#12311yescharacteristic
117C23×C19#12411yescharacteristic
118C23×C19#12411yescharacteristic
119C2×C4×C19—24no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—44no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—82no—
130C2×C4×C19#11712yes—
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D412yes—
133C2×C4×C19C4×Q811yescharacteristic
134C2×C4×C19#12112yes—
135C2×C4×C19C22⋊Q812yes—
136C2×C4×C19C22⋊Q812yes—
137C2×C4×C19#12312yes—
138C2×C4×C19#12312yes—
139C2×C4×C19#12412yes—
140C2×C4×C19#12512yes—
141C2×C4×C19#12512yes—
142C2×C4×C19#12511yescharacteristic
143C2×C4×C19#12612yes—
144C2×C4×C19#12612yes—
145C2×C4×C19C4⋊Q811yescharacteristic
146C2×Dic19—24no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—44no—
154C2×Dic19—42no—
155C2×Dic19—82no—
156C2×Dic19—81no—
157C2×Dic19—81no—
158C19⋊C8—44no—
159#2316D1911yescharacteristic
160C2×#343—191no—
161#1736—192no—
162C2×#339—192no—
163C4⋊#95—191no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19#38211yescharacteristic
177C22×C19#38511yescharacteristic
178C22×C19#38911yescharacteristic
179C22×C19#39311yescharacteristic
180C22×C19#39411yescharacteristic
181C22×C19#39711yescharacteristic
182C22×C19#40011yescharacteristic
183C22×C19#45311yescharacteristic
184C22×C19#45411yescharacteristic
185C22×C19#45511yescharacteristic
186C22×C19#45611yescharacteristic
187C4×C19—44no—
188C4×C19—82no—
189C4×C19—82no—
190C4×C19#38712yes—
191C4×C19#38812yes—
192C4×C19#39812yes—
193C4×C19#40012yes—
194Dic19—44no—
195Dic19—82no—
196C22×M16—192no—
197C2×#117C2×D1912yes—
198C22×C4⋊C4—191no—
199C22×C4⋊C4C2×D1911yescharacteristic
200C22×C42—191no—
201#389—22no—
202#389—22no—
203#380—22no—
204C2×#95—382no—
205#343—194no—
206#340—382no—
207#340—382no—
208#339—384no—
209C2×C19—21no—
210C2×C19—21no—
211C2×C19—21no—
212C2×C19—21no—
213C2×C19#144211yescharacteristic
214C2×C19#185611yescharacteristic
215C2×C19#185711yescharacteristic
216C2×C19#202711yescharacteristic
217C2×C19#202811yescharacteristic
218C2×C19#203911yescharacteristic
219C2×C19#204011yescharacteristic
220C23×C4—381no—
221C23×C4—381no—
222C23×C4C22⋊D1912yes—
223C23×C4C22×D1911yescharacteristic
224C2×M16—194no—
225C2×M16—382no—
226C2×M16—382no—
227C2×M16—382no—
228C2×M16—382no—
229C2×M16—382no—
230C22×C8—382no—
231#117—22no—
232#117—22no—
233#117—22no—
234#117—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—192no—
240C2×C4⋊C4—382no—
241C2×C4⋊C4—382no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4Dic3812yes—
244C2×C4⋊C4C4×D1912yes—
245C2×C4⋊C4C22⋊D1912yes—
246C2×C4⋊C4C22⋊D1912yes—
247C2×C22⋊C4—22no—
248C2×C42—22no—
249C2×C42—192no—
250C2×C42—382no—
251C2×C42—382no—
252C2×C42—381no—
253#95—24no—
254#95—764no—
255C19#1129611yescharacteristic, complemented, Sylow
256C24C2×C22⋊D1911yescharacteristic
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—382no—
264C22×C4—382no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—761no—
268C22×C4—761no—
269C22×C4—761no—
270C22×C4—761no—
271C22×C4—762no—
272C22×C4—762no—
273C22×C4—761no—
274C22×C4—761no—
275C22×C4Dic19⋊C414yes—
276C22×C4C2×Dic3811yescharacteristic
277C22×C4C2×C4×D1911yescharacteristic
278C22×C4#6454112yes—
279C22×C4D4×D1911yescharacteristic
280C22×C4#6454311yescharacteristic
281C22×C4#6454312yes—
282C22×C4Q8×D1911yescharacteristic
283C22×C4#6454512yes—
284C22×C4#6454511yescharacteristic
285C22×C4C2×C22⋊D1912yes—
286M16—384no—
287M16—384no—
288M16—762no—
289M16—762no—
290C2×C8—384no—
291C2×C8—762no—
292C2×C8—762no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—82no—
300C4⋊C4—82no—
301C4⋊C4—384no—
302C4⋊C4—762no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C42—42no—
306C42—42no—
307C42—384no—
308C42—762no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23C2×Dic19⋊C411yescharacteristic
314C23#1059737511yescharacteristic
315C23#1059738211yescharacteristic
316C23#1059738411yescharacteristic
317C23#1059739211yescharacteristic
318C23#1059739311yescharacteristic
319C23#1059739911yescharacteristic
320C2×C4—24no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—384no—
332C2×C4—762no—
333C2×C4—762no—
334C2×C4—762no—
335C2×C4—762no—
336C2×C4—762no—
337C2×C4—762no—
338C2×C4—764no—
339C2×C4—762no—
340C2×C4—1522no—
341C2×C4—1521no—
342C2×C4—1521no—
343C2×C4#1059733311yescharacteristic
344C2×C4#1059733411yescharacteristic
345C2×C4#1059733512yes—
346C2×C4#1059733612yes—
347C2×C4#1059733611yescharacteristic
348C2×C4#1059733812yes—
349C2×C4#1059733911yescharacteristic
350C2×C4#1059734012yes—
351C2×C4#1059734412yes—
352C2×C4#1059734412yes—
353C2×C4#1059737012yes—
354C2×C4C4×C22⋊D1912yes—
355C2×C4#1059738112yes—
356C2×C4#1059738512yes—
357C2×C4#1059739212yes—
358C2×C4#1059739312yes—
359C8—764no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22#1192640911yescharacteristic
373C22#1192641711yescharacteristic
374C22#1192644011yescharacteristic
375C22#1192645511yescharacteristic
376C22#1192645811yescharacteristic
377C22#1192647011yescharacteristic
378C22#1192648211yescharacteristic
379C22#1192671211yescharacteristic
380C22#1192671711yescharacteristic
381C22#1192672211yescharacteristic
382C22#1192672711yescharacteristic
383C4—44no—
384C4—82no—
385C4—82no—
386C4—764no—
387C4—1522no—
388C4#1192642512yes—
389C4#1192643412yes—
390C4#1192647712yes—
391C4#1192648312yes—
392C2—21no—
393C2—21no—
394C2—21no—
395C2—21no—
396C2#1456189411yescharacteristic
397C2#1456384511yescharacteristic
398C2#1456385011yescharacteristic
399C2#1456478811yescharacteristic
400C2#1456479311yescharacteristic
401C2#1456485611yescharacteristic
402C2#1456486111yescharacteristic
subgroupG/H
centerC23#10597399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2316C2
socleC23×C19#120
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2316D19
hypocenterC19#11296
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
10. #11926313C4semidirect
255. C19#11296semidirect

Maximal subgroups

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

subgroupindex
C2×#119263132
#145633562
C2×#119263032
#145618642
C19×#23162
#1129619