Finite Group Databasebeta

← #18071416

Subgroups — #18071416

Order 4864.

446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564963C211yesmaximal, characteristic, complemented
2#14564881C211yesmaximal, characteristic, complemented
3#14564771C211yesmaximal, characteristic
4#14561458C211yesmaximal, characteristic, complemented
5#14561458C211yesmaximal, characteristic, complemented
6#14561456C211yesmaximal, characteristic
7C19×#2727C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597264—21no—
10C2×#10597267—21no—
11C2×#10597267—21no—
12C2×#10597289—21no—
13#11926306—21no—
14#11926306—21no—
15#11926299C2211yescharacteristic
16#11926299C2211yescharacteristic
17#11926299C2211yescharacteristic
18C2×C19×#126—21no—
19C19×#399—21no—
20C19×#396—21no—
21C19×#394—21no—
22C19×#390C2211yescharacteristic
23C19×#389—21no—
24C19×#389C2211yescharacteristic
25C19×#389C2211yescharacteristic
26C19×#388—21no—
27C22×D4×C19D411yescharacteristic
28C22×Dic38—21no—
29C19×#126—42no—
30C19×#126—42no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19C2311yescharacteristic
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8—21no—
52C22×C19⋊C8—21no—
53#10597315—42no—
54C19×#95—21no—
55C19×#95—21no—
56C19×#95—21no—
57#10597289—42no—
58#10597267—42no—
59#10597267—42no—
60#10597264—42no—
61C24×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—21no—
64C2×D4×C19—41no—
65C2×D4×C19—41no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×Dic19—41no—
75C2×Dic38—22no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C2×Dic38—41no—
79C2×Dic38—41no—
80C2×Dic38—41no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19—42no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—81no—
93C4⋊C4×C19D812yes—
94C22⋊C4×C19—42no—
95C22⋊C4×C19—42no—
96C22⋊C4×C19—41no—
97C22⋊C4×C19—41no—
98C22⋊C4×C19—41no—
99C22⋊C4×C19—41no—
100C22⋊C4×C19—81no—
101C22⋊C4×C19—81no—
102C42×C19—41no—
103C42×C19—42no—
104C4⋊Dic19—22no—
105C4⋊Dic19—22no—
106C4⋊Dic19—41no—
107C4⋊Dic19—41no—
108C2×C19⋊C8—22no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—41no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117#7765—191nomaximal, Sylow
118C23×C19—41no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19#12011yescharacteristic
126D4×C19—42no—
127D4×C19—81no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—22no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19C2×D811yescharacteristic
150C2×C4×C19#13511yescharacteristic
151C2×C4×C19#13511yescharacteristic
152C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C19#13711yescharacteristic
154C2×C4×C19#13711yescharacteristic
155C2×Dic19—42no—
156C2×Dic19—81no—
157C2×Dic19—81no—
158Dic38—42no—
159Dic38—42no—
160Dic38—81no—
161Dic38—81no—
162C19⋊C8—42no—
163C19⋊C8—81no—
164C19⋊C8—81no—
165#2727D1911yescharacteristic
166#2057—191no—
167#2043—191no—
168#2023—191no—
169#1271—191no—
170#1271—191no—
171#1270—191no—
172C22×C19—81no—
173C22×C19—81no—
174C22×C19—81no—
175C22×C19—81no—
176C22×C19—81no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19#44711yescharacteristic
180C22×C19#45211yescharacteristic
181C22×C19#45211yescharacteristic
182C22×C19#45411yescharacteristic
183C22×C19#45511yescharacteristic
184C22×C19#45611yescharacteristic
185C22×C19B(4,𝔽2)11yescharacteristic
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—42no—
193C4×C19—81no—
194C4×C19—81no—
195C4×C19—81no—
196C4×C19—81no—
197Dic19—82no—
198C2×C4⋊Q8—191no—
199C2×#126—21no—
200C2×#107—381no—
201C2×#103—381no—
202C2×#103—381no—
203C2×#102—381no—
204#399—21no—
205#396—21no—
206#394—21no—
207#390C2×D1911yescharacteristic
208#389—21no—
209#389C2×D1911yescharacteristic
210#389C2×D1911yescharacteristic
211#388—21no—
212#340—381no—
213#340—381no—
214#336—191no—
215#336—191no—
216#336—191no—
217C2×C19—161no—
218C2×C19#159811yescharacteristic
219C2×C19#160311yescharacteristic
220C2×C19#160611yescharacteristic
221C2×C19#163811yescharacteristic
222C2×C19#164111yescharacteristic
223C2×C19#164711yescharacteristic
224C2×C19#166411yescharacteristic
225C22×Q8—381no—
226C22×D4C22⋊D1911yescharacteristic
227C22×C8—381no—
228C22×C8—381no—
229C22×C8—381no—
230C4⋊Q8—762no—
231#126—42no—
232#126—42no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—381no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4C22⋊D1911yescharacteristic
240C2×C4⋊C4C22⋊D1911yescharacteristic
241C2×C4⋊C4C22⋊D1911yescharacteristic
242C2×C4⋊C4C22⋊D1911yescharacteristic
243C2×C4⋊C4C22⋊D1911yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C42—21no—
251C2×C42C22×D1911yescharacteristic
252#107—762no—
253#103—762no—
254#103—762no—
255#102—762no—
256#95—21no—
257#95—21no—
258#95—21no—
259C19#776511yescharacteristic, complemented, Sylow
260C24—21no—
261C2×Q8—382no—
262C2×Q8—761no—
263C2×Q8—761no—
264C2×Q8—761no—
265C2×Q8—761no—
266C2×Q8—761no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—761no—
277C22×C4C2×C22⋊D1911yescharacteristic
278C22×C4C2×C22⋊D1911yescharacteristic
279C22×C4C2×C22⋊D1911yescharacteristic
280C2×C8—382no—
281C2×C8—761no—
282C2×C8—761no—
283C2×C8—761no—
284C2×C8—761no—
285C2×C8—761no—
286C2×C8—761no—
287C2×C8—761no—
288C2×C8—761no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4—382no—
302C4⋊C4—382no—
303C4⋊C4—761no—
304C4⋊C4—761no—
305C4⋊C4#6452512yes—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—81no—
313C22⋊C4—81no—
314C42—41no—
315C42—42no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23#1059739911yescharacteristic
324Q8—762no—
325Q8—762no—
326Q8—1521no—
327Q8—1521no—
328D4—42no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—762no—
352C2×C4—1521no—
353C2×C4—1521no—
354C2×C4C2×#6452511yescharacteristic
355C2×C4#1059737811yescharacteristic
356C2×C4#1059739611yescharacteristic
357C2×C4#1059739611yescharacteristic
358C2×C4#1059739711yescharacteristic
359C2×C4#1059739711yescharacteristic
360C8—762no—
361C8—1521no—
362C8—1521no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22#1192667811yescharacteristic
371C22#1192670611yescharacteristic
372C22#1192670611yescharacteristic
373C22#1192671711yescharacteristic
374C22#1192672211yescharacteristic
375C22#1192672711yescharacteristic
376C22#1192673111yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—42no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—1522no—
389C2—161no—
390C2#1456257011yescharacteristic
391C2#1456259811yescharacteristic
392C2#1456261511yescharacteristic
393C2#1456280711yescharacteristic
394C2#1456282811yescharacteristic
395C2#1456287011yescharacteristic
396C2#1456296911yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2727C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2727D19
hypocenterC19#7765
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2727

Complements

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

NH ≅ G/Ntype
1. #14564963C2semidirect
2. #14564881C2semidirect
4. #14561458C2semidirect
5. #14561458C2semidirect
259. C19#7765semidirect

Maximal subgroups

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

subgroupindex
#145649632
#145648812
#145647712
#145614582
#145614562
C19×#27272
#776519