Finite Group Databasebeta

← #18078330

Subgroups — #18078330

Order 4864.

980 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#11926407C211yesmaximal, characteristic, complemented
2#14563545C211yesmaximal, characteristic, complemented
3C2×#11926278C212yesmaximal, complemented
4#14561513C212yesmaximal, complemented
5C19×#2847C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×C22⋊(C19⋊C8)—22no—
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926407—24no—
10C2×C19⋊#95—21no—
11C2×C19⋊#95C2212yes—
12#11926278—24no—
13C24×C4×C19C2211yescharacteristic
14C2×C19×#121C412yescomplemented
15C2×C19×#121C2211yescharacteristic
16C2×C19×#120—21no—
17C19×#386—22no—
18C19×#386—21no—
19C19×#380C412yescomplemented
20C19×#380C2211yescharacteristic
21C25×C19D411yescharacteristic
22C22×D4×C19—22no—
23C22×D4×C19—21no—
24C22×D4×C19C2×C411yescharacteristic
25C23×C4×C19—22no—
26C23×C4×C19—22no—
27C23×C4×C19—44no—
28C23×C4×C19C2×C412yes—
29C23×C4×C19D412yes—
30C23×C4×C19D411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C23×Dic19—22no—
33C19×#121—22no—
34C19×#121—22no—
35C19×#121—44no—
36C19×#120—44no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C4⋊C4×C19C2×C412yes—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—22no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊Dic19—24no—
44C2×C22⋊Dic19—44no—
45C22×C19⋊C8—22no—
46C19×#95—22no—
47C19×#95—21no—
48C19⋊#95—24no—
49C19⋊#95—22no—
50C19⋊#95D414yescomplemented
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—44no—
54C24×C19—24no—
55C24×C19—21no—
56C24×C19—21no—
57C24×C19—22no—
58C24×C19—22no—
59C24×C19—21no—
60C24×C19—42no—
61C24×C19C22⋊C412yes—
62C24×C19C2×D411yescharacteristic
63C2×D4×C19—22no—
64C2×D4×C19—42no—
65C2×D4×C19—44no—
66C2×D4×C19—44no—
67C2×D4×C19—44no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C2×D4×C19—42no—
71C2×D4×C19—42no—
72C22×C4×C19—24no—
73C22×C4×C19—24no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—24no—
77C22×C4×C19—24no—
78C22×C4×C19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—42no—
81C22×C4×C19—42no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19—48no—
85C22×C4×C19—48no—
86C22×C4×C19C22⋊C412yes—
87C22×C4×C19C22×C411yescharacteristic
88C22×C4×C19C2×D412yes—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4112yes—
91C22×Dic19—24no—
92C22×Dic19—44no—
93C22×Dic19—44no—
94C22×Dic19—42no—
95C22×Dic19—42no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—42no—
98C22⋊C4×C19—44no—
99C22⋊C4×C19—44no—
100C22⋊C4×C19—42no—
101C22⋊C4×C19—42no—
102C22⋊Dic19—48no—
103C2×C19⋊C8—44no—
104C2×C19⋊C8—42no—
105#9158—191nomaximal, Sylow
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—24no—
109C23×C19—24no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—48no—
117C23×C19—48no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19—41no—
123C23×C19—42no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—42no—
127C23×C19#9914yes—
128C23×C19C2×C22⋊C411yescharacteristic
129C23×C19#12011yescharacteristic
130C23×C19#12311yescharacteristic
131C23×C19#13512yes—
132C23×C19AGL(1,ℤ/8)12yes—
133D4×C19—82no—
134D4×C19—88no—
135D4×C19—82no—
136D4×C19—82no—
137C2×C4×C19—22no—
138C2×C4×C19—22no—
139C2×C4×C19—22no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—48no—
145C2×C4×C19—48no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19C4×D412yes—
155C2×C4×C19#12112yes—
156C2×Dic19—44no—
157C2×Dic19—44no—
158C2×Dic19—44no—
159C2×Dic19—84no—
160C2×Dic19—84no—
161C19⋊C8—82no—
162#2847D1911yescharacteristic
163C2×#381—191no—
164#1779—191no—
165C2×#327—192no—
166#1294—192no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—24no—
172C22×C19—24no—
173C22×C19—24no—
174C22×C19—24no—
175C22×C19—24no—
176C22×C19—48no—
177C22×C19—48no—
178C22×C19—42no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—42no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19—82no—
186C22×C19—82no—
187C22×C19#38611yescharacteristic
188C22×C19C2×#9912yes—
189C22×C19#41611yescharacteristic
190C22×C19#41811yescharacteristic
191C22×C19#42112yes—
192C22×C19#44912yes—
193C22×C19#48212yes—
194C4×C19—22no—
195C4×C19—22no—
196C4×C19—42no—
197C4×C19—81no—
198C4×C19—82no—
199Dic19—84no—
200C24×C4C2×D1911yescharacteristic
201C2×#121Dic1912yescomplemented
202C2×#121C2×D1911yescharacteristic
203C2×#120—21no—
204C22×C22⋊C4—381no—
205C2×C22⋊C8—192no—
206C2×C22⋊C8—382no—
207#386—21no—
208#386—22no—
209#381—384no—
210#380Dic1912yescomplemented
211#380C2×D1911yescharacteristic
212C2×#95—192no—
213C2×#95—381no—
214#327—384no—
215C2×C19—22no—
216C2×C19—22no—
217C2×C19—44no—
218C2×C19—161no—
219C2×C19#151012yes—
220C2×C19#151612yes—
221C2×C19#187511yescharacteristic
222C2×C19#189711yescharacteristic
223C2×C19#189811yescharacteristic
224C25C22⋊D1911yescharacteristic
225C22×D4—22no—
226C22×D4—21no—
227C22×D4C2×Dic1911yescharacteristic
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—44no—
231C23×C4—382no—
232C23×C4C2×Dic1912yes—
233C23×C4C22⋊D1912yes—
234C23×C4C22⋊D1911yescharacteristic
235C23×C4C22×D1911yescharacteristic
236C22×C8—382no—
237#121—22no—
238#121—22no—
239#121—44no—
240#120—44no—
241C2×C4⋊C4C2×Dic1911yescharacteristic
242C2×C4⋊C4C2×Dic1912yes—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—384no—
248C2×C22⋊C4—764no—
249C22⋊C8—382no—
250C22⋊C8—382no—
251C22⋊C8—764no—
252#95—22no—
253#95—21no—
254#95—194no—
255#95—384no—
256#95—382no—
257C19#915811yescharacteristic, complemented, Sylow
258C24—21no—
259C24—21no—
260C24—24no—
261C24—22no—
262C24—22no—
263C24—21no—
264C24—42no—
265C24C22⋊Dic1912yes—
266C24C2×C22⋊D1911yescharacteristic
267C2×D4—22no—
268C2×D4—42no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—44no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—48no—
289C22×C4—48no—
290C22×C4—384no—
291C22×C4—764no—
292C22×C4—764no—
293C22×C4—762no—
294C22×C4—762no—
295C22×C4C22⋊Dic1912yes—
296C22×C4D4×D1912yes—
297C22×C4#6454312yes—
298C22×C4C22×Dic1911yescharacteristic
299C22×C4C2×C22⋊D1911yescharacteristic
300C2×C8—764no—
301C2×C8—762no—
302C4⋊C4—22no—
303C4⋊C4—42no—
304C22⋊C4—44no—
305C22⋊C4—44no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—768no—
309C23—22no—
310C23—22no—
311C23—24no—
312C23—24no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—48no—
320C23—48no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—41no—
329C23—42no—
330C23#1059729114yes—
331C23#1059737812yes—
332C23#1059738111yescharacteristic
333C23#1059738311yescharacteristic
334C23#1059739612yes—
335C23C2×C22⋊Dic1911yescharacteristic
336D4—82no—
337D4—88no—
338D4—82no—
339D4—82no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—764no—
358C2×C4—764no—
359C2×C4—764no—
360C2×C4—1524no—
361C2×C4—1524no—
362C2×C4D4×Dic1912yes—
363C2×C4#1059738512yes—
364C8—1522no—
365C22—24no—
366C22—24no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—48no—
375C22—48no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—82no—
383C22—81no—
384C22—81no—
385C22#1192642411yescharacteristic
386C22C2×#1059729112yes—
387C22#1192654011yescharacteristic
388C22#1192654911yescharacteristic
389C22#1192656112yes—
390C22#1192668712yes—
391C22#1192686512yes—
392C4—22no—
393C4—22no—
394C4—42no—
395C4—82no—
396C4—81no—
397C4—1524no—
398C2—22no—
399C2—22no—
400C2—44no—
401C2—161no—
402C2#1456216412yes—
403C2#1456219112yes—
404C2#1456395811yescharacteristic
405C2#1456408411yescharacteristic
406C2#1456408911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2847C2
socleC23×C19C2×C22⋊C4
cosocleC23×C4×C19C23
hypercenter#2847D19
hypocenterC19#9158
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#11926407C2semidirect
2. #14563545C2semidirect
3. C2×#11926278C2semidirect
4. #14561513C2semidirect
14. C2×C19×#121C4semidirect
19. C19×#380C4semidirect
50. C19⋊#95D4semidirect
201. C2×#121Dic19semidirect
210. #380Dic19semidirect
257. C19#9158semidirect

Maximal subgroups

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

subgroupindex
C2×#119264072
#145635452
C2×#119262782
#145615132
C19×#28472
#915819