Finite Group Databasebeta

← #18078513

Subgroups — #18078513

Order 4864.

582 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 107 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#14572664C211yesmaximal, characteristic, complemented
2C4×#10597291C211yesmaximal, characteristic, complemented
3#14562151C212yesmaximal, complemented
4#14561487C212yesmaximal, complemented
5C19×#2635C211yesmaximal, characteristic
6#11926616—24no—
7#11926601—21no—
8C2×#10597291—21no—
9#11926508C2212yes—
10C2×C22⋊(C19⋊C8)—21no—
11C4×C22⋊Dic19C2212yes—
12#11926311—21no—
13#11926278—24no—
14C2×C19×#121C2211yescharacteristic
15C2×C4×D4×C19C2211yescharacteristic
16C19×#400C411yescharacteristic, complemented
17C19×#399C411yescharacteristic, complemented
18C19×#394—21no—
19C19×#394C411yescharacteristic, complemented
20C19×#392—21no—
21C19×#392C411yescharacteristic, complemented
22C19×#388—21no—
23C19×#386—21no—
24C19×#381C2211yescharacteristic
25C22×D4×C19—21no—
26C22×D4×C19—21no—
27C22×D4×C19C2×C411yescharacteristic
28C22×D4×C19D411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C23×C4×C19C2311yescharacteristic
31C19×#121—22no—
32C19×#121—22no—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19C2×C411yescharacteristic
45C2×C22⋊C4×C19D411yescharacteristic
46C2×C42×C19D411yescharacteristic
47C2×C22⋊Dic19—22no—
48C2×C4×Dic19—22no—
49C2×#64520—22no—
50C22×C19⋊C8—22no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95C2×C411yescharacteristic
55C19×#95C2×C411yescharacteristic
56#10597291—24no—
57C19⋊#95—22no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)D414yescomplemented
61C4⋊(C19⋊C8)—22no—
62#10597260—22no—
63C24×C19—21no—
64C24×C19C22⋊C411yescharacteristic
65C24×C19C2×D411yescharacteristic
66C2×D4×C19—22no—
67C2×D4×C19—22no—
68C2×D4×C19—22no—
69C2×D4×C19—41no—
70C2×D4×C19—42no—
71C2×D4×C19—42no—
72C2×D4×C19—81no—
73C2×D4×C19—81no—
74C2×D4×C19—81no—
75C2×D4×C19—81no—
76C2×D4×C19—81no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—81no—
83C22×C4×C19—81no—
84C22×C4×C19C22⋊C411yescharacteristic
85C22×C4×C19C22⋊C411yescharacteristic
86C22×C4×C19C22⋊C411yescharacteristic
87C22×C4×C19C22×C411yescharacteristic
88C22×C4×C19C2×D412yes—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4112yes—
91C22×Dic19—42no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—22no—
94C4⋊C4×C19—81no—
95C22⋊C4×C19—22no—
96C22⋊C4×C19—22no—
97C22⋊C4×C19—42no—
98C22⋊C4×C19—41no—
99C22⋊C4×C19—41no—
100C22⋊C4×C19—81no—
101C22⋊C4×C19—81no—
102C22⋊C4×C19—81no—
103C22⋊C4×C19—81no—
104C42×C19—21no—
105C42×C19—21no—
106C22⋊Dic19—24no—
107C22⋊Dic19—42no—
108C4×Dic19—82no—
109#64520—82no—
110C2×C19⋊C8—24no—
111C2×C19⋊C8—82no—
112#9185—191nomaximal, Sylow
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19#10412yes—
129C23×C19C2×C22⋊C411yescharacteristic
130C23×C19#12112yes—
131D4×C19—44no—
132D4×C19—82no—
133D4×C19—84no—
134D4×C19—84no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—42no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—81no—
157C2×C4×C19C4×D412yes—
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12311yescharacteristic
160C2×Dic19—44no—
161C2×Dic19—82no—
162C2×Dic19—82no—
163C19⋊C8—44no—
164#2973—191no—
165#2635D1911yescharacteristic
166C4×#99—191no—
167#1507—192no—
168#1284—192no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—22no—
172C22×C19—22no—
173C22×C19—22no—
174C22×C19—22no—
175C22×C19—42no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—81no—
179C22×C19—81no—
180C22×C19—81no—
181C22×C19—81no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19—81no—
188C22×C19#38611yescharacteristic
189C22×C19C2×#10411yescharacteristic
190C22×C19#42111yescharacteristic
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—22no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19—41no—
197C4×C19—81no—
198C4×C19—81no—
199C4×C19—81no—
200Dic19—84no—
201C2×#121C2×D1911yescharacteristic
202C2×C4×D4C2×D1911yescharacteristic
203#435—384no—
204#432—381no—
205C2×#99—381no—
206#407—192no—
207C2×C22⋊C8—381no—
208#400Dic1911yescharacteristic, complemented
209#399Dic1911yescharacteristic, complemented
210#394—21no—
211#394Dic1911yescharacteristic, complemented
212#392—21no—
213#392Dic1911yescharacteristic, complemented
214#388—21no—
215#386—21no—
216#381C2×D1911yescharacteristic
217C4×C22⋊C4—192no—
218#342—381no—
219#327—384no—
220C2×C19—21no—
221C2×C19—21no—
222C2×C19—42no—
223C2×C19—42no—
224C2×C19—161no—
225C2×C19#187111yescharacteristic
226C2×C19#191011yescharacteristic
227C2×C19#191311yescharacteristic
228C22×D4—21no—
229C22×D4—21no—
230C22×D4C2×Dic1911yescharacteristic
231C22×D4C22⋊D1911yescharacteristic
232C23×C4C22⋊D1911yescharacteristic
233C23×C4C22×D1911yescharacteristic
234C2×M16—382no—
235C22×C8—382no—
236#121—22no—
237#121—22no—
238C4×D4—22no—
239C4×D4—22no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×Dic1911yescharacteristic
242C2×C4⋊C4C2×Dic1911yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—382no—
250C2×C22⋊C4C2×Dic1911yescharacteristic
251C2×C22⋊C4C22⋊D1911yescharacteristic
252C2×C42—382no—
253C2×C42C22⋊D1911yescharacteristic
254C4⋊C8—382no—
255#99—384no—
256C22⋊C8—194no—
257C22⋊C8—382no—
258C22⋊C8—382no—
259#97—382no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—382no—
264#95C2×Dic1911yescharacteristic
265#95C2×Dic1911yescharacteristic
266C19#918511yescharacteristic, complemented, Sylow
267C24—21no—
268C24C22⋊Dic1911yescharacteristic
269C24C2×C22⋊D1911yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—81no—
277C2×D4—81no—
278C2×D4—81no—
279C2×D4—81no—
280C2×D4—81no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—762no—
289C22×C4C22⋊Dic1911yescharacteristic
290C22×C4C22⋊Dic1911yescharacteristic
291C22×C4C22⋊Dic1911yescharacteristic
292C22×C4D4×D1912yes—
293C22×C4#6454312yes—
294C22×C4C22×Dic1911yescharacteristic
295C22×C4C2×C22⋊D1911yescharacteristic
296M16—1522no—
297C2×C8—384no—
298C2×C8—1522no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—81no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—384no—
312C22⋊C4—762no—
313C42—21no—
314C42—21no—
315C42—1522no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23#1059729412yes—
332C23#1059738512yes—
333C23C2×C22⋊Dic1911yescharacteristic
334D4—44no—
335D4—82no—
336D4—84no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—764no—
361C2×C4—1522no—
362C2×C4—1522no—
363C2×C4D4×Dic1912yes—
364C2×C4#1059738111yescharacteristic
365C2×C4#1059738311yescharacteristic
366C8—764no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#1192642411yescharacteristic
387C22C2×#1059729411yescharacteristic
388C22#1192656111yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—1524no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—161no—
404C2#1456393811yescharacteristic
405C2#1456416311yescharacteristic
406C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2635C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2635D19
hypocenterC19#9185
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. #14572664C2semidirect
2. C4×#10597291C2semidirect
3. #14562151C2semidirect
4. #14561487C2semidirect
16. C19×#400C4semidirect
17. C19×#399C4semidirect
19. C19×#394C4semidirect
21. C19×#392C4semidirect
60. C22⋊(C19⋊C8)D4semidirect
208. #400Dic19semidirect
209. #399Dic19semidirect
211. #394Dic19semidirect
213. #392Dic19semidirect
266. C19#9185semidirect

Maximal subgroups

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

subgroupindex
#145726642
C4×#105972912
#145621512
#145614872
C19×#26352
#918519