Finite Group Databasebeta

← #18080359

Subgroups — #18080359

Order 4864.

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

normal subgroups only

This group has 838 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#14566233C211yesmaximal, characteristic, complemented
2#14563579C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561487C212yesmaximal, complemented
5C19×#2404C211yesmaximal, characteristic
6C2×#10597294—24no—
7#11926508C2212yes—
8#11926437—24no—
9#11926404—21no—
10#11926400—21no—
11C4×C22⋊Dic19C2212yes—
12#11926268—22no—
13C22×#41×C19C2211yescharacteristic
14C2×C19×#120—21no—
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#393C412yescomplemented
17C19×#392C412yescomplemented
18C19×#386—21no—
19C19×#386—22no—
20C19×#381C2211yescharacteristic
21C25×C19D411yescharacteristic
22C2×#41×C19—22no—
23C2×#41×C19—22no—
24C2×#41×C19—44no—
25C22×Q8×C19C2×C411yescharacteristic
26C22×D4×C19—21no—
27C22×D4×C19—22no—
28C22×D4×C19C2×C411yescharacteristic
29C23×C4×C19—21no—
30C23×C4×C19D411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C19×#120—44no—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19C2×C412yes—
39C2×C22⋊C4×C19D412yes—
40C2×C22⋊Dic19—22no—
41C2×C22⋊Dic19—22no—
42C2×C22⋊Dic19—22no—
43C2×C4⋊Dic19—22no—
44C2×C4×Dic19D414yescomplemented
45C2×#64520—22no—
46C19×#95—22no—
47C19×#95—21no—
48C19×#95C2×C412yes—
49#10597294—48no—
50C19⋊#95—22no—
51C19⋊#95—22no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C24×C19—21no—
55C24×C19—21no—
56C24×C19—21no—
57C24×C19—42no—
58C24×C19—42no—
59C24×C19—81no—
60C24×C19C22⋊C412yes—
61C24×C19C2×D411yescharacteristic
62#41×C19—28no—
63#41×C19—44no—
64#41×C19—44no—
65#41×C19—44no—
66C2×Q8×C19—22no—
67C2×Q8×C19—42no—
68C2×D4×C19—24no—
69C2×D4×C19—22no—
70C2×D4×C19—42no—
71C2×D4×C19—42no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C2×D4×C19—44no—
75C2×D4×C19—44no—
76C2×D4×C19—82no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—22no—
81C22×C4×C19—42no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19—81no—
86C22×C4×C19C22⋊C412yes—
87C22×C4×C19C22×C411yescharacteristic
88C22×C4×C19C2×D412yes—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4112yes—
91C22×Dic19—24no—
92C22⋊C4×C19—24no—
93C22⋊C4×C19—24no—
94C22⋊C4×C19—44no—
95C22⋊C4×C19—42no—
96C22⋊C4×C19—82no—
97C22⋊Dic19—44no—
98C22⋊Dic19—82no—
99C22⋊Dic19—82no—
100C4⋊Dic19—82no—
101C4×Dic19—44no—
102#64520—44no—
103C2×C19⋊C8—42no—
104#9479—191nomaximal, Sylow
105C23×C19—22no—
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—41no—
112C23×C19—42no—
113C23×C19—42no—
114C23×C19—42no—
115C23×C19—42no—
116C23×C19—41no—
117C23×C19—42no—
118C23×C19—42no—
119C23×C19—41no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19—81no—
123C23×C19—81no—
124C23×C19—88no—
125C23×C19C2×C22⋊C411yescharacteristic
126C23×C19#12011yescharacteristic
127C23×C19#12311yescharacteristic
128Q8×C19—24no—
129Q8×C19—42no—
130D4×C19—24no—
131D4×C19—42no—
132D4×C19—44no—
133D4×C19—44no—
134D4×C19—88no—
135C2×C4×C19—24no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—48no—
142C2×C4×C19—42no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—81no—
150C2×C4×C19C4×D412yes—
151C2×C4×C19#12112yes—
152C2×Dic19—44no—
153C2×Dic19—44no—
154C2×Dic19—44no—
155C19⋊C8—82no—
156#2404D1911yescharacteristic
157#2312—191no—
158#1789—192no—
159#1462—191no—
160#1284—192no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—44no—
169C22×C19—44no—
170C22×C19—44no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—42no—
174C22×C19—42no—
175C22×C19—82no—
176C22×C19—82no—
177C22×C19—84no—
178C22×C19—84no—
179C22×C19—81no—
180C22×C19—81no—
181C22×C19#38611yescharacteristic
182C22×C19#42112yes—
183C22×C19B(4,𝔽2)12yes—
184C4×C19—22no—
185C4×C19—22no—
186C4×C19—42no—
187C4×C19—42no—
188C4×C19—82no—
189Dic19—84no—
190C22×#41C2×D1911yescharacteristic
191C2×#120—21no—
192C22×C22⋊C4C2×D1911yescharacteristic
193C2×#104—384no—
194#407—192no—
195#393Dic1912yescomplemented
196#392Dic1912yescomplemented
197#388—384no—
198#386—21no—
199#386—22no—
200#381C2×D1911yescharacteristic
201#380—381no—
202#379—381no—
203C4×C22⋊C4—192no—
204#323—382no—
205C2×C19—22no—
206C2×C19—22no—
207C2×C19—41no—
208C2×C19—82no—
209C2×C19—82no—
210C2×C19#188911yescharacteristic
211C2×C19#189711yescharacteristic
212C2×C19#191111yescharacteristic
213C25C22⋊D1911yescharacteristic
214C2×#41—22no—
215C2×#41—22no—
216C2×#41—44no—
217C22×Q8C2×Dic1911yescharacteristic
218C22×D4—21no—
219C22×D4—22no—
220C22×D4C2×Dic1911yescharacteristic
221C23×C4—21no—
222C23×C4C22⋊D1911yescharacteristic
223C23×C4C22×D1911yescharacteristic
224C2×M16—382no—
225#120—44no—
226C2×C4⋊C4—382no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—382no—
233C2×C22⋊C4—382no—
234C2×C22⋊C4—382no—
235C2×C22⋊C4C2×Dic1912yes—
236C2×C22⋊C4C22⋊D1912yes—
237C2×C42—194no—
238#104—768no—
239C22⋊C8—382no—
240C22⋊C8—382no—
241#95—22no—
242#95—21no—
243#95—382no—
244#95—382no—
245#95C2×Dic1912yes—
246C19#947911yescharacteristic, complemented, Sylow
247C24—21no—
248C24—21no—
249C24—21no—
250C24—42no—
251C24—42no—
252C24—81no—
253C24C22⋊Dic1912yes—
254C24C2×C22⋊D1911yescharacteristic
255#41—28no—
256#41—44no—
257#41—44no—
258#41—44no—
259C2×Q8—22no—
260C2×Q8—42no—
261C2×D4—24no—
262C2×D4—22no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—82no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—81no—
279C22×C4—384no—
280C22×C4C22⋊Dic1912yes—
281C22×C4D4×D1912yes—
282C22×C4#6454312yes—
283C22×C4C22×Dic1911yescharacteristic
284C22×C4C2×C22⋊D1911yescharacteristic
285M16—764no—
286C2×C8—762no—
287C4⋊C4—1522no—
288C22⋊C4—24no—
289C22⋊C4—24no—
290C22⋊C4—44no—
291C22⋊C4—42no—
292C22⋊C4—82no—
293C22⋊C4—764no—
294C22⋊C4—1522no—
295C22⋊C4—1522no—
296C42—764no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—22no—
302C23—22no—
303C23—41no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—88no—
317C23#1059738111yescharacteristic
318C23#1059738311yescharacteristic
319C23C2×C22⋊Dic1911yescharacteristic
320Q8—24no—
321Q8—42no—
322D4—24no—
323D4—42no—
324D4—44no—
325D4—44no—
326D4—88no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—48no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—764no—
343C2×C4—764no—
344C2×C4—764no—
345C2×C4D4×Dic1912yes—
346C2×C4#1059738512yes—
347C8—1522no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—44no—
356C22—44no—
357C22—44no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—82no—
363C22—84no—
364C22—82no—
365C22—84no—
366C22—81no—
367C22—81no—
368C22#1192642411yescharacteristic
369C22#1192656112yes—
370C22#1192673012yes—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—42no—
375C4—82no—
376C4—1524no—
377C2—22no—
378C2—22no—
379C2—41no—
380C2—82no—
381C2—82no—
382C2#1456404411yescharacteristic
383C2#1456408411yescharacteristic
384C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2404C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2404D19
hypocenterC19#9479
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. #14566233C2semidirect
2. #14563579C2semidirect
3. #14561962C2semidirect
4. #14561487C2semidirect
16. C19×#393C4semidirect
17. C19×#392C4semidirect
44. C2×C4×Dic19D4semidirect
195. #393Dic19semidirect
196. #392Dic19semidirect
246. C19#9479semidirect

Maximal subgroups

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

subgroupindex
#145662332
#145635792
#145619622
#145614872
C19×#24042
#947919