Finite Group Databasebeta

← #18077541

Subgroups — #18077541

Order 4864.

836 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11926456C211yesmaximal, characteristic
2#14566233C211yesmaximal, characteristic
3#14563571C212yesmaximal, complemented
4#14561515C212yesmaximal, complemented
5C2×C19×#323C211yesmaximal, characteristic
6C23×Dic38C2211yescharacteristic
7C22×C22⋊Dic19—21no—
8C2×#10597273—24no—
9#11926456—22no—
10#11926456C414yescomplemented
11#11926437—24no—
12#11926404C2212yes—
13#11926400—21no—
14C4×C22⋊Dic19—21no—
15C2×C19⋊#95—21no—
16C2×C19⋊#95C2211yescharacteristic
17C22×C22⋊C4×C19C2211yescharacteristic
18C2×C19×C22⋊C8C2212yes—
19C19×#323—22no—
20C25×C19D411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19C2311yescharacteristic
23C23×Dic19—21no—
24C23×Dic19—21no—
25C22×Dic38—22no—
26C22×Dic38—22no—
27C22×Dic38—21no—
28C22×Dic38—44no—
29C22×Dic38C2×C412yes—
30C22×C8×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19—22no—
33C2×C22⋊C4×C19C2×C412yes—
34C2×C22⋊C4×C19D412yes—
35C2×C22⋊Dic19—24no—
36C2×C22⋊Dic19—22no—
37C2×C22⋊Dic19—22no—
38C2×C22⋊Dic19—22no—
39C2×C22⋊Dic19—44no—
40C2×C4⋊Dic19D414yes—
41C2×C4×Dic19—22no—
42C19×C22⋊C8—22no—
43C19×C22⋊C8—22no—
44C19⋊#95—22no—
45C19⋊#95—24no—
46C19⋊#95—21no—
47C19⋊#95—22no—
48C19⋊#95C2×C412yes—
49#10597273—48no—
50C24×C19—21no—
51C24×C19—22no—
52C24×C19—21no—
53C24×C19—22no—
54C24×C19—42no—
55C24×C19—42no—
56C24×C19C22⋊C412yes—
57C24×C19C2×D411yescharacteristic
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—42no—
61C22×C4×C19—42no—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19#4112yes—
67C22×Dic19—24no—
68C22×Dic19—22no—
69C22×Dic19—22no—
70C22×Dic19—24no—
71C22×Dic19—42no—
72C22×Dic19—41no—
73C22×Dic19—41no—
74C22×Dic19—42no—
75C22×Dic19—42no—
76C22×Dic19—42no—
77C2×Dic38—28no—
78C2×Dic38—24no—
79C2×Dic38—44no—
80C2×Dic38—48no—
81C2×Dic38—44no—
82C2×Dic38—44no—
83C2×Dic38—42no—
84C2×C8×C19—44no—
85C2×C8×C19—42no—
86C22⋊C4×C19—24no—
87C22⋊C4×C19—24no—
88C22⋊Dic19—48no—
89C22⋊Dic19—42no—
90C22⋊Dic19—42no—
91C22⋊Dic19—82no—
92C22⋊Dic19—82no—
93C4⋊Dic19—44no—
94C4×Dic19—82no—
95#9016—191nomaximal, Sylow
96C23×C19—22no—
97C23×C19—22no—
98C23×C19—22no—
99C23×C19—22no—
100C23×C19—22no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19—48no—
104C23×C19—42no—
105C23×C19—42no—
106C23×C19—42no—
107C23×C19—42no—
108C23×C19—81no—
109C23×C19—81no—
110C23×C19—84no—
111C23×C19C2×C22⋊C411yescharacteristic
112C23×C19#12011yescharacteristic
113C23×C19#12311yescharacteristic
114C23×C19#13512yes—
115C23×C19#13712yes—
116C2×C4×C19—24no—
117C2×C4×C19—22no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—81no—
124C2×C4×C19C4×D412yes—
125C2×C4×C19#12112yes—
126C2×Dic19—24no—
127C2×Dic19—42no—
128C2×Dic19—44no—
129C2×Dic19—42no—
130C2×Dic19—44no—
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—44no—
135C2×Dic19—44no—
136C2×Dic19—44no—
137C2×Dic19—84no—
138Dic38—28no—
139Dic38—48no—
140Dic38—44no—
141C8×C19—82no—
142C2×#393—191no—
143#2312—191no—
144#1787—192no—
145C2×#323D1911yescharacteristic
146#1294—192no—
147C22×C19—24no—
148C22×C19—24no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—44no—
154C22×C19—42no—
155C22×C19—42no—
156C22×C19—42no—
157C22×C19—82no—
158C22×C19—84no—
159C22×C19—84no—
160C22×C19#38611yescharacteristic
161C22×C19#41611yescharacteristic
162C22×C19#41911yescharacteristic
163C22×C19#45212yes—
164C22×C19#45512yes—
165C22×C19B(4,𝔽2)12yes—
166C22×C19#48512yes—
167C4×C19—22no—
168C4×C19—22no—
169C4×C19—42no—
170Dic19—44no—
171Dic19—82no—
172Dic19—84no—
173C23×Q8—191no—
174C22×C22⋊C4—381no—
175C22×C22⋊C4C2×D1911yescharacteristic
176C2×#103—384no—
177C2×C22⋊C8C2×D1912yes—
178#393—194no—
179#393—382no—
180#388—384no—
181#380—192no—
182#379—381no—
183C4×C22⋊C4—381no—
184C2×#95—191no—
185C2×#95—381no—
186#323—22no—
187C2×C19—21no—
188C2×C19—21no—
189C2×C19—22no—
190C2×C19—82no—
191C2×C19#160614yes—
192C2×C19#187311yescharacteristic
193C2×C19#188511yescharacteristic
194C2×C19#188911yescharacteristic
195C25D7611yescharacteristic
196C22×Q8—192no—
197C22×Q8—381no—
198C22×Q8—382no—
199C22×Q8—382no—
200C22×Q8—764no—
201C23×C4—381no—
202C23×C4—381no—
203C23×C4D7611yescharacteristic
204C23×C4C22×D1911yescharacteristic
205C22×C8—22no—
206C2×C4⋊C4—194no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—384no—
210C2×C22⋊C4—382no—
211C2×C22⋊C4—382no—
212C2×C22⋊C4—382no—
213C2×C22⋊C4—764no—
214C2×C22⋊C4C4×D1912yes—
215C2×C22⋊C4C22⋊D1912yes—
216C2×C42—382no—
217#103—768no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220#95—192no—
221#95—382no—
222#95—384no—
223#95—382no—
224#95—381no—
225C19#901611yescharacteristic, complemented, Sylow
226C24—21no—
227C24—22no—
228C24—21no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24(C2×D19)⋊C412yes—
233C24C2×D7611yescharacteristic
234C2×Q8—388no—
235C2×Q8—384no—
236C2×Q8—764no—
237C2×Q8—764no—
238C2×Q8—764no—
239C2×Q8—768no—
240C2×Q8—762no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—384no—
246C22×C4—382no—
247C22×C4—384no—
248C22×C4—382no—
249C22×C4—762no—
250C22×C4—761no—
251C22×C4—761no—
252C22×C4—762no—
253C22×C4—762no—
254C22×C4—762no—
255C22×C4(C2×D19)⋊C412yes—
256C22×C4C2×C4×D1911yescharacteristic
257C22×C4D4×D1912yes—
258C22×C4#6454312yes—
259C22×C4C2×C22⋊D1911yescharacteristic
260C2×C8—44no—
261C2×C8—42no—
262C4⋊C4—764no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—768no—
266C22⋊C4—762no—
267C22⋊C4—762no—
268C22⋊C4—1522no—
269C22⋊C4—1522no—
270C42—1522no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—42no—
277C23—42no—
278C23—48no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—81no—
284C23—81no—
285C23—84no—
286C23#1059732811yescharacteristic
287C23#1059733211yescharacteristic
288C23#1059735012yes—
289C23#1059735512yes—
290C23C2×(C2×D19)⋊C411yescharacteristic
291Q8—388no—
292Q8—768no—
293Q8—764no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—384no—
303C2×C4—762no—
304C2×C4—764no—
305C2×C4—762no—
306C2×C4—764no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—762no—
310C2×C4—764no—
311C2×C4—764no—
312C2×C4—764no—
313C2×C4—1524no—
314C2×C4(C22⋊D19)⋊C412yes—
315C2×C4#1059738512yes—
316C8—82no—
317C22—24no—
318C22—24no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—44no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—82no—
328C22—84no—
329C22—84no—
330C22#1192642111yescharacteristic
331C22#1192654111yescharacteristic
332C22#1192655411yescharacteristic
333C22#1192670812yes—
334C22#1192672412yes—
335C22#1192673212yes—
336C22#1192688612yes—
337C4—22no—
338C4—22no—
339C4—42no—
340C4—764no—
341C4—1522no—
342C4—1524no—
343C2—21no—
344C2—21no—
345C2—22no—
346C2—82no—
347C2#1456261714yes—
348C2#1456394511yescharacteristic
349C2#1456402111yescharacteristic
350C2#1456404111yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#323C2
socleC23×C19#120
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenterC2×#323D19
hypocenterC19#9016
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #14563571C2semidirect
4. #14561515C2semidirect
10. #11926456C4semidirect
225. C19#9016semidirect

Maximal subgroups

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

subgroupindex
C2×#119264562
#145662332
#145635712
#145615152
C2×C19×#3232
#901619