Finite Group Databasebeta

← #18075172

Subgroups — #18075172

Order 4864.

1026 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C22×#10597334C211yesmaximal, characteristic
2#14563558C212yesmaximal
3#14561965C211yesmaximal, characteristic
4#14561964C212yesmaximal
5C19×#1463C211yesmaximal, characteristic
6C23×Dic38C411yescharacteristic
7C23×Dic38C2211yescharacteristic
8C2×#10597334—24no—
9C2×#10597334—24no—
10C2×#10597334—22no—
11C2×#10597334—22no—
12C22×C4⋊Dic19C411yescharacteristic
13C22×Dic19⋊C4C411yescharacteristic
14C22×Dic19⋊C4C2211yescharacteristic
15C22×C4×Dic19C411yescharacteristic
16C2×#10597281—24no—
17#11926508C2212yes—
18#11926270—22no—
19#11926269—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#324—22no—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19C2×C411yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×Dic38—22no—
31C22×Dic38—21no—
32C22×Dic38—22no—
33C22×Dic38—21no—
34C22×Dic38—22no—
35C22×Dic38—22no—
36C22×Dic38—44no—
37C22×Dic38—44no—
38C22×Dic38D414yes—
39C2×M16×C19—22no—
40C2×C4⋊C4×C19—22no—
41C2×C4⋊C4×C19—22no—
42C2×C4⋊C4×C19D412yes—
43C2×C4⋊C4×C19D412yes—
44C2×C4⋊Dic19—22no—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19—22no—
47C2×Dic19⋊C4—22no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—22no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—22no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4D414yes—
54C2×C4×Dic19—22no—
55C2×C4×Dic19—22no—
56C2×C4×Dic19—22no—
57C2×#64520—22no—
58#10597334—216no—
59#10597334—216no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64#10597281—48no—
65C24×C19C22×C411yescharacteristic
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—24no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—42no—
72C22×C4×C19—42no—
73C22×C4×C19C22⋊C412yes—
74C22×C4×C19C22⋊C412yes—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D412yes—
77C22×C4×C19C2×D412yes—
78C22×C4×C19C2×D411yescharacteristic
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—24no—
84C22×Dic19—24no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—42no—
90C22×Dic19—42no—
91C22×Dic19C22⋊C412yes—
92C22×Dic19C22⋊C412yes—
93C22×Dic19C22⋊C412yes—
94C22×Dic19C22⋊C412yes—
95C2×Dic38—28no—
96C2×Dic38—24no—
97C2×Dic38—24no—
98C2×Dic38—28no—
99C2×Dic38—44no—
100C2×Dic38—44no—
101C2×Dic38—48no—
102C2×Dic38—44no—
103C2×Dic38—48no—
104C2×Dic38—48no—
105C2×Dic38—44no—
106C2×Dic38—44no—
107M16×C19—44no—
108C2×C8×C19—42no—
109C4⋊C4×C19—24no—
110C4⋊C4×C19—24no—
111C4⋊Dic19—28no—
112Dic19⋊C4—28no—
113Dic19⋊C4—24no—
114Dic19⋊C4—24no—
115C4×Dic19—28no—
116#64520—44no—
117C2×C19⋊C8—42no—
118#8551—191nomaximal, Sylow
119C23×C19—22no—
120C23×C19—22no—
121C23×C19—22no—
122C23×C19C2×C22⋊C411yescharacteristic
123C23×C19C2×C22⋊C411yescharacteristic
124C23×C19C2×C22⋊C411yescharacteristic
125C2×C4×C19—24no—
126C2×C4×C19—24no—
127C2×C4×C19—22no—
128C2×C4×C19—24no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—41no—
132C2×C4×C19—42no—
133C2×C4×C19—41no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19#10114yescomplemented
138C2×C4×C19#12012yes—
139C2×C4×C19#12012yes—
140C2×Dic19—24no—
141C2×Dic19—24no—
142C2×Dic19—24no—
143C2×Dic19—24no—
144C2×Dic19—22no—
145C2×Dic19—22no—
146C2×Dic19—22no—
147C2×Dic19—22no—
148C2×Dic19—22no—
149C2×Dic19—22no—
150C2×Dic19—24no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19#9914yes—
157C2×Dic19#10114yescomplemented
158Dic38—48no—
159Dic38—48no—
160Dic38—416no—
161C8×C19—82no—
162C19⋊C8—82no—
163C22×C4⋊Q8—191no—
164#1784—192no—
165#1463—192no—
166#1463—191no—
167#1463D1911yescharacteristic
168C22×C19—28no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19#37911yescharacteristic
176C22×C19C2×#9912yes—
177C22×C19C2×#10112yes—
178C22×C19C2×#10112yes—
179C4×C19—22no—
180C4×C19—22no—
181C4×C19—24no—
182C4×C19—42no—
183Dic19—24no—
184Dic19—24no—
185Dic19—42no—
186Dic19—42no—
187C23×Q8—191no—
188C23×Q8—191no—
189C2×C4⋊Q8—384no—
190C2×C4⋊Q8—384no—
191C2×C4⋊Q8—382no—
192C2×C4⋊Q8—382no—
193C22×C4⋊C4—191no—
194C22×C4⋊C4—191no—
195C22×C4⋊C4—191no—
196C22×C4⋊C4C2×D1911yescharacteristic
197C22×C42—191no—
198C2×#101—384no—
199#407—192no—
200#407C2×D1912yes—
201#324—22no—
202#324—384no—
203#324—382no—
204C2×C19—22no—
205C2×C19—22no—
206C2×C19—22no—
207C2×C19#178111yescharacteristic
208C2×C19#178411yescharacteristic
209C2×C19#178411yescharacteristic
210C22×Q8—194no—
211C22×Q8—382no—
212C22×Q8—382no—
213C22×Q8—382no—
214C22×Q8—381no—
215C22×Q8—382no—
216C22×Q8—381no—
217C22×Q8—764no—
218C22×Q8—764no—
219C23×C4—191no—
220C23×C4—191no—
221C23×C4—191no—
222C23×C4—191no—
223C23×C4C4×D1911yescharacteristic
224C23×C4C4×D1911yescharacteristic
225C23×C4C22×D1911yescharacteristic
226C2×M16—22no—
227C2×M16—382no—
228C4⋊Q8—3816no—
229C4⋊Q8—3816no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—194no—
233C2×C4⋊C4—382no—
234C2×C4⋊C4—382no—
235C2×C4⋊C4—382no—
236C2×C4⋊C4—382no—
237C2×C4⋊C4—382no—
238C2×C4⋊C4—382no—
239C2×C4⋊C4—381no—
240C2×C4⋊C4—382no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4D7612yes—
243C2×C4⋊C4C22⋊D1912yes—
244C2×C42—382no—
245C2×C42—382no—
246C2×C42—382no—
247#101—768no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—382no—
251C22⋊C8—382no—
252C19#855111yescharacteristic, complemented, Sylow
253C24C2×C4×D1911yescharacteristic
254C2×Q8—388no—
255C2×Q8—388no—
256C2×Q8—384no—
257C2×Q8—384no—
258C2×Q8—764no—
259C2×Q8—764no—
260C2×Q8—764no—
261C2×Q8—768no—
262C2×Q8—764no—
263C2×Q8—768no—
264C2×Q8—764no—
265C2×Q8—768no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—24no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—192no—
274C22×C4—192no—
275C22×C4—192no—
276C22×C4—192no—
277C22×C4—384no—
278C22×C4—384no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4—381no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—762no—
288C22×C4—762no—
289C22×C4(C2×D19)⋊C412yes—
290C22×C4(C2×D19)⋊C412yes—
291C22×C4C2×D7611yescharacteristic
292C22×C4D4×D1912yes—
293C22×C4D4×D1912yes—
294C22×C4C2×C22⋊D1911yescharacteristic
295M16—44no—
296M16—764no—
297C2×C8—42no—
298C2×C8—762no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—388no—
302C4⋊C4—388no—
303C4⋊C4—384no—
304C4⋊C4—384no—
305C42—388no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23C22⋊C4×D1911yescharacteristic
310C23C22⋊C4×D1911yescharacteristic
311C23C2×(C2×D19)⋊C411yescharacteristic
312Q8—768no—
313Q8—768no—
314Q8—7616no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—194no—
328C2×C4—194no—
329C2×C4—384no—
330C2×C4—384no—
331C2×C4—384no—
332C2×C4—384no—
333C2×C4—382no—
334C2×C4—382no—
335C2×C4—382no—
336C2×C4—382no—
337C2×C4—382no—
338C2×C4—382no—
339C2×C4—384no—
340C2×C4—762no—
341C2×C4—762no—
342C2×C4—762no—
343C2×C4—762no—
344C2×C4—762no—
345C2×C4#1059728114yescomplemented
346C2×C4#1059732812yes—
347C2×C4#1059738312yes—
348C8—82no—
349C8—1522no—
350C22—28no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22#1192639911yescharacteristic
358C22#99×D1912yes—
359C22#101×D1912yes—
360C22C2×#1059728112yes—
361C4—22no—
362C4—22no—
363C4—24no—
364C4—42no—
365C4—384no—
366C4—384no—
367C4—762no—
368C4—762no—
369C2—22no—
370C2—22no—
371C2—22no—
372C2#1456354811yescharacteristic
373C2#1456355711yescharacteristic
374C2#1456355811yescharacteristic
subgroupG/H
centerC22#11926399
commutator, prime radicalC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1463C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#1463D19
hypocenterC19#8551
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
137. C2×C4×C19#101semidirect
157. C2×Dic19#101semidirect
252. C19#8551semidirect
345. C2×C4#10597281semidirect

Maximal subgroups

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

subgroupindex
C22×#105973342
#145635582
#145619652
#145619642
C19×#14632
#855119