Finite Group Databasebeta

← #18075049

Subgroups — #18075049

Order 4864.

976 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11927115C211yesmaximal, characteristic
2#14563563C211yesmaximal, characteristic
3#14562167C214yesmaximal, complemented
4C19×#1782C211yesmaximal, characteristic
5C23×Dic38C411yescharacteristic, complemented
6#11927115—28no—
7C2×#10597390—21no—
8C2×#10597382—21no—
9C2×#10597381—21no—
10C2×#10597381—21no—
11C2×#10597370C412yescomplemented
12C2×#10597370C2212yes—
13C2×#10597372C411yescharacteristic, complemented
14C2×#10597293—21no—
15C2×#10597290—21no—
16#11926508C2212yes—
17#11926280—28no—
18C22×#41×C19C2211yescharacteristic
19C2×C19×#99—21no—
20C2×C19×#99—21no—
21C19×#381C2212yes—
22C2×#41×C19—24no—
23C2×#41×C19—42no—
24C2×#41×C19—42no—
25C22×Q8×C19D411yescharacteristic
26C22×D4×C19D411yescharacteristic
27C22×D4×C19D411yescharacteristic
28C22×D4×C19D411yescharacteristic
29C23×C4×C19C2×C411yescharacteristic
30C23×C4×C19C2×C411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C23×Dic19—21no—
33C22×Dic38—21no—
34C22×Dic38—24no—
35C22×Dic38—42no—
36C22×Dic38—42no—
37C22×Dic38C2×C412yes—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊Dic19—22no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—22no—
42#10597390—28no—
43#10597382—28no—
44#10597381—28no—
45#10597381—28no—
46#10597372—24no—
47C2×C4⋊Dic19C2×C412yes—
48#10597370—24no—
49#10597370—24no—
50#10597370—24no—
51#10597370D418yes—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—22no—
54C2×C4×Dic19—21no—
55C2×#64520—22no—
56C19×#99—42no—
57C19×#99—42no—
58C19×#95—24no—
59#10597293—42no—
60#10597290—42no—
61C22⋊(C19⋊C8)—24no—
62C24×C19C22⋊C411yescharacteristic
63C24×C19C22⋊C411yescharacteristic
64C24×C19C2×D411yescharacteristic
65#41×C19—416no—
66C2×Q8×C19—22no—
67C2×Q8×C19—22no—
68C2×Q8×C19—41no—
69C2×D4×C19—22no—
70C2×D4×C19—22no—
71C2×D4×C19—22no—
72C2×D4×C19—22no—
73C2×D4×C19—22no—
74C2×D4×C19—22no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C2×D4×C19—41no—
78C22×C4×C19—22no—
79C22×C4×C19—22no—
80C22×C4×C19—22no—
81C22×C4×C19—22no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—42no—
87C22×C4×C19C22⋊C411yescharacteristic
88C22×C4×C19C22⋊C411yescharacteristic
89C22×C4×C19C22×C411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D414yes—
92C22×Dic19—24no—
93C22×Dic19—22no—
94C22×Dic19—22no—
95C22×Dic19—42no—
96C22×Dic19—42no—
97C2×Dic38—24no—
98C2×Dic38—22no—
99C2×Dic38—42no—
100C2×Dic38—416no—
101C2×Dic38—42no—
102C2×Dic38—42no—
103C2×Dic38—42no—
104C2×Dic38C22⋊C414yes—
105C22⋊C4×C19—42no—
106C22⋊C4×C19—42no—
107C22⋊Dic19—24no—
108C22⋊Dic19—28no—
109C22⋊Dic19—28no—
110C4⋊Dic19—22no—
111C4⋊Dic19C22⋊C414yes—
112Dic19⋊C4—28no—
113Dic19⋊C4—28no—
114C4×Dic19—24no—
115#64520—42no—
116#64520—42no—
117C2×C19⋊C8—42no—
118#8520—191nomaximal, Sylow
119C23×C19—21no—
120C23×C19—21no—
121C23×C19—21no—
122C23×C19—21no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—21no—
126C23×C19—42no—
127C23×C19—42no—
128C23×C19—42no—
129C23×C19#9912yes—
130C23×C19C2×C22⋊C411yescharacteristic
131C23×C19#12012yes—
132Q8×C19—44no—
133D4×C19—44no—
134D4×C19—44no—
135D4×C19—44no—
136C2×C4×C19—28no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—44no—
147C2×C4×C19—44no—
148C2×C4×C19—82no—
149C2×C4×C19—84no—
150C2×C4×C19#9912yes—
151C2×C4×C19C2×C22⋊C412yes—
152C2×C4×C19#12012yes—
153C2×Dic19—24no—
154C2×Dic19—24no—
155C2×Dic19—48no—
156C2×Dic19—44no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159Dic38—44no—
160Dic38—48no—
161Dic38—44no—
162C19⋊C8—82no—
163C2×#536—191no—
164#1785—191no—
165#1782D1911yescharacteristic
166#1511—194no—
167C22×C19—22no—
168C22×C19—24no—
169C22×C19—22no—
170C22×C19—22no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—42no—
174C22×C19—42no—
175C22×C19—41no—
176C22×C19—81no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19—81no—
180C22×C19#37911yescharacteristic
181C22×C19C2×#9911yescharacteristic
182C22×C19C2×#9911yescharacteristic
183C4×C19—22no—
184C4×C19—22no—
185C4×C19—22no—
186C4×C19—41no—
187C4×C19—162no—
188Dic19—44no—
189Dic19—44no—
190C22×#41C2×D1911yescharacteristic
191C23×Q8—191no—
192#536—388no—
193C2×C4⋊Q8—381no—
194C2×#124—381no—
195C2×#123—381no—
196C2×#123—381no—
197C2×C22⋊Q8—192no—
198C2×C22⋊Q8—192no—
199C2×#117—191no—
200C2×#101—381no—
201C2×#100—381no—
202C2×#99—21no—
203C2×#99—21no—
204#407—192no—
205#381C2×D1912yes—
206#328—388no—
207C2×C19—21no—
208C2×C19—21no—
209C2×C19—42no—
210C2×C19—42no—
211C2×C19—81no—
212C2×C19#178111yescharacteristic
213C2×C19#179612yes—
214C2×#41—24no—
215C2×#41—42no—
216C2×#41—42no—
217C22×Q8—192no—
218C22×Q8—384no—
219C22×Q8—381no—
220C22×Q8—762no—
221C22×Q8—762no—
222C22×Q8D7611yescharacteristic
223C22×D4D7611yescharacteristic
224C22×D4C22⋊D1911yescharacteristic
225C22×D4C22⋊D1911yescharacteristic
226C23×C4—381no—
227C23×C4C4×D1911yescharacteristic
228C23×C4C4×D1911yescharacteristic
229C23×C4C22×D1911yescharacteristic
230C2×M16—382no—
231C4⋊Q8—388no—
232#124—388no—
233#123—388no—
234#123—388no—
235C22⋊Q8—198no—
236C22⋊Q8—384no—
237C22⋊Q8—384no—
238C22⋊Q8—384no—
239#117—384no—
240C2×C4⋊C4—192no—
241C2×C4⋊C4—382no—
242C2×C4⋊C4—382no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—381no—
245C2×C22⋊C4—382no—
246C2×C22⋊C4—382no—
247C2×C42—381no—
248#101—762no—
249#100—762no—
250#99—42no—
251#99—42no—
252C22⋊C8—384no—
253#95—24no—
254C19#852011yescharacteristic, complemented, Sylow
255C24(C2×D19)⋊C411yescharacteristic
256C24(C2×D19)⋊C411yescharacteristic
257C24C2×C22⋊D1911yescharacteristic
258#41—416no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—194no—
263C2×Q8—384no—
264C2×Q8—382no—
265C2×Q8—7616no—
266C2×Q8—762no—
267C2×Q8—762no—
268C2×Q8—762no—
269C2×Q8—762no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—42no—
288C22×C4—384no—
289C22×C4—382no—
290C22×C4—382no—
291C22×C4—762no—
292C22×C4—762no—
293C22×C4(C2×D19)⋊C411yescharacteristic
294C22×C4(C2×D19)⋊C411yescharacteristic
295C22×C4C2×C4×D1911yescharacteristic
296C22×C4C2×D7611yescharacteristic
297C22×C4D4×D1914yes—
298M16—762no—
299M16—762no—
300C2×C8—762no—
301C4⋊C4—194no—
302C4⋊C4—388no—
303C4⋊C4—382no—
304C4⋊C4—388no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—384no—
308C22⋊C4—388no—
309C22⋊C4—388no—
310C42—384no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23#1059726312yes—
322C23C2×(C2×D19)⋊C411yescharacteristic
323C23#1059738312yes—
324Q8—44no—
325Q8—764no—
326Q8—764no—
327Q8—768no—
328D4—44no—
329D4—44no—
330D4—44no—
331C2×C4—28no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—82no—
344C2×C4—84no—
345C2×C4—384no—
346C2×C4—384no—
347C2×C4—768no—
348C2×C4—764no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4#1059726312yes—
352C2×C4C22⋊C4×D1912yes—
353C2×C4#1059732812yes—
354C8—1522no—
355C22—22no—
356C22—24no—
357C22—22no—
358C22—22no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22#1192639911yescharacteristic
369C22C2×#1059726311yescharacteristic
370C22C2×#1059726311yescharacteristic
371C4—22no—
372C4—22no—
373C4—22no—
374C4—41no—
375C4—162no—
376C4—764no—
377C4—764no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—42no—
382C2—81no—
383C2#1456354911yescharacteristic
384C2#1456360812yes—
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1782C2
socleC22×C19#379
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#1782D19
hypocenterC19#8520
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
3. #14562167C2semidirect
5. C23×Dic38C4semidirect
11. C2×#10597370C4semidirect
13. C2×#10597372C4semidirect
254. C19#8520semidirect

Maximal subgroups

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

subgroupindex
C2×#119271152
#145635632
#145621672
C19×#17822
#852019