Finite Group Databasebeta

← #14569375

Subgroups — #14569375

Order 2432.

824 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597385C211yesmaximal, characteristic, complemented
2C2×#10597328C211yesmaximal, characteristic, complemented
3C2×#10597383C211yesmaximal, characteristic, complemented
4C22×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
5#11926473C212yesmaximal, complemented
6#11926462C212yesmaximal, complemented
7#11926459C212yesmaximal, complemented
8#11926453C212yesmaximal, complemented
9#11926423C211yesmaximal, characteristic, complemented
10#11926402C211yesmaximal, characteristic, complemented
11C19×#386C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19C2211yescharacteristic
15C22×C22⋊D19C2211yescharacteristic
16C22×C22⋊D19C2212yes—
17C22×C22⋊D19C2211yescharacteristic, complemented
18C23×Dic19C2211yescharacteristic
19C22×D76C2212yes—
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19C2212yescomplemented
22C2×C22⋊Dic19C2211yescharacteristic
23C2×C22⋊Dic19C2211yescharacteristic, complemented
24#10597385—24no—
25#10597383—24no—
26C2×(C2×D19)⋊C4—24no—
27C2×(C2×D19)⋊C4C2212yes—
28C2×(C2×D19)⋊C4C2212yes—
29C2×(C2×D19)⋊C4C2212yes—
30C2×(C2×D19)⋊C4C2212yes—
31C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
32C2×(C2×D19)⋊C4C2212yescomplemented
33C2×Dic19⋊C4C2211yescharacteristic, complemented
34C2×Dic19⋊C4C2212yescomplemented
35#10597328—24no—
36C19×#95C2212yescomplemented
37C19⋊#95C2212yescomplemented
38C19⋊#95C2212yescomplemented
39C24×C19C2311yescharacteristic
40C24×C19C2311yescharacteristic
41C23×D19—22no—
42C23×D19—22no—
43C23×D19—42no—
44C23×D19—42no—
45C23×D19D414yescomplemented
46C23×D19C2311yescharacteristic
47C23×D19C2312yes—
48C2×D4×C19—22no—
49C2×D4×C19—22no—
50C2×D4×C19—22no—
51C22×C4×C19—22no—
52C22×C4×C19—42no—
53C22×C4×C19C2312yes—
54C22×C4×C19C2312yes—
55C22×C4×C19C2311yescharacteristic
56C2×C22⋊D19—22no—
57C2×C22⋊D19—22no—
58C2×C22⋊D19—22no—
59C2×C22⋊D19—24no—
60C2×C22⋊D19—22no—
61C2×C22⋊D19—42no—
62C2×C22⋊D19—42no—
63C2×C22⋊D19—42no—
64C22×Dic19—42no—
65C22×Dic19D414yescomplemented
66C22×Dic19C2312yes—
67C22×Dic19C2311yescharacteristic
68C22×Dic19C2311yescharacteristic
69C22×Dic19C2311yescharacteristic
70C2×D76—24no—
71C2×D76—42no—
72C2×D76—42no—
73C22⋊C4×C19—22no—
74C22⋊C4×C19—42no—
75C22⋊Dic19—22no—
76C22⋊Dic19—22no—
77(C2×D19)⋊C4—24no—
78(C2×D19)⋊C4—24no—
79(C2×D19)⋊C4—22no—
80(C2×D19)⋊C4—24no—
81(C2×D19)⋊C4—24no—
82(C2×D19)⋊C4—42no—
83Dic19⋊C4—22no—
84Dic19⋊C4—42no—
85C23×C19—22no—
86C23×C19—22no—
87C23×C19—21no—
88C23×C19—21no—
89C23×C19—21no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19C2×D412yes—
93C23×C19C2×D412yes—
94C23×C19#4112yes—
95C23×C19C2411yescharacteristic
96C22×D19—28no—
97C22×D19—22no—
98C22×D19—22no—
99C22×D19—22no—
100C22×D19—22no—
101C22×D19—22no—
102C22×D19—22no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19—21no—
106C22×D19—22no—
107C22×D19—22no—
108C22×D19—48no—
109C22×D19—44no—
110C22×D19—44no—
111C22×D19—48no—
112C22×D19C2×D414yes—
113D4×C19—44no—
114C2×C4×C19—21no—
115C2×C4×C19—22no—
116C2×C4×C19—21no—
117C2×C4×C19—22no—
118C2×C4×C19—21no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—44no—
124C22⋊D19—44no—
125C22⋊D19—48no—
126C22⋊D19—44no—
127C2×Dic19—22no—
128C2×Dic19—22no—
129C2×Dic19—21no—
130C2×Dic19—21no—
131C2×Dic19—22no—
132C2×Dic19—21no—
133C2×Dic19—22no—
134C2×Dic19—22no—
135C2×Dic19—44no—
136C2×Dic19C2×D412yes—
137C2×Dic19C2×D412yes—
138D76—48no—
139#2617—191nomaximal, Sylow
140C22×C19—22no—
141C22×C19—24no—
142C22×C19—22no—
143C22×C19—24no—
144C22×C19—41no—
145C22×C19—42no—
146C22×C19—41no—
147C22×C19—41no—
148C22×C19—42no—
149C22×C19#12114yes—
150C22×C19C22×D411yescharacteristic
151C22×C19C22×D411yescharacteristic
152C22×C19C2×#4111yescharacteristic
153C22×C19H(5,𝔽2)12yes—
154C22×C19H(5,𝔽2)12yes—
155C2×D19—24no—
156C2×D19—24no—
157C2×D19—24no—
158C2×D19—416no—
159C2×D19—42no—
160C2×D19—42no—
161C2×D19—42no—
162C2×D19—42no—
163C2×D19—41no—
164C2×D19—42no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—42no—
168C4×C19—41no—
169C4×C19—42no—
170C4×C19—42no—
171Dic19—22no—
172Dic19—22no—
173Dic19—41no—
174Dic19—42no—
175C2×#121—191no—
176C2×#120—191no—
177C2×#120—191no—
178C22×C22⋊C4—191no—
179#397—192no—
180#394—192no—
181#394—192no—
182#392—192no—
183#386—191no—
184#386D1911yescharacteristic, complemented
185#380—191no—
186C2×C19—24no—
187C2×C19—81no—
188C2×C19C2×#12111yescharacteristic
189C2×C19#53412yes—
190C2×C19#53411yescharacteristic
191C2×C19#53511yescharacteristic
192C2×C19#53812yes—
193D19—44no—
194D19—81no—
195C25—191no—
196C22×D4—191no—
197C22×D4—192no—
198C22×D4—191no—
199C22×D4—192no—
200C22×D4C2×D1911yescharacteristic
201C23×C4—191no—
202C23×C4C2×D1911yescharacteristic
203#121—384no—
204#120—384no—
205#120—384no—
206C2×C4⋊C4—191no—
207C2×C4⋊C4—192no—
208C2×C22⋊C4—191no—
209C2×C22⋊C4—191no—
210C2×C22⋊C4—192no—
211C2×C22⋊C4—192no—
212C2×C22⋊C4—192no—
213C2×C22⋊C4—192no—
214C2×C22⋊C4—191no—
215C2×C22⋊C4—192no—
216C2×C22⋊C4—384no—
217C2×C22⋊C4C2×D1911yescharacteristic
218C2×C22⋊C4C2×D1912yescomplemented
219#95—192no—
220#95—192no—
221#95C2×D1912yescomplemented
222C19#261711yescharacteristic, complemented, Sylow
223C24—192no—
224C24—194no—
225C24—191no—
226C24—382no—
227C24—382no—
228C24—762no—
229C24—762no—
230C24C22×D1911yescharacteristic
231C24C22×D1911yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—384no—
236C2×D4—382no—
237C2×D4—384no—
238C2×D4—382no—
239C2×D4—382no—
240C2×D4—382no—
241C2×D4—762no—
242C2×D4—762no—
243C2×D4—762no—
244C2×D4—762no—
245C2×D4—762no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4—191no—
249C22×C4—191no—
250C22×C4—194no—
251C22×C4—191no—
252C22×C4—192no—
253C22×C4—762no—
254C22×C4C22×D1912yes—
255C22×C4C22×D1912yes—
256C22×C4C22×D1911yescharacteristic
257C4⋊C4—382no—
258C4⋊C4—762no—
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—384no—
262C22⋊C4—384no—
263C22⋊C4—382no—
264C22⋊C4—384no—
265C22⋊C4—384no—
266C22⋊C4—382no—
267C22⋊C4—382no—
268C22⋊C4—762no—
269C23—22no—
270C23—22no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—22no—
275C23—22no—
276C23—194no—
277C23—382no—
278C23—382no—
279C23—382no—
280C23—382no—
281C23—382no—
282C23—382no—
283C23—388no—
284C23—381no—
285C23—381no—
286C23—381no—
287C23—382no—
288C23—382no—
289C23—768no—
290C23—764no—
291C23—764no—
292C23—768no—
293C23#6454112yes—
294C23D4×D1912yes—
295C23D4×D1912yes—
296C23C23×D1911yescharacteristic
297D4—44no—
298D4—768no—
299D4—764no—
300D4—768no—
301D4—764no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—44no—
312C2×C4—192no—
313C2×C4—192no—
314C2×C4—382no—
315C2×C4—382no—
316C2×C4—381no—
317C2×C4—382no—
318C2×C4—381no—
319C2×C4—381no—
320C2×C4—382no—
321C2×C4—382no—
322C2×C4—764no—
323C22—24no—
324C22—22no—
325C22—22no—
326C22—24no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—42no—
331C22—41no—
332C22—384no—
333C22—384no—
334C22—384no—
335C22—7616no—
336C22—762no—
337C22—762no—
338C22—762no—
339C22—762no—
340C22—762no—
341C22—761no—
342C22—761no—
343C22—762no—
344C22—761no—
345C22#1059733014yes—
346C22C2×#6454111yescharacteristic
347C22C2×D4×D1911yescharacteristic
348C22C2×D4×D1911yescharacteristic
349C22#1059743012yes—
350C22#1059743512yes—
351C4—42no—
352C4—42no—
353C4—41no—
354C4—382no—
355C4—382no—
356C4—762no—
357C4—761no—
358C2—24no—
359C2—81no—
360C2—764no—
361C2—1521no—
362C2C2×#1059733011yescharacteristic
363C2#1192710212yes—
364C2#1192710511yescharacteristic
365C2#1192710911yescharacteristic
366C2#1192712712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#386C2
hypercenter#386D19
hypocenterC19#2617
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#10597385C2semidirect
2. C2×#10597328C2semidirect
3. C2×#10597383C2semidirect
4. C22×(C2×D19)⋊C4C2semidirect
5. #11926473C2semidirect
6. #11926462C2semidirect
7. #11926459C2semidirect
8. #11926453C2semidirect
9. #11926423C2semidirect
10. #11926402C2semidirect
11. C19×#386C2semidirect
17. C22×C22⋊D19C22semidirect
21. C2×C22⋊C4×C19C22semidirect
23. C2×C22⋊Dic19C22semidirect
31. C2×(C2×D19)⋊C4C22semidirect
32. C2×(C2×D19)⋊C4C22semidirect
33. C2×Dic19⋊C4C22semidirect
34. C2×Dic19⋊C4C22semidirect
36. C19×#95C22semidirect
37. C19⋊#95C22semidirect
38. C19⋊#95C22semidirect
45. C23×D19D4semidirect
65. C22×Dic19D4semidirect
184. #386D19semidirect
218. C2×C22⋊C4C2×D19semidirect
221. #95C2×D19semidirect
222. C19#2617semidirect

Maximal subgroups

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

subgroupindex
C2×#105973852
C2×#105973282
C2×#105973832
C22×(C2×D19)⋊C42
#119264732
#119264622
#119264592
#119264532
#119264232
#119264022
C19×#3862
#261719