Finite Group Databasebeta

← #14578045

Subgroups — #14578045

Order 2432.

1002 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927298C212yesmaximal, complemented
2#11927294C211yesmaximal, characteristic, complemented
3#11927278C212yesmaximal, complemented
4#11927274C212yesmaximal, complemented
5#11927261C214yesmaximal, complemented
6#11927207C214yesmaximal, complemented
7#11927164C214yesmaximal, complemented
8#11927160C214yesmaximal, complemented
9#11927119C212yesmaximal, complemented
10#11927116C212yesmaximal, complemented
11#11927100C212yesmaximal, complemented
12#11927093C211yesmaximal, characteristic
13C19×#563C211yesmaximal, characteristic, complemented
14C2×#64545C2211yescharacteristic
15C2×Q8×D19C2212yes—
16C2×#64543C2211yescharacteristic
17C22×Dic38C2212yes—
18C19×C4⋊Q8C2212yes—
19C19×#126C2214yes—
20C19×#125C2212yes—
21C19×#124C2211yescharacteristic
22C19×#123C2212yes—
23C19×C22⋊Q8C2214yes—
24#10597393C2212yes—
25#10597390C2211yescharacteristic
26#10597390C2212yes—
27#10597390C2214yes—
28#10597386C2211yescharacteristic
29#10597381C2212yes—
30#10597375C2212yes—
31C4×C22⋊D19C2214yes—
32#10597344C2214yes—
33#10597344C2214yes—
34#10597343C2214yes—
35#10597342C2214yes—
36#10597342C2214yes—
37#10597342C2214yes—
38#10597342C2214yes—
39#10597340C2214yes—
40#10597340C2214yes—
41#10597338C2212yes—
42#10597338C2212yes—
43#10597334C2214yes—
44#10597334C2212yes—
45#10597334C2212yes—
46#10597334C2214yes—
47#10597333C2214yes—
48#10597333C2214yes—
49#10597333C2214yes—
50#10597332C2212yes—
51#10597331C2214yes—
52#10597331C2214yes—
53#10597331C2214yes—
54#10597330C2214yes—
55(C22⋊D19)⋊C4C2214yes—
56(C22⋊D19)⋊C4C2214yes—
57#10597325C2214yes—
58#10597324C2214yes—
59#10597324C2214yes—
60#10597323C2212yes—
61#10597321C2211yescharacteristic
62#10597321C2212yes—
63#10597318C2212yes—
64C42×D19C2211yescharacteristic
65#10597316C2212yes—
66C4×Dic38C2214yes—
67C2×Q8×C19C2311yescharacteristic
68C2×Q8×C19C2312yes—
69C2×D4×C19C2311yescharacteristic
70C22×C4×C19C2312yes—
71C2×C22⋊D19C2314yes—
72C2×C22⋊D19C2312yes—
73C22×Dic19C2312yes—
74C22×Dic19C2312yes—
75#64545—42no—
76Q8×D19—44no—
77#64543—42no—
78C2×D76C2311yescharacteristic
79C2×D76C2312yes—
80C2×C4×D19C2311yescharacteristic
81C2×C4×D19C2312yes—
82C2×C4×D19C2312yes—
83C2×C4×D19C2314yes—
84C2×Dic38—44no—
85C2×Dic38C2314yes—
86C2×Dic38C2314yes—
87C2×Dic38C2314yes—
88C2×Dic38C2311yescharacteristic
89C2×Dic38C2312yes—
90C4⋊C4×C19C2312yes—
91C4⋊C4×C19C2314yes—
92C4⋊C4×C19C2314yes—
93C4⋊C4×C19C2314yes—
94C4⋊C4×C19C2312yes—
95C22⋊C4×C19C2314yes—
96C22⋊C4×C19C2314yes—
97C22⋊C4×C19C2312yes—
98C42×C19C2311yescharacteristic
99C42×C19C2312yes—
100C22⋊Dic19C2312yes—
101C22⋊Dic19C2314yes—
102(C2×D19)⋊C4C2314yes—
103(C2×D19)⋊C4C2314yes—
104(C2×D19)⋊C4C2314yes—
105(C2×D19)⋊C4C2314yes—
106(C2×D19)⋊C4C2314yes—
107(C2×D19)⋊C4C2314yes—
108C4⋊Dic19C2314yes—
109C4⋊Dic19C2312yes—
110C4⋊Dic19C2312yes—
111Dic19⋊C4C2314yes—
112Dic19⋊C4C2314yes—
113Dic19⋊C4C2314yes—
114Dic19⋊C4C2314yes—
115Dic19⋊C4C2314yes—
116Dic19⋊C4C2314yes—
117Dic19⋊C4C2314yes—
118C4×Dic19C2311yescharacteristic
119C4×Dic19C2312yes—
120C4×Dic19C2314yes—
121C4×Dic19C2314yes—
122C4×Dic19C2314yes—
123C4×Dic19C2312yes—
124C23×C19C2412yes—
125C22×D19C2412yes—
126C22×D19C2411yescharacteristic
127Q8×C19—42no—
128Q8×C19—41no—
129D4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19C2414yes—
132C2×C4×C19C2412yes—
133C2×C4×C19C2411yescharacteristic
134C2×C4×C19C2412yes—
135C2×C4×C19C2414yes—
136C22⋊D19—28no—
137C22⋊D19—42no—
138C2×Dic19—24no—
139C2×Dic19—42no—
140C2×Dic19C2414yes—
141C2×Dic19C2412yes—
142C2×Dic19C2414yes—
143C2×Dic19C2411yescharacteristic
144C2×Dic19C2412yes—
145D76—41no—
146D76—42no—
147C4×D19—22no—
148C4×D19—24no—
149C4×D19—24no—
150C4×D19—44no—
151Dic38—28no—
152Dic38—28no—
153Dic38—44no—
154Dic38—41no—
155Dic38—42no—
156#3550—191nomaximal, Sylow
157C22×C19—22no—
158C22×C19—24no—
159C22×C19C2511yescharacteristic
160C2×D19—22no—
161C2×D19—21no—
162C2×D19—22no—
163C2×D19—24no—
164C4×C19—24no—
165C4×C19—21no—
166C4×C19—22no—
167C4×C19—24no—
168C4×C19—22no—
169Dic19—24no—
170Dic19—22no—
171Dic19—24no—
172Dic19H(5,𝔽2)12yes—
173Dic192−1+414yes—
174#563—192no—
175#563—191no—
176#563D1911yescharacteristic, complemented
177#559—192no—
178Q82—192no—
179#556—194no—
180D4×Q8—194no—
181#542—194no—
182#542—194no—
183#536—192no—
184#536—192no—
185#533—192no—
186#532—191no—
187C2×C19—42no—
188C2×C19C2×H(5,𝔽2)11yescharacteristic
189C2×C19C2×2−1+412yes—
190D19—42no—
191D19—41no—
192C2×#41—191no—
193C2×#41—191no—
194C22×Q8—192no—
195C22×Q8—192no—
196C4⋊Q8—191no—
197C4⋊Q8—192no—
198C4⋊Q8—194no—
199C4⋊Q8—192no—
200C4⋊Q8—192no—
201C4⋊Q8—194no—
202C4⋊Q8—194no—
203C4⋊Q8C2×D1912yes—
204#127—191no—
205#126—194no—
206#126—194no—
207#126—194no—
208#126C2×D1914yes—
209#125—192no—
210#125C2×D1912yes—
211#124—192no—
212#124—194no—
213#124—194no—
214#124—194no—
215#124—191no—
216#124—192no—
217#124C2×D1911yescharacteristic
218#123—192no—
219#123—192no—
220#123—194no—
221#123—194no—
222#123—192no—
223#123C2×D1912yes—
224C22⋊Q8—194no—
225C22⋊Q8—194no—
226C22⋊Q8—194no—
227C22⋊Q8—194no—
228C22⋊Q8—194no—
229C22⋊Q8—194no—
230C22⋊Q8—194no—
231C22⋊Q8C2×D1914yes—
232#121—194no—
233C4×Q8—194no—
234C4×Q8—194no—
235C4×Q8—194no—
236C4×Q8—194no—
237C4×D4—194no—
238C4×D4—194no—
239C4×D4—194no—
240#117—192no—
241#117—192no—
242#117—192no—
243#117—192no—
244C2×C42—191no—
245C19#355011yescharacteristic, complemented, Sylow
246#41—762no—
247#41—762no—
248C2×Q8—194no—
249C2×Q8—194no—
250C2×Q8—194no—
251C2×Q8—192no—
252C2×Q8—191no—
253C2×Q8—764no—
254C2×Q8—764no—
255C2×Q8C22×D1912yes—
256C2×Q8C22×D1911yescharacteristic
257C2×D4—194no—
258C2×D4—192no—
259C2×D4—192no—
260C2×D4—191no—
261C2×D4C22×D1911yescharacteristic
262C22×C4—192no—
263C22×C4—192no—
264C22×C4—192no—
265C22×C4—191no—
266C22×C4—192no—
267C22×C4—194no—
268C22×C4C22×D1912yes—
269C4⋊C4—194no—
270C4⋊C4—194no—
271C4⋊C4—194no—
272C4⋊C4—194no—
273C4⋊C4—194no—
274C4⋊C4—194no—
275C4⋊C4—194no—
276C4⋊C4—192no—
277C4⋊C4—192no—
278C4⋊C4—194no—
279C4⋊C4C22×D1912yes—
280C4⋊C4C22×D1912yes—
281C4⋊C4C22×D1914yes—
282C4⋊C4C22×D1914yes—
283C4⋊C4C22×D1914yes—
284C22⋊C4—192no—
285C22⋊C4—194no—
286C22⋊C4—194no—
287C22⋊C4—194no—
288C22⋊C4—194no—
289C22⋊C4—194no—
290C22⋊C4—194no—
291C22⋊C4—194no—
292C22⋊C4C22×D1912yes—
293C22⋊C4C22×D1914yes—
294C22⋊C4C22×D1914yes—
295C42—192no—
296C42—191no—
297C42—194no—
298C42—194no—
299C42—192no—
300C42—194no—
301C42C22×D1911yescharacteristic
302C42C22×D1912yes—
303C23—192no—
304C23—191no—
305C23C23×D1912yes—
306Q8—42no—
307Q8—41no—
308Q8—388no—
309Q8—388no—
310Q8—764no—
311Q8—762no—
312Q8—761no—
313D4—41no—
314D4—388no—
315D4—761no—
316D4—762no—
317D4—762no—
318C2×C4—42no—
319C2×C4—192no—
320C2×C4—191no—
321C2×C4—194no—
322C2×C4—192no—
323C2×C4—194no—
324C2×C4—384no—
325C2×C4—382no—
326C2×C4—384no—
327C2×C4—384no—
328C2×C4—764no—
329C2×C4—762no—
330C2×C4C23×D1914yes—
331C2×C4C23×D1912yes—
332C2×C4C23×D1912yes—
333C2×C4C23×D1911yescharacteristic
334C2×C4C23×D1914yes—
335C22—22no—
336C22—24no—
337C22—382no—
338C22—381no—
339C22—382no—
340C22—384no—
341C22C24×D1911yescharacteristic
342C4—24no—
343C4—21no—
344C4—22no—
345C4—22no—
346C4—24no—
347C4—192no—
348C4—194no—
349C4—382no—
350C4—384no—
351C4—384no—
352C2—42no—
353C2—762no—
354C2—761no—
355C2H(5,𝔽2)×D1911yescharacteristic
356C22−1+4×D1912yes—
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#563C2
prime radical#11927093C2
hypercenter#563D19
hypocenterC19#3550
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #11927298C2semidirect
2. #11927294C2semidirect
3. #11927278C2semidirect
4. #11927274C2semidirect
5. #11927261C2semidirect
6. #11927207C2semidirect
7. #11927164C2semidirect
8. #11927160C2semidirect
9. #11927119C2semidirect
10. #11927116C2semidirect
11. #11927100C2semidirect
13. C19×#563C2semidirect
176. #563D19semidirect
245. C19#3550semidirect

Maximal subgroups

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

subgroupindex
#119272982
#119272942
#119272782
#119272742
#119272612
#119272072
#119271642
#119271602
#119271192
#119271162
#119271002
#119270932
C19×#5632
#355019