Finite Group Databasebeta

← #14578241

Subgroups — #14578241

Order 2432.

912 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19⋊#564C212yesmaximal, complemented
2#11927298C212yesmaximal, complemented
3#11927271C212yesmaximal, complemented
4#11927249C212yesmaximal, complemented
5#11927232C212yesmaximal, complemented
6#11927229C214yesmaximal, complemented
7#11927229C212yesmaximal, complemented
8#11927175C212yesmaximal, complemented
9#11927174C212yesmaximal, complemented
10#11927157C212yesmaximal, complemented
11#11927153C214yesmaximal, complemented
12#11927141C212yesmaximal
13#11927101C211yesmaximal, characteristic, complemented
14#11927078C211yesmaximal, characteristic
15C2×C19×#125C211yesmaximal, characteristic, complemented
16C19×#125C2212yes—
17C19×#125C2212yes—
18C19×#125C2212yes—
19C19×#125C2212yes—
20C2×C4⋊C4×C19C2212yes—
21C2×C4⋊C4×C19C2212yes—
22C2×C4⋊C4×C19C2211yescharacteristic
23C2×C4⋊C4×C19C2211yescharacteristic
24C2×C42×C19C2211yescharacteristic
25#10597376C2211yescharacteristic
26#10597375C2212yes—
27#10597375C2214yes—
28C4×C22⋊D19C2212yes—
29C4×C22⋊D19C2214yes—
30#10597372C2212yes—
31#10597372C2214yes—
32#10597370C2211yescharacteristic
33#10597370C2212yes—
34#10597370C2212yes—
35#10597370C2214yes—
36#10597344C2214yes—
37#10597344C2214yes—
38#10597344C2214yes—
39#10597344C2214yes—
40#10597343C2214yes—
41#10597343C2212yes—
42#10597343C2212yes—
43#10597342C2214yes—
44#10597342C2214yes—
45#10597340C2214yes—
46#10597338C2214yes—
47#10597338C2212yes—
48C4⋊C4×D19C2212yes—
49#10597336C2214yes—
50#10597336C2214yes—
51#10597336C2214yes—
52#10597336C2212yes—
53#10597335C2214yes—
54#10597335C2214yes—
55#10597335C2214yes—
56#10597335C2214yes—
57#10597335C2214yes—
58#10597334C2214yes—
59#10597334C2214yes—
60#10597334C2212yes—
61#10597333C2214yes—
62#10597333C2212yes—
63#10597333C2212yes—
64#10597322C2212yes—
65#10597321C2211yescharacteristic
66C4×D76C2211yescharacteristic
67#10597318C2212yes—
68#10597316C2212yes—
69#10597316C2211yescharacteristic
70#10597315C2211yescharacteristic
71#10597315C2211yescharacteristic
72C4×Dic38C2211yescharacteristic
73C4×Dic38C2212yes—
74C4×Dic38C2212yes—
75C22×C4×C19C2311yescharacteristic
76C22×C4×C19C2311yescharacteristic
77C22×C4×C19C2312yes—
78C22×C4×C19C2311yescharacteristic
79C22×C4×C19C2312yes—
80C2×C22⋊D19C2312yes—
81C2×D76C2311yescharacteristic
82C2×C4×D19C2312yes—
83C2×C4×D19C2314yes—
84C2×Dic38C2312yes—
85C2×Dic38C2312yes—
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2314yes—
88C4⋊C4×C19C2312yes—
89C4⋊C4×C19C2314yes—
90C4⋊C4×C19C2312yes—
91C4⋊C4×C19C2314yes—
92C4⋊C4×C19C2314yes—
93C4⋊C4×C19C2312yes—
94C4⋊C4×C19C2312yes—
95C4⋊C4×C19C2314yes—
96C42×C19C2311yescharacteristic
97C42×C19C2311yescharacteristic
98C42×C19C2311yescharacteristic
99C42×C19C2311yescharacteristic
100C22⋊Dic19C2314yes—
101C22⋊Dic19C2312yes—
102(C2×D19)⋊C4C2312yes—
103(C2×D19)⋊C4C2312yes—
104(C2×D19)⋊C4C2312yes—
105(C2×D19)⋊C4C2312yes—
106(C2×D19)⋊C4C2314yes—
107(C2×D19)⋊C4C2314yes—
108(C2×D19)⋊C4C2314yes—
109C4⋊Dic19C2311yescharacteristic
110C4⋊Dic19C2312yes—
111C4⋊Dic19C2312yes—
112C4⋊Dic19C2312yes—
113C4⋊Dic19C2312yes—
114C4⋊Dic19C2311yescharacteristic
115C4⋊Dic19C2314yes—
116C4⋊Dic19C2314yes—
117C4⋊Dic19C2314yes—
118Dic19⋊C4C2314yes—
119Dic19⋊C4C2314yes—
120Dic19⋊C4C2312yes—
121Dic19⋊C4C2312yes—
122Dic19⋊C4C2312yes—
123Dic19⋊C4C2312yes—
124Dic19⋊C4C2314yes—
125Dic19⋊C4C2314yes—
126Dic19⋊C4C2314yes—
127Dic19⋊C4C2314yes—
128Dic19⋊C4C2314yes—
129C4×Dic19C2314yes—
130C4×Dic19C2312yes—
131C4×Dic19C2314yes—
132C4×Dic19C2314yes—
133C4×Dic19C2314yes—
134C23×C19C2411yescharacteristic
135C22×D19C2412yes—
136C2×C4×C19—22no—
137C2×C4×C19—24no—
138C2×C4×C19—22no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19C2411yescharacteristic
142C2×C4×C19C2414yes—
143C2×C4×C19C2414yes—
144C2×C4×C19C2411yescharacteristic
145C2×C4×C19C2411yescharacteristic
146C2×C4×C19C2411yescharacteristic
147C2×C4×C19C2411yescharacteristic
148C2×C4×C19C2411yescharacteristic
149C22⋊D19—24no—
150C2×Dic19C2412yes—
151C2×Dic19C2414yes—
152C2×Dic19C2412yes—
153C2×Dic19C2412yes—
154C2×Dic19C2414yes—
155D76—41no—
156C4×D19—24no—
157C4×D19—44no—
158Dic38—24no—
159Dic38—41no—
160Dic38—44no—
161Dic38—42no—
162#3563—191nomaximal, Sylow
163C22×C19—21no—
164C22×C19—21no—
165C22×C192−1+412yes—
166C22×C19C2511yescharacteristic
167C2×D19—22no—
168C2×D19—22no—
169C2×D19—22no—
170C4×C19—21no—
171C4×C19—24no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—24no—
176C4×C19—21no—
177C4×C192−1+412yes—
178Dic19—24no—
179Dic19—22no—
180Dic19—22no—
181Dic19—22no—
182Dic19—24no—
183#564—192no—
184#563—192no—
185#557—192no—
186#554—192no—
187#552—192no—
188#552—194no—
189#552—192no—
190#544—192no—
191#544—192no—
192#541—194no—
193#541—192no—
194#539—192no—
195#533—191no—
196#529—191no—
197C2×#125D1911yescharacteristic, complemented
198C2×C19—22no—
199C2×C19C2×2−1+411yescharacteristic
200C2×C19C2×2−1+411yescharacteristic
201C2×C19#58511yescharacteristic
202D19—42no—
203C4⋊Q8—194no—
204C4⋊Q8—192no—
205C4⋊Q8—194no—
206C4⋊Q8—191no—
207C4⋊Q8—191no—
208#126—194no—
209#126—194no—
210#126—194no—
211#126—194no—
212#126—192no—
213#125—194no—
214#125—194no—
215#125—194no—
216#125—194no—
217#125—194no—
218#125—194no—
219#125—192no—
220#125—194no—
221#125—194no—
222#125—191no—
223#125—192no—
224#125C2×D1912yes—
225#125C2×D1912yes—
226#125C2×D1912yes—
227#125C2×D1912yes—
228#124—191no—
229#123—192no—
230#123—194no—
231#123—194no—
232C22⋊Q8—191no—
233C22⋊Q8—192no—
234C22⋊Q8—192no—
235C22⋊Q8—194no—
236C22⋊Q8—194no—
237C22⋊Q8—192no—
238C22⋊Q8—192no—
239C22⋊Q8—194no—
240C22⋊Q8—194no—
241#121—191no—
242C4×Q8—194no—
243C4×Q8—192no—
244C4×Q8—192no—
245C4×Q8—191no—
246C4×Q8—192no—
247C4×Q8—192no—
248C4×D4—192no—
249C4×D4—194no—
250C4×D4—191no—
251#117—192no—
252#117—194no—
253#117—194no—
254#117—192no—
255#117—192no—
256C2×C4⋊C4—192no—
257C2×C4⋊C4C2×D1912yes—
258C2×C4⋊C4C2×D1911yescharacteristic
259C2×C4⋊C4C2×D1912yes—
260C2×C4⋊C4C2×D1911yescharacteristic
261C2×C42C2×D1911yescharacteristic
262C19#356311yescharacteristic, complemented, Sylow
263C2×Q8—192no—
264C2×Q8—194no—
265C2×Q8—192no—
266C2×Q8—191no—
267C2×D4—192no—
268C2×D4—191no—
269C22×C4—192no—
270C22×C4—194no—
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C22×C4C22×D1912yes—
274C22×C4C22×D1911yescharacteristic
275C22×C4C22×D1912yes—
276C4⋊C4—194no—
277C4⋊C4—192no—
278C4⋊C4—192no—
279C4⋊C4—194no—
280C4⋊C4—192no—
281C4⋊C4—192no—
282C4⋊C4—194no—
283C4⋊C4—194no—
284C4⋊C4—194no—
285C4⋊C4—194no—
286C4⋊C4—194no—
287C4⋊C4—192no—
288C4⋊C4—194no—
289C4⋊C4—192no—
290C4⋊C4—194no—
291C4⋊C4—194no—
292C4⋊C4—192no—
293C4⋊C4—191no—
294C4⋊C4—191no—
295C4⋊C4—192no—
296C4⋊C4C22×D1912yes—
297C4⋊C4C22×D1912yes—
298C4⋊C4C22×D1914yes—
299C4⋊C4C22×D1912yes—
300C4⋊C4C22×D1914yes—
301C4⋊C4C22×D1914yes—
302C4⋊C4C22×D1914yes—
303C4⋊C4C22×D1912yes—
304C22⋊C4—194no—
305C22⋊C4—192no—
306C22⋊C4—192no—
307C22⋊C4—192no—
308C22⋊C4—194no—
309C22⋊C4—192no—
310C22⋊C4—194no—
311C22⋊C4—194no—
312C22⋊C4—192no—
313C42—194no—
314C42—194no—
315C42—192no—
316C42—194no—
317C42—194no—
318C42C22×D1911yescharacteristic
319C42C22×D1911yescharacteristic
320C42C22×D1911yescharacteristic
321C42C22×D1911yescharacteristic
322C23—192no—
323C23C23×D1911yescharacteristic
324Q8—384no—
325Q8—764no—
326Q8—761no—
327Q8—762no—
328D4—384no—
329D4—761no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—194no—
336C2×C4—192no—
337C2×C4—192no—
338C2×C4—192no—
339C2×C4—194no—
340C2×C4—384no—
341C2×C4—764no—
342C2×C4C23×D1911yescharacteristic
343C2×C4C23×D1914yes—
344C2×C4C23×D1914yes—
345C2×C4C23×D1911yescharacteristic
346C2×C4C23×D1911yescharacteristic
347C2×C4C23×D1911yescharacteristic
348C2×C4C23×D1911yescharacteristic
349C2×C4C23×D1911yescharacteristic
350C22—21no—
351C22—21no—
352C22—382no—
353C22—382no—
354C22—382no—
355C22#1059743612yes—
356C22C24×D1911yescharacteristic
357C4—21no—
358C4—24no—
359C4—21no—
360C4—21no—
361C4—24no—
362C4—21no—
363C4—21no—
364C4—382no—
365C4—382no—
366C4—384no—
367C4—384no—
368C4—382no—
369C4#1059743312yes—
370C2—22no—
371C2—762no—
372C2C2×#1059743611yescharacteristic
373C2C2×#1059743311yescharacteristic
374C2#1192738011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC2×C19×#125C2
prime radical#10597376C22
hypercenterC2×#125D19
hypocenterC19#3563
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C19⋊#564C2semidirect
2. #11927298C2semidirect
3. #11927271C2semidirect
4. #11927249C2semidirect
5. #11927232C2semidirect
6. #11927229C2semidirect
7. #11927229C2semidirect
8. #11927175C2semidirect
9. #11927174C2semidirect
10. #11927157C2semidirect
11. #11927153C2semidirect
13. #11927101C2semidirect
15. C2×C19×#125C2semidirect
197. C2×#125D19semidirect
262. C19#3563semidirect

Maximal subgroups

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

subgroupindex
C19⋊#5642
#119272982
#119272712
#119272492
#119272322
#119272292
#119271752
#119271742
#119271572
#119271532
#119271412
#119271012
#119270782
C2×C19×#1252
#356319