Finite Group Databasebeta

← #14578169

Subgroups — #14578169

Order 2432.

1024 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927298C212yesmaximal, complemented
2#11927292C212yesmaximal, complemented
3#11927250C212yesmaximal, complemented
4#11927247C212yesmaximal, complemented
5#11927242C212yesmaximal, complemented
6#11927195C212yesmaximal, complemented
7#11927195C214yesmaximal, complemented
8#11927174C212yesmaximal, complemented
9#11927150C212yesmaximal, complemented
10#11927142C214yesmaximal, complemented
11#11927141C212yesmaximal, complemented
12#11927125C212yesmaximal, complemented
13#11927094C211yesmaximal, characteristic, complemented
14#11927078C211yesmaximal, characteristic, complemented
15C2×C19×#125C211yesmaximal, characteristic, complemented
16C2×#64541C2212yes—
17C2×#64541C2214yes—
18C19×#125C2212yes—
19C19×#125C2212yes—
20C19×#125C2212yes—
21C19×#125C2212yes—
22C2×C4⋊C4×C19C2212yes—
23C2×C4⋊C4×C19C2211yescharacteristic
24C2×C4⋊C4×C19C2212yes—
25C2×C4⋊C4×C19C2211yescharacteristic
26C2×C42×C19C2211yescharacteristic
27#10597376C2211yescharacteristic
28#10597376C2212yes—
29#10597376C2212yes—
30#10597376C2214yes—
31#10597375C2212yes—
32#10597375C2214yes—
33C4×C22⋊D19C2212yes—
34C4×C22⋊D19C2214yes—
35#10597370C2211yescharacteristic
36#10597344C2214yes—
37#10597344C2214yes—
38#10597343C2214yes—
39#10597343C2214yes—
40#10597342C2214yes—
41#10597342C2214yes—
42#10597342C2214yes—
43#10597342C2214yes—
44#10597341C2214yes—
45#10597341C2214yes—
46#10597341C2212yes—
47#10597341C2214yes—
48#10597341C2212yes—
49#10597340C2214yes—
50#10597340C2214yes—
51#10597340C2214yes—
52#10597340C2214yes—
53#10597340C2214yes—
54#10597339C2214yes—
55#10597339C2212yes—
56#10597339C2212yes—
57#10597338C2212yes—
58C4⋊C4×D19C2214yes—
59C4⋊C4×D19C2212yes—
60#10597336C2212yes—
61#10597335C2214yes—
62#10597334C2214yes—
63#10597334C2212yes—
64#10597322C2212yes—
65#10597321C2212yes—
66#10597321C2211yescharacteristic
67#10597320C2211yescharacteristic
68C4×D76C2211yescharacteristic
69C4×D76C2212yes—
70C4×D76C2212yes—
71#10597318C2212yes—
72#10597316C2211yescharacteristic
73#10597315C2211yescharacteristic
74C4×Dic38C2211yescharacteristic
75C22×C4×C19C2311yescharacteristic
76C22×C4×C19C2311yescharacteristic
77C22×C4×C19C2312yes—
78C22×C4×C19C2311yescharacteristic
79C22×C4×C19C2312yes—
80C2×C22⋊D19C2312yes—
81C2×C22⋊D19C2314yes—
82#64541—44no—
83#64541—48no—
84C2×D76C2312yes—
85C2×D76C2312yes—
86C2×D76C2311yescharacteristic
87C2×D76C2314yes—
88C2×D76C2312yes—
89C2×D76C2314yes—
90C2×C4×D19C2312yes—
91C2×C4×D19C2314yes—
92C2×C4×D19C2314yes—
93C2×C4×D19C2314yes—
94C2×C4×D19C2314yes—
95C2×Dic38C2312yes—
96C2×Dic38C2314yes—
97C2×Dic38C2311yescharacteristic
98C4⋊C4×C19C2312yes—
99C4⋊C4×C19C2314yes—
100C4⋊C4×C19C2314yes—
101C4⋊C4×C19C2312yes—
102C4⋊C4×C19C2314yes—
103C4⋊C4×C19C2312yes—
104C4⋊C4×C19C2312yes—
105C4⋊C4×C19C2314yes—
106C42×C19C2311yescharacteristic
107C42×C19C2311yescharacteristic
108C42×C19C2311yescharacteristic
109C42×C19C2311yescharacteristic
110C22⋊Dic19C2312yes—
111(C2×D19)⋊C4C2312yes—
112(C2×D19)⋊C4C2314yes—
113(C2×D19)⋊C4C2314yes—
114(C2×D19)⋊C4C2314yes—
115(C2×D19)⋊C4C2314yes—
116(C2×D19)⋊C4C2312yes—
117(C2×D19)⋊C4C2312yes—
118(C2×D19)⋊C4C2312yes—
119(C2×D19)⋊C4C2314yes—
120(C2×D19)⋊C4C2314yes—
121(C2×D19)⋊C4C2314yes—
122C4⋊Dic19C2311yescharacteristic
123C4⋊Dic19C2312yes—
124C4⋊Dic19C2312yes—
125C4⋊Dic19C2314yes—
126C4⋊Dic19C2311yescharacteristic
127Dic19⋊C4C2312yes—
128Dic19⋊C4C2312yes—
129Dic19⋊C4C2312yes—
130Dic19⋊C4C2312yes—
131Dic19⋊C4C2314yes—
132Dic19⋊C4C2314yes—
133Dic19⋊C4C2314yes—
134C4×Dic19C2312yes—
135C4×Dic19C2314yes—
136C23×C19C2411yescharacteristic
137C22×D19C2412yes—
138C22×D19C2414yes—
139C2×C4×C19—22no—
140C2×C4×C19—24no—
141C2×C4×C19—22no—
142C2×C4×C19—41no—
143C2×C4×C19—42no—
144C2×C4×C19C2414yes—
145C2×C4×C19C2411yescharacteristic
146C2×C4×C19C2411yescharacteristic
147C2×C4×C19C2411yescharacteristic
148C2×C4×C19C2411yescharacteristic
149C2×C4×C19C2414yes—
150C2×C4×C19C2411yescharacteristic
151C2×C4×C19C2411yescharacteristic
152C22⋊D19—28no—
153C22⋊D19—24no—
154C2×Dic19C2412yes—
155C2×Dic19C2412yes—
156C2×Dic19C2412yes—
157C2×Dic19C2414yes—
158D76—24no—
159D76—41no—
160D76—44no—
161D76—42no—
162D76—42no—
163D76—44no—
164C4×D19—24no—
165C4×D19—44no—
166C4×D19—44no—
167C4×D19—44no—
168C4×D19—44no—
169Dic38—41no—
170Dic38—42no—
171Dic38—44no—
172#3559—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19H(5,𝔽2)12yes—
176C22×C19C2511yescharacteristic
177C2×D19—22no—
178C2×D19—24no—
179C2×D19—22no—
180C2×D19—24no—
181C2×D19—24no—
182C2×D19—22no—
183C4×C19—21no—
184C4×C19—24no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—24no—
189C4×C19—21no—
190C4×C192−1+412yes—
191Dic19—24no—
192Dic19—22no—
193Dic19—22no—
194Dic19—22no—
195#563—192no—
196#562—192no—
197#554—192no—
198#553—192no—
199#553—192no—
200#547—194no—
201#547—192no—
202#544—192no—
203#540—192no—
204#539—194no—
205#539—192no—
206#537—192no—
207#532—191no—
208#529—191no—
209C2×#125D1911yescharacteristic, complemented
210C2×C19—22no—
211C2×C19C2×H(5,𝔽2)11yescharacteristic
212C2×C19C2×2−1+411yescharacteristic
213C2×C19#58511yescharacteristic
214D19—42no—
215D19—44no—
216C2×#41—192no—
217C2×#41—194no—
218C4⋊Q8—192no—
219C4⋊Q8—194no—
220C4⋊Q8—191no—
221#127—191no—
222#126—194no—
223#126—194no—
224#126—192no—
225#125—194no—
226#125—192no—
227#125—191no—
228#125C2×D1912yes—
229#125C2×D1912yes—
230#125C2×D1912yes—
231#125C2×D1912yes—
232#124—191no—
233#124—192no—
234#123—192no—
235#123—194no—
236#123—194no—
237#123—194no—
238#123—194no—
239#123—194no—
240#123—194no—
241C22⋊Q8—191no—
242C22⋊Q8—194no—
243C22⋊Q8—194no—
244C22⋊Q8—194no—
245C22⋊Q8—194no—
246C22⋊Q8—194no—
247C22⋊Q8—194no—
248#121—191no—
249#121—192no—
250#121—192no—
251#121—194no—
252#121—194no—
253#121—194no—
254#121—192no—
255#121—194no—
256#121—192no—
257C4×Q8—191no—
258C4×D4—192no—
259C4×D4—194no—
260C4×D4—194no—
261C4×D4—192no—
262C4×D4—192no—
263C4×D4—191no—
264C4×D4—192no—
265C4×D4—192no—
266#117—192no—
267#117—192no—
268C2×C4⋊C4—194no—
269C2×C4⋊C4—192no—
270C2×C4⋊C4C2×D1912yes—
271C2×C4⋊C4C2×D1911yescharacteristic
272C2×C4⋊C4C2×D1912yes—
273C2×C4⋊C4C2×D1911yescharacteristic
274C2×C42C2×D1911yescharacteristic
275C19#355911yescharacteristic, complemented, Sylow
276#41—764no—
277#41—768no—
278C2×Q8—191no—
279C2×Q8—194no—
280C2×Q8—192no—
281C2×D4—192no—
282C2×D4—194no—
283C2×D4—192no—
284C2×D4—194no—
285C2×D4—191no—
286C2×D4—192no—
287C2×D4—194no—
288C2×D4—192no—
289C22×C4—192no—
290C22×C4—194no—
291C22×C4—194no—
292C22×C4—194no—
293C22×C4—194no—
294C22×C4C22×D1911yescharacteristic
295C22×C4C22×D1911yescharacteristic
296C22×C4C22×D1912yes—
297C22×C4C22×D1911yescharacteristic
298C22×C4C22×D1912yes—
299C4⋊C4—192no—
300C4⋊C4—194no—
301C4⋊C4—194no—
302C4⋊C4—192no—
303C4⋊C4—192no—
304C4⋊C4—194no—
305C4⋊C4—192no—
306C4⋊C4—192no—
307C4⋊C4—194no—
308C4⋊C4—192no—
309C4⋊C4—191no—
310C4⋊C4—191no—
311C4⋊C4C22×D1912yes—
312C4⋊C4C22×D1914yes—
313C4⋊C4C22×D1912yes—
314C4⋊C4C22×D1914yes—
315C4⋊C4C22×D1914yes—
316C4⋊C4C22×D1914yes—
317C4⋊C4C22×D1912yes—
318C4⋊C4C22×D1912yes—
319C22⋊C4—192no—
320C22⋊C4—192no—
321C22⋊C4—194no—
322C22⋊C4—192no—
323C22⋊C4—192no—
324C22⋊C4—194no—
325C22⋊C4—194no—
326C22⋊C4—194no—
327C22⋊C4—194no—
328C22⋊C4—194no—
329C22⋊C4—194no—
330C22⋊C4—192no—
331C42—192no—
332C42—194no—
333C42C22×D1911yescharacteristic
334C42C22×D1911yescharacteristic
335C42C22×D1911yescharacteristic
336C42C22×D1911yescharacteristic
337C23—192no—
338C23—194no—
339C23C23×D1911yescharacteristic
340Q8—764no—
341Q8—762no—
342Q8—761no—
343D4—384no—
344D4—388no—
345D4—384no—
346D4—764no—
347D4—762no—
348D4—764no—
349D4—762no—
350D4—761no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—192no—
357C2×C4—192no—
358C2×C4—192no—
359C2×C4—194no—
360C2×C4—384no—
361C2×C4—764no—
362C2×C4—764no—
363C2×C4—764no—
364C2×C4—764no—
365C2×C4C23×D1914yes—
366C2×C4C23×D1911yescharacteristic
367C2×C4C23×D1911yescharacteristic
368C2×C4C23×D1911yescharacteristic
369C2×C4C23×D1911yescharacteristic
370C2×C4C23×D1911yescharacteristic
371C2×C4C23×D1914yes—
372C2×C4C23×D1911yescharacteristic
373C22—21no—
374C22—21no—
375C22—382no—
376C22—384no—
377C22—382no—
378C22—384no—
379C22—384no—
380C22—382no—
381C22#1059743512yes—
382C22C24×D1911yescharacteristic
383C4—21no—
384C4—24no—
385C4—21no—
386C4—21no—
387C4—24no—
388C4—21no—
389C4—21no—
390C4—382no—
391C4—384no—
392C4—382no—
393C4—382no—
394C4#1059743312yes—
395C2—22no—
396C2—762no—
397C2—764no—
398C2C2×#1059743511yescharacteristic
399C2C2×#1059743311yescharacteristic
400C2#1192738011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC2×C19×#125C2
hypercenterC2×#125D19
hypocenterC19#3559
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #11927298C2semidirect
2. #11927292C2semidirect
3. #11927250C2semidirect
4. #11927247C2semidirect
5. #11927242C2semidirect
6. #11927195C2semidirect
7. #11927195C2semidirect
8. #11927174C2semidirect
9. #11927150C2semidirect
10. #11927142C2semidirect
11. #11927141C2semidirect
12. #11927125C2semidirect
13. #11927094C2semidirect
14. #11927078C2semidirect
15. C2×C19×#125C2semidirect
209. C2×#125D19semidirect
275. C19#3559semidirect

Maximal subgroups

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

subgroupindex
#119272982
#119272922
#119272502
#119272472
#119272422
#119271952
#119271742
#119271502
#119271422
#119271412
#119271252
#119270942
#119270782
C2×C19×#1252
#355919