Finite Group Databasebeta

← #14578173

Subgroups — #14578173

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#11927294C212yesmaximal, complemented
2#11927288C212yesmaximal, complemented
3#11927253C212yesmaximal, complemented
4#11927246C212yesmaximal, complemented
5#11927244C212yesmaximal, complemented
6#11927194C212yesmaximal, complemented
7#11927193C214yesmaximal, complemented
8#11927171C212yesmaximal, complemented
9#11927148C212yesmaximal, complemented
10#11927139C212yesmaximal, complemented
11#11927136C214yesmaximal, complemented
12#11927121C212yesmaximal, complemented
13#11927078C211yesmaximal, characteristic, complemented
14C2×#10597316C211yesmaximal, characteristic, complemented
15C19×#532C211yesmaximal, characteristic, complemented
16C2×#41×C19C2212yes—
17C2×#64543C2214yes—
18C19×C4⋊Q8C2211yescharacteristic
19C19×#127C2211yescharacteristic
20C19×#124C2212yes—
21C19×#121C2212yes—
22C19×#121C2212yes—
23C4×D4×C19C2212yes—
24C4×D4×C19C2212yes—
25C2×C42×C19C2211yescharacteristic
26#10597392C2214yes—
27#10597390C2214yes—
28#10597385C2214yes—
29#10597385C2214yes—
30#10597385C2214yes—
31#10597384C2212yes—
32#10597384C2212yes—
33#10597381C2214yes—
34#10597381C2214yes—
35#10597381C2214yes—
36D4×Dic19C2214yes—
37D4×Dic19C2212yes—
38D4×Dic19C2212yes—
39#10597376C2211yescharacteristic
40#10597375C2212yes—
41#10597375C2214yes—
42C4×C22⋊D19C2212yes—
43C4×C22⋊D19C2214yes—
44C2×C4⋊Dic19C2211yescharacteristic
45C2×C4⋊Dic19C2211yescharacteristic
46#10597370C2211yescharacteristic
47#10597370C2214yes—
48C2×Dic19⋊C4C2212yes—
49C2×Dic19⋊C4C2212yes—
50C2×Dic19⋊C4C2214yes—
51#10597342C2214yes—
52#10597338C2212yes—
53C4⋊C4×D19C2212yes—
54#10597336C2212yes—
55#10597335C2214yes—
56#10597334C2212yes—
57#10597332C2214yes—
58#10597330C2214yes—
59#10597329C2214yes—
60#10597325C2214yes—
61#10597325C2214yes—
62#10597324C2214yes—
63#10597324C2214yes—
64#10597324C2214yes—
65#10597322C2212yes—
66#10597321C2211yescharacteristic
67C4×D76C2211yescharacteristic
68#10597318C2212yes—
69#10597316C2212yes—
70#10597316C2212yes—
71#10597316C2212yes—
72#10597316C2212yes—
73#10597316C2211yescharacteristic
74C4×Dic38C2211yescharacteristic
75#41×C19—44no—
76C2×Q8×C19C2312yes—
77C2×D4×C19C2312yes—
78C2×D4×C19C2314yes—
79C2×D4×C19C2312yes—
80C2×D4×C19C2312yes—
81C22×C4×C19C2311yescharacteristic
82C22×C4×C19C2311yescharacteristic
83C22×C4×C19C2311yescharacteristic
84C22×C4×C19C2314yes—
85C2×C22⋊D19C2312yes—
86C2×C22⋊D19C2314yes—
87C2×C22⋊D19C2314yes—
88C22×Dic19C2312yes—
89C22×Dic19C2314yes—
90C22×Dic19C2312yes—
91C22×Dic19C2314yes—
92#64543—48no—
93C2×D76C2311yescharacteristic
94C2×C4×D19C2312yes—
95C2×C4×D19C2314yes—
96C2×Dic38C2314yes—
97C2×Dic38C2311yescharacteristic
98C4⋊C4×C19C2312yes—
99C4⋊C4×C19C2312yes—
100C22⋊C4×C19C2314yes—
101C22⋊C4×C19C2314yes—
102C42×C19C2311yescharacteristic
103C42×C19C2311yescharacteristic
104C42×C19C2311yescharacteristic
105C42×C19C2311yescharacteristic
106C22⋊Dic19C2312yes—
107C22⋊Dic19C2314yes—
108C22⋊Dic19C2314yes—
109C22⋊Dic19C2314yes—
110C22⋊Dic19C2314yes—
111(C2×D19)⋊C4C2312yes—
112(C2×D19)⋊C4C2312yes—
113(C2×D19)⋊C4C2314yes—
114(C2×D19)⋊C4C2312yes—
115(C2×D19)⋊C4C2312yes—
116C4⋊Dic19C2311yescharacteristic
117C4⋊Dic19C2312yes—
118C4⋊Dic19C2312yes—
119C4⋊Dic19C2314yes—
120C4⋊Dic19C2312yes—
121C4⋊Dic19C2312yes—
122C4⋊Dic19C2311yescharacteristic
123Dic19⋊C4C2312yes—
124Dic19⋊C4C2312yes—
125Dic19⋊C4C2314yes—
126Dic19⋊C4C2314yes—
127Dic19⋊C4C2314yes—
128Dic19⋊C4C2314yes—
129Dic19⋊C4C2314yes—
130Dic19⋊C4C2312yes—
131Dic19⋊C4C2314yes—
132Dic19⋊C4C2314yes—
133Dic19⋊C4C2312yes—
134C4×Dic19C2312yes—
135C4×Dic19C2314yes—
136C23×C19C2414yes—
137C23×C19C2411yescharacteristic
138C22×D19C2412yes—
139Q8×C19—42no—
140D4×C19—28no—
141D4×C19—24no—
142D4×C19—42no—
143D4×C19—42no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—41no—
147C2×C4×C19—44no—
148C2×C4×C19C2414yes—
149C2×C4×C19C2411yescharacteristic
150C2×C4×C19C2411yescharacteristic
151C2×C4×C19C2411yescharacteristic
152C2×C4×C19C2411yescharacteristic
153C2×C4×C19C2411yescharacteristic
154C2×C4×C19C2411yescharacteristic
155C22⋊D19—24no—
156C22⋊D19—44no—
157C22⋊D19—44no—
158C2×Dic19—24no—
159C2×Dic19—44no—
160C2×Dic19—44no—
161C2×Dic19—42no—
162C2×Dic19C2412yes—
163C2×Dic19C2414yes—
164C2×Dic19C2412yes—
165C2×Dic19C2412yes—
166C2×Dic19C2414yes—
167D76—41no—
168C4×D19—24no—
169C4×D19—44no—
170Dic38—41no—
171Dic38—44no—
172#3559—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—24no—
176C22×C19—24no—
177C22×C19—24no—
178C22×C19H(5,𝔽2)12yes—
179C22×C19C2511yescharacteristic
180C2×D19—22no—
181C2×D19—22no—
182C2×D19—22no—
183C4×C19—24no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C192−1+412yes—
190Dic19—22no—
191Dic19—24no—
192Dic19—22no—
193Dic19—22no—
194Dic19—24no—
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—192no—
205#539—194no—
206#537—192no—
207#532D1911yescharacteristic, complemented
208#529—191no—
209C2×#125—191no—
210C2×C19—22no—
211C2×C19—44no—
212C2×C19C2×H(5,𝔽2)11yescharacteristic
213C2×C19C2×2−1+411yescharacteristic
214C2×C19#58511yescharacteristic
215D19—42no—
216C2×#41—194no—
217C2×#41C2×D1912yes—
218C4⋊Q8—194no—
219C4⋊Q8—192no—
220C4⋊Q8C2×D1911yescharacteristic
221#127C2×D1911yescharacteristic
222#126—194no—
223#126—194no—
224#126—192no—
225#125—194no—
226#125—192no—
227#125—192no—
228#125—192no—
229#125—192no—
230#125—192no—
231#125—191no—
232#124—191no—
233#124C2×D1912yes—
234#123—194no—
235#123—194no—
236#123—194no—
237#123—192no—
238#123—194no—
239#123—194no—
240#123—194no—
241C22⋊Q8—194no—
242C22⋊Q8—191no—
243C22⋊Q8—194no—
244C22⋊Q8—194no—
245C22⋊Q8—194no—
246C22⋊Q8—194no—
247C22⋊Q8—194no—
248#121—192no—
249#121—192no—
250#121—194no—
251#121—194no—
252#121—194no—
253#121—191no—
254#121—194no—
255#121C2×D1912yes—
256#121C2×D1912yes—
257C4×Q8—191no—
258C4×D4—194no—
259C4×D4—192no—
260C4×D4—192no—
261C4×D4—192no—
262C4×D4—194no—
263C4×D4—191no—
264C4×D4C2×D1912yes—
265C4×D4C2×D1912yes—
266#117—192no—
267#117—192no—
268C2×C4⋊C4—192no—
269C2×C4⋊C4—192no—
270C2×C4⋊C4—191no—
271C2×C4⋊C4—191no—
272C2×C4⋊C4—194no—
273C2×C4⋊C4—192no—
274C2×C42C2×D1911yescharacteristic
275C19#355911yescharacteristic, complemented, Sylow
276#41—44no—
277#41—768no—
278C2×Q8—191no—
279C2×Q8—194no—
280C2×Q8C22×D1912yes—
281C2×D4—192no—
282C2×D4—194no—
283C2×D4—194no—
284C2×D4—191no—
285C2×D4C22×D1912yes—
286C2×D4C22×D1914yes—
287C2×D4C22×D1912yes—
288C2×D4C22×D1912yes—
289C22×C4—192no—
290C22×C4—192no—
291C22×C4—194no—
292C22×C4—194no—
293C22×C4—192no—
294C22×C4—194no—
295C22×C4C22×D1911yescharacteristic
296C22×C4C22×D1911yescharacteristic
297C22×C4C22×D1911yescharacteristic
298C22×C4C22×D1914yes—
299C4⋊C4—194no—
300C4⋊C4—192no—
301C4⋊C4—194no—
302C4⋊C4—194no—
303C4⋊C4—194no—
304C4⋊C4—194no—
305C4⋊C4—194no—
306C4⋊C4—194no—
307C4⋊C4—192no—
308C4⋊C4—192no—
309C4⋊C4—192no—
310C4⋊C4—192no—
311C4⋊C4—192no—
312C4⋊C4—192no—
313C4⋊C4—192no—
314C4⋊C4—194no—
315C4⋊C4—191no—
316C4⋊C4—191no—
317C4⋊C4C22×D1912yes—
318C4⋊C4C22×D1912yes—
319C22⋊C4—192no—
320C22⋊C4—194no—
321C22⋊C4—194no—
322C22⋊C4—194no—
323C22⋊C4—194no—
324C22⋊C4—192no—
325C22⋊C4—194no—
326C22⋊C4—192no—
327C22⋊C4—192no—
328C22⋊C4—192no—
329C22⋊C4C22×D1914yes—
330C22⋊C4C22×D1914yes—
331C42—192no—
332C42—194no—
333C42C22×D1911yescharacteristic
334C42C22×D1911yescharacteristic
335C42C22×D1911yescharacteristic
336C42C22×D1911yescharacteristic
337C23—192no—
338C23C23×D1914yes—
339C23C23×D1911yescharacteristic
340Q8—42no—
341Q8—764no—
342Q8—761no—
343D4—28no—
344D4—24no—
345D4—42no—
346D4—42no—
347D4—384no—
348D4—761no—
349D4—764no—
350D4—764no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—44no—
354C2×C4—41no—
355C2×C4—192no—
356C2×C4—192no—
357C2×C4—194no—
358C2×C4—192no—
359C2×C4—194no—
360C2×C4—384no—
361C2×C4—384no—
362C2×C4—764no—
363C2×C4—764no—
364C2×C4—762no—
365C2×C4—764no—
366C2×C4C23×D1914yes—
367C2×C4C23×D1911yescharacteristic
368C2×C4C23×D1911yescharacteristic
369C2×C4C23×D1911yescharacteristic
370C2×C4C23×D1911yescharacteristic
371C2×C4C23×D1911yescharacteristic
372C2×C4C23×D1911yescharacteristic
373C22—21no—
374C22—21no—
375C22—24no—
376C22—24no—
377C22—24no—
378C22—382no—
379C22—382no—
380C22—382no—
381C22#1059743012yes—
382C22C24×D1911yescharacteristic
383C4—21no—
384C4—21no—
385C4—24no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—384no—
390C4—382no—
391C4—382no—
392C4—384no—
393C4—382no—
394C4#1059743612yes—
395C2—22no—
396C2—44no—
397C2—762no—
398C2C2×#1059743011yescharacteristic
399C2C2×#1059743611yescharacteristic
400C2#1192738011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#532C2
hypercenter#532D19
hypocenterC19#3559
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #11927294C2semidirect
2. #11927288C2semidirect
3. #11927253C2semidirect
4. #11927246C2semidirect
5. #11927244C2semidirect
6. #11927194C2semidirect
7. #11927193C2semidirect
8. #11927171C2semidirect
9. #11927148C2semidirect
10. #11927139C2semidirect
11. #11927136C2semidirect
12. #11927121C2semidirect
13. #11927078C2semidirect
14. C2×#10597316C2semidirect
15. C19×#532C2semidirect
207. #532D19semidirect
275. C19#3559semidirect

Maximal subgroups

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

subgroupindex
#119272942
#119272882
#119272532
#119272462
#119272442
#119271942
#119271932
#119271712
#119271482
#119271392
#119271362
#119271212
#119270782
C2×#105973162
C19×#5322
#355919