Finite Group Databasebeta

← #14577417

Subgroups — #14577417

Order 2432.

1476 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597433C211yesmaximal, characteristic, complemented
2C2×#10597436C211yesmaximal, characteristic, complemented
3#11927207C214yesmaximal, complemented
4#11927196C214yesmaximal, complemented
5#11927192C218yesmaximal, complemented
6#11927120C211yesmaximal, characteristic, complemented
7#11927119C212yesmaximal, complemented
8#11927114C212yesmaximal, complemented
9#11927093C212yesmaximal, complemented
10#11927090C211yesmaximal, characteristic, complemented
11C2×#10597390C211yesmaximal, characteristic, complemented
12C4⋊Q8×D19C212yesmaximal, complemented
13#11927012C211yesmaximal, characteristic, complemented
14C19×#536C211yesmaximal, characteristic, complemented
15C2×#41×C19C2211yescharacteristic
16C22×Q8×C19C2211yescharacteristic
17#10597436—28no—
18#10597433—28no—
19C2×#64545C2212yes—
20C2×#64545C2212yes—
21C2×Q8×D19C2212yes—
22C2×Q8×D19C2212yes—
23C2×Q8×D19C2212yes—
24C2×#64543C2212yes—
25C2×#64543C2214yes—
26C2×#64541C2211yescharacteristic
27C2×#64541C2212yes—
28C2×#64541C2214yes—
29C2×#64541C2211yescharacteristic
30C22×Dic38C2211yescharacteristic
31C22×Dic38C2212yes—
32C19×C4⋊Q8C2212yes—
33C19×#124C2212yes—
34C19×#123C2214yes—
35C19×C22⋊Q8C2214yes—
36C19×#117C2211yescharacteristic
37#10597393C2211yescharacteristic
38#10597390C2211yescharacteristic
39#10597390C2212yes—
40#10597390C2212yes—
41#10597390C2214yes—
42#10597386C2211yescharacteristic
43#10597385C2214yes—
44#10597382C2211yescharacteristic
45C4×C22⋊D19C2214yes—
46C2×Dic19⋊C4C2214yes—
47C2×C4×Dic19C2211yescharacteristic
48#10597343C2214yes—
49#10597342C2218yes—
50#10597340C2218yes—
51#10597339C2212yes—
52C4⋊C4×D19C2218yes—
53#10597334C2218yes—
54#10597333C2212yes—
55#10597332C2214yes—
56#10597330C2218yes—
57#10597329C2218yes—
58(C22⋊D19)⋊C4C2218yes—
59(C22⋊D19)⋊C4C2214yes—
60#10597324C2218yes—
61#10597321C2212yes—
62#10597318C2212yes—
63C42×D19C2212yes—
64#10597315C2212yes—
65#41×C19—24no—
66C2×Q8×C19—24no—
67C2×Q8×C19C2312yes—
68C2×Q8×C19C2312yes—
69C2×Q8×C19C2311yescharacteristic
70C2×D4×C19C2311yescharacteristic
71C2×D4×C19C2312yes—
72C22×C4×C19C2312yes—
73C22×C4×C19C2312yes—
74C22×C4×C19C2311yescharacteristic
75C2×C22⋊D19C2312yes—
76C2×C22⋊D19C2314yes—
77C2×C22⋊D19C2314yes—
78C2×C22⋊D19C2312yes—
79C22×Dic19C2312yes—
80C22×Dic19C2314yes—
81C22×Dic19C2312yes—
82#64545—28no—
83#64545—28no—
84Q8×D19—28no—
85Q8×D19—28no—
86Q8×D19—28no—
87#64543—216no—
88#64543—28no—
89#64541—24no—
90#64541—216no—
91#64541—28no—
92#64541D418yescomplemented
93C2×D76C2311yescharacteristic
94C2×D76C2314yes—
95C2×D76C2311yescharacteristic
96C2×C4×D19C2314yes—
97C2×C4×D19C2314yes—
98C2×C4×D19C2314yes—
99C2×C4×D19C2312yes—
100C2×C4×D19C2314yes—
101C2×C4×D19C2312yes—
102C2×Dic38—24no—
103C2×Dic38—28no—
104C2×Dic38C2311yescharacteristic
105C2×Dic38C2312yes—
106C2×Dic38C2312yes—
107C2×Dic38C2314yes—
108C2×Dic38C2314yes—
109C2×Dic38C2311yescharacteristic
110C4⋊C4×C19C2312yes—
111C4⋊C4×C19C2318yes—
112C22⋊C4×C19C2312yes—
113C22⋊C4×C19C2318yes—
114C42×C19C2312yes—
115C22⋊Dic19C2314yes—
116(C2×D19)⋊C4C2314yes—
117(C2×D19)⋊C4C2314yes—
118(C2×D19)⋊C4C2318yes—
119C4⋊Dic19C2318yes—
120Dic19⋊C4C2314yes—
121Dic19⋊C4C2318yes—
122Dic19⋊C4C2318yes—
123Dic19⋊C4C2314yes—
124C4×Dic19C2311yescharacteristic
125C4×Dic19C2311yescharacteristic
126C4×Dic19C2312yes—
127C4×Dic19C2314yes—
128C23×C19C2412yes—
129C23×C19C2411yescharacteristic
130C22×D19C2412yes—
131C22×D19C2412yes—
132Q8×C19—22no—
133Q8×C19—24no—
134Q8×C19—24no—
135D4×C19—24no—
136D4×C19—22no—
137C2×C4×C19—24no—
138C2×C4×C19—24no—
139C2×C4×C19C2×D414yes—
140C2×C4×C19C2414yes—
141C2×C4×C19C2414yes—
142C2×C4×C19C2412yes—
143C2×C4×C19C2411yescharacteristic
144C2×C4×C19C2411yescharacteristic
145C22⋊D19—24no—
146C22⋊D19—28no—
147C22⋊D19—28no—
148C22⋊D19C2×D418yes—
149C2×Dic19—24no—
150C2×Dic19—28no—
151C2×Dic19—24no—
152C2×Dic19C2412yes—
153C2×Dic19C2414yes—
154C2×Dic19C2412yes—
155C2×Dic19C2412yes—
156C2×Dic19C2412yes—
157D76—28no—
158D76—22no—
159D76C2×D414yes—
160C4×D19—28no—
161C4×D19—28no—
162C4×D19—24no—
163C4×D19—28no—
164C4×D19—28no—
165C4×D19C2×D418yes—
166Dic38—24no—
167Dic38—24no—
168Dic38—22no—
169Dic38—28no—
170Dic38—28no—
171Dic38C2×D414yes—
172#3499—191nomaximal, Sylow
173C22×C19—22no—
174C22×C19—22no—
175C22×C19—24no—
176C22×C19C22×D412yes—
177C22×C19C2511yescharacteristic
178C2×D19—24no—
179C2×D19—22no—
180C2×D19—24no—
181C2×D19C22×D414yes—
182C4×C19—22no—
183C4×C19—24no—
184C4×C19—24no—
185C4×C19C22×D412yes—
186C4×C19C22×D412yes—
187Dic19—22no—
188Dic19—24no—
189Dic19—22no—
190Dic19C22×D414yes—
191Dic192−1+414yescomplemented
192C2×2−1+4—191no—
193C2×2−1+4—191no—
194D4×Q8—194no—
195#547—198no—
196#547—194no—
197#536—192no—
198#536—192no—
199#536—191no—
200#536D1911yescharacteristic, complemented
201#532—191no—
202#532—192no—
203C2×C4⋊Q8—191no—
204C2×C4⋊Q8—192no—
205C4×#41—191no—
206C2×C19—22no—
207C2×C19—42no—
208C2×C19C23×D411yescharacteristic
209C2×C19C2×2−1+412yes—
210D19—24no—
211D19—42no—
2122−1+4—388no—
2132−1+4—388no—
214C2×#41—192no—
215C2×#41—192no—
216C2×#41—192no—
217C2×#41—194no—
218C2×#41—191no—
219C2×#41—191no—
220C2×#41—192no—
221C2×#41—194no—
222C2×#41C2×D1911yescharacteristic
223C22×Q8—192no—
224C22×Q8—192no—
225C22×Q8—192no—
226C22×Q8—191no—
227C22×Q8—192no—
228C22×Q8C2×D1911yescharacteristic
229C4⋊Q8—191no—
230C4⋊Q8—192no—
231C4⋊Q8—192no—
232C4⋊Q8—194no—
233C4⋊Q8—198no—
234C4⋊Q8—192no—
235C4⋊Q8C2×D1912yes—
236#127—191no—
237#124—191no—
238#124—191no—
239#124—192no—
240#124C2×D1912yes—
241#123—198no—
242#123—198no—
243#123—194no—
244#123C2×D1914yes—
245C22⋊Q8—198no—
246C22⋊Q8—194no—
247C22⋊Q8—198no—
248C22⋊Q8C2×D1914yes—
249#121—194no—
250#121—198no—
251C4×Q8—192no—
252C4×D4—194no—
253C4×D4—192no—
254C4×D4—194no—
255C4×D4—198no—
256#117—192no—
257#117C2×D1911yescharacteristic
258C2×C4⋊C4—194no—
259C2×C4⋊C4—198no—
260C2×C42—191no—
261C2×C42—192no—
262C19#349911yescharacteristic, complemented, Sylow
263#41—24no—
264#41—198no—
265#41—3816no—
266#41—388no—
267#41—388no—
268#41—388no—
269#41—3816no—
270#41—388no—
271#41—384no—
272C2×Q8—24no—
273C2×Q8—191no—
274C2×Q8—194no—
275C2×Q8—194no—
276C2×Q8—192no—
277C2×Q8—191no—
278C2×Q8—192no—
279C2×Q8—388no—
280C2×Q8—388no—
281C2×Q8—388no—
282C2×Q8—388no—
283C2×Q8—384no—
284C2×Q8C22×D1912yes—
285C2×Q8C22×D1911yescharacteristic
286C2×Q8C22×D1912yes—
287C2×D4—192no—
288C2×D4—194no—
289C2×D4—194no—
290C2×D4—192no—
291C2×D4—191no—
292C2×D4—194no—
293C2×D4—191no—
294C2×D4C22×D1912yes—
295C2×D4C22×D1911yescharacteristic
296C22×C4—192no—
297C22×C4—192no—
298C22×C4—192no—
299C22×C4—194no—
300C22×C4—194no—
301C22×C4—194no—
302C22×C4—194no—
303C22×C4—194no—
304C22×C4—192no—
305C22×C4C22×D1912yes—
306C22×C4C22×D1912yes—
307C22×C4C22×D1911yescharacteristic
308C4⋊C4—194no—
309C4⋊C4—198no—
310C4⋊C4—198no—
311C4⋊C4—194no—
312C4⋊C4—198no—
313C4⋊C4C22×D1918yes—
314C4⋊C4C22×D1912yes—
315C22⋊C4—194no—
316C22⋊C4—194no—
317C22⋊C4—194no—
318C22⋊C4—198no—
319C22⋊C4C22×D1912yes—
320C22⋊C4C22×D1918yes—
321C42—191no—
322C42—191no—
323C42—194no—
324C42—192no—
325C42C22×D1912yes—
326C23—192no—
327C23—192no—
328C23C23×D1912yes—
329C23C23×D1911yescharacteristic
330Q8—24no—
331Q8—24no—
332Q8—22no—
333Q8—194no—
334Q8—388no—
335Q8—388no—
336Q8—384no—
337Q8—382no—
338Q8—384no—
339D4—24no—
340D4—22no—
341D4—198no—
342D4—194no—
343D4—388no—
344D4—388no—
345D4—388no—
346D4—384no—
347D4—382no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—192no—
351C2×C4—192no—
352C2×C4—198no—
353C2×C4—192no—
354C2×C4—192no—
355C2×C4—194no—
356C2×C4—388no—
357C2×C4—388no—
358C2×C4—388no—
359C2×C4—388no—
360C2×C4—388no—
361C2×C4—384no—
362C2×C4—384no—
363C2×C4—384no—
364C2×C4D4×D1914yes—
365C2×C4C23×D1914yes—
366C2×C4C23×D1912yes—
367C2×C4C23×D1914yes—
368C2×C4C23×D1911yescharacteristic
369C2×C4C23×D1911yescharacteristic
370C22—22no—
371C22—22no—
372C22—24no—
373C22—194no—
374C22—384no—
375C22—382no—
376C22—384no—
377C22C2×D4×D1912yes—
378C22C24×D1911yescharacteristic
379C4—22no—
380C4—24no—
381C4—24no—
382C4—194no—
383C4—194no—
384C4—382no—
385C4—384no—
386C4—382no—
387C4C2×D4×D1912yes—
388C4C2×D4×D1912yes—
389C2—22no—
390C2—42no—
391C2—384no—
392C2—762no—
393C2C22×D4×D1911yescharacteristic
394C22−1+4×D1912yes—
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#536C2
hypercenter#536D19
hypocenterC19#3499
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#10597433C2semidirect
2. C2×#10597436C2semidirect
3. #11927207C2semidirect
4. #11927196C2semidirect
5. #11927192C2semidirect
6. #11927120C2semidirect
7. #11927119C2semidirect
8. #11927114C2semidirect
9. #11927093C2semidirect
10. #11927090C2semidirect
11. C2×#10597390C2semidirect
12. C4⋊Q8×D19C2semidirect
13. #11927012C2semidirect
14. C19×#536C2semidirect
92. #64541D4semidirect
191. Dic192−1+4semidirect
200. #536D19semidirect
262. C19#3499semidirect

Maximal subgroups

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

subgroupindex
C2×#105974332
C2×#105974362
#119272072
#119271962
#119271922
#119271202
#119271192
#119271142
#119270932
#119270902
C2×#105973902
C4⋊Q8×D192
#119270122
C19×#5362
#349919