Finite Group Databasebeta

← C2×#11927360 #14578401

Subgroups — C2×#11927360 #14578401

Order 2432.

1408 conjugacy classes of subgroups.

The subgroup lattice has 392 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#11927360C2116yesmaximal, direct product factor
4C2×#10597355C211yesmaximal, characteristic, complemented
5C2×#10597364C212yesmaximal, complemented
6C2×#10597361C212yesmaximal, complemented
7C2×#10597362C212yesmaximal, complemented
8C2×#10597396C211yesmaximal, characteristic, complemented
9C22×#64528C211yesmaximal, characteristic, complemented
10C2×Q16×D19C212yesmaximal, complemented
11C2×#10597353C211yesmaximal, characteristic, complemented
12C2×C19×#137C211yesmaximal, characteristic, complemented
13C2×#41×C19C2211yescharacteristic
14C22×Q8×C19C2211yescharacteristic
15#10597436—24no—
16#10597436C2218yescomplemented
17#10597433—24no—
18#10597433C2218yescomplemented
19C2×#64545—21no—
20C2×#64545C2212yes—
21C2×Q8×D19—21no—
22C2×Q8×D19C2212yes—
23C2×Q8×D19C2212yes—
24C2×#64543—22no—
25C2×#64543C2212yes—
26C2×#64541—22no—
27C2×#64541—21no—
28C2×#64541C2211yescharacteristic
29C2×#64541C2211yescharacteristic
30C22×Dic38—21no—
31C22×Dic38C2211yescharacteristic
32C19×#137C2218yescomplemented
33C2×Q16×C19C2212yes—
34C2×SD16×C19C2212yes—
35C2×M16×C19C2211yescharacteristic
36#10597396C2218yescomplemented
37C2×#64528C2211yescharacteristic
38C2×#64528C2212yes—
39C2×#64528C2212yes—
40C2×#64528C2218yescomplemented
41C2×#64527C2211yescharacteristic
42C2×#64526C2211yescharacteristic
43C2×#64525C2211yescharacteristic
44C22×C19⋊C8C2211yescharacteristic
45#10597364C22116yescomplemented
46Q16×D19C22116yescomplemented
47#10597362C22116yescomplemented
48#10597361C22116yescomplemented
49#10597355C2218yescomplemented
50#10597353C2218yescomplemented
51C2×Dic76C2212yes—
52C2×#64516C2212yes—
53C2×#64515C2212yes—
54C2×C8×D19C2212yes—
55#41×C19—22no—
56#41×C19C2314yes—
57C2×Q8×C19—21no—
58C2×Q8×C19—22no—
59C2×Q8×C19C2311yescharacteristic
60C2×Q8×C19C2312yes—
61C2×Q8×C19C2314yes—
62C2×D4×C19—21no—
63C2×D4×C19C2311yescharacteristic
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—22no—
69C2×C22⋊D19D412yes—
70C22×Dic19—21no—
71C22×Dic19—22no—
72#64545—28no—
73#64545—24no—
74#64545C2318yes—
75Q8×D19—24no—
76Q8×D19—24no—
77Q8×D19—28no—
78Q8×D19C2318yes—
79Q8×D19C2318yes—
80#64543—216no—
81#64543—24no—
82#64543C2318yes—
83#64541—22no—
84#64541—216no—
85#64541—28no—
86#64541D414yes—
87#64541C2314yes—
88#64541C2314yes—
89C2×D76—22no—
90C2×D76D411yescharacteristic
91C2×D76C2311yescharacteristic
92C2×C4×D19—22no—
93C2×C4×D19—22no—
94C2×C4×D19—21no—
95C2×C4×D19—22no—
96C2×C4×D19C2312yes—
97C2×Dic38—21no—
98C2×Dic38—22no—
99C2×Dic38—22no—
100C2×Dic38—22no—
101C2×Dic38—28no—
102C2×Dic38D411yescharacteristic
103C2×Dic38C2311yescharacteristic
104C2×Dic38C2312yes—
105C2×Dic38C2314yes—
106Q16×C19C2318yes—
107SD16×C19C2318yes—
108M16×C19C2314yes—
109C2×C8×C19C2312yes—
110#64528C2318yes—
111#64528C2318yes—
112#64528C2314yes—
113#64527C2314yes—
114#64526C2314yes—
115#64525C2314yes—
116C2×C19⋊C8C2311yescharacteristic
117C2×C19⋊C8C2311yescharacteristic
118C2×C19⋊C8C2314yes—
119Dic76C2318yes—
120#64516C2318yes—
121#64515C2318yes—
122C8×D19C2318yes—
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
126C22×D19C2×D412yes—
127Q8×C19—21no—
128Q8×C19—22no—
129Q8×C19—24no—
130Q8×C19C2412yes—
131Q8×C19C2414yes—
132D4×C19—24no—
133D4×C19—21no—
134D4×C19C2412yes—
135C2×C4×C19—21no—
136C2×C4×C19—22no—
137C2×C4×C19—24no—
138C2×C4×C19—24no—
139C2×C4×C19C2×D411yescharacteristic
140C2×C4×C19C2×D412yes—
141C2×C4×C19C2411yescharacteristic
142C2×C4×C19C2412yes—
143C22⋊D19—24no—
144C22⋊D19—28no—
145C22⋊D19C2×D418yes—
146C2×Dic19—21no—
147C2×Dic19—22no—
148C2×Dic19—24no—
149C2×Dic19—28no—
150C2×Dic19C2×D412yes—
151D76—28no—
152D76—21no—
153D76C2×D414yes—
154D76C2412yes—
155C4×D19—28no—
156C4×D19—28no—
157C4×D19—24no—
158C4×D19—28no—
159C4×D19C2×D414yes—
160C4×D19C2414yes—
161Dic38—24no—
162Dic38—22no—
163Dic38—21no—
164Dic38—28no—
165Dic38—28no—
166Dic38C2×D414yes—
167Dic38C2414yes—
168Dic38C2412yes—
169C8×C19C2414yes—
170C19⋊C8C2412yes—
171C19⋊C8C2412yes—
172C2×#578—191nomaximal, Sylow
173C22×C19—22no—
174C22×C19—22no—
175C22×C19—42no—
176C22×C19C22×D412yes—
177C22×C19C22×D411yescharacteristic
178C2×D19—24no—
179C2×D19—22no—
180C2×D19—42no—
181C2×D19C22×D414yes—
182C4×C19—22no—
183C4×C19—24no—
184C4×C19C22×D411yescharacteristic
185C4×C19C22×D412yes—
186C4×C19C2511yescharacteristic
187Dic19—22no—
188Dic19—24no—
189Dic19C22×D414yes—
190C2×2−1+4—191no—
191C2×2−1+4—191no—
192#578—1916no—
193C2×#137—192no—
194C2×#137—192no—
195C2×#137—191no—
196C2×#137D1911yescharacteristic, complemented
197C2×#135—191no—
198C2×#135—192no—
199C22×Q16—191no—
200C22×Q16—192no—
201C2×#131—191no—
202C2×C19—22no—
203C2×C19—42no—
204C2×C19#57812yescomplemented
205C2×C19C23×D411yescharacteristic
206D19—24no—
207D19—42no—
2082−1+4—198no—
2092−1+4—198no—
2102−1+4—384no—
2112−1+4—384no—
212C2×#41—191no—
213C2×#41—192no—
214C2×#41—192no—
215C2×#41—191no—
216C2×#41—382no—
217C2×#41—381no—
218C2×#41—382no—
219C2×#41—381no—
220C2×#41C2×D1911yescharacteristic
221C22×Q8—192no—
222C22×Q8—192no—
223C22×Q8—191no—
224C22×Q8—381no—
225C22×Q8—381no—
226C22×Q8C2×D1911yescharacteristic
227#137—1916no—
228#137—1916no—
229#137—198no—
230#137C2×D1918yescomplemented
231#135—198no—
232#135—1916no—
233C2×Q16—191no—
234C2×Q16—192no—
235C2×Q16—192no—
236C2×Q16—198no—
237C2×Q16—1916no—
238C2×Q16—192no—
239C2×Q16C2×D1912yes—
240C2×SD16—191no—
241C2×SD16—191no—
242C2×SD16—192no—
243C2×SD16C2×D1912yes—
244C2×D8—191no—
245#131—198no—
246C2×M16—192no—
247C2×M16C2×D1911yescharacteristic
248C22×C8—191no—
249C22×C8—192no—
250C19C2×#57811yescharacteristic, complemented, Sylow
251#41—22no—
252#41—194no—
253#41—194no—
254#41—198no—
255#41—198no—
256#41—194no—
257#41—3816no—
258#41—388no—
259#41—384no—
260#41—384no—
261#41—3816no—
262#41—388no—
263#41—382no—
264#41C22×D1914yes—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—191no—
268C2×Q8—198no—
269C2×Q8—198no—
270C2×Q8—191no—
271C2×Q8—192no—
272C2×Q8—194no—
273C2×Q8—382no—
274C2×Q8—382no—
275C2×Q8—388no—
276C2×Q8—384no—
277C2×Q8—384no—
278C2×Q8—388no—
279C2×Q8—381no—
280C2×Q8—382no—
281C2×Q8C22×D1911yescharacteristic
282C2×Q8C22×D1912yes—
283C2×Q8C22×D1914yes—
284C2×D4—21no—
285C2×D4—192no—
286C2×D4—191no—
287C2×D4—191no—
288C2×D4—382no—
289C2×D4—382no—
290C2×D4—381no—
291C2×D4C22×D1911yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—192no—
295C22×C4—382no—
296C22×C4—382no—
297C22×C4—382no—
298C22×C4—382no—
299C22×C4—381no—
300C22×C4—381no—
301C22×C4C22×D1911yescharacteristic
302Q16—194no—
303Q16—198no—
304Q16—198no—
305Q16—198no—
306Q16C22×D1918yes—
307SD16—194no—
308SD16—194no—
309SD16—198no—
310SD16C22×D1918yes—
311D8—194no—
312M16—198no—
313M16C22×D1914yes—
314C2×C8—191no—
315C2×C8—191no—
316C2×C8—194no—
317C2×C8—198no—
318C2×C8C22×D1912yes—
319C23—21no—
320C23—192no—
321C23—381no—
322C23D4×D1911yescharacteristic
323Q8—24no—
324Q8—22no—
325Q8—21no—
326Q8—194no—
327Q8—192no—
328Q8—194no—
329Q8—388no—
330Q8—388no—
331Q8—384no—
332Q8—381no—
333Q8—382no—
334Q8C23×D1912yes—
335Q8C23×D1914yes—
336D4—24no—
337D4—21no—
338D4—198no—
339D4—194no—
340D4—192no—
341D4—388no—
342D4—388no—
343D4—384no—
344D4—381no—
345D4C23×D1912yes—
346C2×C4—24no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—192no—
351C2×C4—194no—
352C2×C4—194no—
353C2×C4—388no—
354C2×C4—388no—
355C2×C4—388no—
356C2×C4—388no—
357C2×C4—384no—
358C2×C4—381no—
359C2×C4—382no—
360C2×C4—384no—
361C2×C4D4×D1912yes—
362C2×C4D4×D1911yescharacteristic
363C2×C4C23×D1912yes—
364C2×C4C23×D1911yescharacteristic
365C8—192no—
366C8—192no—
367C8C23×D1914yes—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—194no—
372C22—384no—
373C22—382no—
374C22—762no—
375C22C2×D4×D1912yes—
376C22C2×D4×D1911yescharacteristic
377C4—22no—
378C4—24no—
379C4—194no—
380C4—382no—
381C4—384no—
382C4C2×D4×D1912yes—
383C4C2×D4×D1911yescharacteristic
384C4C24×D1911yescharacteristic
385C2—22no—
386C2—42no—
387C2—384no—
388C2—762no—
389C2#1192736012yesdirect product factor
390C2C22×D4×D1911yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC2×C19×#137C2
socleC22×C19C22×D4
hypercenterC2×#137D19
hypocenterC19C2×#578
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#10597433C2semidirect
2. C2×#10597436C2semidirect
3. #11927360C2direct (N × H)
4. C2×#10597355C2semidirect
5. C2×#10597364C2semidirect
6. C2×#10597361C2semidirect
7. C2×#10597362C2semidirect
8. C2×#10597396C2semidirect
9. C22×#64528C2semidirect
10. C2×Q16×D19C2semidirect
11. C2×#10597353C2semidirect
12. C2×C19×#137C2semidirect
16. #10597436C22semidirect
18. #10597433C22semidirect
32. C19×#137C22semidirect
36. #10597396C22semidirect
40. C2×#64528C22semidirect
45. #10597364C22semidirect
46. Q16×D19C22semidirect
47. #10597362C22semidirect
48. #10597361C22semidirect
49. #10597355C22semidirect
50. #10597353C22semidirect
196. C2×#137D19semidirect
204. C2×C19#578semidirect
230. #137C2×D19semidirect
250. C19C2×#578semidirect
389. C2#11927360direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105974332
C2×#105974362
#119273602
C2×#105973552
C2×#105973642
C2×#105973612
C2×#105973622
C2×#105973962
C22×#645282
C2×Q16×D192
C2×#105973532
C2×C19×#1372
C2×#57819