Finite Group Databasebeta

← #14574246

Subgroups — #14574246

Order 2432.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927165C211yesmaximal, characteristic, complemented
2#11926940C211yesmaximal, characteristic, complemented
3#11926926C211yesmaximal, characteristic, complemented
4#11926906C211yesmaximal, characteristic, complemented
5#11926903C211yesmaximal, characteristic, complemented
6#11926800C211yesmaximal, characteristic, complemented
7#11926795C211yesmaximal, characteristic
8#11926775C211yesmaximal, characteristic, complemented
9#11926771C211yesmaximal, characteristic, complemented
10#11926654C211yesmaximal, characteristic, complemented
11#11926649C211yesmaximal, characteristic, complemented
12C4×#64527C211yesmaximal, characteristic, complemented
13C4×#64526C211yesmaximal, characteristic, complemented
14#11926500C211yesmaximal, characteristic, complemented
15C19×#542C211yesmaximal, characteristic, complemented
16C19×C4⋊Q8C2211yescharacteristic
17C19×#126—21no—
18C19×#124—21no—
19C19×#124C2211yescharacteristic
20C19×#123—21no—
21C19×C22⋊Q8—21no—
22C19×C22⋊Q8C2211yescharacteristic
23C19×#121C2211yescharacteristic
24C4×Q8×C19C2211yescharacteristic
25C4×D4×C19C2211yescharacteristic
26C19×#117C2211yescharacteristic
27C2×#64528C2211yescharacteristic
28C2×#64527C2211yescharacteristic
29C2×#64526C2211yescharacteristic
30C2×#64525C2211yescharacteristic
31#10597376C2211yescharacteristic
32#10597370C2211yescharacteristic
33C2×#64520C2211yescharacteristic
34C22×C19⋊C8C2211yescharacteristic
35#10597344—21no—
36#10597342—21no—
37#10597331—21no—
38#10597329—21no—
39#10597321C2211yescharacteristic
40C4×D76C2211yescharacteristic
41#10597315C2211yescharacteristic
42C4×Dic38C2211yescharacteristic
43#10597292C2211yescharacteristic
44#10597292C2211yescharacteristic
45#10597289C2211yescharacteristic
46#10597289C2211yescharacteristic
47#10597267C2211yescharacteristic
48#10597267C2211yescharacteristic
49#10597266C2211yescharacteristic
50#10597266C2211yescharacteristic
51#10597265C2211yescharacteristic
52#10597265C2211yescharacteristic
53#10597265C2211yescharacteristic
54#10597265C2211yescharacteristic
55#10597260C2211yescharacteristic
56#10597260C2211yescharacteristic
57C4×C19⋊C8C2211yescharacteristic
58C4×C19⋊C8C2211yescharacteristic
59C2×Q8×C19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19—21no—
64C22×C4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×D76C2311yescharacteristic
67C2×C4×D19—21no—
68C2×Dic38—21no—
69C2×Dic38C2311yescharacteristic
70C4⋊C4×C19—21no—
71C4⋊C4×C19—21no—
72C4⋊C4×C19—21no—
73C4⋊C4×C19D411yescharacteristic
74C4⋊C4×C19D411yescharacteristic
75C4⋊C4×C19C2311yescharacteristic
76C4⋊C4×C19C2311yescharacteristic
77C22⋊C4×C19—21no—
78C22⋊C4×C19—21no—
79C22⋊C4×C19—21no—
80C22⋊C4×C19—21no—
81C22⋊C4×C19—21no—
82C22⋊C4×C19D411yescharacteristic
83C22⋊C4×C19D411yescharacteristic
84C42×C19—21no—
85C42×C19C2311yescharacteristic
86C42×C19C2311yescharacteristic
87C22⋊Dic19—21no—
88#64528—22no—
89#64527—22no—
90#64526—22no—
91#64525—22no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96C4⋊Dic19—21no—
97C4⋊Dic19C2311yescharacteristic
98C4⋊Dic19C2311yescharacteristic
99Dic19⋊C4—21no—
100Dic19⋊C4—21no—
101C4×Dic19—21no—
102#64520—22no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8C2311yescharacteristic
105C2×C19⋊C8C2311yescharacteristic
106C2×C19⋊C8C2311yescharacteristic
107C2×C19⋊C8C2311yescharacteristic
108C23×C19—21no—
109C23×C19C2×D411yescharacteristic
110C22×D19—21no—
111Q8×C19—21no—
112Q8×C19—21no—
113Q8×C19—81no—
114D4×C19—21no—
115D4×C19—21no—
116D4×C19—81no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—81no—
123C2×C4×C19C2×D411yescharacteristic
124C2×C4×C19C2×D411yescharacteristic
125C2×C4×C19C2×D411yescharacteristic
126C2×C4×C19C2×D411yescharacteristic
127C2×C4×C19C2×D411yescharacteristic
128C2×C4×C19C2411yescharacteristic
129C22⋊D19—81no—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133D76—21no—
134D76—21no—
135C4×D19—81no—
136Dic38—21no—
137Dic38—21no—
138Dic38—81no—
139C19⋊C8—21no—
140C19⋊C8—21no—
141C19⋊C8#4112yes—
142C19⋊C8#4112yes—
143#3173—191nomaximal, Sylow
144C22×C19—21no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19—41no—
148C22×C19—41no—
149C22×C19—41no—
150C22×C19C22×D411yescharacteristic
151C2×D19—41no—
152C2×D19—41no—
153C2×D19—41no—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—41no—
160C4×C19—41no—
161C4×C19—41no—
162C4×C19C2×#4111yescharacteristic
163C4×C19C2×#4111yescharacteristic
164Dic19—41no—
165Dic19—41no—
166Dic19—41no—
167#542—191no—
168#542D1911yescharacteristic, complemented
169#498—191no—
170#495—191no—
171#489—191no—
172#489—191no—
173#470—191no—
174#469—191no—
175#465—191no—
176#465—191no—
177#442—191no—
178#441—191no—
179C4×SD16—191no—
180C4×SD16—191no—
181#405—191no—
182C2×C19—41no—
183C2×C19—81no—
184C2×C19#53211yescharacteristic
185C2×C19#57711yescharacteristic
186C2×C19#57711yescharacteristic
187D19—81no—
188C2×Q16—191no—
189C2×SD16—191no—
190C2×SD16—191no—
191C2×D8—191no—
192C2×M16—191no—
193C22×C8—191no—
194C4⋊Q8—191no—
195C4⋊Q8C2×D1911yescharacteristic
196#126—21no—
197#126—381no—
198#124—21no—
199#124—191no—
200#124—381no—
201#124C2×D1911yescharacteristic
202#123—21no—
203#123—381no—
204C22⋊Q8—21no—
205C22⋊Q8—191no—
206C22⋊Q8—381no—
207C22⋊Q8C2×D1911yescharacteristic
208#121—191no—
209#121C2×D1911yescharacteristic
210C4×Q8—191no—
211C4×Q8C2×D1911yescharacteristic
212C4×D4—191no—
213C4×D4C2×D1911yescharacteristic
214#117C2×D1911yescharacteristic
215#106—191no—
216#106—191no—
217#106—191no—
218#106—191no—
219#103—191no—
220#103—191no—
221#103—191no—
222#103—191no—
223#102—191no—
224#102—191no—
225#102—191no—
226#102—191no—
227#97—191no—
228#97—191no—
229C4×C8—191no—
230C4×C8—191no—
231C19#317311yescharacteristic, complemented, Sylow
232C2×Q8—21no—
233C2×Q8—191no—
234C2×Q8—381no—
235C2×Q8C22×D1911yescharacteristic
236C2×D4—21no—
237C2×D4—191no—
238C2×D4—381no—
239C2×D4C22×D1911yescharacteristic
240C22×C4—21no—
241C22×C4—381no—
242C22×C4C22×D1911yescharacteristic
243Q16—382no—
244SD16—382no—
245SD16—382no—
246D8—382no—
247M16—382no—
248C2×C8—191no—
249C2×C8—191no—
250C2×C8—191no—
251C2×C8—191no—
252C2×C8—382no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—191no—
257C4⋊C4—191no—
258C4⋊C4—381no—
259C4⋊C4—381no—
260C4⋊C4—381no—
261C4⋊C4C22⋊D1911yescharacteristic
262C4⋊C4C22⋊D1911yescharacteristic
263C4⋊C4C22×D1911yescharacteristic
264C4⋊C4C22×D1911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—381no—
271C22⋊C4—381no—
272C22⋊C4—381no—
273C22⋊C4—381no—
274C22⋊C4—381no—
275C22⋊C4C22⋊D1911yescharacteristic
276C22⋊C4C22⋊D1911yescharacteristic
277C42—21no—
278C42—381no—
279C42C22×D1911yescharacteristic
280C42C22×D1911yescharacteristic
281C23—21no—
282C23—381no—
283C23C2×C22⋊D1911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—381no—
288Q8—381no—
289Q8—1521no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—381no—
294D4—381no—
295D4—1521no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—381no—
303C2×C4—381no—
304C2×C4—381no—
305C2×C4—1521no—
306C2×C4C2×C22⋊D1911yescharacteristic
307C2×C4C2×C22⋊D1911yescharacteristic
308C2×C4C2×C22⋊D1911yescharacteristic
309C2×C4C2×C22⋊D1911yescharacteristic
310C2×C4C2×C22⋊D1911yescharacteristic
311C2×C4C23×D1911yescharacteristic
312C8—192no—
313C8—192no—
314C8—381no—
315C8—381no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—761no—
323C22—761no—
324C22—761no—
325C22C22×C22⋊D1911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—761no—
335C4—761no—
336C4—761no—
337C4#41×D1911yescharacteristic
338C4#41×D1911yescharacteristic
339C2—41no—
340C2—81no—
341C2—1521no—
342C2#1192709011yescharacteristic
343C2#1192735211yescharacteristic
344C2#1192735511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#542C2
socleC22×C19C22×D4
prime radical#11926795C2
hypercenter#542D19
hypocenterC19#3173
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #11927165C2semidirect
2. #11926940C2semidirect
3. #11926926C2semidirect
4. #11926906C2semidirect
5. #11926903C2semidirect
6. #11926800C2semidirect
8. #11926775C2semidirect
9. #11926771C2semidirect
10. #11926654C2semidirect
11. #11926649C2semidirect
12. C4×#64527C2semidirect
13. C4×#64526C2semidirect
14. #11926500C2semidirect
15. C19×#542C2semidirect
168. #542D19semidirect
231. C19#3173semidirect

Maximal subgroups

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

subgroupindex
#119271652
#119269402
#119269262
#119269062
#119269032
#119268002
#119267952
#119267752
#119267712
#119266542
#119266492
C4×#645272
C4×#645262
#119265002
C19×#5422
#317319