Finite Group Databasebeta

← #14572708

Subgroups — #14572708

Order 2432.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927090C211yesmaximal, characteristic
2#11926620C211yesmaximal, characteristic, complemented
3#11926619C211yesmaximal, characteristic, complemented
4#11926618C211yesmaximal, characteristic, complemented
5#11926615C211yesmaximal, characteristic, complemented
6#11926613C211yesmaximal, characteristic, complemented
7#11926612C211yesmaximal, characteristic, complemented
8C8×C22⋊D19C211yesmaximal, characteristic, complemented
9(C22⋊D19)⋊C8C211yesmaximal, characteristic, complemented
10#11926598C211yesmaximal, characteristic, complemented
11#11926594C211yesmaximal, characteristic, complemented
12#11926511C211yesmaximal, characteristic, complemented
13#11926509C211yesmaximal, characteristic, complemented
14#11926509C211yesmaximal, characteristic, complemented
15C19×#408C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#64541C2211yescharacteristic
18C2×M16×C19C2211yescharacteristic
19C22×C8×C19C2211yescharacteristic
20#10597393C411yescharacteristic
21#10597390C411yescharacteristic
22#10597386C411yescharacteristic
23#10597385C411yescharacteristic
24#10597385C411yescharacteristic
25#10597385C411yescharacteristic
26#10597385C411yescharacteristic
27#10597382C411yescharacteristic
28C4×C22⋊D19C2211yescharacteristic
29C4×C22⋊D19C2211yescharacteristic
30C4×C22⋊D19C2211yescharacteristic
31C4×C22⋊D19C2211yescharacteristic
32C2×C4×Dic19C2211yescharacteristic
33C2×#64520C2211yescharacteristic
34C22×C19⋊C8C2211yescharacteristic
35C2×#64515C2211yescharacteristic
36C2×#64515C2211yescharacteristic
37C2×C8×D19C2211yescharacteristic
38C2×C8×D19C2211yescharacteristic
39C19×C22⋊C8C2211yescharacteristic
40C19×C22⋊C8C2211yescharacteristic
41C19×C22⋊C8C2211yescharacteristic
42C19×C22⋊C8C2211yescharacteristic
43C22⋊(C19⋊C8)C2211yescharacteristic
44C22⋊(C19⋊C8)C2211yescharacteristic
45C22⋊(C19⋊C8)C2211yescharacteristic
46C22⋊(C19⋊C8)C2211yescharacteristic
47(C2×D19)⋊C8C2211yescharacteristic
48(C2×D19)⋊C8C2211yescharacteristic
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51#10597272C2211yescharacteristic
52#10597272C2211yescharacteristic
53Dic19⋊C8C2211yescharacteristic
54Dic19⋊C8C2211yescharacteristic
55Dic19⋊C8C2211yescharacteristic
56Dic19⋊C8C2211yescharacteristic
57C8×Dic19C2211yescharacteristic
58C8×Dic19C2211yescharacteristic
59#41×C19—41no—
60#41×C19—41no—
61C2×Q8×C19C2×C411yescharacteristic
62C2×D4×C19C2×C411yescharacteristic
63C2×D4×C19C2×C411yescharacteristic
64C2×D4×C19C2×C411yescharacteristic
65C22×C4×C19C2311yescharacteristic
66C22×C4×C19C2311yescharacteristic
67C22×C4×C19C2311yescharacteristic
68C2×C22⋊D19C2×C411yescharacteristic
69C2×C22⋊D19C2×C411yescharacteristic
70C2×C22⋊D19C2×C411yescharacteristic
71C2×C22⋊D19C2×C411yescharacteristic
72C2×C22⋊D19C2×C411yescharacteristic
73C2×C22⋊D19C2×C411yescharacteristic
74C22×Dic19C2×C411yescharacteristic
75C22×Dic19C2×C411yescharacteristic
76#64541—41no—
77#64541—41no—
78C2×D76C2×C411yescharacteristic
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38C2×C411yescharacteristic
82M16×C19—41no—
83C2×C8×C19—41no—
84C2×C8×C19C2311yescharacteristic
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C22⋊Dic19C2×C411yescharacteristic
89C22⋊Dic19C2×C411yescharacteristic
90C22⋊Dic19C2×C411yescharacteristic
91C22⋊Dic19C2×C411yescharacteristic
92(C2×D19)⋊C4C2×C411yescharacteristic
93(C2×D19)⋊C4C2×C411yescharacteristic
94(C2×D19)⋊C4C2×C411yescharacteristic
95(C2×D19)⋊C4C2×C411yescharacteristic
96Dic19⋊C4C2×C411yescharacteristic
97Dic19⋊C4C2×C411yescharacteristic
98Dic19⋊C4C2×C411yescharacteristic
99Dic19⋊C4C2×C411yescharacteristic
100C4×Dic19C2×C411yescharacteristic
101C4×Dic19C2×C411yescharacteristic
102C4×Dic19C2311yescharacteristic
103C4×Dic19C2311yescharacteristic
104#64520—41no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8C2311yescharacteristic
107C2×C19⋊C8C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109C2×C19⋊C8C2311yescharacteristic
110#64515—41no—
111#64515—41no—
112C8×D19—41no—
113C8×D19—41no—
114C23×C19C22×C411yescharacteristic
115C23×C19C22×C411yescharacteristic
116C23×C19C22×C411yescharacteristic
117C22×D19C22×C411yescharacteristic
118C22×D19C22×C411yescharacteristic
119Q8×C19—41no—
120D4×C19—41no—
121D4×C19—41no—
122D4×C19—41no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19C22×C411yescharacteristic
130C2×C4×C19C22×C411yescharacteristic
131C2×C4×C19C22×C411yescharacteristic
132C2×C4×C19C2411yescharacteristic
133C22⋊D19—22no—
134C22⋊D19—22no—
135C22⋊D19—41no—
136C22⋊D19—41no—
137C22⋊D19—41no—
138C22⋊D19—41no—
139C2×Dic19—22no—
140C2×Dic19—41no—
141C2×Dic19C22×C411yescharacteristic
142C2×Dic19C22×C411yescharacteristic
143C2×Dic19C22×C411yescharacteristic
144C2×Dic19C22×C411yescharacteristic
145C2×Dic19C22×C411yescharacteristic
146C2×Dic19C22×C411yescharacteristic
147D76—41no—
148C4×D19—21no—
149C4×D19—21no—
150C4×D19—21no—
151C4×D19—21no—
152Dic38—41no—
153C8×C19—21no—
154C8×C19—21no—
155C8×C19—21no—
156C8×C19—21no—
157C19⋊C8—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161#2981—191nomaximal, Sylow
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19C23×C411yescharacteristic
172C2×D19—21no—
173C2×D19—21no—
174C2×D19—21no—
175C2×D19—21no—
176C2×D19—21no—
177C2×D19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19H(5,𝔽2)11yescharacteristic
182C4×C19H(5,𝔽2)11yescharacteristic
183Dic19—21no—
184Dic19—21no—
185Dic19—21no—
186Dic19—21no—
187Dic19—21no—
188Dic19#13112yes—
189#532—191no—
190#436—191no—
191#436—191no—
192#435—191no—
193#435—191no—
194#435—191no—
195#435—191no—
196C8×D4—191no—
197C8×D4—191no—
198#432—191no—
199#431—191no—
200#408—191no—
201#408—191no—
202#408—191no—
203#408D1911yescharacteristic, complemented
204C2×C19—41no—
205C2×C19—41no—
206C2×C19—41no—
207C2×C19#51811yescharacteristic
208C2×C19C2×#13111yescharacteristic
209C2×C19#56811yescharacteristic
210D19—41no—
211D19—41no—
212C2×#41—191no—
213C2×#41C2×D1911yescharacteristic
214C2×M16—191no—
215C2×M16—191no—
216C2×M16—191no—
217C2×M16C2×D1911yescharacteristic
218C22×C8—191no—
219C22×C8—191no—
220C22×C8—191no—
221C22×C8C2×D1911yescharacteristic
222C4⋊Q8—191no—
223#127—191no—
224#124—191no—
225#124—191no—
226#121—191no—
227#121—191no—
228#121—191no—
229#121—191no—
230C4×D4—191no—
231C4×D4—191no—
232C4×D4—191no—
233C4×D4—191no—
234C2×C42—191no—
235C4⋊C8—191no—
236C4⋊C8—191no—
237C4⋊C8—191no—
238C4⋊C8—191no—
239C22⋊C8—191no—
240C22⋊C8—191no—
241C22⋊C8—191no—
242C22⋊C8—191no—
243C22⋊C8—191no—
244C22⋊C8—191no—
245C22⋊C8—191no—
246C22⋊C8—191no—
247C22⋊C8C2×D1911yescharacteristic
248C22⋊C8C2×D1911yescharacteristic
249C22⋊C8C2×D1911yescharacteristic
250C22⋊C8C2×D1911yescharacteristic
251#97—191no—
252#97—191no—
253C4×C8—191no—
254C4×C8—191no—
255C19#298111yescharacteristic, complemented, Sylow
256#41—41no—
257#41—41no—
258#41—761no—
259#41—761no—
260C2×Q8—191no—
261C2×Q8C4×D1911yescharacteristic
262C2×D4—191no—
263C2×D4—191no—
264C2×D4—191no—
265C2×D4—191no—
266C2×D4—191no—
267C2×D4—191no—
268C2×D4—191no—
269C2×D4C4×D1911yescharacteristic
270C2×D4C4×D1911yescharacteristic
271C2×D4C4×D1911yescharacteristic
272C22×C4—191no—
273C22×C4—191no—
274C22×C4—191no—
275C22×C4—191no—
276C22×C4C22×D1911yescharacteristic
277C22×C4C22×D1911yescharacteristic
278C22×C4C22×D1911yescharacteristic
279M16—41no—
280M16—761no—
281M16—761no—
282M16—761no—
283C2×C8—41no—
284C2×C8—191no—
285C2×C8—191no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8—761no—
289C2×C8—761no—
290C2×C8—761no—
291C2×C8C22×D1911yescharacteristic
292C2×C8C22×D1911yescharacteristic
293C2×C8C22×D1911yescharacteristic
294C2×C8C22×D1911yescharacteristic
295C4⋊C4—191no—
296C4⋊C4—191no—
297C4⋊C4—191no—
298C4⋊C4—191no—
299C22⋊C4—191no—
300C22⋊C4—191no—
301C22⋊C4—191no—
302C22⋊C4—191no—
303C22⋊C4—191no—
304C22⋊C4—191no—
305C22⋊C4—191no—
306C22⋊C4—191no—
307C42—191no—
308C42—191no—
309C42—191no—
310C42—191no—
311C23—191no—
312C23—191no—
313C23C2×C4×D1911yescharacteristic
314C23C2×C4×D1911yescharacteristic
315C23C2×C4×D1911yescharacteristic
316Q8—41no—
317Q8—761no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—382no—
322D4—382no—
323D4—761no—
324D4—761no—
325D4—761no—
326D4—761no—
327D4—761no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—191no—
335C2×C4—191no—
336C2×C4—191no—
337C2×C4—191no—
338C2×C4—191no—
339C2×C4—191no—
340C2×C4—382no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—761no—
346C2×C4C2×C4×D1911yescharacteristic
347C2×C4C2×C4×D1911yescharacteristic
348C2×C4C2×C4×D1911yescharacteristic
349C2×C4C23×D1911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—381no—
355C8—381no—
356C8—381no—
357C8—381no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—381no—
368C22—381no—
369C22—381no—
370C22—381no—
371C22—381no—
372C22—381no—
373C22C22×C4×D1911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—192no—
378C4—381no—
379C4—381no—
380C4—381no—
381C4—381no—
382C4—381no—
383C4#1059743011yescharacteristic
384C4#1059743011yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—761no—
389C2—761no—
390C2#1192701711yescharacteristic
391C2#131×D1911yescharacteristic
392C2#1192730911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D19
commutator, socleC22×C19C23×C4
FittingC19×#408C2
prime radical#11927090C2
cosocleC2×C4×C19C24
hypercenter#408D19
hypocenterC19#2981
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #11926620C2semidirect
3. #11926619C2semidirect
4. #11926618C2semidirect
5. #11926615C2semidirect
6. #11926613C2semidirect
7. #11926612C2semidirect
8. C8×C22⋊D19C2semidirect
9. (C22⋊D19)⋊C8C2semidirect
10. #11926598C2semidirect
11. #11926594C2semidirect
12. #11926511C2semidirect
13. #11926509C2semidirect
14. #11926509C2semidirect
15. C19×#408C2semidirect
203. #408D19semidirect
255. C19#2981semidirect

Maximal subgroups

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

subgroupindex
#119270902
#119266202
#119266192
#119266182
#119266152
#119266132
#119266122
C8×C22⋊D192
(C22⋊D19)⋊C82
#119265982
#119265942
#119265112
#119265092
C19×#4082
#298119