Finite Group Databasebeta

← #14568883

Subgroups — #14568883

Order 2432.

476 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11926485C211yesmaximal, characteristic, complemented
2#11926462C211yesmaximal, characteristic
3#11926457C211yesmaximal, characteristic, complemented
4#11926457C211yesmaximal, characteristic, complemented
5#11926448C211yesmaximal, characteristic, complemented
6#11926435C211yesmaximal, characteristic, complemented
7#11926433C211yesmaximal, characteristic, complemented
8#11926422C211yesmaximal, characteristic
9#11926422C211yesmaximal, characteristic
10#11926411C211yesmaximal, characteristic, complemented
11#11926406C211yesmaximal, characteristic, complemented
12#11926406C211yesmaximal, characteristic, complemented
13C4×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
14#11926391C211yesmaximal, characteristic, complemented
15C19×#383C211yesmaximal, characteristic, complemented
16C22×D76C2211yescharacteristic
17C22×C4×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C2×C42×C19C2211yescharacteristic
21C2×(C2×D19)⋊C4C2211yescharacteristic
22C2×(C2×D19)⋊C4C2211yescharacteristic
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2211yescharacteristic
32C2×Dic19⋊C4C2211yescharacteristic
33C2×C4×Dic19C2211yescharacteristic
34C2×C4×Dic19C2211yescharacteristic
35C19×#95C2211yescharacteristic
36C19×#95C2211yescharacteristic
37C19×#95C2211yescharacteristic
38C19×#95C2211yescharacteristic
39C19×#95C2211yescharacteristic
40C19×#95C2211yescharacteristic
41C19⋊#95C2211yescharacteristic
42C19⋊#95C2211yescharacteristic
43C19⋊#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C23×D19C2311yescharacteristic
52C23×D19C2311yescharacteristic
53C22×C4×C19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×Dic19C2311yescharacteristic
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C2×D76—22no—
67C2×D76—22no—
68C2×D76—41no—
69C2×C4×D19—22no—
70C2×C4×D19—22no—
71C2×C4×D19—22no—
72C2×C4×D19—22no—
73C2×C4×D19—41no—
74C2×C4×D19—41no—
75C2×Dic38—22no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C42×C19—22no—
79(C2×D19)⋊C4—22no—
80(C2×D19)⋊C4—22no—
81(C2×D19)⋊C4—22no—
82(C2×D19)⋊C4—22no—
83(C2×D19)⋊C4—22no—
84(C2×D19)⋊C4—22no—
85(C2×D19)⋊C4—41no—
86(C2×D19)⋊C4—41no—
87(C2×D19)⋊C4—41no—
88(C2×D19)⋊C4—41no—
89Dic19⋊C4—41no—
90Dic19⋊C4—41no—
91C4×Dic19—22no—
92C4×Dic19—41no—
93C23×C19C2411yescharacteristic
94C22×D19—21no—
95C22×D19—21no—
96C22×D19—21no—
97C22×D19—21no—
98C22×D19—21no—
99C22×D19—21no—
100C22×D19—21no—
101C22×D19—21no—
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19—21no—
106C22×D19#4112yes—
107C22×D19#4112yes—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19#4112yes—
129C2×Dic19—21no—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19#4112yes—
146C2×Dic19#4112yes—
147D76—44no—
148C4×D19—44no—
149C4×D19—44no—
150Dic38—44no—
151#2572—191nomaximal, Sylow
152C22×C19C2×#4111yescharacteristic
153C22×C19C2×#4111yescharacteristic
154C22×C19C2×#4111yescharacteristic
155C22×C19C2×#4111yescharacteristic
156C22×C19C2×#4111yescharacteristic
157C22×C19H(5,𝔽2)11yescharacteristic
158C22×C19H(5,𝔽2)11yescharacteristic
159C2×D19—22no—
160C2×D19—22no—
161C2×D19—22no—
162C2×D19—22no—
163C2×D19—22no—
164C2×D19—22no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C4×C19—22no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19—41no—
180Dic19—22no—
181Dic19—22no—
182Dic19—41no—
183Dic19—41no—
184Dic19—41no—
185Dic19—41no—
186#400—191no—
187#394—191no—
188#393—191no—
189#393—191no—
190#391—191no—
191#388—191no—
192#388—191no—
193#386—191no—
194#386—191no—
195#383—191no—
196#383D1911yescharacteristic, complemented
197#381—191no—
198#381—191no—
199C4×C22⋊C4—191no—
200C4×C22⋊C4—191no—
201C2×C19#52911yescharacteristic
202C2×C19#52911yescharacteristic
203C2×C19#53811yescharacteristic
204C2×C19#55111yescharacteristic
205C2×C19#55111yescharacteristic
206C2×C19#55111yescharacteristic
207C2×C19#55511yescharacteristic
208D19—42no—
209D19—42no—
210C22×Q8—191no—
211C22×D4—191no—
212C23×C4—191no—
213C23×C4—191no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C22⋊C4—191no—
217C2×C22⋊C4—191no—
218C2×C22⋊C4—191no—
219C2×C22⋊C4—191no—
220C2×C22⋊C4—191no—
221C2×C22⋊C4—191no—
222C2×C22⋊C4—191no—
223C2×C22⋊C4—191no—
224C2×C22⋊C4—191no—
225C2×C22⋊C4—191no—
226C2×C42—191no—
227C2×C42—191no—
228C2×C42C2×D1911yescharacteristic
229#95—191no—
230#95—191no—
231#95—191no—
232#95—191no—
233#95—191no—
234#95—191no—
235#95—191no—
236#95—191no—
237#95—191no—
238#95—191no—
239#95C2×D1911yescharacteristic
240#95C2×D1911yescharacteristic
241#95C2×D1911yescharacteristic
242#95C2×D1911yescharacteristic
243#95C2×D1911yescharacteristic
244#95C2×D1911yescharacteristic
245C19#257211yescharacteristic, complemented, Sylow
246C24—191no—
247C24—191no—
248C2×Q8—382no—
249C2×Q8—761no—
250C2×Q8—761no—
251C2×D4—382no—
252C2×D4—382no—
253C2×D4—761no—
254C22×C4—191no—
255C22×C4—191no—
256C22×C4—191no—
257C22×C4—191no—
258C22×C4—191no—
259C22×C4—191no—
260C22×C4—382no—
261C22×C4—382no—
262C22×C4—382no—
263C22×C4—382no—
264C22×C4—761no—
265C22×C4—761no—
266C22×C4C22×D1911yescharacteristic
267C22×C4C22×D1911yescharacteristic
268C22×C4C22×D1911yescharacteristic
269C22×C4C22×D1911yescharacteristic
270C22×C4C22×D1911yescharacteristic
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C4⋊C4—761no—
274C4⋊C4—761no—
275C22⋊C4—382no—
276C22⋊C4—382no—
277C22⋊C4—382no—
278C22⋊C4—382no—
279C22⋊C4—382no—
280C22⋊C4—382no—
281C22⋊C4—761no—
282C22⋊C4—761no—
283C22⋊C4—761no—
284C22⋊C4—761no—
285C42—22no—
286C42—382no—
287C42—761no—
288C23—192no—
289C23—192no—
290C23—381no—
291C23—381no—
292C23—381no—
293C23—381no—
294C23—381no—
295C23—381no—
296C23—381no—
297C23—381no—
298C23—381no—
299C23—381no—
300C23—381no—
301C23—381no—
302C23C23×D1911yescharacteristic
303Q8—764no—
304D4—764no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—192no—
326C2×C4—192no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—764no—
344C2×C4—764no—
345C2×C4#6454112yes—
346C22—382no—
347C22—382no—
348C22—382no—
349C22—382no—
350C22—382no—
351C22—382no—
352C22—761no—
353C22—761no—
354C22—761no—
355C22—761no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22C2×#6454111yescharacteristic
361C22#41×D1911yescharacteristic
362C22#41×D1911yescharacteristic
363C22#41×D1911yescharacteristic
364C22#41×D1911yescharacteristic
365C22#1059743511yescharacteristic
366C22#1059743511yescharacteristic
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—382no—
375C4—382no—
376C4—761no—
377C4—761no—
378C4—761no—
379C4—761no—
380C2—762no—
381C2—762no—
382C2#1192707211yescharacteristic
383C2#1192707711yescharacteristic
384C2#1192713311yescharacteristic
385C2#1192721811yescharacteristic
386C2#1192721911yescharacteristic
387C2#1192721911yescharacteristic
388C2#1192725711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#383C2
prime radicalC22×D76C22
hypercenter#383D19
hypocenterC19#2572
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. #11926485C2semidirect
3. #11926457C2semidirect
4. #11926457C2semidirect
5. #11926448C2semidirect
6. #11926435C2semidirect
7. #11926433C2semidirect
10. #11926411C2semidirect
11. #11926406C2semidirect
12. #11926406C2semidirect
13. C4×(C2×D19)⋊C4C2semidirect
14. #11926391C2semidirect
15. C19×#383C2semidirect
196. #383D19semidirect
245. C19#2572semidirect

Maximal subgroups

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

subgroupindex
#119264852
#119264622
#119264572
#119264482
#119264352
#119264332
#119264222
#119264112
#119264062
C4×(C2×D19)⋊C42
#119263912
C19×#3832
#257219