Finite Group Databasebeta

← #14574329

Subgroups — #14574329

Order 2432.

410 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927091C211yesmaximal, characteristic, complemented
2#11927081C211yesmaximal, characteristic, complemented
3#11926952C211yesmaximal, characteristic, complemented
4#11926930C211yesmaximal, characteristic, complemented
5#11926907C211yesmaximal, characteristic, complemented
6#11926905C211yesmaximal, characteristic, complemented
7#11926781C211yesmaximal, characteristic, complemented
8#11926779C211yesmaximal, characteristic, complemented
9#11926776C211yesmaximal, characteristic, complemented
10#11926770C211yesmaximal, characteristic, complemented
11#11926657C211yesmaximal, characteristic, complemented
12#11926654C211yesmaximal, characteristic, complemented
13#11926642C211yesmaximal, characteristic, complemented
14#97×D19C211yesmaximal, characteristic, complemented
15C19×#440C211yesmaximal, characteristic, complemented
16C2×#64541—21no—
17C2×SD16×C19C2211yescharacteristic
18C4×Q8×C19C2211yescharacteristic
19C4×D4×C19C2211yescharacteristic
20#10597393C2211yescharacteristic
21#10597392C2211yescharacteristic
22C2×#64527C2211yescharacteristic
23#10597386C2211yescharacteristic
24#10597384C2211yescharacteristic
25C2×#64525C2211yescharacteristic
26C4×C22⋊D19—21no—
27C2×D152C2211yescharacteristic
28C2×C8×D19C2211yescharacteristic
29C2×C8×D19C2211yescharacteristic
30#10597344—21no—
31#10597341C2211yescharacteristic
32#10597341C2211yescharacteristic
33#10597340—21no—
34#10597336C2211yescharacteristic
35#10597334C2211yescharacteristic
36#10597331—21no—
37#10597330—21no—
38C4×D76—21no—
39C4×D76C2211yescharacteristic
40C4×D76C2211yescharacteristic
41#10597318—21no—
42C42×D19C2211yescharacteristic
43C19×#107C2211yescharacteristic
44C19×#103C2211yescharacteristic
45C19×#102C2211yescharacteristic
46C19×#97C2211yescharacteristic
47#10597292C2211yescharacteristic
48#10597289C2211yescharacteristic
49#10597278C2211yescharacteristic
50#10597278C2211yescharacteristic
51#10597274C2211yescharacteristic
52#10597272C2211yescharacteristic
53#10597272C2211yescharacteristic
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic
56#10597265C2211yescharacteristic
57#10597264C2211yescharacteristic
58#10597260C2211yescharacteristic
59C2×Q8×C19C2311yescharacteristic
60C2×D4×C19C2311yescharacteristic
61C22×C4×C19—21no—
62C2×C22⋊D19—21no—
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65#64541—44no—
66C2×D76—21no—
67C2×D76—21no—
68C2×D76C2311yescharacteristic
69C2×D76C2311yescharacteristic
70C2×C4×D19—21no—
71C2×C4×D19—21no—
72C2×C4×D19D411yescharacteristic
73C2×C4×D19D411yescharacteristic
74C2×C4×D19C2311yescharacteristic
75C2×Dic38—21no—
76SD16×C19—22no—
77C2×C8×C19C2311yescharacteristic
78C2×C8×C19C2311yescharacteristic
79C4⋊C4×C19—21no—
80C4⋊C4×C19C2311yescharacteristic
81C4⋊C4×C19C2311yescharacteristic
82C22⋊C4×C19—21no—
83C42×C19—21no—
84C42×C19C2311yescharacteristic
85C22⋊Dic19—21no—
86#64527—22no—
87#64525—22no—
88(C2×D19)⋊C4—21no—
89(C2×D19)⋊C4—21no—
90(C2×D19)⋊C4—21no—
91(C2×D19)⋊C4—21no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95C4⋊Dic19—21no—
96C4⋊Dic19C2311yescharacteristic
97C4⋊Dic19C2311yescharacteristic
98Dic19⋊C4—21no—
99Dic19⋊C4—21no—
100Dic19⋊C4—21no—
101C4×Dic19D411yescharacteristic
102C4×Dic19D411yescharacteristic
103C4×Dic19C2311yescharacteristic
104C2×C19⋊C8C2311yescharacteristic
105C2×C19⋊C8C2311yescharacteristic
106D152—22no—
107C8×D19—22no—
108C8×D19—22no—
109C23×C19—21no—
110C22×D19—21no—
111C22×D19—21no—
112C22×D19C2×D411yescharacteristic
113Q8×C19—21no—
114Q8×C19—21no—
115D4×C19—21no—
116D4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—42no—
121C2×C4×C19C2×D411yescharacteristic
122C2×C4×C19C2×D411yescharacteristic
123C2×C4×C19C2411yescharacteristic
124C22⋊D19—42no—
125C22⋊D19—42no—
126C22⋊D19—42no—
127C2×Dic19—21no—
128C2×Dic19—21no—
129C2×Dic19C2×D411yescharacteristic
130C2×Dic19C2×D411yescharacteristic
131C2×Dic19C2×D411yescharacteristic
132D76—21no—
133D76—21no—
134D76—21no—
135D76—21no—
136D76—42no—
137D76—42no—
138C4×D19—22no—
139C4×D19—21no—
140C4×D19—21no—
141C4×D19—41no—
142C4×D19—42no—
143C4×D19—42no—
144Dic38—42no—
145C8×C19—21no—
146C8×C19#4112yescomplemented
147C19⋊C8—21no—
148C19⋊C8#4112yescomplemented
149#3180—191nomaximal, Sylow
150C22×C19—41no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19C22×D411yescharacteristic
154C2×D19—21no—
155C2×D19—21no—
156C2×D19—41no—
157C2×D19—41no—
158C2×D19—41no—
159C2×D19—41no—
160C2×D19—41no—
161C2×D19—41no—
162C2×D19AGL(1,ℤ/8)12yes—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—41no—
166C4×C19—41no—
167C4×C19—41no—
168C4×C19C2×#4111yescharacteristic
169C4×C19C2×#4111yescharacteristic
170Dic19—21no—
171Dic19—21no—
172Dic19—21no—
173Dic19—41no—
174Dic19—41no—
175#532—191no—
176#529—191no—
177#501—191no—
178#496—191no—
179#490—191no—
180#489—191no—
181#466—191no—
182#466—191no—
183#465—191no—
184#465—191no—
185#442—191no—
186#442—191no—
187#440—191no—
188#440D1911yescharacteristic, complemented
189C2×#97—191no—
190C2×C19—81no—
191C2×C19#53211yescharacteristic
192C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C19#57511yescharacteristic
194D19—22no—
195D19—81no—
196D19—81no—
197C2×#41—381no—
198C2×SD16—191no—
199C2×SD16C2×D1911yescharacteristic
200C2×D8—191no—
201C2×D8—191no—
202C22×C8—191no—
203C22×C8—191no—
204C4⋊Q8—191no—
205#127—191no—
206#126—381no—
207#125—191no—
208#124—191no—
209#124—381no—
210#123—381no—
211C22⋊Q8—191no—
212#121—191no—
213#121—191no—
214#121—191no—
215#121—381no—
216C4×Q8C2×D1911yescharacteristic
217C4×D4—191no—
218C4×D4—191no—
219C4×D4—381no—
220C4×D4—381no—
221C4×D4C2×D1911yescharacteristic
222#117—381no—
223C2×C42—191no—
224#107—191no—
225#107C2×D1911yescharacteristic
226#106—191no—
227#106—191no—
228#103—191no—
229#103C2×D1911yescharacteristic
230#102—191no—
231#102—191no—
232#102—191no—
233#102—191no—
234#102—191no—
235#102C2×D1911yescharacteristic
236#97—191no—
237#97—191no—
238#97—191no—
239#97C2×D1911yescharacteristic
240C19#318011yescharacteristic, complemented, Sylow
241#41—764no—
242C2×Q8—381no—
243C2×Q8C22×D1911yescharacteristic
244C2×D4—191no—
245C2×D4—191no—
246C2×D4—381no—
247C2×D4—381no—
248C2×D4—381no—
249C2×D4—381no—
250C2×D4—381no—
251C2×D4C22×D1911yescharacteristic
252C22×C4—21no—
253C22×C4—191no—
254C22×C4—191no—
255C22×C4—191no—
256C22×C4—381no—
257C22×C4—381no—
258SD16—22no—
259SD16—382no—
260D8—382no—
261D8—382no—
262C2×C8—191no—
263C2×C8—191no—
264C2×C8—382no—
265C2×C8—382no—
266C2×C8C22×D1911yescharacteristic
267C2×C8C22×D1911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—191no—
270C4⋊C4—191no—
271C4⋊C4—381no—
272C4⋊C4—381no—
273C4⋊C4—381no—
274C4⋊C4—381no—
275C4⋊C4C22×D1911yescharacteristic
276C4⋊C4C22×D1911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—381no—
279C22⋊C4—381no—
280C22⋊C4—381no—
281C22⋊C4—381no—
282C22⋊C4—381no—
283C22⋊C4—381no—
284C22⋊C4—381no—
285C22⋊C4—381no—
286C42—21no—
287C42—191no—
288C42—191no—
289C42—191no—
290C42C22×D1911yescharacteristic
291C23—21no—
292C23—191no—
293C23—381no—
294C23—381no—
295Q8—21no—
296Q8—21no—
297Q8—762no—
298D4—21no—
299D4—21no—
300D4—381no—
301D4—381no—
302D4—381no—
303D4—381no—
304D4—762no—
305D4—762no—
306D4—762no—
307D4—762no—
308D4—762no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—191no—
314C2×C4—191no—
315C2×C4—191no—
316C2×C4—382no—
317C2×C4—381no—
318C2×C4—381no—
319C2×C4—381no—
320C2×C4—381no—
321C2×C4—761no—
322C2×C4—762no—
323C2×C4—762no—
324C2×C4D4×D1911yescharacteristic
325C2×C4D4×D1911yescharacteristic
326C2×C4C23×D1911yescharacteristic
327C8—21no—
328C8—192no—
329C8—381no—
330C8#6454112yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—192no—
335C22—381no—
336C22—381no—
337C22—761no—
338C22—761no—
339C22—761no—
340C22—761no—
341C22—761no—
342C22—761no—
343C22C2×D4×D1911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—381no—
350C4—381no—
351C4—381no—
352C4—761no—
353C4—761no—
354C4C2×#6454111yescharacteristic
355C4#41×D1911yescharacteristic
356C2—81no—
357C2—382no—
358C2—1521no—
359C2—1521no—
360C2#1192709111yescharacteristic
361C2AGL(1,ℤ/8)×D1911yescharacteristic
362C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#440C2
socleC22×C19C22×D4
hypercenter#440D19
hypocenterC19#3180
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #11927091C2semidirect
2. #11927081C2semidirect
3. #11926952C2semidirect
4. #11926930C2semidirect
5. #11926907C2semidirect
6. #11926905C2semidirect
7. #11926781C2semidirect
8. #11926779C2semidirect
9. #11926776C2semidirect
10. #11926770C2semidirect
11. #11926657C2semidirect
12. #11926654C2semidirect
13. #11926642C2semidirect
14. #97×D19C2semidirect
15. C19×#440C2semidirect
146. C8×C19#41semidirect
148. C19⋊C8#41semidirect
188. #440D19semidirect
240. C19#3180semidirect
330. C8#64541semidirect

Maximal subgroups

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

subgroupindex
#119270912
#119270812
#119269522
#119269302
#119269072
#119269052
#119267812
#119267792
#119267762
#119267702
#119266572
#119266542
#119266422
#97×D192
C19×#4402
#318019