Finite Group Databasebeta

← #14575041

Subgroups — #14575041

Order 2432.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927167C211yesmaximal, characteristic, complemented
2#11927147C211yesmaximal, characteristic, complemented
3#11926849C211yesmaximal, characteristic, complemented
4#11926847C211yesmaximal, characteristic, complemented
5#11926832C211yesmaximal, characteristic, complemented
6#11926823C211yesmaximal, characteristic, complemented
7#11926797C211yesmaximal, characteristic, complemented
8#11926778C211yesmaximal, characteristic, complemented
9#11926775C211yesmaximal, characteristic, complemented
10#11926762C211yesmaximal, characteristic, complemented
11#11926761C211yesmaximal, characteristic, complemented
12#11926742C211yesmaximal, characteristic, complemented
13#11926738C211yesmaximal, characteristic, complemented
14#11926572C211yesmaximal, characteristic, complemented
15C19×#468C211yesmaximal, characteristic, complemented
16C2×SD16×C19C2211yescharacteristic
17C2×M16×C19C2211yescharacteristic
18C19×C22⋊Q8C2211yescharacteristic
19C19×#121C2211yescharacteristic
20#10597393C2211yescharacteristic
21Q8×Dic19C2211yescharacteristic
22C2×#64527C2211yescharacteristic
23#10597386C2211yescharacteristic
24#10597385—21no—
25#10597384—21no—
26D4×Dic19C2211yescharacteristic
27C2×#64525C2211yescharacteristic
28#10597376C2211yescharacteristic
29#10597376C2211yescharacteristic
30#10597372C2211yescharacteristic
31C22×C19⋊C8C2211yescharacteristic
32C2×D152C2211yescharacteristic
33#10597344—21no—
34#10597343—21no—
35#10597339C2211yescharacteristic
36#10597339C2211yescharacteristic
37#10597336C2211yescharacteristic
38#10597334C2211yescharacteristic
39#10597332—21no—
40#10597331—21no—
41#10597329—21no—
42#10597329—21no—
43C19×#107C2211yescharacteristic
44C19×#103C2211yescharacteristic
45C19×#102C2211yescharacteristic
46#10597292C2211yescharacteristic
47#10597289C2211yescharacteristic
48#10597278C2211yescharacteristic
49#10597278C2211yescharacteristic
50#10597274C2211yescharacteristic
51Dic19⋊C8C2211yescharacteristic
52Dic19⋊C8C2211yescharacteristic
53Dic19⋊C8C2211yescharacteristic
54Dic19⋊C8C2211yescharacteristic
55#10597266C2211yescharacteristic
56#10597266C2211yescharacteristic
57#10597265C2211yescharacteristic
58#10597264C2211yescharacteristic
59C2×Q8×C19C2311yescharacteristic
60C2×D4×C19—21no—
61C2×D4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C22×Dic19—21no—
68C2×D76C2311yescharacteristic
69C2×D76C2311yescharacteristic
70C2×C4×D19—21no—
71C2×C4×D19—21no—
72C2×Dic38—21no—
73SD16×C19—41no—
74M16×C19—41no—
75C2×C8×C19C2311yescharacteristic
76C2×C8×C19C2311yescharacteristic
77C4⋊C4×C19—21no—
78C4⋊C4×C19C2311yescharacteristic
79C4⋊C4×C19C2311yescharacteristic
80C22⋊C4×C19—21no—
81C22⋊C4×C19—21no—
82C22⋊Dic19—21no—
83C22⋊Dic19D411yescharacteristic
84C22⋊Dic19D411yescharacteristic
85#64527—41no—
86#64525—41no—
87(C2×D19)⋊C4—21no—
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—
93C4⋊Dic19—21no—
94C4⋊Dic19—21no—
95C4⋊Dic19D411yescharacteristic
96C4⋊Dic19D411yescharacteristic
97C4⋊Dic19C2311yescharacteristic
98C4⋊Dic19C2311yescharacteristic
99Dic19⋊C4—21no—
100Dic19⋊C4—21no—
101C4×Dic19—21no—
102C4×Dic19C2311yescharacteristic
103C4×Dic19C2311yescharacteristic
104C2×C19⋊C8—41no—
105C2×C19⋊C8C2311yescharacteristic
106C2×C19⋊C8C2311yescharacteristic
107D152—41no—
108C23×C19—21no—
109C23×C19C2×D411yescharacteristic
110C22×D19—21no—
111C22×D19—21no—
112Q8×C19—21no—
113Q8×C19—21no—
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×C19C2×D411yescharacteristic
123C2×C4×C19C2411yescharacteristic
124C22⋊D19—81no—
125C22⋊D19—81no—
126C22⋊D19—81no—
127C22⋊D19—81no—
128C2×Dic19—21no—
129C2×Dic19—21no—
130C2×Dic19—81no—
131C2×Dic19C2×D411yescharacteristic
132C2×Dic19C2×D411yescharacteristic
133C2×Dic19C2×D411yescharacteristic
134C2×Dic19C2×D411yescharacteristic
135D76—21no—
136D76—21no—
137D76—21no—
138D76—21no—
139C4×D19—81no—
140C4×D19—81no—
141Dic38—81no—
142C8×C19—21no—
143C8×C19—21no—
144C19⋊C8—21no—
145C19⋊C8—21no—
146#3257—191nomaximal, Sylow
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—41no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19C22×D411yescharacteristic
154C2×D19—41no—
155C2×D19—41no—
156C2×D19—41no—
157C2×D19—41no—
158C2×D19—41no—
159C2×D19—41no—
160C4×C19—21no—
161C4×C19—41no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19H(5,𝔽2)11yescharacteristic
165C4×C192−1+411yescharacteristic
166Dic19—21no—
167Dic19—21no—
168Dic19—21no—
169Dic19—21no—
170Dic19—41no—
171Dic19—41no—
172#542—191no—
173#540—191no—
174#479—191no—
175#478—191no—
176#476—191no—
177#474—191no—
178#469—191no—
179#468D1911yescharacteristic, complemented
180#466—191no—
181#465—191no—
182#463—191no—
183#463—191no—
184#460—191no—
185#459—191no—
186#424—191no—
187C2×C19—41no—
188C2×C19—81no—
189C2×C19#53711yescharacteristic
190C2×C19#57611yescharacteristic
191C2×C19#57711yescharacteristic
192D19—81no—
193D19—81no—
194C2×SD16—191no—
195C2×SD16C2×D1911yescharacteristic
196C2×D8—191no—
197C2×D8—191no—
198C2×M16C2×D1911yescharacteristic
199C22×C8—191no—
200C4⋊Q8—191no—
201#127—191no—
202#126—381no—
203#125—191no—
204#124—191no—
205#124—381no—
206#123—381no—
207#123—381no—
208#123—381no—
209C22⋊Q8—381no—
210C22⋊Q8C2×D1911yescharacteristic
211#121—191no—
212#121—191no—
213#121—381no—
214#121—381no—
215#121C2×D1911yescharacteristic
216C4×Q8—191no—
217C4×D4—191no—
218C4×D4—191no—
219C4×D4—191no—
220#117—191no—
221#107—191no—
222#107C2×D1911yescharacteristic
223#106—191no—
224#106—191no—
225C4⋊C8—191no—
226C4⋊C8—191no—
227C4⋊C8—191no—
228C4⋊C8—191no—
229#103—191no—
230#103C2×D1911yescharacteristic
231#102—191no—
232#102—191no—
233#102—191no—
234#102—191no—
235#102—191no—
236#102C2×D1911yescharacteristic
237C19#325711yescharacteristic, complemented, Sylow
238C2×Q8—381no—
239C2×Q8C22×D1911yescharacteristic
240C2×D4—21no—
241C2×D4—191no—
242C2×D4—191no—
243C2×D4—381no—
244C2×D4—381no—
245C2×D4—381no—
246C2×D4—381no—
247C2×D4C22×D1911yescharacteristic
248C22×C4—381no—
249C22×C4—381no—
250C22×C4—381no—
251C22×C4C22×D1911yescharacteristic
252SD16—41no—
253SD16—761no—
254D8—761no—
255D8—761no—
256M16—41no—
257C2×C8—191no—
258C2×C8—191no—
259C2×C8—761no—
260C2×C8C22×D1911yescharacteristic
261C2×C8C22×D1911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—191no—
264C4⋊C4—191no—
265C4⋊C4—191no—
266C4⋊C4—191no—
267C4⋊C4—381no—
268C4⋊C4—381no—
269C4⋊C4—381no—
270C4⋊C4—381no—
271C4⋊C4C22×D1911yescharacteristic
272C4⋊C4C22×D1911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—191no—
276C22⋊C4—191no—
277C22⋊C4—381no—
278C22⋊C4—381no—
279C22⋊C4—381no—
280C22⋊C4—381no—
281C22⋊C4—381no—
282C22⋊C4—381no—
283C22⋊C4—381no—
284C42—191no—
285C42—191no—
286C42—381no—
287C23—21no—
288C23—381no—
289C23—381no—
290C23D4×D1911yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—1521no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—381no—
298D4—381no—
299D4—381no—
300D4—381no—
301D4—1521no—
302D4—1521no—
303D4—1521no—
304D4—1521no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—191no—
311C2×C4—191no—
312C2×C4—191no—
313C2×C4—191no—
314C2×C4—381no—
315C2×C4—381no—
316C2×C4—1521no—
317C2×C4—1521no—
318C2×C4—1521no—
319C2×C4D4×D1911yescharacteristic
320C2×C4C23×D1911yescharacteristic
321C8—21no—
322C8—21no—
323C8—381no—
324C8—381no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—761no—
332C22—761no—
333C22—761no—
334C22—761no—
335C22—761no—
336C22—761no—
337C22C2×D4×D1911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—381no—
343C4—381no—
344C4—381no—
345C4—381no—
346C4—761no—
347C4—761no—
348C4#1059743011yescharacteristic
349C4#1059743611yescharacteristic
350C2—41no—
351C2—81no—
352C2—1521no—
353C2—1521no—
354C2#1192712111yescharacteristic
355C2#1192734811yescharacteristic
356C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#468C2
socleC22×C19C22×D4
hypercenter#468D19
hypocenterC19#3257
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11927167C2semidirect
2. #11927147C2semidirect
3. #11926849C2semidirect
4. #11926847C2semidirect
5. #11926832C2semidirect
6. #11926823C2semidirect
7. #11926797C2semidirect
8. #11926778C2semidirect
9. #11926775C2semidirect
10. #11926762C2semidirect
11. #11926761C2semidirect
12. #11926742C2semidirect
13. #11926738C2semidirect
14. #11926572C2semidirect
15. C19×#468C2semidirect
179. #468D19semidirect
237. C19#3257semidirect

Maximal subgroups

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

subgroupindex
#119271672
#119271472
#119268492
#119268472
#119268322
#119268232
#119267972
#119267782
#119267752
#119267622
#119267612
#119267422
#119267382
#119265722
C19×#4682
#325719