Finite Group Databasebeta

← #14575643

Subgroups — #14575643

Order 2432.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927240C211yesmaximal, characteristic, complemented
2#11927215C211yesmaximal, characteristic, complemented
3#11926909C211yesmaximal, characteristic, complemented
4#11926869C211yesmaximal, characteristic, complemented
5#11926858C211yesmaximal, characteristic, complemented
6#11926852C211yesmaximal, characteristic, complemented
7#11926797C211yesmaximal, characteristic, complemented
8#11926780C211yesmaximal, characteristic, complemented
9#11926740C211yesmaximal, characteristic, complemented
10#11926691C211yesmaximal, characteristic, complemented
11#11926691C211yesmaximal, characteristic, complemented
12#11926646C211yesmaximal, characteristic, complemented
13#11926546C211yesmaximal, characteristic, complemented
14#11926541C211yesmaximal, characteristic, complemented
15C19×#435C211yesmaximal, characteristic, complemented
16C2×#64541C2211yescharacteristic
17C2×#64541C2211yescharacteristic
18C2×M16×C19C2211yescharacteristic
19C22×C8×C19C2211yescharacteristic
20C4×D4×C19C2211yescharacteristic
21#10597386—21no—
22#10597385—21no—
23#10597376C2211yescharacteristic
24#10597376C2211yescharacteristic
25#10597376C2211yescharacteristic
26#10597376C2211yescharacteristic
27#10597372C2211yescharacteristic
28C2×C4⋊Dic19C2211yescharacteristic
29C2×D152C2211yescharacteristic
30C2×D152C2211yescharacteristic
31C2×#64516C2211yescharacteristic
32#10597344—21no—
33#10597339—21no—
34#10597330—21no—
35#10597330—21no—
36#10597329—21no—
37(C22⋊D19)⋊C4—21no—
38#10597320C2211yescharacteristic
39C4×D76C2211yescharacteristic
40#10597316C2211yescharacteristic
41C4×Dic38C2211yescharacteristic
42C19×C4⋊C8C2211yescharacteristic
43C19×C22⋊C8C2211yescharacteristic
44C19×C22⋊C8C2211yescharacteristic
45C19×#97C2211yescharacteristic
46#10597278C2211yescharacteristic
47#10597278C2211yescharacteristic
48#10597278C2211yescharacteristic
49#10597278C2211yescharacteristic
50#10597278C2211yescharacteristic
51#10597278C2211yescharacteristic
52#10597278C2211yescharacteristic
53#10597275C2211yescharacteristic
54#10597275C2211yescharacteristic
55#10597274C2211yescharacteristic
56#10597273C2211yescharacteristic
57#10597273C2211yescharacteristic
58#10597273C2211yescharacteristic
59C2×D4×C19D411yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C2×C22⋊D19—21no—
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C22×Dic19—21no—
69#64541—22no—
70#64541—22no—
71#64541—41no—
72#64541—41no—
73C2×D76—21no—
74C2×D76—21no—
75C2×D76C2311yescharacteristic
76C2×D76C2311yescharacteristic
77C2×D76C2311yescharacteristic
78C2×C4×D19—21no—
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×Dic38C2311yescharacteristic
82M16×C19—41no—
83C2×C8×C19—41no—
84C2×C8×C19C2311yescharacteristic
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19D411yescharacteristic
89C22⋊C4×C19D411yescharacteristic
90C22⋊C4×C19D411yescharacteristic
91C42×C19C2311yescharacteristic
92C22⋊Dic19—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98C4⋊Dic19—21no—
99C4⋊Dic19C2311yescharacteristic
100C4⋊Dic19C2311yescharacteristic
101C4⋊Dic19C2311yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106C4×Dic19—21no—
107C4×Dic19—21no—
108D152—41no—
109D152—41no—
110#64516—22no—
111C23×C19C2×D411yescharacteristic
112C23×C19C2×D411yescharacteristic
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—21no—
116D4×C19—41no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19C2×D411yescharacteristic
122C2×C4×C19C2×D411yescharacteristic
123C2×C4×C19C2×D411yescharacteristic
124C2×C4×C19C2×D411yescharacteristic
125C2×C4×C19C2411yescharacteristic
126C22⋊D19—42no—
127C22⋊D19—42no—
128C22⋊D19—42no—
129C22⋊D19—81no—
130C22⋊D19—81no—
131C22⋊D19—81no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—81no—
138D76—21no—
139D76—21no—
140D76—21no—
141D76—21no—
142D76—21no—
143D76—21no—
144D76—42no—
145D76—81no—
146C4×D19—42no—
147C4×D19—42no—
148C4×D19—81no—
149Dic38—21no—
150Dic38#4112yes—
151C8×C19—21no—
152C8×C19—21no—
153C8×C19—21no—
154C8×C19—21no—
155#3309—191nomaximal, Sylow
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19C22×D411yescharacteristic
163C2×D19—41no—
164C2×D19—41no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19C2×#4111yescharacteristic
177C4×C19H(5,𝔽2)11yescharacteristic
178Dic19—22no—
179Dic19—41no—
180Dic19—41no—
181Dic19—41no—
182Dic19—41no—
183#553—191no—
184#550—191no—
185#490—191no—
186#482—191no—
187#480—191no—
188#479—191no—
189#469—191no—
190#466—191no—
191#459—191no—
192#449—191no—
193#449—191no—
194#440—191no—
195#435D1911yescharacteristic, complemented
196#417—191no—
197#416—191no—
198C2×C19—41no—
199C2×C19—41no—
200C2×C19#54611yescharacteristic
201C2×C19#57511yescharacteristic
202C2×C19#57611yescharacteristic
203D19—81no—
204D19—81no—
205D19—81no—
206C2×#41—191no—
207C2×#41—191no—
208C2×SD16—191no—
209C2×D8—191no—
210C2×D8—191no—
211C2×M16C2×D1911yescharacteristic
212C22×C8C2×D1911yescharacteristic
213#127—191no—
214#127—381no—
215#126—381no—
216#125—191no—
217#123—381no—
218#121—191no—
219#121—191no—
220#121—191no—
221#121—191no—
222#121—381no—
223#121—381no—
224#121—381no—
225C4×Q8—191no—
226C4×D4—191no—
227C4×D4—381no—
228C4×D4—381no—
229C4×D4C2×D1911yescharacteristic
230#117—191no—
231C2×C4⋊C4—191no—
232#107—191no—
233#107—191no—
234#106—191no—
235C4⋊C8C2×D1911yescharacteristic
236#103—191no—
237#103—191no—
238#103—191no—
239#102—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245#102—191no—
246C22⋊C8C2×D1911yescharacteristic
247C22⋊C8C2×D1911yescharacteristic
248#97C2×D1911yescharacteristic
249C19#330911yescharacteristic, complemented, Sylow
250#41—382no—
251#41—382no—
252#41—761no—
253#41—761no—
254C2×Q8—191no—
255C2×D4—191no—
256C2×D4—191no—
257C2×D4—191no—
258C2×D4—381no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4—381no—
266C2×D4D7611yescharacteristic
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273SD16—382no—
274D8—761no—
275D8—761no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D1911yescharacteristic
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C2×C8C22×D1911yescharacteristic
282C4⋊C4—191no—
283C4⋊C4—191no—
284C4⋊C4—191no—
285C4⋊C4—191no—
286C4⋊C4—381no—
287C4⋊C4—381no—
288C4⋊C4—381no—
289C4⋊C4—381no—
290C4⋊C4D7611yescharacteristic
291C22⋊C4—381no—
292C22⋊C4—381no—
293C22⋊C4—381no—
294C22⋊C4—381no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4D7611yescharacteristic
298C22⋊C4D7611yescharacteristic
299C42—381no—
300C42—381no—
301C42C22×D1911yescharacteristic
302C23—381no—
303C23—381no—
304C23—381no—
305C23C2×D7611yescharacteristic
306C23C2×D7611yescharacteristic
307Q8—192no—
308Q8—381no—
309D4—41no—
310D4—381no—
311D4—381no—
312D4—381no—
313D4—381no—
314D4—381no—
315D4—381no—
316D4—762no—
317D4—762no—
318D4—762no—
319D4—762no—
320D4—1521no—
321D4—1521no—
322D4—1521no—
323D4—1521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—762no—
334C2×C4—762no—
335C2×C4—1521no—
336C2×C4—1521no—
337C2×C4C2×D7611yescharacteristic
338C2×C4C2×D7611yescharacteristic
339C2×C4C2×D7611yescharacteristic
340C2×C4C2×D7611yescharacteristic
341C2×C4C23×D1911yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—761no—
353C22—761no—
354C22—761no—
355C22—761no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—761no—
361C22C22×D7611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—382no—
367C4—761no—
368C4—761no—
369C4—761no—
370C4—761no—
371C4#1059743011yescharacteristic
372C4#41×D1911yescharacteristic
373C2—41no—
374C2—41no—
375C2—1521no—
376C2—1521no—
377C2—1521no—
378C2#1192718911yescharacteristic
379C2#1192734411yescharacteristic
380C2#1192734911yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#435C2
socleC22×C19C22×D4
hypercenter#435D19
hypocenterC19#3309
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #11927240C2semidirect
2. #11927215C2semidirect
3. #11926909C2semidirect
4. #11926869C2semidirect
5. #11926858C2semidirect
6. #11926852C2semidirect
7. #11926797C2semidirect
8. #11926780C2semidirect
9. #11926740C2semidirect
10. #11926691C2semidirect
11. #11926691C2semidirect
12. #11926646C2semidirect
13. #11926546C2semidirect
14. #11926541C2semidirect
15. C19×#435C2semidirect
195. #435D19semidirect
249. C19#3309semidirect

Maximal subgroups

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

subgroupindex
#119272402
#119272152
#119269092
#119268692
#119268582
#119268522
#119267972
#119267802
#119267402
#119266912
#119266462
#119265462
#119265412
C19×#4352
#330919