Finite Group Databasebeta

← #14575635

Subgroups — #14575635

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#11927215C211yesmaximal, characteristic, complemented
2#11926910C211yesmaximal, characteristic, complemented
3#11926868C211yesmaximal, characteristic, complemented
4#11926857C211yesmaximal, characteristic, complemented
5#11926848C211yesmaximal, characteristic, complemented
6#11926795C211yesmaximal, characteristic, complemented
7#11926778C211yesmaximal, characteristic, complemented
8#11926739C211yesmaximal, characteristic, complemented
9#11926687C211yesmaximal, characteristic, complemented
10#11926687C211yesmaximal, characteristic, complemented
11#11926644C211yesmaximal, characteristic, complemented
12#11926616C211yesmaximal, characteristic, complemented
13#11926543C211yesmaximal, characteristic, complemented
14#11926538C211yesmaximal, characteristic, complemented
15C19×#553C211yesmaximal, characteristic, complemented
16C2×#64541C2211yescharacteristic
17C2×#64541C2211yescharacteristic
18C19×#126—21no—
19C19×#125C2211yescharacteristic
20C19×#123—21no—
21C19×#121—21no—
22C19×#121C2211yescharacteristic
23C19×#121C2211yescharacteristic
24C4×D4×C19—21no—
25C4×D4×C19C2211yescharacteristic
26C4×D4×C19C2211yescharacteristic
27C19×#117C2211yescharacteristic
28C2×C4⋊C4×C19C2211yescharacteristic
29#10597386—21no—
30C2×#64526C2211yescharacteristic
31C2×#64525C2211yescharacteristic
32C2×#64525C2211yescharacteristic
33#10597376C2211yescharacteristic
34#10597376C2211yescharacteristic
35C2×#64520C2211yescharacteristic
36C22×C19⋊C8C2211yescharacteristic
37#10597339—21no—
38#10597330—21no—
39#10597330—21no—
40#10597320C2211yescharacteristic
41C4×Dic38C2211yescharacteristic
42#10597289C2211yescharacteristic
43C22⋊(C19⋊C8)C2211yescharacteristic
44C22⋊(C19⋊C8)C2211yescharacteristic
45#10597267C2211yescharacteristic
46#10597267C2211yescharacteristic
47#10597267C2211yescharacteristic
48#10597266C2211yescharacteristic
49#10597266C2211yescharacteristic
50#10597266C2211yescharacteristic
51#10597266C2211yescharacteristic
52#10597266C2211yescharacteristic
53#10597266C2211yescharacteristic
54#10597265C2211yescharacteristic
55#10597264C2211yescharacteristic
56#10597264C2211yescharacteristic
57C4⋊(C19⋊C8)C2211yescharacteristic
58#10597260C2211yescharacteristic
59C2×D4×C19—21no—
60C2×D4×C19—21no—
61C2×D4×C19D411yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19C2311yescharacteristic
66C22×C4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71#64541—22no—
72#64541—22no—
73#64541—41no—
74#64541—41no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76C2311yescharacteristic
78C2×D76C2311yescharacteristic
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×Dic38C2311yescharacteristic
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19D411yescharacteristic
86C4⋊C4×C19C2311yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊C4×C19D411yescharacteristic
94C22⋊C4×C19D411yescharacteristic
95C42×C19—21no—
96C42×C19C2311yescharacteristic
97#64526—22no—
98#64525—41no—
99#64525—41no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102C4⋊Dic19C2311yescharacteristic
103Dic19⋊C4—21no—
104C4×Dic19—21no—
105#64520—41no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109C2×C19⋊C8C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C23×C19—21no—
112C23×C19C2×D411yescharacteristic
113C23×C19C2×D411yescharacteristic
114C22×D19—21no—
115C22×D19—21no—
116D4×C19—21no—
117D4×C19—21no—
118D4×C19—41no—
119D4×C19—42no—
120D4×C19—81no—
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—81no—
129C2×C4×C19—81no—
130C2×C4×C19C2×D411yescharacteristic
131C2×C4×C19C2×D411yescharacteristic
132C2×C4×C19C2×D411yescharacteristic
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—42no—
136C22⋊D19—42no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141D76—21no—
142D76—21no—
143D76—21no—
144D76—21no—
145D76—42no—
146D76—81no—
147C4×D19—42no—
148C4×D19—42no—
149Dic38—21no—
150Dic38#4112yes—
151C19⋊C8—21no—
152C19⋊C8—21no—
153C19⋊C8—21no—
154C19⋊C8—21no—
155#3309—191nomaximal, Sylow
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19C22×D411yescharacteristic
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×C19—41no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19C2×#4111yescharacteristic
180C4×C19H(5,𝔽2)11yescharacteristic
181Dic19—22no—
182Dic19—41no—
183#553D1911yescharacteristic, complemented
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#435—191no—
196#417—191no—
197#416—191no—
198C2×C19—41no—
199C2×C19—41no—
200C2×C19—81no—
201C2×C19#54611yescharacteristic
202C2×C19#57511yescharacteristic
203C2×C19#57611yescharacteristic
204D19—81no—
205D19—81no—
206C2×#41—191no—
207C2×#41—191no—
208C2×SD16—191no—
209C2×D8—191no—
210C2×D8—191no—
211C2×M16—191no—
212C22×C8—191no—
213#127—191no—
214#127—381no—
215#126—21no—
216#125C2×D1911yescharacteristic
217#123—21no—
218#121—21no—
219#121—191no—
220#121—191no—
221#121—381no—
222#121—381no—
223#121C2×D1911yescharacteristic
224#121C2×D1911yescharacteristic
225C4×Q8—191no—
226C4×D4—21no—
227C4×D4—381no—
228C4×D4C2×D1911yescharacteristic
229C4×D4C2×D1911yescharacteristic
230#117C2×D1911yescharacteristic
231C2×C4⋊C4C2×D1911yescharacteristic
232#107—191no—
233#107—191no—
234#106—191no—
235C4⋊C8—191no—
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⋊C8—191no—
247C22⋊C8—191no—
248#97—191no—
249C19#330911yescharacteristic, complemented, Sylow
250#41—382no—
251#41—382no—
252#41—761no—
253#41—761no—
254C2×Q8—191no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—191no—
258C2×D4—191no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4C22⋊D1911yescharacteristic
266C2×D4C22×D1911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273SD16—382no—
274D8—761no—
275D8—761no—
276M16—761no—
277C2×C8—191no—
278C2×C8—191no—
279C2×C8—191no—
280C2×C8—191no—
281C2×C8—761no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—191no—
286C4⋊C4—381no—
287C4⋊C4C22⋊D1911yescharacteristic
288C4⋊C4C22×D1911yescharacteristic
289C4⋊C4C22×D1911yescharacteristic
290C4⋊C4C22×D1911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4C22⋊D1911yescharacteristic
298C22⋊C4C22⋊D1911yescharacteristic
299C42—21no—
300C42—381no—
301C42C22×D1911yescharacteristic
302C23—21no—
303C23—381no—
304C23—381no—
305C23C2×C22⋊D1911yescharacteristic
306C23C2×C22⋊D1911yescharacteristic
307Q8—192no—
308Q8—381no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—381no—
315D4—381no—
316D4—381no—
317D4—381no—
318D4—762no—
319D4—762no—
320D4—762no—
321D4—1521no—
322D4—1521no—
323D4—1521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—762no—
336C2×C4—762no—
337C2×C4C2×C22⋊D1911yescharacteristic
338C2×C4C2×C22⋊D1911yescharacteristic
339C2×C4C2×C22⋊D1911yescharacteristic
340C2×C4C2×C22⋊D1911yescharacteristic
341C2×C4C23×D1911yescharacteristic
342C8—381no—
343C8—381no—
344C8—381no—
345C8—381no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—761no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—761no—
361C22C22×C22⋊D1911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—382no—
370C4—761no—
371C4#41×D1911yescharacteristic
372C4#1059743511yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—1521no—
377C2—1521no—
378C2#1192718211yescharacteristic
379C2#1192734211yescharacteristic
380C2#1192734711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#553C2
socleC22×C19C22×D4
hypercenter#553D19
hypocenterC19#3309
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #11927215C2semidirect
2. #11926910C2semidirect
3. #11926868C2semidirect
4. #11926857C2semidirect
5. #11926848C2semidirect
6. #11926795C2semidirect
7. #11926778C2semidirect
8. #11926739C2semidirect
9. #11926687C2semidirect
10. #11926687C2semidirect
11. #11926644C2semidirect
12. #11926616C2semidirect
13. #11926543C2semidirect
14. #11926538C2semidirect
15. C19×#553C2semidirect
183. #553D19semidirect
249. C19#3309semidirect

Maximal subgroups

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

subgroupindex
#119272152
#119269102
#119268682
#119268572
#119268482
#119267952
#119267782
#119267392
#119266872
#119266442
#119266162
#119265432
#119265382
C19×#5532
#330919