Finite Group Databasebeta

← #14570849

Subgroups — #14570849

Order 2432.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11926480C211yesmaximal, characteristic, complemented
2#11926478C211yesmaximal, characteristic, complemented
3#11926474C211yesmaximal, characteristic, complemented
4#11926466C211yesmaximal, characteristic, complemented
5#11926466C211yesmaximal, characteristic, complemented
6#11926444C211yesmaximal, characteristic
7#11926430C211yesmaximal, characteristic, complemented
8#11926425C211yesmaximal, characteristic, complemented
9#11926421C211yesmaximal, characteristic
10#11926420C211yesmaximal, characteristic
11#11926419C211yesmaximal, characteristic, complemented
12#11926416C211yesmaximal, characteristic, complemented
13#11926403C211yesmaximal, characteristic, complemented
14#11926401C211yesmaximal, characteristic, complemented
15C19×#399C211yesmaximal, characteristic, complemented
16C22×C22⋊D19C2211yescharacteristic
17C23×Dic19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19C2211yescharacteristic
24C2×C22⋊C4×C19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
26C2×C22⋊Dic19C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×C4⋊Dic19C2211yescharacteristic
33C2×C4⋊Dic19C2211yescharacteristic
34C2×C4⋊Dic19C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×Dic19⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39C2×Dic19⋊C4C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41C19×#95C2211yescharacteristic
42C19⋊#95C2211yescharacteristic
43C19⋊#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C24×C19C2311yescharacteristic
52C23×D19C2311yescharacteristic
53C22×C4×C19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C2×C22⋊D19—41no—
60C2×C22⋊D19—41no—
61C2×C22⋊D19Q814yes—
62C22×Dic19—41no—
63C22×Dic19—41no—
64C22×Dic19—41no—
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C22×Dic19C2311yescharacteristic
69C22×Dic19C2311yescharacteristic
70C22×Dic19C2311yescharacteristic
71C22×Dic19C2311yescharacteristic
72C2×C4×D19—22no—
73C2×C4×D19—22no—
74C2×C4×D19—41no—
75C4⋊C4×C19—22no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C22⋊C4×C19—22no—
79C22⋊C4×C19—41no—
80C22⋊C4×C19—41no—
81C22⋊Dic19—22no—
82C22⋊Dic19—41no—
83(C2×D19)⋊C4—41no—
84(C2×D19)⋊C4—41no—
85(C2×D19)⋊C4—41no—
86(C2×D19)⋊C4—41no—
87(C2×D19)⋊C4—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91Dic19⋊C4—22no—
92Dic19⋊C4—41no—
93Dic19⋊C4—41no—
94Dic19⋊C4—41no—
95Dic19⋊C4—41no—
96C4×Dic19—41no—
97C23×C19—21no—
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19C2×Q812yes—
104C23×C19C2411yescharacteristic
105C22×D19—21no—
106C22×D19—21no—
107C22×D19—21no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19C2×Q812yes—
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—21no—
129C2×C4×C19#4112yes—
130C22⋊D19—44no—
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—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—44no—
151C2×Dic19C2×Q812yes—
152C2×Dic19#4112yes—
153C4×D19—44no—
154#2748—191nomaximal, Sylow
155C22×C19—22no—
156C22×C19—22no—
157C22×C19—22no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19C22×Q811yescharacteristic
163C22×C19C2×#4111yescharacteristic
164C22×C19C2×#4111yescharacteristic
165C22×C19H(5,𝔽2)11yescharacteristic
166C22×C19H(5,𝔽2)11yescharacteristic
167C22×C19H(5,𝔽2)11yescharacteristic
168C22×C19H(5,𝔽2)11yescharacteristic
169C2×D19—22no—
170C2×D19—22no—
171C2×D19—22no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C4×C19—22no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19—41no—
180C4×C19—41no—
181C4×C19—41no—
182Dic19—22no—
183Dic19—22no—
184Dic19—41no—
185Dic19—41no—
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189#399—191no—
190#399D1911yescharacteristic, complemented
191#398—191no—
192#398—191no—
193#396—191no—
194#396—191no—
195#390—191no—
196#387—191no—
197#387—191no—
198#386—191no—
199#386—191no—
200#385—191no—
201#385—191no—
202#380—191no—
203#380—191no—
204C2×C19—42no—
205C2×C19#54011yescharacteristic
206C2×C19#54011yescharacteristic
207C2×C19#54311yescharacteristic
208C2×C19#55111yescharacteristic
209C2×C19#55411yescharacteristic
210C2×C19#55411yescharacteristic
211C2×C19#56011yescharacteristic
212D19—42no—
213C22×D4—191no—
214C23×C4—191no—
215C23×C4—191no—
216C2×C4⋊C4—191no—
217C2×C4⋊C4—191no—
218C2×C4⋊C4—191no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4C2×D1911yescharacteristic
225C2×C4⋊C4C2×D1911yescharacteristic
226C2×C4⋊C4C2×D1911yescharacteristic
227C2×C22⋊C4—191no—
228C2×C22⋊C4—191no—
229C2×C22⋊C4—191no—
230C2×C22⋊C4—191no—
231C2×C22⋊C4—191no—
232C2×C22⋊C4—191no—
233C2×C22⋊C4—191no—
234C2×C22⋊C4C2×D1911yescharacteristic
235C2×C22⋊C4C2×D1911yescharacteristic
236C2×C22⋊C4C2×D1911yescharacteristic
237C2×C42—191no—
238#95—191no—
239#95—191no—
240#95—191no—
241#95—191no—
242#95—191no—
243#95—191no—
244#95—191no—
245#95—191no—
246#95—191no—
247#95C2×D1911yescharacteristic
248C19#274811yescharacteristic, complemented, Sylow
249C24—191no—
250C24C22×D1911yescharacteristic
251C2×D4—194no—
252C2×D4—761no—
253C2×D4—761no—
254C22×C4—191no—
255C22×C4—191no—
256C22×C4—191no—
257C22×C4—191no—
258C22×C4—191no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—382no—
262C22×C4—382no—
263C22×C4—761no—
264C22×C4—761no—
265C22×C4—761no—
266C22×C4—761no—
267C22×C4C22×D1911yescharacteristic
268C22×C4C22×D1911yescharacteristic
269C22×C4C22×D1911yescharacteristic
270C22×C4C22×D1911yescharacteristic
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—382no—
277C4⋊C4—761no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C4⋊C4—761no—
281C4⋊C4—761no—
282C4⋊C4—761no—
283C4⋊C4—761no—
284C22⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—382no—
288C22⋊C4—761no—
289C22⋊C4—761no—
290C22⋊C4—761no—
291C22⋊C4—761no—
292C22⋊C4—761no—
293C22⋊C4—761no—
294C42—761no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—192no—
302C23—381no—
303C23—381no—
304C23—381no—
305C23—381no—
306C23—381no—
307C23—381no—
308C23Q8×D1912yes—
309C23C23×D1911yescharacteristic
310D4—764no—
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—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—192no—
329C2×C4—192no—
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—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—381no—
349C2×C4—764no—
350C2×C4—764no—
351C2×C4#6454312yes—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—382no—
360C22—382no—
361C22—382no—
362C22—761no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22C2×#6454311yescharacteristic
367C22#1059743011yescharacteristic
368C22#1059743011yescharacteristic
369C22C2×Q8×D1911yescharacteristic
370C22#41×D1911yescharacteristic
371C22#1059743511yescharacteristic
372C22#1059743511yescharacteristic
373C4—22no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—382no—
380C4—382no—
381C4—761no—
382C4—761no—
383C4—761no—
384C4—761no—
385C4—761no—
386C2—42no—
387C2—762no—
388C2#1192714611yescharacteristic
389C2#1192714811yescharacteristic
390C2#1192716911yescharacteristic
391C2#1192721711yescharacteristic
392C2#1192724811yescharacteristic
393C2#1192725211yescharacteristic
394C2#1192728411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#399C2
prime radicalC22×C22⋊D19C22
hypercenter#399D19
hypocenterC19#2748
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #11926480C2semidirect
2. #11926478C2semidirect
3. #11926474C2semidirect
4. #11926466C2semidirect
5. #11926466C2semidirect
7. #11926430C2semidirect
8. #11926425C2semidirect
11. #11926419C2semidirect
12. #11926416C2semidirect
13. #11926403C2semidirect
14. #11926401C2semidirect
15. C19×#399C2semidirect
190. #399D19semidirect
248. C19#2748semidirect

Maximal subgroups

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

subgroupindex
#119264802
#119264782
#119264742
#119264662
#119264442
#119264302
#119264252
#119264212
#119264202
#119264192
#119264162
#119264032
#119264012
C19×#3992
#274819