Finite Group Databasebeta

← #14566767

Subgroups — #14566767

Order 2432.

552 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597340C211yesmaximal, characteristic
2#11926445C211yesmaximal, characteristic
3#11926436C211yesmaximal, characteristic, complemented
4#11926436C211yesmaximal, characteristic, complemented
5#11926433C211yesmaximal, characteristic, complemented
6#11926433C211yesmaximal, characteristic, complemented
7#11926425C211yesmaximal, characteristic, complemented
8#11926422C211yesmaximal, characteristic
9C4⋊C4×Dic19C211yesmaximal, characteristic, complemented
10#11926395C211yesmaximal, characteristic, complemented
11C4×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
12C4×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
13#11926391C211yesmaximal, characteristic, complemented
14#11926391C211yesmaximal, characteristic, complemented
15C19×#387C211yesmaximal, characteristic, complemented
16C22×D76C2211yescharacteristic
17C22×C4×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C42×C19C2211yescharacteristic
22C2×(C2×D19)⋊C4C2211yescharacteristic
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×C4⋊Dic19C2211yescharacteristic
33C2×Dic19⋊C4C2211yescharacteristic
34C2×Dic19⋊C4C2211yescharacteristic
35C2×C4×Dic19C2211yescharacteristic
36C2×C4×Dic19C2211yescharacteristic
37C2×C4×Dic19C2211yescharacteristic
38C2×C4×Dic19C2211yescharacteristic
39C2×C4×Dic19C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41#10597340C418yescomplemented
42C19×#95C2211yescharacteristic
43C19×#95C2211yescharacteristic
44C19×#95C2211yescharacteristic
45C19×#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C23×D19C2311yescharacteristic
53C23×D19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C2×D76—41no—
68C2×D76—41no—
69C2×D76C2×C414yes—
70C2×C4×D19—22no—
71C2×C4×D19—22no—
72C2×C4×D19—41no—
73C2×C4×D19—41no—
74C2×C4×D19—41no—
75C2×C4×D19C2×C414yescomplemented
76C4⋊C4×C19—41no—
77C4⋊C4×C19C2×C414yescomplemented
78C42×C19—41no—
79(C2×D19)⋊C4—22no—
80(C2×D19)⋊C4—22no—
81(C2×D19)⋊C4—22no—
82(C2×D19)⋊C4—22no—
83(C2×D19)⋊C4—22no—
84(C2×D19)⋊C4—22no—
85(C2×D19)⋊C4—41no—
86(C2×D19)⋊C4C2×C414yes—
87(C2×D19)⋊C4C2×C414yes—
88(C2×D19)⋊C4C2×C414yescomplemented
89C4⋊Dic19—22no—
90Dic19⋊C4—22no—
91Dic19⋊C4C2×C414yescomplemented
92C4×Dic19—22no—
93C4×Dic19—22no—
94C4×Dic19—41no—
95C4×Dic19—41no—
96C4×Dic19—41no—
97C4×Dic19—41no—
98C23×C19C2411yescharacteristic
99C22×D19—21no—
100C22×D19—21no—
101C22×D19—21no—
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19—21no—
106C22×D19—21no—
107C22×D19—21no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19C22×C412yes—
112C22×D19C22×C412yes—
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—21no—
130C2×C4×C19C22×C412yes—
131C2×C4×C19C22×C412yes—
132C2×C4×C19C22×C412yes—
133C2×C4×C19#4112yes—
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×Dic19C22×C412yes—
148C2×Dic19C22×C412yes—
149C2×Dic19#4112yes—
150C2×Dic19#4112yes—
151C2×Dic19#4112yes—
152D76—44no—
153C4×D19—44no—
154C4×D19—44no—
155#2374—191nomaximal, Sylow
156C22×C19C23×C411yescharacteristic
157C22×C19C2×#4111yescharacteristic
158C22×C19C2×#4111yescharacteristic
159C22×C19C2×#4111yescharacteristic
160C22×C19C2×#4111yescharacteristic
161C22×C19H(5,𝔽2)11yescharacteristic
162C22×C19H(5,𝔽2)11yescharacteristic
163C2×D19—22no—
164C2×D19—22no—
165C2×D19—22no—
166C2×D19—22no—
167C2×D19—22no—
168C2×D19—22no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—22no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19—41no—
184Dic19—22no—
185Dic19—22no—
186Dic19—22no—
187Dic19—22no—
188Dic19—22no—
189Dic19—41no—
190C2×#123—191no—
191#390—191no—
192#388—191no—
193#388—191no—
194#388—191no—
195#388—191no—
196#387—191no—
197#387D1911yescharacteristic, complemented
198#386—191no—
199C4×C4⋊C4—191no—
200C4×C4⋊C4—191no—
201C4×C22⋊C4—191no—
202C4×C22⋊C4—191no—
203C4×C22⋊C4—191no—
204C4×C22⋊C4—191no—
205C2×C19C4×#4111yescharacteristic
206C2×C19C4×#4111yescharacteristic
207C2×C19#51811yescharacteristic
208C2×C19#55111yescharacteristic
209C2×C19#55311yescharacteristic
210C2×C19#55311yescharacteristic
211C2×C19#55911yescharacteristic
212D19—42no—
213D19—42no—
214C22×D4—191no—
215C23×C4—191no—
216C23×C4—191no—
217#123—198no—
218C2×C4⋊C4—191no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4C2×D1911yescharacteristic
222C2×C4⋊C4C2×D1911yescharacteristic
223C2×C22⋊C4—191no—
224C2×C22⋊C4—191no—
225C2×C22⋊C4—191no—
226C2×C22⋊C4—191no—
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×C42—191no—
234C2×C42—191no—
235C2×C42—191no—
236C2×C42—191no—
237C2×C42—191no—
238C2×C42—191no—
239C2×C42C2×D1911yescharacteristic
240#95—191no—
241#95—191no—
242#95—191no—
243#95—191no—
244#95—191no—
245#95—191no—
246#95C2×D1911yescharacteristic
247#95C2×D1911yescharacteristic
248#95C2×D1911yescharacteristic
249#95C2×D1911yescharacteristic
250C19#237411yescharacteristic, complemented, Sylow
251C24—191no—
252C24—191no—
253C2×D4—194no—
254C2×D4—761no—
255C2×D4—761no—
256C22×C4—191no—
257C22×C4—191no—
258C22×C4—191no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—194no—
262C22×C4—191no—
263C22×C4—382no—
264C22×C4—382no—
265C22×C4—761no—
266C22×C4—761no—
267C22×C4—761no—
268C22×C4C22×D1911yescharacteristic
269C22×C4C22×D1911yescharacteristic
270C22×C4C22×D1911yescharacteristic
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C22×C4C22×D1911yescharacteristic
274C22×C4C22×D1911yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—194no—
277C4⋊C4—382no—
278C4⋊C4—382no—
279C4⋊C4C4×D1914yescomplemented
280C22⋊C4—194no—
281C22⋊C4—194no—
282C22⋊C4—194no—
283C22⋊C4—382no—
284C22⋊C4—382no—
285C22⋊C4—382no—
286C22⋊C4—382no—
287C22⋊C4—382no—
288C22⋊C4—382no—
289C22⋊C4—761no—
290C42—41no—
291C42—382no—
292C42—382no—
293C42—761no—
294C42—761no—
295C42—761no—
296C42—761no—
297C23—192no—
298C23—192no—
299C23—381no—
300C23—381no—
301C23—381no—
302C23—381no—
303C23—381no—
304C23—381no—
305C23—381no—
306C23—381no—
307C23—381no—
308C23—381no—
309C23—381no—
310C23—381no—
311C23C23×D1911yescharacteristic
312D4—764no—
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—21no—
329C2×C4—21no—
330C2×C4—192no—
331C2×C4—192no—
332C2×C4—192no—
333C2×C4—192no—
334C2×C4—192no—
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—764no—
349C2×C4—764no—
350C2×C4C2×C4×D1912yes—
351C2×C4C2×C4×D1912yes—
352C2×C4C2×C4×D1912yes—
353C2×C4#6454512yes—
354C22—382no—
355C22—382no—
356C22—382no—
357C22—382no—
358C22—382no—
359C22—382no—
360C22—761no—
361C22—761no—
362C22—761no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22C22×C4×D1911yescharacteristic
369C22#1059743011yescharacteristic
370C22C2×#6454511yescharacteristic
371C22#41×D1911yescharacteristic
372C22#41×D1911yescharacteristic
373C22#41×D1911yescharacteristic
374C22#1059743511yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—382no—
383C4—382no—
384C4—382no—
385C4—382no—
386C4—382no—
387C4—761no—
388C2—762no—
389C2—762no—
390C2#1192701211yescharacteristic
391C2C4×#6454511yescharacteristic
392C2#1192701611yescharacteristic
393C2#1192722111yescharacteristic
394C2#1192724511yescharacteristic
395C2#1192724711yescharacteristic
396C2#1192727811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC19×#387C2
socle, cosocleC23×C19C24
prime radicalC22×D76C22
hypercenter#387D19
hypocenterC19#2374
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. #11926436C2semidirect
4. #11926436C2semidirect
5. #11926433C2semidirect
6. #11926433C2semidirect
7. #11926425C2semidirect
9. C4⋊C4×Dic19C2semidirect
10. #11926395C2semidirect
11. C4×(C2×D19)⋊C4C2semidirect
12. C4×(C2×D19)⋊C4C2semidirect
13. #11926391C2semidirect
14. #11926391C2semidirect
15. C19×#387C2semidirect
41. #10597340C4semidirect
75. C2×C4×D19C2×C4semidirect
77. C4⋊C4×C19C2×C4semidirect
88. (C2×D19)⋊C4C2×C4semidirect
91. Dic19⋊C4C2×C4semidirect
197. #387D19semidirect
250. C19#2374semidirect
279. C4⋊C4C4×D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973402
#119264452
#119264362
#119264332
#119264252
#119264222
C4⋊C4×Dic192
#119263952
C4×(C2×D19)⋊C42
#119263912
C19×#3872
#237419