Finite Group Databasebeta

← #14566635

Subgroups — #14566635

Order 2432.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597324C211yesmaximal, characteristic
2C2×#10597333C211yesmaximal, characteristic, complemented
3C22×Dic19⋊C4C211yesmaximal, characteristic
4#11926448C211yesmaximal, characteristic, complemented
5#11926440C211yesmaximal, characteristic, complemented
6#11926439C211yesmaximal, characteristic, complemented
7#11926439C211yesmaximal, characteristic, complemented
8#11926429C211yesmaximal, characteristic, complemented
9#11926426C211yesmaximal, characteristic, complemented
10#11926416C211yesmaximal, characteristic
11#11926395C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic19C211yesmaximal, characteristic
13C22⋊C4×Dic19C211yesmaximal, characteristic
14C4×C22⋊Dic19C211yesmaximal, characteristic
15C19×#385C211yesmaximal, characteristic
16C23×C4×C19C2211yescharacteristic
17C23×Dic19C2211yescharacteristic
18C23×Dic19C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19C2211yescharacteristic
24C2×C22⋊Dic19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
26C2×C4⋊Dic19C2211yescharacteristic
27C2×Dic19⋊C4—24no—
28C2×Dic19⋊C4C2211yescharacteristic
29C2×Dic19⋊C4C2211yescharacteristic
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2211yescharacteristic
32C2×Dic19⋊C4C2211yescharacteristic
33C2×Dic19⋊C4C2211yescharacteristic
34C2×Dic19⋊C4C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×C4×Dic19C2211yescharacteristic
37C2×C4×Dic19C2211yescharacteristic
38C2×C4×Dic19C2211yescharacteristic
39C2×C4×Dic19C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41C2×C4×Dic19C2211yescharacteristic
42#10597333—24no—
43#10597324C418yescomplemented
44C19×#95C2211yescharacteristic
45C19×#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C19⋊#95C2211yescharacteristic
54C24×C19C2311yescharacteristic
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—41no—
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C22×Dic19—22no—
65C22×Dic19—22no—
66C22×Dic19—22no—
67C22×Dic19—22no—
68C22×Dic19—41no—
69C22×Dic19C2×C414yes—
70C22×Dic19C2311yescharacteristic
71C22×Dic19C2311yescharacteristic
72C22×Dic19C2311yescharacteristic
73C22×Dic19C2311yescharacteristic
74C22×Dic19C2311yescharacteristic
75C22×Dic19C2311yescharacteristic
76C22×Dic19C2311yescharacteristic
77C22×Dic19C2311yescharacteristic
78C2×Dic38—22no—
79C2×Dic38—22no—
80C2×Dic38C2×C414yescomplemented
81C4⋊C4×C19—22no—
82C4⋊C4×C19—41no—
83C22⋊C4×C19—22no—
84C22⋊C4×C19C2×C414yes—
85C22⋊Dic19C2×C414yes—
86C22⋊Dic19Q814yescomplemented
87C4⋊Dic19C2×C414yescomplemented
88Dic19⋊C4—22no—
89Dic19⋊C4—22no—
90Dic19⋊C4—22no—
91Dic19⋊C4—22no—
92Dic19⋊C4—41no—
93Dic19⋊C4C2×C414yescomplemented
94Dic19⋊C4C2×C414yescomplemented
95Dic19⋊C4D414yes—
96C4×Dic19—22no—
97C4×Dic19—22no—
98C4×Dic19—22no—
99C4×Dic19—22no—
100C4×Dic19—41no—
101C4×Dic19—41no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—21no—
106C23×C19C22×C412yes—
107C23×C19C2×Q812yes—
108C23×C19#4112yes—
109C23×C19C2411yescharacteristic
110C2×C4×C19—21no—
111C2×C4×C19—21no—
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—44no—
126C2×C4×C19C22×C412yes—
127C2×C4×C19C22×C412yes—
128C2×C4×C19C2×D412yes—
129C2×Dic19—21no—
130C2×Dic19—21no—
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—28no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—44no—
146C2×Dic19C22×C412yes—
147C2×Dic19C22×C412yes—
148C2×Dic19C22×C412yes—
149C2×Dic19C22×C412yes—
150C2×Dic19C2×D412yes—
151C2×Dic19C2×D412yes—
152C2×Dic19C2×Q812yes—
153C2×Dic19C2×Q812yes—
154C2×Dic19#4112yes—
155Dic38—28no—
156#2360—191nomaximal, Sylow
157C22×C19—22no—
158C22×C19—22no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19C4×Q814yescomplemented
164C22×C19C23×C411yescharacteristic
165C22×C19C22×D411yescharacteristic
166C22×C19C22×Q811yescharacteristic
167C22×C19C2×#4111yescharacteristic
168C22×C19C2×#4111yescharacteristic
169C22×C19H(5,𝔽2)11yescharacteristic
170C22×C192−1+411yescharacteristic
171C4×C19—22no—
172C4×C19—22no—
173C4×C19—22no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177Dic19—22no—
178Dic19—22no—
179Dic19—22no—
180Dic19—22no—
181Dic19—22no—
182Dic19—22no—
183Dic19—41no—
184Dic19C4×D414yes—
185C2×C22⋊Q8—191no—
186C2×C4×Q8—191no—
187C22×C4⋊C4—191no—
188#391—191no—
189#389—191no—
190#389—191no—
191#389—191no—
192#387—191no—
193#387—191no—
194#385—191no—
195#385D1911yescharacteristic
196C4×C4⋊C4—191no—
197C4×C22⋊C4—191no—
198C4×C22⋊C4—191no—
199C4×C22⋊C4—191no—
200C2×C19—24no—
201C2×C19C2×C4×D411yescharacteristic
202C2×C19C2×C4×Q811yescharacteristic
203C2×C19#52011yescharacteristic
204C2×C19#54611yescharacteristic
205C2×C19D4×Q811yescharacteristic
206C2×C19#55211yescharacteristic
207C2×C19#55411yescharacteristic
208C22×Q8—191no—
209C23×C4—191no—
210C23×C4—191no—
211C23×C4C2×D1911yescharacteristic
212C22⋊Q8—198no—
213C4×Q8—384no—
214C2×C4⋊C4—191no—
215C2×C4⋊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—384no—
224C2×C4⋊C4C2×D1911yescharacteristic
225C2×C4⋊C4C2×D1911yescharacteristic
226C2×C22⋊C4—191no—
227C2×C22⋊C4—191no—
228C2×C22⋊C4C2×D1911yescharacteristic
229C2×C22⋊C4C2×D1911yescharacteristic
230C2×C42—191no—
231C2×C42—191no—
232C2×C42—191no—
233C2×C42—191no—
234C2×C42—191no—
235C2×C42—191no—
236#95—191no—
237#95—191no—
238#95—191no—
239#95—191no—
240#95—191no—
241#95—191no—
242#95—191no—
243#95—191no—
244#95C2×D1911yescharacteristic
245#95C2×D1911yescharacteristic
246C19#236011yescharacteristic, complemented, Sylow
247C24C22×D1911yescharacteristic
248C2×Q8—194no—
249C2×Q8—382no—
250C2×Q8—382no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—191no—
255C22×C4—194no—
256C22×C4—191no—
257C22×C4—191no—
258C22×C4—191no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—191no—
262C22×C4—191no—
263C22×C4—382no—
264C22×C4—382no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—761no—
268C22×C4C22×D1911yescharacteristic
269C22×C4C22×D1911yescharacteristic
270C22×C4C22×D1911yescharacteristic
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C22×C4C22×D1911yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—194no—
277C4⋊C4—194no—
278C4⋊C4—194no—
279C4⋊C4—194no—
280C4⋊C4—382no—
281C4⋊C4—382no—
282C4⋊C4—382no—
283C4⋊C4—382no—
284C4⋊C4—761no—
285C22⋊C4—22no—
286C22⋊C4—194no—
287C22⋊C4—194no—
288C22⋊C4C4×D1914yes—
289C42—382no—
290C42—382no—
291C42—382no—
292C42—382no—
293C42—761no—
294C42—761no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×C4×D1912yes—
300C23#6454312yes—
301C23Q8×D1912yes—
302C23C23×D1911yescharacteristic
303Q8—388no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
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—44no—
320C2×C4—192no—
321C2×C4—192no—
322C2×C4—192no—
323C2×C4—192no—
324C2×C4—192no—
325C2×C4—192no—
326C2×C4—192no—
327C2×C4—192no—
328C2×C4—192no—
329C2×C4—388no—
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—764no—
346C2×C4C2×C4×D1912yes—
347C2×C4C2×C4×D1912yes—
348C2×C4D4×D1912yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22#1059733314yescomplemented
356C22C22×C4×D1911yescharacteristic
357C22C2×D4×D1911yescharacteristic
358C22C2×#6454311yescharacteristic
359C22#1059743011yescharacteristic
360C22C2×Q8×D1911yescharacteristic
361C22#41×D1911yescharacteristic
362C22#1059743611yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—194no—
370C4—382no—
371C4—382no—
372C4—382no—
373C4—382no—
374C4—382no—
375C4—382no—
376C4—761no—
377C2—24no—
378C2C4×D4×D1911yescharacteristic
379C2C2×#1059733311yescharacteristic
380C2#1192702311yescharacteristic
381C2#1192718111yescharacteristic
382C2#1192720711yescharacteristic
383C2#1192723111yescharacteristic
384C2#1192724811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC19×#385C2
socle, cosocleC23×C19C24
prime radicalC24×C19C23
hypercenter#385D19
hypocenterC19#2360
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#10597333C2semidirect
4. #11926448C2semidirect
5. #11926440C2semidirect
6. #11926439C2semidirect
7. #11926439C2semidirect
8. #11926429C2semidirect
9. #11926426C2semidirect
11. #11926395C2semidirect
43. #10597324C4semidirect
80. C2×Dic38C2×C4semidirect
86. C22⋊Dic19Q8semidirect
87. C4⋊Dic19C2×C4semidirect
93. Dic19⋊C4C2×C4semidirect
94. Dic19⋊C4C2×C4semidirect
163. C22×C19C4×Q8semidirect
246. C19#2360semidirect
355. C22#10597333semidirect

Maximal subgroups

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

subgroupindex
C2×#105973242
C2×#105973332
C22×Dic19⋊C42
#119264482
#119264402
#119264392
#119264292
#119264262
#119264162
#119263952
C22⋊C4×Dic192
C4×C22⋊Dic192
C19×#3852
#236019