Finite Group Databasebeta

← #14569499

Subgroups — #14569499

Order 2432.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597331C211yesmaximal, characteristic
2C2×C4×Dic38C211yesmaximal, characteristic, complemented
3#11926480C211yesmaximal, characteristic, complemented
4#11926479C211yesmaximal, characteristic, complemented
5#11926465C211yesmaximal, characteristic, complemented
6#11926464C211yesmaximal, characteristic, complemented
7#11926460C211yesmaximal, characteristic
8#11926459C211yesmaximal, characteristic
9#11926457C211yesmaximal, characteristic, complemented
10#11926456C211yesmaximal, characteristic, complemented
11#11926436C211yesmaximal, characteristic, complemented
12#11926435C211yesmaximal, characteristic, complemented
13#11926432C211yesmaximal, characteristic, complemented
14#11926411C211yesmaximal, characteristic, complemented
15C19×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D19C2211yescharacteristic
17C22×Dic38C2211yescharacteristic
18C22×Dic38C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19C2211yescharacteristic
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C42×C19C2211yescharacteristic
24C2×C22⋊Dic19C2211yescharacteristic
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×(C2×D19)⋊C4C2211yescharacteristic
33C2×C4⋊Dic19C2211yescharacteristic
34C2×C4⋊Dic19C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×Dic19⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39C2×C4×Dic19C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41#10597331—24no—
42C4×Dic38—24no—
43C19×#95C2211yescharacteristic
44C19×#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C24×C19C2311yescharacteristic
54C23×D19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C2×C22⋊D19—22no—
62C2×C22⋊D19—41no—
63C2×C22⋊D19—41no—
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C22×Dic19C2311yescharacteristic
69C22×Dic19C2311yescharacteristic
70C22×Dic19C2311yescharacteristic
71C2×Dic38—22no—
72C2×Dic38—22no—
73C2×Dic38—22no—
74C2×Dic38—22no—
75C2×Dic38—41no—
76C2×Dic38—41no—
77C4⋊C4×C19—41no—
78C22⋊C4×C19—22no—
79C22⋊C4×C19—22no—
80C22⋊C4×C19—41no—
81C42×C19—22no—
82C22⋊Dic19—22no—
83C22⋊Dic19—22no—
84C22⋊Dic19—41no—
85(C2×D19)⋊C4—22no—
86(C2×D19)⋊C4—22no—
87(C2×D19)⋊C4—22no—
88(C2×D19)⋊C4—22no—
89(C2×D19)⋊C4—41no—
90(C2×D19)⋊C4—41no—
91C4⋊Dic19—22no—
92C4⋊Dic19—41no—
93Dic19⋊C4—22no—
94Dic19⋊C4—22no—
95Dic19⋊C4—41no—
96Dic19⋊C4—41no—
97C4×Dic19—22no—
98C4×Dic19D414yes—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—21no—
106C23×C19C2411yescharacteristic
107C22×D19—21no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19—21no—
112C22×D19—21no—
113C22×D19—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×C19C2×D412yes—
131C2×C4×C19#4112yes—
132C22⋊D19—44no—
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—21no—
151C2×Dic19C2×D412yes—
152C2×Dic19C2×D412yes—
153C2×Dic19#4112yes—
154Dic38—28no—
155Dic38—44no—
156#2632—191nomaximal, Sylow
157C22×C19—41no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19C22×D411yescharacteristic
165C22×C19C2×#4111yescharacteristic
166C22×C19C2×#4111yescharacteristic
167C22×C19H(5,𝔽2)11yescharacteristic
168C22×C19H(5,𝔽2)11yescharacteristic
169C22×C192−1+411yescharacteristic
170C22×C192−1+411yescharacteristic
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19—41no—
184Dic19—22no—
185Dic19—22no—
186Dic19—22no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190Dic19—41no—
191C2×#124—191no—
192C2×C4×Q8—191no—
193#399—191no—
194#399—191no—
195#395—191no—
196#395—191no—
197#394—191no—
198#394—191no—
199#393—191no—
200#393—191no—
201#388—191no—
202#388—191no—
203#388—191no—
204#388D1911yescharacteristic, complemented
205#383—191no—
206C2×C19—81no—
207C2×C19#52511yescharacteristic
208C2×C19#53511yescharacteristic
209C2×C19#53611yescharacteristic
210C2×C19#54211yescharacteristic
211C2×C19#54211yescharacteristic
212C2×C19#54211yescharacteristic
213C2×C19#54211yescharacteristic
214D19—81no—
215C22×Q8—191no—
216C22×Q8—191no—
217C22×D4—191no—
218#124—384no—
219C4×Q8—384no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
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⋊C4—191no—
235C2×C22⋊C4—191no—
236C2×C22⋊C4C2×D1911yescharacteristic
237C2×C22⋊C4C2×D1911yescharacteristic
238C2×C22⋊C4C2×D1911yescharacteristic
239C2×C42—191no—
240C2×C42—191no—
241C2×C42C2×D1911yescharacteristic
242#95—191no—
243#95—191no—
244#95—191no—
245#95—191no—
246#95—191no—
247#95—191no—
248#95—191no—
249#95—191no—
250#95C2×D1911yescharacteristic
251#95C2×D1911yescharacteristic
252C19#263211yescharacteristic, complemented, Sylow
253C24—191no—
254C24C22×D1911yescharacteristic
255C2×Q8—382no—
256C2×Q8—382no—
257C2×Q8—382no—
258C2×Q8—382no—
259C2×Q8—761no—
260C2×Q8—761no—
261C2×D4—382no—
262C2×D4—761no—
263C2×D4—761no—
264C22×C4—191no—
265C22×C4—191no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—191no—
270C22×C4—191no—
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C22×C4C22×D1911yescharacteristic
274C22×C4C22×D1911yescharacteristic
275C22×C4C22×D1911yescharacteristic
276C22×C4C22×D1911yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—382no—
279C4⋊C4—382no—
280C4⋊C4—382no—
281C4⋊C4—761no—
282C4⋊C4—761no—
283C4⋊C4—761no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—382no—
288C22⋊C4—382no—
289C22⋊C4—382no—
290C22⋊C4—382no—
291C22⋊C4—382no—
292C22⋊C4—382no—
293C22⋊C4—761no—
294C22⋊C4—761no—
295C22⋊C4—761no—
296C42—22no—
297C42—194no—
298C42—382no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—381no—
307C23—381no—
308C23—381no—
309C23—381no—
310C23—381no—
311C23—381no—
312C23—381no—
313C23C23×D1911yescharacteristic
314Q8—388no—
315Q8—764no—
316D4—764no—
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—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—192no—
334C2×C4—192no—
335C2×C4—192no—
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—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4#6454112yes—
355C2×C4D4×D1912yes—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22C2×#6454111yescharacteristic
371C22C2×D4×D1911yescharacteristic
372C22#1059743011yescharacteristic
373C22#41×D1911yescharacteristic
374C22#1059743511yescharacteristic
375C22#1059743611yescharacteristic
376C22#1059743611yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—382no—
384C4—382no—
385C4—382no—
386C4—761no—
387C4—761no—
388C4—761no—
389C4—761no—
390C2—81no—
391C2—1521no—
392C2#1192705311yescharacteristic
393C2#1192711011yescharacteristic
394C2#1192711611yescharacteristic
395C2#1192715811yescharacteristic
396C2#1192715911yescharacteristic
397C2#1192716011yescharacteristic
398C2#1192716511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#388C2
prime radicalC22×C22⋊D19C22
hypercenter#388D19
hypocenterC19#2632
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic38C2semidirect
3. #11926480C2semidirect
4. #11926479C2semidirect
5. #11926465C2semidirect
6. #11926464C2semidirect
9. #11926457C2semidirect
10. #11926456C2semidirect
11. #11926436C2semidirect
12. #11926435C2semidirect
13. #11926432C2semidirect
14. #11926411C2semidirect
15. C19×#388C2semidirect
204. #388D19semidirect
252. C19#2632semidirect

Maximal subgroups

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

subgroupindex
C2×#105973312
C2×C4×Dic382
#119264802
#119264792
#119264652
#119264642
#119264602
#119264592
#119264572
#119264562
#119264362
#119264352
#119264322
#119264112
C19×#3882
#263219