Finite Group Databasebeta

← #14566663

Subgroups — #14566663

Order 2432.

576 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597342C211yesmaximal, characteristic
2C2×C4×Dic38C211yesmaximal, characteristic, complemented
3C2×#10597318C211yesmaximal, characteristic
4#11926448C211yesmaximal, characteristic, complemented
5#11926439C211yesmaximal, characteristic, complemented
6#11926436C211yesmaximal, characteristic
7#11926435C211yesmaximal, characteristic
8#11926435C211yesmaximal, characteristic
9#11926434C211yesmaximal, characteristic
10#11926430C211yesmaximal, characteristic, complemented
11#11926428C211yesmaximal, characteristic, complemented
12C4×Dic19⋊C4C211yesmaximal, characteristic, complemented
13#11926395C211yesmaximal, characteristic, complemented
14#11926391C211yesmaximal, characteristic
15C4×C4⋊C4×C19C211yesmaximal, characteristic, complemented
16C22×C4×D19C2211yescharacteristic
17C22×Dic38C2211yescharacteristic
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C42×C19C2211yescharacteristic
21C2×C42×C19C2211yescharacteristic
22C2×C42×C19C2211yescharacteristic
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×C4⋊Dic19C2211yescharacteristic
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
41#10597342C418yescomplemented
42#10597318—24no—
43C4×Dic38—24no—
44C19×#95C2211yescharacteristic
45C19×#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C19⋊#95C2211yescharacteristic
54C23×D19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C22×Dic19C2311yescharacteristic
69C2×C4×D19—22no—
70C2×C4×D19—22no—
71C2×C4×D19C2×C414yes—
72C2×Dic38—22no—
73C2×Dic38—22no—
74C2×Dic38C2×C414yes—
75C4⋊C4×C19—22no—
76C4⋊C4×C19C2×C414yes—
77C42×C19—22no—
78C42×C19—22no—
79C42×C19—22no—
80(C2×D19)⋊C4—22no—
81(C2×D19)⋊C4—22no—
82(C2×D19)⋊C4—22no—
83(C2×D19)⋊C4—22no—
84(C2×D19)⋊C4C2×C414yes—
85(C2×D19)⋊C4C2×C414yes—
86C4⋊Dic19—22no—
87Dic19⋊C4—22no—
88Dic19⋊C4—22no—
89Dic19⋊C4—22no—
90Dic19⋊C4C2×C414yes—
91Dic19⋊C4C2×C414yes—
92Dic19⋊C4D414yes—
93C4×Dic19—22no—
94C4×Dic19—22no—
95C4×Dic19—22no—
96C4×Dic19—22no—
97C4×Dic19—22no—
98C23×C19C2411yescharacteristic
99C22×D19—21no—
100C22×D19—21no—
101C22×D19—21no—
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19C22×C412yes—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
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×C19C22×C412yes—
122C2×C4×C19C22×C412yes—
123C2×C4×C19C22×C412yes—
124C2×C4×C19C2×D412yes—
125C2×C4×C19#4112yes—
126C2×C4×C19#4112yes—
127C2×Dic19—21no—
128C2×Dic19—21no—
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—21no—
142C2×Dic19C22×C412yes—
143C2×Dic19C22×C412yes—
144C2×Dic19C22×C412yes—
145C2×Dic19C2×D412yes—
146C2×Dic19C2×D412yes—
147C2×Dic19#4112yes—
148C4×D19—28no—
149Dic38—28no—
150#2362—191nomaximal, Sylow
151C22×C19C23×C411yescharacteristic
152C22×C19C22×D411yescharacteristic
153C22×C19C2×#4111yescharacteristic
154C22×C19C2×#4111yescharacteristic
155C22×C19C2×#4111yescharacteristic
156C22×C192−1+411yescharacteristic
157C22×C192−1+411yescharacteristic
158C2×D19—22no—
159C2×D19—22no—
160C2×D19—22no—
161C2×D19—41no—
162C2×D19—41no—
163C2×D19—41no—
164C2×D19—41no—
165C4×C19—22no—
166C4×C19—22no—
167C4×C19—22no—
168C4×C19—22no—
169C4×C19—22no—
170C4×C19—22no—
171C4×C19—41no—
172Dic19—22no—
173Dic19—22no—
174Dic19—22no—
175Dic19—41no—
176Dic19—41no—
177Dic19—41no—
178Dic19C4×D414yes—
179C2×C22⋊Q8—191no—
180C2×C4×Q8—191no—
181C2×#117—191no—
182#391—191no—
183#389—191no—
184#388—191no—
185#388—191no—
186#388—191no—
187#388—191no—
188#387—191no—
189#387—191no—
190C4×C4⋊C4—191no—
191C4×C4⋊C4—191no—
192C4×C4⋊C4D1911yescharacteristic, complemented
193C4×C22⋊C4—191no—
194C2×C19C2×C4×D411yescharacteristic
195C2×C19C4×#4111yescharacteristic
196C2×C19#51911yescharacteristic
197C2×C19#54711yescharacteristic
198C2×C19#54811yescharacteristic
199C2×C19#55211yescharacteristic
200C2×C19#55611yescharacteristic
201D19—42no—
202C22×Q8—191no—
203C23×C4—191no—
204C22⋊Q8—198no—
205C4×Q8—384no—
206#117—384no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4—191no—
209C2×C4⋊C4—191no—
210C2×C4⋊C4—191no—
211C2×C4⋊C4—191no—
212C2×C4⋊C4—191no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4C2×D1911yescharacteristic
215C2×C4⋊C4C2×D1911yescharacteristic
216C2×C22⋊C4—191no—
217C2×C22⋊C4—191no—
218C2×C22⋊C4—191no—
219C2×C22⋊C4—191no—
220C2×C22⋊C4—191no—
221C2×C22⋊C4—191no—
222C2×C42—191no—
223C2×C42—191no—
224C2×C42—191no—
225C2×C42—191no—
226C2×C42—191no—
227C2×C42C2×D1911yescharacteristic
228C2×C42C2×D1911yescharacteristic
229C2×C42C2×D1911yescharacteristic
230#95—191no—
231#95—191no—
232#95—191no—
233#95—191no—
234#95—191no—
235#95—191no—
236#95—191no—
237#95—191no—
238#95C2×D1911yescharacteristic
239#95C2×D1911yescharacteristic
240C19#236211yescharacteristic, complemented, Sylow
241C24—191no—
242C2×Q8—194no—
243C2×Q8—382no—
244C2×Q8—382no—
245C22×C4—191no—
246C22×C4—191no—
247C22×C4—191no—
248C22×C4—191no—
249C22×C4—194no—
250C22×C4—191no—
251C22×C4—191no—
252C22×C4—191no—
253C22×C4—382no—
254C22×C4—382no—
255C22×C4C22×D1911yescharacteristic
256C22×C4C22×D1911yescharacteristic
257C22×C4C22×D1911yescharacteristic
258C22×C4C22×D1911yescharacteristic
259C22×C4C22×D1911yescharacteristic
260C22×C4C22×D1911yescharacteristic
261C22×C4C22×D1911yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—194no—
264C4⋊C4—194no—
265C4⋊C4—194no—
266C4⋊C4—382no—
267C4⋊C4—382no—
268C4⋊C4—382no—
269C4⋊C4—382no—
270C4⋊C4C4×D1914yes—
271C22⋊C4—194no—
272C22⋊C4—194no—
273C22⋊C4—382no—
274C22⋊C4—382no—
275C22⋊C4—382no—
276C22⋊C4—382no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—382no—
281C42—382no—
282C42—382no—
283C42—382no—
284C42—382no—
285C23—192no—
286C23—381no—
287C23—381no—
288C23—381no—
289C23—381no—
290C23—381no—
291C23—381no—
292C23C23×D1911yescharacteristic
293Q8—388no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—192no—
310C2×C4—192no—
311C2×C4—192no—
312C2×C4—192no—
313C2×C4—192no—
314C2×C4—192no—
315C2×C4—388no—
316C2×C4—381no—
317C2×C4—381no—
318C2×C4—381no—
319C2×C4—381no—
320C2×C4—381no—
321C2×C4—381no—
322C2×C4—381no—
323C2×C4—381no—
324C2×C4—381no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4C2×C4×D1912yes—
332C2×C4C2×C4×D1912yes—
333C2×C4C2×C4×D1912yes—
334C2×C4#6454112yes—
335C2×C4#6454112yes—
336C2×C4D4×D1912yes—
337C22—382no—
338C22—382no—
339C22—382no—
340C22—761no—
341C22—761no—
342C22—761no—
343C22—761no—
344C22C22×C4×D1911yescharacteristic
345C22C2×#6454111yescharacteristic
346C22C2×#6454111yescharacteristic
347C22C2×D4×D1911yescharacteristic
348C22#1059743311yescharacteristic
349C22#41×D1911yescharacteristic
350C22#1059743611yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—194no—
359C4—382no—
360C4—382no—
361C4—382no—
362C4—761no—
363C4—761no—
364C4—761no—
365C2—762no—
366C2C4×D4×D1911yescharacteristic
367C2C4×#6454111yescharacteristic
368C2#1192702011yescharacteristic
369C2#1192719511yescharacteristic
370C2#1192720311yescharacteristic
371C2#1192722711yescharacteristic
372C2#1192726611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC4×C4⋊C4×C19C2
socle, cosocleC23×C19C24
prime radicalC23×D19C23
hypercenterC4×C4⋊C4D19
hypocenterC19#2362
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic38C2semidirect
4. #11926448C2semidirect
5. #11926439C2semidirect
10. #11926430C2semidirect
11. #11926428C2semidirect
12. C4×Dic19⋊C4C2semidirect
13. #11926395C2semidirect
15. C4×C4⋊C4×C19C2semidirect
41. #10597342C4semidirect
192. C4×C4⋊C4D19semidirect
240. C19#2362semidirect

Maximal subgroups

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

subgroupindex
C2×#105973422
C2×C4×Dic382
C2×#105973182
#119264482
#119264392
#119264362
#119264352
#119264342
#119264302
#119264282
C4×Dic19⋊C42
#119263952
#119263912
C4×C4⋊C4×C192
#236219