Finite Group Databasebeta

← #14567955

Subgroups — #14567955

Order 2432.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597332C211yesmaximal, characteristic
2C2×#10597324C211yesmaximal, characteristic, complemented
3#11926484C211yesmaximal, characteristic, complemented
4#11926484C211yesmaximal, characteristic, complemented
5#11926471C211yesmaximal, characteristic, complemented
6#11926457C211yesmaximal, characteristic, complemented
7#11926450C211yesmaximal, characteristic, complemented
8#11926435C211yesmaximal, characteristic, complemented
9#11926435C211yesmaximal, characteristic, complemented
10#11926423C211yesmaximal, characteristic
11#11926421C211yesmaximal, characteristic
12#11926410C211yesmaximal, characteristic, complemented
13#11926405C211yesmaximal, characteristic, complemented
14C2×C19⋊#95C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C19C211yesmaximal, characteristic, complemented
16C23×C4×C19C2211yescharacteristic
17C22×C22⋊D19C2211yescharacteristic
18C23×Dic19C2211yescharacteristic
19C23×Dic19C2211yescharacteristic
20C22×Dic38C2211yescharacteristic
21C2×C22⋊C4×C19C2211yescharacteristic
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C42×C19C2211yescharacteristic
24C2×C42×C19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
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×C4⋊Dic19C2211yescharacteristic
34C2×C4⋊Dic19C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37#10597332—24no—
38#10597324—24no—
39C19×#95C2211yescharacteristic
40C19×#95C2211yescharacteristic
41C19⋊#95C2211yescharacteristic
42C19⋊#95C2211yescharacteristic
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×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
64C2×C22⋊D19—22no—
65C2×C22⋊D19—22no—
66C2×C22⋊D19—22no—
67C22×Dic19—22no—
68C22×Dic19—22no—
69C22×Dic19—22no—
70C22×Dic19—22no—
71C22×Dic19—22no—
72C22×Dic19—41no—
73C22×Dic19C2311yescharacteristic
74C22×Dic19C2311yescharacteristic
75C22×Dic19C2311yescharacteristic
76C22×Dic19C2311yescharacteristic
77C22×Dic19C2311yescharacteristic
78C22×Dic19C2311yescharacteristic
79C22×Dic19C2311yescharacteristic
80C2×Dic38—22no—
81C2×Dic38—22no—
82C2×Dic38—41no—
83C22⋊C4×C19—22no—
84C22⋊C4×C19D414yes—
85C42×C19—22no—
86C42×C19—41no—
87C22⋊Dic19—22no—
88(C2×D19)⋊C4—22no—
89(C2×D19)⋊C4—22no—
90(C2×D19)⋊C4—22no—
91(C2×D19)⋊C4—22no—
92(C2×D19)⋊C4—41no—
93(C2×D19)⋊C4—41no—
94C4⋊Dic19—22no—
95C4⋊Dic19—22no—
96C4⋊Dic19—22no—
97Dic19⋊C4—22no—
98Dic19⋊C4—22no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19C2×D412yes—
104C23×C19#4112yes—
105C23×C19#4112yes—
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—44no—
130C2×C4×C19C2×D412yes—
131C2×C4×C19C2×D412yes—
132C2×C4×C19#4112yes—
133C22⋊D19—44no—
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×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—44no—
155C2×Dic19—44no—
156C2×Dic19#4112yes—
157Dic38—44no—
158#2488—191nomaximal, Sylow
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—22no—
165C22×C19#12414yes—
166C22×C19C22×D411yescharacteristic
167C22×C19C2×#4111yescharacteristic
168C22×C19C2×#4111yescharacteristic
169C22×C19C2×#4111yescharacteristic
170C22×C19C2×#4111yescharacteristic
171C22×C19H(5,𝔽2)11yescharacteristic
172C22×C192−1+411yescharacteristic
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
179C2×D19—41no—
180C4×C19—22no—
181C4×C19—22no—
182C4×C19—22no—
183C4×C19—41no—
184C4×C19—41no—
185C4×C19—41no—
186Dic19—22no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190Dic19—41no—
191Dic19—41no—
192Dic19—41no—
193C2×#123—191no—
194C2×C22⋊Q8—191no—
195#400—191no—
196#400—191no—
197#397—191no—
198#393—191no—
199#391—191no—
200#388—191no—
201#388—191no—
202#386—191no—
203#386—191no—
204#382—191no—
205#381—191no—
206C4×C22⋊C4D1911yescharacteristic, complemented
207C2×#95—191no—
208C2×C19—24no—
209C2×C19C2×#12411yescharacteristic
210C2×C19#52911yescharacteristic
211C2×C19#53911yescharacteristic
212C2×C19#54611yescharacteristic
213C2×C19#54711yescharacteristic
214C2×C19#55111yescharacteristic
215C2×C19#55211yescharacteristic
216D19—81no—
217C22×Q8—191no—
218C22×D4—191no—
219C23×C4—191no—
220C23×C4—191no—
221C23×C4C2×D1911yescharacteristic
222#123—384no—
223C22⋊Q8—384no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—191no—
227C2×C4⋊C4—191no—
228C2×C4⋊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×C42C2×D1911yescharacteristic
239C2×C42C2×D1911yescharacteristic
240#95—191no—
241#95—191no—
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#95—191no—
251#95—191no—
252#95C2×D1911yescharacteristic
253#95C2×D1911yescharacteristic
254C19#248811yescharacteristic, complemented, Sylow
255C24—191no—
256C24C22×D1911yescharacteristic
257C2×Q8—382no—
258C2×Q8—382no—
259C2×Q8—761no—
260C2×D4—382no—
261C2×D4—382no—
262C2×D4—382no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—191no—
270C22×C4—191no—
271C22×C4—191no—
272C22×C4—191no—
273C22×C4—382no—
274C22×C4—382no—
275C22×C4—382no—
276C22×C4—382no—
277C22×C4—382no—
278C22×C4—761no—
279C22×C4C22×D1911yescharacteristic
280C22×C4C22×D1911yescharacteristic
281C22×C4C22×D1911yescharacteristic
282C22×C4C22×D1911yescharacteristic
283C22×C4C22×D1911yescharacteristic
284C22×C4C22×D1911yescharacteristic
285C4⋊C4—382no—
286C4⋊C4—382no—
287C4⋊C4—382no—
288C4⋊C4—382no—
289C4⋊C4—382no—
290C22⋊C4—22no—
291C22⋊C4—382no—
292C22⋊C4—382no—
293C22⋊C4—382no—
294C22⋊C4—382no—
295C22⋊C4—382no—
296C22⋊C4—761no—
297C22⋊C4—761no—
298C22⋊C4D7614yes—
299C42—22no—
300C42—41no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—381no—
306C23—381no—
307C23—381no—
308C23—381no—
309C23—381no—
310C23—381no—
311C23—381no—
312C23C2×D7612yes—
313C23#6454112yes—
314C23#6454112yes—
315C23C23×D1911yescharacteristic
316Q8—764no—
317D4—764no—
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—44no—
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—381no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—764no—
356C2×C4—764no—
357C2×C4C2×D7612yes—
358C2×C4C2×D7612yes—
359C2×C4#6454312yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22—761no—
373C22#1059732114yes—
374C22C22×D7611yescharacteristic
375C22C2×#6454111yescharacteristic
376C22C2×#6454111yescharacteristic
377C22C2×#6454311yescharacteristic
378C22#1059743011yescharacteristic
379C22#41×D1911yescharacteristic
380C22#1059743611yescharacteristic
381C4—22no—
382C4—22no—
383C4—22no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—382no—
388C4—761no—
389C4—761no—
390C4—761no—
391C4—761no—
392C4—761no—
393C4—761no—
394C2—24no—
395C2—1521no—
396C2C2×#1059732111yescharacteristic
397C2#1192707411yescharacteristic
398C2#1192713611yescharacteristic
399C2#1192718911yescharacteristic
400C2#1192719811yescharacteristic
401C2#1192722011yescharacteristic
402C2#1192722711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC4×C22⋊C4×C19C2
prime radicalC22×C22⋊D19C22
hypercenterC4×C22⋊C4D19
hypocenterC19#2488
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10597324C2semidirect
3. #11926484C2semidirect
4. #11926484C2semidirect
5. #11926471C2semidirect
6. #11926457C2semidirect
7. #11926450C2semidirect
8. #11926435C2semidirect
9. #11926435C2semidirect
12. #11926410C2semidirect
13. #11926405C2semidirect
14. C2×C19⋊#95C2semidirect
15. C4×C22⋊C4×C19C2semidirect
206. C4×C22⋊C4D19semidirect
254. C19#2488semidirect

Maximal subgroups

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

subgroupindex
C2×#105973322
C2×#105973242
#119264842
#119264712
#119264572
#119264502
#119264352
#119264232
#119264212
#119264102
#119264052
C2×C19⋊#952
C4×C22⋊C4×C192
#248819