Finite Group Databasebeta

← C2×#1464×C151 #50322281

Subgroups — C2×#1464×C151 #50322281

Order 38656.

1326 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C151C211yesmaximal, characteristic
2C2×#432×C151C212yesmaximal, complemented
3#1464×C151C218yesmaximal, direct product factor
4C2×#324×C151C212yesmaximal, complemented
5C2×#323×C151C212yesmaximal
6C24×C4×C151C411yescharacteristic
7C2×#117×C151—22no—
8C2×#117×C151—22no—
9C2×#117×C151—24no—
10C2×#117×C151C414yes—
11C2×#117×C151C2214yes—
12C22×C4⋊C4×C151C411yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C22⋊C4×C151C411yescharacteristic
15C22×C22⋊C4×C151C2211yescharacteristic
16C22×C42×C151C411yescharacteristic
17C22×C42×C151C2211yescharacteristic
18#432×C151—24no—
19#432×C151C2218yescomplemented
20C2×C4⋊C8×C151—22no—
21C2×C22⋊C8×C151C2214yes—
22C2×#97×C151—22no—
23#324×C151C2218yescomplemented
24#323×C151C2218yes—
25C25×C151C2×C411yescharacteristic
26C23×C4×C151—22no—
27C23×C4×C151—21no—
28C23×C4×C151—21no—
29C23×C4×C151—24no—
30C23×C4×C151—24no—
31C23×C4×C151C2×C414yes—
32C23×C4×C151C2×C411yescharacteristic
33C23×C4×C151C2×C411yescharacteristic
34C23×C4×C151C2×C411yescharacteristic
35C23×C4×C151C2×C411yescharacteristic
36C23×C4×C151C2×C411yescharacteristic
37C23×C4×C151C2311yescharacteristic
38C22×C8×C151—24no—
39#117×C151—28no—
40#117×C151—28no—
41#117×C151—28no—
42#117×C151—28no—
43C2×C4⋊C4×C151—22no—
44C2×C4⋊C4×C151—22no—
45C2×C4⋊C4×C151—22no—
46C2×C4⋊C4×C151—22no—
47C2×C4⋊C4×C151C2×C414yes—
48C2×C4⋊C4×C151C2×C412yes—
49C2×C4⋊C4×C151C2312yes—
50C2×C22⋊C4×C151—22no—
51C2×C22⋊C4×C151—22no—
52C2×C22⋊C4×C151—22no—
53C2×C22⋊C4×C151—22no—
54C2×C22⋊C4×C151C2×C414yes—
55C2×C22⋊C4×C151C2×C412yes—
56C2×C22⋊C4×C151C2312yes—
57C2×C42×C151—22no—
58C2×C42×C151—21no—
59C2×C42×C151—21no—
60C2×C42×C151C2×C414yes—
61C2×C42×C151C2×C412yes—
62C2×C42×C151D412yes—
63C2×C42×C151D412yes—
64C2×C42×C151D414yes—
65C2×C42×C151C2312yes—
66C4⋊C8×C151—28no—
67C22⋊C8×C151—24no—
68C22⋊C8×C151C2318yes—
69#97×C151—28no—
70C24×C151—21no—
71C24×C151—21no—
72C24×C151—22no—
73C24×C151—42no—
74C24×C151—42no—
75C24×C151M1614yes—
76C24×C151C22×C411yescharacteristic
77C24×C151C22×C412yes—
78C22×C4×C151—216no—
79C22×C4×C151—28no—
80C22×C4×C151—28no—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—28no—
84C22×C4×C151—22no—
85C22×C4×C151—22no—
86C22×C4×C151—22no—
87C22×C4×C151—24no—
88C22×C4×C151—24no—
89C22×C4×C151—28no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—42no—
95C22×C4×C151—42no—
96C22×C4×C151—42no—
97C22×C4×C151—42no—
98C22×C4×C151C22⋊C412yes—
99C22×C4×C151C22⋊C411yescharacteristic
100C22×C4×C151C22⋊C411yescharacteristic
101C22×C4×C151C22⋊C412yes—
102C22×C4×C151C22⋊C412yes—
103C22×C4×C151M1614yes—
104C22×C4×C151C22×C412yes—
105C22×C4×C151C22×C412yes—
106C22×C4×C151C22×C412yes—
107C22×C4×C151C22×C412yes—
108C22×C4×C151C22×C411yescharacteristic
109C22×C4×C151C22×C412yes—
110C22×C4×C151C2×D412yes—
111C22×C4×C151C2×D412yes—
112C22×C4×C151C2411yescharacteristic
113C2×C8×C151—28no—
114C2×C8×C151—48no—
115C4⋊C4×C151—24no—
116C4⋊C4×C151—28no—
117C4⋊C4×C151—24no—
118C22⋊C4×C151—24no—
119C22⋊C4×C151—28no—
120C22⋊C4×C151—24no—
121C42×C151—24no—
122C42×C151—24no—
123C42×C151C22⋊C414yes—
124C42×C151C22⋊C414yes—
125C42×C151C2×D414yes—
126C42×C151C2×D414yes—
127C23×C151—22no—
128C23×C151—22no—
129C23×C151—22no—
130C23×C151—22no—
131C23×C151—24no—
132C23×C151—24no—
133C23×C151—48no—
134C23×C151—42no—
135C23×C151—42no—
136C23×C151—42no—
137C23×C151—42no—
138C23×C151—48no—
139C23×C151—42no—
140C23×C151—42no—
141C23×C151C2×C22⋊C411yescharacteristic
142C23×C151C2×C22⋊C411yescharacteristic
143C23×C151C2×M1612yes—
144C23×C151C2×M1612yes—
145C23×C151C2×M1614yes—
146C23×C151C23×C411yescharacteristic
147C2×C4×C151—216no—
148C2×C4×C151—216no—
149C2×C4×C151—22no—
150C2×C4×C151—22no—
151C2×C4×C151—22no—
152C2×C4×C151—22no—
153C2×C4×C151—24no—
154C2×C4×C151—22no—
155C2×C4×C151—22no—
156C2×C4×C151—24no—
157C2×C4×C151—24no—
158C2×C4×C151—24no—
159C2×C4×C151—24no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—42no—
163C2×C4×C151—41no—
164C2×C4×C151—42no—
165C2×C4×C151—42no—
166C2×C4×C151—41no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151C2×C22⋊C412yes—
174C2×C4×C151C2×C22⋊C412yes—
175C2×C4×C151C2×C22⋊C412yes—
176C2×C4×C151C2×C22⋊C414yes—
177C2×C4×C151C2×M1614yes—
178C2×C4×C151C22×D412yes—
179C8×C151—48no—
180C22×C151—21no—
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—21no—
184C22×C151—24no—
185C22×C151—24no—
186C22×C151—24no—
187C22×C151—44no—
188C22×C151—44no—
189C22×C151—48no—
190C22×C151—42no—
191C22×C151—42no—
192C22×C151—48no—
193C22×C151#40712yes—
194C22×C151#40712yes—
195C22×C151#41012yes—
196C22×C151#41312yes—
197C22×C151C22×C22⋊C411yescharacteristic
198C22×C151C22×M1611yescharacteristic
199C22×C151C22×M1611yescharacteristic
200C4×C151—22no—
201C4×C151—22no—
202C4×C151—24no—
203C4×C151—22no—
204C4×C151—22no—
205C4×C151—24no—
206C4×C151—42no—
207C4×C151—42no—
208C2×C151—21no—
209C2×C151—21no—
210C2×C151—22no—
211C2×C151—44no—
212C2×C151#146414yesdirect product factor
213C2×C151C2×#40711yescharacteristic
214C2×C151C2×#41011yescharacteristic
215C2×C151C2×#41311yescharacteristic
216C2×#1464C15111yesmaximal, characteristic, direct product factor, Sylow
217C151C2×#146411yescharacteristic, direct product factor, Sylow
218C22×#117C2×C15111yescharacteristic
219C2×#432C2×C15112yescomplemented
220#1464C2×C15118yesdirect product factor
221C2×#324C2×C15112yescomplemented
222C2×#323C2×C15112yes—
223C24×C4C4×C15111yescharacteristic
224C2×#117—22no—
225C2×#117—22no—
226C2×#117—24no—
227C2×#117C4×C15114yes—
228C2×#117C22×C15114yes—
229C22×C4⋊C4C4×C15111yescharacteristic
230C22×C4⋊C4C22×C15111yescharacteristic
231C22×C22⋊C4C4×C15111yescharacteristic
232C22×C22⋊C4C22×C15111yescharacteristic
233C22×C42C4×C15111yescharacteristic
234C22×C42C22×C15111yescharacteristic
235#432—24no—
236#432C22×C15118yescomplemented
237C2×C4⋊C8—22no—
238C2×C22⋊C8C22×C15114yes—
239C2×#97—22no—
240#324C22×C15118yescomplemented
241#323C22×C15118yes—
242C25C2×C4×C15111yescharacteristic
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—24no—
248C23×C4C2×C4×C15114yes—
249C23×C4C2×C4×C15111yescharacteristic
250C23×C4C2×C4×C15111yescharacteristic
251C23×C4C2×C4×C15111yescharacteristic
252C23×C4C2×C4×C15111yescharacteristic
253C23×C4C2×C4×C15111yescharacteristic
254C23×C4C23×C15111yescharacteristic
255C22×C8—24no—
256#117—28no—
257#117—28no—
258#117—28no—
259#117—28no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4C2×C4×C15114yes—
265C2×C4⋊C4C2×C4×C15112yes—
266C2×C4⋊C4C23×C15112yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4C2×C4×C15114yes—
272C2×C22⋊C4C2×C4×C15112yes—
273C2×C22⋊C4C23×C15112yes—
274C2×C42—22no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42C2×C4×C15114yes—
278C2×C42C2×C4×C15112yes—
279C2×C42D4×C15112yes—
280C2×C42D4×C15112yes—
281C2×C42D4×C15114yes—
282C2×C42C23×C15112yes—
283C4⋊C8—28no—
284C22⋊C8—24no—
285C22⋊C8C23×C15118yes—
286#97—28no—
287C24—21no—
288C24—21no—
289C24—22no—
290C24—42no—
291C24—42no—
292C24M16×C15114yes—
293C24C22×C4×C15111yescharacteristic
294C24C22×C4×C15112yes—
295C22×C4—216no—
296C22×C4—28no—
297C22×C4—28no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—28no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—28no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4C22⋊C4×C15112yes—
316C22×C4C22⋊C4×C15111yescharacteristic
317C22×C4C22⋊C4×C15111yescharacteristic
318C22×C4C22⋊C4×C15112yes—
319C22×C4C22⋊C4×C15112yes—
320C22×C4M16×C15114yes—
321C22×C4C22×C4×C15112yes—
322C22×C4C22×C4×C15112yes—
323C22×C4C22×C4×C15112yes—
324C22×C4C22×C4×C15112yes—
325C22×C4C22×C4×C15111yescharacteristic
326C22×C4C22×C4×C15112yes—
327C22×C4C2×D4×C15112yes—
328C22×C4C2×D4×C15112yes—
329C22×C4C24×C15111yescharacteristic
330C2×C8—28no—
331C2×C8—48no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—28no—
337C22⋊C4—24no—
338C42—24no—
339C42—24no—
340C42C22⋊C4×C15114yes—
341C42C22⋊C4×C15114yes—
342C42C2×D4×C15114yes—
343C42C2×D4×C15114yes—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—24no—
348C23—22no—
349C23—22no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—48no—
356C23—42no—
357C23—42no—
358C23C2×C22⋊C4×C15111yescharacteristic
359C23C2×C22⋊C4×C15111yescharacteristic
360C23C2×M16×C15112yes—
361C23C2×M16×C15112yes—
362C23C2×M16×C15114yes—
363C23C23×C4×C15111yescharacteristic
364C2×C4—216no—
365C2×C4—216no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4C2×C22⋊C4×C15112yes—
391C2×C4C2×C22⋊C4×C15112yes—
392C2×C4C2×C22⋊C4×C15112yes—
393C2×C4C2×C22⋊C4×C15114yes—
394C2×C4C2×M16×C15114yes—
395C2×C4C22×D4×C15112yes—
396C8—48no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—24no—
402C22—24no—
403C22—24no—
404C22—44no—
405C22—48no—
406C22—44no—
407C22—42no—
408C22—42no—
409C22—48no—
410C22#407×C15112yes—
411C22#407×C15112yes—
412C22#410×C15112yes—
413C22#413×C15112yes—
414C22C22×C22⋊C4×C15111yescharacteristic
415C22C22×M16×C15111yescharacteristic
416C22C22×M16×C15111yescharacteristic
417C4—22no—
418C4—22no—
419C4—24no—
420C4—22no—
421C4—22no—
422C4—24no—
423C4—42no—
424C4—42no—
425C2—22no—
426C2—21no—
427C2—21no—
428C2—44no—
429C2#1464×C15114yesdirect product factor
430C2C2×#407×C15111yescharacteristic
431C2C2×#410×C15111yescharacteristic
432C2C2×#413×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC25×C151C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#432×C151C2semidirect
3. #1464×C151C2direct (N × H)
4. C2×#324×C151C2semidirect
19. #432×C151C22semidirect
23. #324×C151C22semidirect
212. C2×C151#1464direct (N × H)
216. C2×#1464C151direct (N × H)
217. C151C2×#1464direct (N × H)
219. C2×#432C2×C151semidirect
220. #1464C2×C151direct (N × H)
221. C2×#324C2×C151semidirect
236. #432C22×C151semidirect
240. #324C22×C151semidirect
429. C2#1464×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#117×C1512
C2×#432×C1512
#1464×C1512
C2×#324×C1512
C2×#323×C1512
C2×#1464151