Finite Group Databasebeta

← C2×#1632×C151 #50323402

Subgroups — C2×#1632×C151 #50323402

Order 38656.

1054 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2C2×#494×C151C211yesmaximal, characteristic, complemented
3C2×#477×C151C211yesmaximal, characteristic, complemented
4C2×#476×C151C211yesmaximal, characteristic
5#1632×C151C218yesmaximal, direct product factor
6C2×#333×C151C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C151C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C151C211yesmaximal, characteristic
9C22×Q16×C151—22no—
10#554×C151—22no—
11#554×C151—22no—
12#554×C151—22no—
13#554×C151C2214yes—
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151—21no—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151—22no—
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×D4×C151—21no—
21C2×C4×D4×C151C2211yescharacteristic
22C22×C4⋊C4×C151—21no—
23#494×C151—22no—
24#494×C151C2214yescomplemented
25#477×C151—22no—
26#477×C151C2214yescomplemented
27#476×C151—22no—
28#476×C151C2214yes—
29C2×#107×C151—21no—
30C2×#106×C151—21no—
31C2×C4⋊C8×C151C2211yescharacteristic
32C2×C4⋊C8×C151C2211yescharacteristic
33C2×#103×C151—21no—
34C2×#102×C151—21no—
35C2×C4×C8×C151C2211yescharacteristic
36#333×C151C2214yescomplemented
37Q8⋊C8×C151C2214yescomplemented
38D4⋊C8×C151C2214yes—
39C22×Q8×C151—21no—
40C22×Q8×C151D411yescharacteristic
41C22×Q8×C151D412yes—
42C22×D4×C151D411yescharacteristic
43C23×C4×C151—22no—
44C23×C4×C151—21no—
45C2×Q16×C151—28no—
46C2×Q16×C151—48no—
47C22×C8×C151—21no—
48C22×C8×C151—21no—
49C22×C8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151—21no—
55C4⋊Q8×C151D412yes—
56C4⋊Q8×C151C2312yes—
57C4⋊Q8×C151C2312yes—
58#125×C151—24no—
59#125×C151—24no—
60C22⋊Q8×C151—24no—
61C22⋊Q8×C151—28no—
62C22⋊Q8×C151—24no—
63C22⋊Q8×C151—28no—
64C4×Q8×C151—21no—
65C4×Q8×C151—21no—
66C4×Q8×C151D412yes—
67C4×Q8×C151C2312yes—
68C4×D4×C151—24no—
69C4×D4×C151—24no—
70C4×D4×C151—21no—
71C4×D4×C151—21no—
72C4×D4×C151D412yes—
73C4×D4×C151C2312yes—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—24no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—24no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151C2311yescharacteristic
89#107×C151—24no—
90#106×C151—24no—
91C4⋊C8×C151—21no—
92C4⋊C8×C151—21no—
93C4⋊C8×C151C2312yes—
94C4⋊C8×C151C2312yes—
95#103×C151—24no—
96#102×C151—24no—
97C4×C8×C151—21no—
98C4×C8×C151C2312yes—
99C24×C151—21no—
100C2×Q8×C151—21no—
101C2×Q8×C151—22no—
102C2×Q8×C151—22no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151—44no—
106C2×Q8×C151—44no—
107C2×Q8×C151—41no—
108C2×Q8×C151C2×D412yes—
109C2×Q8×C151C2×D414yes—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151Q1614yescomplemented
113C2×D4×C151C2×D412yes—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—21no—
117C22×C4×C151—22no—
118C22×C4×C151—28no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—42no—
122C22×C4×C151—42no—
123C22×C4×C151—41no—
124C22×C4×C151—84no—
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128Q16×C151—416no—
129C2×C8×C151—24no—
130C2×C8×C151—22no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C2×C8×C151—42no—
134C2×C8×C151—42no—
135C4⋊C4×C151—28no—
136C4⋊C4×C151—28no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—41no—
148C4⋊C4×C151—41no—
149C4⋊C4×C151C2×D412yes—
150C4⋊C4×C151C2×D412yes—
151C22⋊C4×C151—28no—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—22no—
154C42×C151—22no—
155C42×C151—22no—
156C42×C151C2×D411yescharacteristic
157C42×C151C2×D411yescharacteristic
158C42×C151C2×D411yescharacteristic
159C42×C151C2411yescharacteristic
160C23×C151—22no—
161C23×C151—24no—
162C23×C151—42no—
163C23×C151—42no—
164C23×C151#12011yescharacteristic
165Q8×C151—22no—
166Q8×C151—22no—
167Q8×C151—44no—
168Q8×C151—44no—
169Q8×C151—42no—
170Q8×C151—82no—
171Q8×C151—82no—
172D4×C151—22no—
173D4×C151—24no—
174D4×C151C2×Q1614yescomplemented
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—24no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—44no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—44no—
187C2×C4×C151—42no—
188C2×C4×C151—88no—
189C2×C4×C151—82no—
190C2×C4×C151#12011yescharacteristic
191C2×C4×C151#12011yescharacteristic
192C2×C4×C151#12011yescharacteristic
193C2×C4×C151C2×Q1612yes—
194C2×C4×C151#13512yes—
195C2×C4×C151#13712yes—
196C2×C4×C151#13712yes—
197C2×C4×C151C22×D411yescharacteristic
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C22×D411yescharacteristic
200C8×C151—24no—
201C8×C151—42no—
202C8×C151—42no—
203C22×C151—24no—
204C22×C151—48no—
205C22×C151—42no—
206C22×C151—42no—
207C22×C151#45112yes—
208C22×C151#45212yes—
209C22×C151#45312yes—
210C22×C151C2×#12011yescharacteristic
211C4×C151—21no—
212C4×C151—21no—
213C4×C151—42no—
214C4×C151—42no—
215C4×C151—42no—
216C4×C151—44no—
217C4×C151—82no—
218C4×C151#45112yes—
219C4×C151#45212yes—
220C4×C151C22×Q1611yescharacteristic
221C4×C151C2×#13511yescharacteristic
222C4×C151C2×#13711yescharacteristic
223C4×C151C2×#13711yescharacteristic
224C2×C151—44no—
225C2×C151#163214yesdirect product factor
226C2×C151C2×#45111yescharacteristic
227C2×C151C2×#45211yescharacteristic
228C2×C151C2×#45311yescharacteristic
229C2×#1632C15111yesmaximal, characteristic, direct product factor, Sylow
230C151C2×#163211yescharacteristic, direct product factor, Sylow
231C2×#554C2×C15111yescharacteristic
232C2×#494C2×C15111yescharacteristic, complemented
233C2×#477C2×C15111yescharacteristic, complemented
234C2×#476C2×C15111yescharacteristic
235#1632C2×C15118yesdirect product factor
236C2×#333C2×C15111yescharacteristic, complemented
237C2×Q8⋊C8C2×C15111yescharacteristic, complemented
238C2×D4⋊C8C2×C15111yescharacteristic
239C22×Q16—22no—
240#554—22no—
241#554—22no—
242#554—22no—
243#554C22×C15114yes—
244C2×C4⋊Q8C22×C15111yescharacteristic
245C2×C4⋊Q8C22×C15111yescharacteristic
246C2×#125—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—22no—
249C2×C4×Q8C22×C15111yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4C22×C15111yescharacteristic
252C22×C4⋊C4—21no—
253#494—22no—
254#494C22×C15114yescomplemented
255#477—22no—
256#477C22×C15114yescomplemented
257#476—22no—
258#476C22×C15114yes—
259C2×#107—21no—
260C2×#106—21no—
261C2×C4⋊C8C22×C15111yescharacteristic
262C2×C4⋊C8C22×C15111yescharacteristic
263C2×#103—21no—
264C2×#102—21no—
265C2×C4×C8C22×C15111yescharacteristic
266#333C22×C15114yescomplemented
267Q8⋊C8C22×C15114yescomplemented
268D4⋊C8C22×C15114yes—
269C22×Q8—21no—
270C22×Q8D4×C15111yescharacteristic
271C22×Q8D4×C15112yes—
272C22×D4D4×C15111yescharacteristic
273C23×C4—22no—
274C23×C4—21no—
275C2×Q16—28no—
276C2×Q16—48no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8D4×C15112yes—
286C4⋊Q8C23×C15112yes—
287C4⋊Q8C23×C15112yes—
288#125—24no—
289#125—24no—
290C22⋊Q8—24no—
291C22⋊Q8—28no—
292C22⋊Q8—24no—
293C22⋊Q8—28no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8D4×C15112yes—
297C4×Q8C23×C15112yes—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4D4×C15112yes—
303C4×D4C23×C15112yes—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4D4×C15111yescharacteristic
314C2×C4⋊C4D4×C15111yescharacteristic
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C42—21no—
318C2×C42C23×C15111yescharacteristic
319#107—24no—
320#106—24no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8C23×C15112yes—
324C4⋊C8C23×C15112yes—
325#103—24no—
326#102—24no—
327C4×C8—21no—
328C4×C8C23×C15112yes—
329C24—21no—
330C2×Q8—21no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—41no—
338C2×Q8C2×D4×C15112yes—
339C2×Q8C2×D4×C15114yes—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4Q16×C15114yescomplemented
343C2×D4C2×D4×C15112yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—28no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—84no—
355C22×C4C2×D4×C15111yescharacteristic
356C22×C4C2×D4×C15111yescharacteristic
357C22×C4C2×D4×C15111yescharacteristic
358Q16—416no—
359C2×C8—24no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—42no—
365C4⋊C4—28no—
366C4⋊C4—28no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C15112yes—
380C4⋊C4C2×D4×C15112yes—
381C22⋊C4—28no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C42—22no—
385C42—22no—
386C42C2×D4×C15111yescharacteristic
387C42C2×D4×C15111yescharacteristic
388C42C2×D4×C15111yescharacteristic
389C42C24×C15111yescharacteristic
390C23—24no—
391C23—22no—
392C23—42no—
393C23—42no—
394C23#120×C15111yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—44no—
398Q8—44no—
399Q8—42no—
400Q8—82no—
401Q8—82no—
402D4—24no—
403D4—22no—
404D4C2×Q16×C15114yescomplemented
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—88no—
419C2×C4—82no—
420C2×C4#120×C15111yescharacteristic
421C2×C4#120×C15111yescharacteristic
422C2×C4#120×C15111yescharacteristic
423C2×C4C2×Q16×C15112yes—
424C2×C4#135×C15112yes—
425C2×C4#137×C15112yes—
426C2×C4#137×C15112yes—
427C2×C4C22×D4×C15111yescharacteristic
428C2×C4C22×D4×C15111yescharacteristic
429C2×C4C22×D4×C15111yescharacteristic
430C8—24no—
431C8—42no—
432C8—42no—
433C22—24no—
434C22—48no—
435C22—42no—
436C22—42no—
437C22#451×C15112yes—
438C22#452×C15112yes—
439C22#453×C15112yes—
440C22C2×#120×C15111yescharacteristic
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—44no—
447C4—82no—
448C4#451×C15112yes—
449C4#452×C15112yes—
450C4C22×Q16×C15111yescharacteristic
451C4C2×#135×C15111yescharacteristic
452C4C2×#137×C15111yescharacteristic
453C4C2×#137×C15111yescharacteristic
454C2—44no—
455C2#1632×C15114yesdirect product factor
456C2C2×#451×C15111yescharacteristic
457C2C2×#452×C15111yescharacteristic
458C2C2×#453×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#494×C151C2semidirect
3. C2×#477×C151C2semidirect
5. #1632×C151C2direct (N × H)
6. C2×#333×C151C2semidirect
7. C2×Q8⋊C8×C151C2semidirect
24. #494×C151C22semidirect
26. #477×C151C22semidirect
36. #333×C151C22semidirect
37. Q8⋊C8×C151C22semidirect
112. C2×D4×C151Q16semidirect
174. D4×C151C2×Q16semidirect
225. C2×C151#1632direct (N × H)
229. C2×#1632C151direct (N × H)
230. C151C2×#1632direct (N × H)
232. C2×#494C2×C151semidirect
233. C2×#477C2×C151semidirect
235. #1632C2×C151direct (N × H)
236. C2×#333C2×C151semidirect
237. C2×Q8⋊C8C2×C151semidirect
254. #494C22×C151semidirect
256. #477C22×C151semidirect
266. #333C22×C151semidirect
267. Q8⋊C8C22×C151semidirect
342. C2×D4Q16×C151semidirect
404. D4C2×Q16×C151semidirect
455. C2#1632×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#494×C1512
C2×#477×C1512
C2×#476×C1512
#1632×C1512
C2×#333×C1512
C2×Q8⋊C8×C1512
C2×D4⋊C8×C1512
C2×#1632151