Finite Group Databasebeta

← C151×#21844 #50326769

Subgroups — C151×#21844 #50326769

Order 38656.

1100 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C151C211yesmaximal, characteristic
2#2920×C151C211yesmaximal, characteristic
3C4×#117×C151C211yesmaximal, characteristic
4#1994×C151C214yesmaximal, complemented
5#1986×C151C214yesmaximal, complemented
6#1826×C151C214yesmaximal
7#533×C151—21no—
8#533×C151—21no—
9#533×C151—21no—
10#533×C151—21no—
11#533×C151C412yescomplemented
12#533×C151C412yescomplemented
13#533×C151C2212yes—
14#533×C151C2212yes—
15C2×C4⋊Q8×C151C411yescharacteristic, complemented
16C2×C4⋊Q8×C151C411yescharacteristic, complemented
17C2×#125×C151C412yescomplemented
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151—21no—
20C2×C4×Q8×C151—21no—
21C2×C4×Q8×C151—21no—
22C2×#117×C151—21no—
23C2×#117×C151C2212yes—
24C22×C42×C151C2211yescharacteristic
25#432×C151—21no—
26#432×C151—21no—
27#431×C151—21no—
28#431×C151—21no—
29#423×C151C2212yes—
30#407×C151C2212yes—
31C4×M16×C151C2212yes—
32C4×C4⋊C4×C151—21no—
33C4×C4⋊C4×C151C2212yes—
34C4×C22⋊C4×C151—21no—
35C4×C22⋊C4×C151C2212yes—
36#376×C151—21no—
37C43×C151C2212yes—
38#339×C151C22116yes—
39C22×Q8×C151—21no—
40C22×Q8×C151—21no—
41C23×C4×C151D411yescharacteristic
42C23×C4×C151D411yescharacteristic
43C23×C4×C151C2311yescharacteristic
44C2×M16×C151C2314yes—
45C4⋊Q8×C151—21no—
46C4⋊Q8×C151—21no—
47C4⋊Q8×C151—21no—
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151C2×C412yes—
50C4⋊Q8×C151C2×C412yes—
51C4⋊Q8×C151C2×C412yes—
52C4⋊Q8×C151C2×C412yes—
53#125×C151—22no—
54#125×C151—22no—
55#125×C151C2×C414yes—
56#125×C151C2×C414yes—
57C22⋊Q8×C151—22no—
58C22⋊Q8×C151—22no—
59C22⋊Q8×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—22no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C4×Q8×C151—22no—
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C4×Q8×C151—22no—
72C4×Q8×C151—22no—
73#117×C151—28no—
74#117×C151—22no—
75#117×C151—22no—
76#117×C151C2×C414yes—
77#117×C151C2314yes—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151C2×C412yes—
84C2×C4⋊C4×C151C2×C412yes—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—22no—
87C2×C42×C151—22no—
88C2×C42×C151—22no—
89C2×C42×C151—22no—
90C2×C42×C151C2×C411yescharacteristic
91C2×C42×C151C2×C411yescharacteristic
92C2×C42×C151C2×C411yescharacteristic
93C2×C42×C151C2×C411yescharacteristic
94C2×C42×C151D411yescharacteristic
95C2×C42×C151D411yescharacteristic
96C2×C42×C151D411yescharacteristic
97C2×C42×C151D411yescharacteristic
98C2×C42×C151D411yescharacteristic
99C2×C42×C151D411yescharacteristic
100C2×C42×C151C2314yes—
101C2×C42×C151C2311yescharacteristic
102C2×C42×C151C2311yescharacteristic
103C4⋊C8×C151—22no—
104C4⋊C8×C151—22no—
105C22⋊C8×C151—22no—
106C22⋊C8×C151—22no—
107#97×C151—22no—
108C4×C8×C151—22no—
109#95×C151—22no—
110#95×C151—22no—
111C24×C151C2×D411yescharacteristic
112C2×Q8×C151—22no—
113C2×Q8×C151—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—44no—
117C2×Q8×C151—44no—
118C22×C4×C151—24no—
119C22×C4×C151—24no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—24no—
123C22×C4×C151—42no—
124C22×C4×C151C22⋊C411yescharacteristic
125C22×C4×C151C22⋊C411yescharacteristic
126C22×C4×C151C22⋊C411yescharacteristic
127C22×C4×C151C22⋊C411yescharacteristic
128C22×C4×C151C22⋊C411yescharacteristic
129C22×C4×C151C22⋊C411yescharacteristic
130C22×C4×C151C22⋊C411yescharacteristic
131C22×C4×C151C22⋊C411yescharacteristic
132C22×C4×C151C22×C411yescharacteristic
133C22×C4×C151C22×C411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2411yescharacteristic
142M16×C151—28no—
143C2×C8×C151—24no—
144C4⋊C4×C151—28no—
145C4⋊C4×C151—24no—
146C4⋊C4×C151—24no—
147C4⋊C4×C151—24no—
148C4⋊C4×C151—24no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151C22×C414yes—
156C4⋊C4×C151C22×C414yes—
157C22⋊C4×C151—28no—
158C22⋊C4×C151—24no—
159C22⋊C4×C151—24no—
160C42×C151—28no—
161C42×C151—24no—
162C42×C151—24no—
163C42×C151—28no—
164C42×C151—44no—
165C42×C151C22⋊C411yescharacteristic
166C42×C151C22⋊C411yescharacteristic
167C42×C151C22⋊C411yescharacteristic
168C42×C151C22⋊C411yescharacteristic
169C42×C151C22⋊C411yescharacteristic
170C42×C151C22⋊C411yescharacteristic
171C42×C151C22⋊C411yescharacteristic
172C42×C151C22⋊C411yescharacteristic
173C42×C151C22×C411yescharacteristic
174C42×C151C22×C411yescharacteristic
175C42×C151C22×C411yescharacteristic
176C42×C151C22×C411yescharacteristic
177C42×C151C2×D411yescharacteristic
178C42×C151C2×D411yescharacteristic
179C42×C151C2×D411yescharacteristic
180C42×C151C2×D411yescharacteristic
181C23×C151—22no—
182C23×C151—22no—
183C23×C151—41no—
184C23×C151C2×C22⋊C411yescharacteristic
185C23×C151C2×C22⋊C411yescharacteristic
186C23×C151C22×D411yescharacteristic
187Q8×C151—44no—
188Q8×C151—44no—
189Q8×C151—44no—
190Q8×C151—44no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—28no—
205C2×C4×C151—24no—
206C2×C4×C151—24no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—44no—
211C2×C4×C151—44no—
212C2×C4×C151—44no—
213C2×C4×C151—44no—
214C2×C4×C151#10414yes—
215C2×C4×C151C2×C22⋊C411yescharacteristic
216C2×C4×C151C2×C22⋊C411yescharacteristic
217C2×C4×C151C2×C22⋊C411yescharacteristic
218C2×C4×C151C2×C22⋊C411yescharacteristic
219C2×C4×C151C2×C22⋊C411yescharacteristic
220C2×C4×C151C2×C22⋊C411yescharacteristic
221C2×C4×C151C2×C22⋊C411yescharacteristic
222C2×C4×C151C2×C22⋊C411yescharacteristic
223C2×C4×C151C2×C22⋊C411yescharacteristic
224C2×C4×C151C2×C22⋊C411yescharacteristic
225C2×C4×C151C23×C411yescharacteristic
226C2×C4×C151C22×D411yescharacteristic
227C2×C4×C1512−1+414yes—
228C8×C151—44no—
229C22×C151—21no—
230C22×C151—21no—
231C22×C151—21no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—21no—
235C22×C151—21no—
236C22×C151—44no—
237C22×C151C2×#10412yes—
238C22×C151C22×C22⋊C411yescharacteristic
239C22×C151#53612yes—
240C4×C151—21no—
241C4×C151—21no—
242C4×C151—21no—
243C4×C151—21no—
244C4×C151—21no—
245C4×C151—21no—
246C4×C151—21no—
247C4×C151—48no—
248C4×C151—44no—
249C4×C151—44no—
250C4×C151C2×#10412yes—
251C4×C151C2×#10412yes—
252C4×C151#42112yes—
253C4×C151#51912yes—
254C4×C151#53612yes—
255C2×C151—22no—
256C2×C151—22no—
257C2×C151—41no—
258C2×C151#231011yescharacteristic
259C2×C151C22×#10411yescharacteristic
260C2×C151C2×#42111yescharacteristic
261#21844C15111yesmaximal, characteristic, direct product factor, Sylow
262C151#2184411yescharacteristic, direct product factor, Sylow
263C2×#533C2×C15111yescharacteristic
264#2920C2×C15111yescharacteristic
265C4×#117C2×C15111yescharacteristic
266#1994C2×C15114yescomplemented
267#1986C2×C15114yescomplemented
268#1826C2×C15114yes—
269#533—21no—
270#533—21no—
271#533—21no—
272#533—21no—
273#533C4×C15112yescomplemented
274#533C4×C15112yescomplemented
275#533C22×C15112yes—
276#533C22×C15112yes—
277C2×C4⋊Q8C4×C15111yescharacteristic, complemented
278C2×C4⋊Q8C4×C15111yescharacteristic, complemented
279C2×#125C4×C15112yescomplemented
280C2×C22⋊Q8—21no—
281C2×C22⋊Q8—21no—
282C2×C4×Q8—21no—
283C2×C4×Q8—21no—
284C2×#117—21no—
285C2×#117C22×C15112yes—
286C22×C42C22×C15111yescharacteristic
287#432—21no—
288#432—21no—
289#431—21no—
290#431—21no—
291#423C22×C15112yes—
292#407C22×C15112yes—
293C4×M16C22×C15112yes—
294C4×C4⋊C4—21no—
295C4×C4⋊C4C22×C15112yes—
296C4×C22⋊C4—21no—
297C4×C22⋊C4C22×C15112yes—
298#376—21no—
299C43C22×C15112yes—
300#339C22×C151116yes—
301C22×Q8—21no—
302C22×Q8—21no—
303C23×C4D4×C15111yescharacteristic
304C23×C4D4×C15111yescharacteristic
305C23×C4C23×C15111yescharacteristic
306C2×M16C23×C15114yes—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C2×C4×C15112yes—
312C4⋊Q8C2×C4×C15112yes—
313C4⋊Q8C2×C4×C15112yes—
314C4⋊Q8C2×C4×C15112yes—
315#125—22no—
316#125—22no—
317#125C2×C4×C15114yes—
318#125C2×C4×C15114yes—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335#117—28no—
336#117—22no—
337#117—22no—
338#117C2×C4×C15114yes—
339#117C23×C15114yes—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4C2×C4×C15112yes—
346C2×C4⋊C4C2×C4×C15112yes—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42C2×C4×C15111yescharacteristic
353C2×C42C2×C4×C15111yescharacteristic
354C2×C42C2×C4×C15111yescharacteristic
355C2×C42C2×C4×C15111yescharacteristic
356C2×C42D4×C15111yescharacteristic
357C2×C42D4×C15111yescharacteristic
358C2×C42D4×C15111yescharacteristic
359C2×C42D4×C15111yescharacteristic
360C2×C42D4×C15111yescharacteristic
361C2×C42D4×C15111yescharacteristic
362C2×C42C23×C15114yes—
363C2×C42C23×C15111yescharacteristic
364C2×C42C23×C15111yescharacteristic
365C4⋊C8—22no—
366C4⋊C8—22no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369#97—22no—
370C4×C8—22no—
371#95—22no—
372#95—22no—
373C24C2×D4×C15111yescharacteristic
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—44no—
379C2×Q8—44no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—42no—
386C22×C4C22⋊C4×C15111yescharacteristic
387C22×C4C22⋊C4×C15111yescharacteristic
388C22×C4C22⋊C4×C15111yescharacteristic
389C22×C4C22⋊C4×C15111yescharacteristic
390C22×C4C22⋊C4×C15111yescharacteristic
391C22×C4C22⋊C4×C15111yescharacteristic
392C22×C4C22⋊C4×C15111yescharacteristic
393C22×C4C22⋊C4×C15111yescharacteristic
394C22×C4C22×C4×C15111yescharacteristic
395C22×C4C22×C4×C15111yescharacteristic
396C22×C4C2×D4×C15111yescharacteristic
397C22×C4C2×D4×C15111yescharacteristic
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15111yescharacteristic
400C22×C4C2×D4×C15111yescharacteristic
401C22×C4C2×D4×C15111yescharacteristic
402C22×C4C2×D4×C15111yescharacteristic
403C22×C4C24×C15111yescharacteristic
404M16—28no—
405C2×C8—24no—
406C4⋊C4—28no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4C22×C4×C15114yes—
418C4⋊C4C22×C4×C15114yes—
419C22⋊C4—28no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C42—28no—
423C42—24no—
424C42—24no—
425C42—28no—
426C42—44no—
427C42C22⋊C4×C15111yescharacteristic
428C42C22⋊C4×C15111yescharacteristic
429C42C22⋊C4×C15111yescharacteristic
430C42C22⋊C4×C15111yescharacteristic
431C42C22⋊C4×C15111yescharacteristic
432C42C22⋊C4×C15111yescharacteristic
433C42C22⋊C4×C15111yescharacteristic
434C42C22⋊C4×C15111yescharacteristic
435C42C22×C4×C15111yescharacteristic
436C42C22×C4×C15111yescharacteristic
437C42C22×C4×C15111yescharacteristic
438C42C22×C4×C15111yescharacteristic
439C42C2×D4×C15111yescharacteristic
440C42C2×D4×C15111yescharacteristic
441C42C2×D4×C15111yescharacteristic
442C42C2×D4×C15111yescharacteristic
443C23—22no—
444C23—22no—
445C23—41no—
446C23C2×C22⋊C4×C15111yescharacteristic
447C23C2×C22⋊C4×C15111yescharacteristic
448C23C22×D4×C15111yescharacteristic
449Q8—44no—
450Q8—44no—
451Q8—44no—
452Q8—44no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—28no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4#104×C15114yes—
477C2×C4C2×C22⋊C4×C15111yescharacteristic
478C2×C4C2×C22⋊C4×C15111yescharacteristic
479C2×C4C2×C22⋊C4×C15111yescharacteristic
480C2×C4C2×C22⋊C4×C15111yescharacteristic
481C2×C4C2×C22⋊C4×C15111yescharacteristic
482C2×C4C2×C22⋊C4×C15111yescharacteristic
483C2×C4C2×C22⋊C4×C15111yescharacteristic
484C2×C4C2×C22⋊C4×C15111yescharacteristic
485C2×C4C2×C22⋊C4×C15111yescharacteristic
486C2×C4C2×C22⋊C4×C15111yescharacteristic
487C2×C4C23×C4×C15111yescharacteristic
488C2×C4C22×D4×C15111yescharacteristic
489C2×C42−1+4×C15114yes—
490C8—44no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—44no—
499C22C2×#104×C15112yes—
500C22C22×C22⋊C4×C15111yescharacteristic
501C22#536×C15112yes—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—48no—
510C4—44no—
511C4—44no—
512C4C2×#104×C15112yes—
513C4C2×#104×C15112yes—
514C4#421×C15112yes—
515C4#519×C15112yes—
516C4#536×C15112yes—
517C2—22no—
518C2—22no—
519C2—41no—
520C2#2310×C15111yescharacteristic
521C2C22×#104×C15111yescharacteristic
522C2C2×#421×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C22×C22⋊C4
prime radicalC24×C151C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1994×C151C2semidirect
5. #1986×C151C2semidirect
11. #533×C151C4semidirect
12. #533×C151C4semidirect
15. C2×C4⋊Q8×C151C4semidirect
16. C2×C4⋊Q8×C151C4semidirect
17. C2×#125×C151C4semidirect
261. #21844C151direct (N × H)
262. C151#21844direct (N × H)
266. #1994C2×C151semidirect
267. #1986C2×C151semidirect
273. #533C4×C151semidirect
274. #533C4×C151semidirect
277. C2×C4⋊Q8C4×C151semidirect
278. C2×C4⋊Q8C4×C151semidirect
279. C2×#125C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1512
#2920×C1512
C4×#117×C1512
#1994×C1512
#1986×C1512
#1826×C1512
#21844151