Finite Group Databasebeta

← C151×#23009 #50327934

Subgroups — C151×#23009 #50327934

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#464×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic
3C2×C4×Q16×C151C211yesmaximal, characteristic, complemented
4#2367×C151C211yesmaximal, characteristic
5Q8×C4⋊C4×C151C211yesmaximal, characteristic, complemented
6#1959×C151C211yesmaximal, characteristic
7#1947×C151C211yesmaximal, characteristic, complemented
8#1935×C151C211yesmaximal, characteristic, complemented
9#1934×C151C211yesmaximal, characteristic
10#1880×C151C211yesmaximal, characteristic
11#1878×C151C211yesmaximal, characteristic, complemented
12#1863×C151C211yesmaximal, characteristic, complemented
13#1862×C151C211yesmaximal, characteristic
14#1771×C151C211yesmaximal, characteristic, complemented
15#1763×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C2×#124×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24#464×C151C418yescomplemented
25#440×C151—24no—
26C4×Q16×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×#107×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#391×C151C2211yescharacteristic
42#390×C151C2211yescharacteristic
43#389×C151—21no—
44#389×C151—21no—
45#389×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#388×C151—21no—
48#388×C151—21no—
49#385×C151—21no—
50#384×C151—21no—
51#384×C151C2211yescharacteristic
52C4×C4⋊C4×C151—21no—
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C22⋊C4×C151—21no—
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×Q8×C151C2311yescharacteristic
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C2×Q16×C151—22no—
67C2×Q16×C151—22no—
68C2×Q16×C151C2×C414yescomplemented
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C2×SD16×C151C2×C414yes—
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76#124×C151—22no—
77#124×C151C2×C414yes—
78C4×Q8×C151—22no—
79C4×Q8×C151—22no—
80C4×Q8×C151—22no—
81C4×Q8×C151—22no—
82C4×Q8×C151—41no—
83C4×Q8×C151—41no—
84C4×Q8×C151—41no—
85C4×Q8×C151C2×C414yescomplemented
86C4×D4×C151—22no—
87C4×D4×C151—41no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151D411yescharacteristic
97C2×C4⋊C4×C151D411yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C42×C151—21no—
109C2×C42×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151—21no—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114C2×C42×C151C2311yescharacteristic
115C2×C42×C151C2311yescharacteristic
116#107×C151—22no—
117#107×C151—22no—
118C4⋊C8×C151C2×C414yescomplemented
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—41no—
122#103×C151C2×C414yescomplemented
123#103×C151D414yes—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151C2×C414yes—
127#97×C151—22no—
128#97×C151—22no—
129C4×C8×C151—22no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151D411yescharacteristic
136#95×C151D411yescharacteristic
137C24×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151C22×C412yes—
147C2×Q8×C151C22×C412yes—
148C2×Q8×C151C2×D412yes—
149C2×Q8×C151#4112yes—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151C22×C412yes—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—42no—
164C22×C4×C151—42no—
165C22×C4×C151—81no—
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2411yescharacteristic
173Q16×C151—28no—
174SD16×C151—28no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151C22×C412yes—
185C2×C8×C151C22×C412yes—
186C2×C8×C151C2×D412yes—
187C4⋊C4×C151—24no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151—42no—
199C4⋊C4×C151—42no—
200C4⋊C4×C151—42no—
201C4⋊C4×C151—42no—
202C4⋊C4×C151—81no—
203C4⋊C4×C151—81no—
204C4⋊C4×C151—81no—
205C4⋊C4×C151C22×C412yes—
206C4⋊C4×C151C2×D412yes—
207C22⋊C4×C151—24no—
208C22⋊C4×C151—24no—
209C22⋊C4×C151—42no—
210C22⋊C4×C151—42no—
211C22⋊C4×C151—81no—
212C42×C151—24no—
213C42×C151—21no—
214C42×C151—21no—
215C42×C151—21no—
216C42×C151—21no—
217C42×C151—42no—
218C42×C151—42no—
219C42×C151—42no—
220C42×C151—81no—
221C42×C151C22×C412yes—
222C42×C151#4112yes—
223C23×C151—22no—
224C23×C151—41no—
225C23×C151—41no—
226C23×C151—41no—
227C23×C151—41no—
228C23×C151—41no—
229C23×C151—41no—
230C23×C151C22×D411yescharacteristic
231Q8×C151—22no—
232Q8×C151—22no—
233Q8×C151—22no—
234Q8×C151—22no—
235Q8×C151—22no—
236Q8×C151—41no—
237Q8×C151—41no—
238Q8×C151C4×D414yes—
239D4×C151—22no—
240D4×C151—22no—
241D4×C151—41no—
242D4×C151—41no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—21no—
246C2×C4×C151—22no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—22no—
253C2×C4×C151—22no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—22no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—84no—
280C2×C4×C151C4×D412yes—
281C2×C4×C151C4×D412yes—
282C2×C4×C151#13712yes—
283C2×C4×C151C23×C411yescharacteristic
284C2×C4×C151C22×D411yescharacteristic
285C2×C4×C151C2×#4111yescharacteristic
286C2×C4×C151C2×#4111yescharacteristic
287C2×C4×C151H(5,𝔽2)11yescharacteristic
288C2×C4×C1512−1+411yescharacteristic
289C8×C151—22no—
290C8×C151—22no—
291C8×C151—22no—
292C8×C151—41no—
293C22×C151—42no—
294C22×C151—42no—
295C22×C151—42no—
296C22×C151—81no—
297C22×C151—81no—
298C22×C151—81no—
299C22×C151—81no—
300C22×C151C2×C4×D411yescharacteristic
301C22×C151D4211yescharacteristic
302C22×C151#54811yescharacteristic
303C22×C151C2×#13711yescharacteristic
304C22×C151#57511yescharacteristic
305C22×C151#57611yescharacteristic
306C22×C151#57811yescharacteristic
307C4×C151—24no—
308C4×C151—22no—
309C4×C151—22no—
310C4×C151—22no—
311C4×C151—42no—
312C4×C151—42no—
313C4×C151—41no—
314C4×C151—41no—
315C4×C151—42no—
316C4×C151—41no—
317C4×C151—81no—
318C4×C151—81no—
319C4×C151—81no—
320C4×C151C2×C4×D411yescharacteristic
321C4×C151#52011yescharacteristic
322C4×C151#54711yescharacteristic
323C4×C151#55311yescharacteristic
324C2×C151—82no—
325C2×C151#236111yescharacteristic
326C2×C151C4×#13711yescharacteristic
327C2×C151#295111yescharacteristic
328C2×C151#326811yescharacteristic
329C2×C151#327011yescharacteristic
330C2×C151#337511yescharacteristic
331C2×C151#337711yescharacteristic
332#23009C15111yesmaximal, characteristic, direct product factor, Sylow
333C151#2300911yescharacteristic, direct product factor, Sylow
334C2×#464C2×C15111yescharacteristic
335C2×#440C2×C15111yescharacteristic
336C2×C4×Q16C2×C15111yescharacteristic, complemented
337#2367C2×C15111yescharacteristic
338Q8×C4⋊C4C2×C15111yescharacteristic, complemented
339#1959C2×C15111yescharacteristic
340#1947C2×C15111yescharacteristic, complemented
341#1935C2×C15111yescharacteristic, complemented
342#1934C2×C15111yescharacteristic
343#1880C2×C15111yescharacteristic
344#1878C2×C15111yescharacteristic, complemented
345#1863C2×C15111yescharacteristic, complemented
346#1862C2×C15111yescharacteristic
347#1771C2×C15111yescharacteristic, complemented
348#1763C2×C15111yescharacteristic, complemented
349C22×Q16C22×C15111yescharacteristic
350C22×SD16C22×C15111yescharacteristic
351C2×#124C22×C15111yescharacteristic
352C2×C4×Q8C22×C15111yescharacteristic
353C2×C4×Q8C22×C15111yescharacteristic
354C2×C4×Q8C22×C15111yescharacteristic
355C2×C4×Q8C22×C15111yescharacteristic
356C2×C4×D4C22×C15111yescharacteristic
357#464C4×C15118yescomplemented
358#440—24no—
359C4×Q16—24no—
360C2×#107C22×C15111yescharacteristic
361C2×#107C22×C15111yescharacteristic
362C2×C4⋊C8C22×C15111yescharacteristic
363C2×#103C22×C15111yescharacteristic
364C2×#103C22×C15111yescharacteristic
365C2×#103C22×C15111yescharacteristic
366C2×#103C22×C15111yescharacteristic
367C2×#103C22×C15111yescharacteristic
368C2×#102C22×C15111yescharacteristic
369C2×#102C22×C15111yescharacteristic
370C2×#102C22×C15111yescharacteristic
371C2×#97C22×C15111yescharacteristic
372C2×#97C22×C15111yescharacteristic
373C2×C4×C8C22×C15111yescharacteristic
374#391C22×C15111yescharacteristic
375#390C22×C15111yescharacteristic
376#389—21no—
377#389—21no—
378#389C22×C15111yescharacteristic
379#389C22×C15111yescharacteristic
380#388—21no—
381#388—21no—
382#385—21no—
383#384—21no—
384#384C22×C15111yescharacteristic
385C4×C4⋊C4—21no—
386C4×C4⋊C4C22×C15111yescharacteristic
387C4×C4⋊C4C22×C15111yescharacteristic
388C4×C22⋊C4—21no—
389#340C22×C15111yescharacteristic
390#340C22×C15111yescharacteristic
391#340C22×C15111yescharacteristic
392#340C22×C15111yescharacteristic
393#336C22×C15111yescharacteristic
394#336C22×C15111yescharacteristic
395C22×Q8C23×C15111yescharacteristic
396C22×Q8C23×C15111yescharacteristic
397C22×D4C23×C15111yescharacteristic
398C23×C4—21no—
399C2×Q16—22no—
400C2×Q16—22no—
401C2×Q16C2×C4×C15114yescomplemented
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16C2×C4×C15114yes—
405C22×C8C23×C15111yescharacteristic
406C22×C8C23×C15111yescharacteristic
407C22×C8C23×C15111yescharacteristic
408C22×C8C23×C15111yescharacteristic
409#124—22no—
410#124C2×C4×C15114yes—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—41no—
416C4×Q8—41no—
417C4×Q8—41no—
418C4×Q8C2×C4×C15114yescomplemented
419C4×D4—22no—
420C4×D4—41no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4D4×C15111yescharacteristic
430C2×C4⋊C4D4×C15111yescharacteristic
431C2×C4⋊C4C23×C15111yescharacteristic
432C2×C4⋊C4C23×C15111yescharacteristic
433C2×C4⋊C4C23×C15111yescharacteristic
434C2×C4⋊C4C23×C15111yescharacteristic
435C2×C4⋊C4C23×C15111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42C23×C15111yescharacteristic
447C2×C42C23×C15111yescharacteristic
448C2×C42C23×C15111yescharacteristic
449#107—22no—
450#107—22no—
451C4⋊C8C2×C4×C15114yescomplemented
452#103—22no—
453#103—22no—
454#103—41no—
455#103C2×C4×C15114yescomplemented
456#103D4×C15114yes—
457#102—22no—
458#102—41no—
459#102C2×C4×C15114yes—
460#97—22no—
461#97—22no—
462C4×C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95D4×C15111yescharacteristic
469#95D4×C15111yescharacteristic
470C24—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×C4×C15112yes—
480C2×Q8C22×C4×C15112yes—
481C2×Q8C2×D4×C15112yes—
482C2×Q8#41×C15112yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C22×C4×C15112yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4C2×D4×C15111yescharacteristic
500C22×C4C2×D4×C15111yescharacteristic
501C22×C4C2×D4×C15111yescharacteristic
502C22×C4C2×D4×C15111yescharacteristic
503C22×C4C2×D4×C15111yescharacteristic
504C22×C4C2×D4×C15111yescharacteristic
505C22×C4C24×C15111yescharacteristic
506Q16—28no—
507SD16—28no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8C22×C4×C15112yes—
518C2×C8C22×C4×C15112yes—
519C2×C8C2×D4×C15112yes—
520C4⋊C4—24no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—41no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4C22×C4×C15112yes—
539C4⋊C4C2×D4×C15112yes—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C42—24no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—42no—
552C42—42no—
553C42—81no—
554C42C22×C4×C15112yes—
555C42#41×C15112yes—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C22×D4×C15111yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8C4×D4×C15114yes—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4C4×D4×C15112yes—
614C2×C4C4×D4×C15112yes—
615C2×C4#137×C15112yes—
616C2×C4C23×C4×C15111yescharacteristic
617C2×C4C22×D4×C15111yescharacteristic
618C2×C4C2×#41×C15111yescharacteristic
619C2×C4C2×#41×C15111yescharacteristic
620C2×C4H(5,𝔽2)×C15111yescharacteristic
621C2×C42−1+4×C15111yescharacteristic
622C8—22no—
623C8—22no—
624C8—22no—
625C8—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C2×C4×D4×C15111yescharacteristic
634C22D42×C15111yescharacteristic
635C22#548×C15111yescharacteristic
636C22C2×#137×C15111yescharacteristic
637C22#575×C15111yescharacteristic
638C22#576×C15111yescharacteristic
639C22#578×C15111yescharacteristic
640C4—24no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—42no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4C2×C4×D4×C15111yescharacteristic
654C4#520×C15111yescharacteristic
655C4#547×C15111yescharacteristic
656C4#553×C15111yescharacteristic
657C2—82no—
658C2#2361×C15111yescharacteristic
659C2C4×#137×C15111yescharacteristic
660C2#2951×C15111yescharacteristic
661C2#3268×C15111yescharacteristic
662C2#3270×C15111yescharacteristic
663C2#3375×C15111yescharacteristic
664C2#3377×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q16×C151C2semidirect
5. Q8×C4⋊C4×C151C2semidirect
7. #1947×C151C2semidirect
8. #1935×C151C2semidirect
11. #1878×C151C2semidirect
12. #1863×C151C2semidirect
14. #1771×C151C2semidirect
15. #1763×C151C2semidirect
24. #464×C151C4semidirect
68. C2×Q16×C151C2×C4semidirect
85. C4×Q8×C151C2×C4semidirect
118. C4⋊C8×C151C2×C4semidirect
122. #103×C151C2×C4semidirect
332. #23009C151direct (N × H)
333. C151#23009direct (N × H)
336. C2×C4×Q16C2×C151semidirect
338. Q8×C4⋊C4C2×C151semidirect
340. #1947C2×C151semidirect
341. #1935C2×C151semidirect
344. #1878C2×C151semidirect
345. #1863C2×C151semidirect
347. #1771C2×C151semidirect
348. #1763C2×C151semidirect
357. #464C4×C151semidirect
401. C2×Q16C2×C4×C151semidirect
418. C4×Q8C2×C4×C151semidirect
451. C4⋊C8C2×C4×C151semidirect
455. #103C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#464×C1512
C2×#440×C1512
C2×C4×Q16×C1512
#2367×C1512
Q8×C4⋊C4×C1512
#1959×C1512
#1947×C1512
#1935×C1512
#1934×C1512
#1880×C1512
#1878×C1512
#1863×C1512
#1862×C1512
#1771×C1512
#1763×C1512
#23009151