Finite Group Databasebeta

← C151×#24127 #50329052

Subgroups — C151×#24127 #50329052

Order 38656.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C151C211yesmaximal, characteristic
2C2×#479×C151C211yesmaximal, characteristic, complemented
3C2×C4×Q16×C151C211yesmaximal, characteristic, complemented
4#2536×C151C211yesmaximal, characteristic
5#2036×C151C211yesmaximal, characteristic, complemented
6#2035×C151C211yesmaximal, characteristic, complemented
7#2001×C151C211yesmaximal, characteristic, complemented
8#2001×C151C211yesmaximal, characteristic, complemented
9#1991×C151C211yesmaximal, characteristic, complemented
10#1954×C151C211yesmaximal, characteristic
11#1873×C151C211yesmaximal, characteristic, complemented
12#1872×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1852×C151C211yesmaximal, characteristic, complemented
15#1805×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17#552×C151—24no—
18#552×C151—24no—
19C2×#126×C151—21no—
20C2×#125×C151—21no—
21C2×#125×C151C2211yescharacteristic
22C2×#123×C151—21no—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×C22⋊Q8×C151C2211yescharacteristic
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C2×#117×C151—21no—
31C2×#117×C151C2211yescharacteristic
32C22×C4⋊C4×C151C2211yescharacteristic
33#479×C151—24no—
34C4×Q16×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×#107×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×C4⋊C8×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic
49C2×C4×C8×C151C2211yescharacteristic
50#398×C151—21no—
51#394×C151—21no—
52#388×C151—21no—
53#388×C151—21no—
54#382×C151C2211yescharacteristic
55#380×C151C2211yescharacteristic
56#380×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63C22×Q8×C151C2311yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×D4×C151D411yescharacteristic
66C23×C4×C151—21no—
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C2×Q16×C151—22no—
70C2×Q16×C151—22no—
71C2×Q16×C151—22no—
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76#126×C151—28no—
77#125×C151—28no—
78#125×C151—22no—
79#125×C151D414yes—
80#123×C151—28no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—41no—
88C22⋊Q8×C151—41no—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151D414yes—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95#117×C151—28no—
96#117×C151—22no—
97#117×C151—22no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—22no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151D411yescharacteristic
124C2×C22⋊C4×C151D411yescharacteristic
125C2×C42×C151—21no—
126C2×C42×C151—21no—
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#107×C151—22no—
130#107×C151—22no—
131#106×C151—22no—
132C4⋊C8×C151—22no—
133#103×C151—22no—
134#103×C151—22no—
135#103×C151—22no—
136#103×C151—22no—
137#103×C151—41no—
138#103×C151—41no—
139C22⋊C8×C151—22no—
140C22⋊C8×C151—22no—
141C22⋊C8×C151—41no—
142C22⋊C8×C151—41no—
143C4×C8×C151—22no—
144#95×C151—21no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151C2×D411yescharacteristic
149C24×C151C2×D411yescharacteristic
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151—21no—
160C2×Q8×C151C2×D412yes—
161C2×Q8×C151#4112yes—
162C2×D4×C151—22no—
163C2×D4×C151—22no—
164C2×D4×C151—41no—
165C22×C4×C151—24no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—42no—
187C22×C4×C151—42no—
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2411yescharacteristic
193Q16×C151—28no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151#4112yes—
206C4⋊C4×C151—24no—
207C4⋊C4×C151—24no—
208C4⋊C4×C151—24no—
209C4⋊C4×C151—24no—
210C4⋊C4×C151—24no—
211C4⋊C4×C151—24no—
212C4⋊C4×C151—22no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—42no—
223C4⋊C4×C151—42no—
224C4⋊C4×C151—42no—
225C4⋊C4×C151C2×D412yes—
226C4⋊C4×C151C2×D412yes—
227C4⋊C4×C151C2×D412yes—
228C22⋊C4×C151—24no—
229C22⋊C4×C151—24no—
230C22⋊C4×C151—24no—
231C22⋊C4×C151—22no—
232C22⋊C4×C151—22no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C42×C151—24no—
238C42×C151—24no—
239C42×C151—42no—
240C42×C151C2×D412yes—
241C42×C151C2×D412yes—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151#13512yes—
256C23×C151C22×D411yescharacteristic
257Q8×C151—22no—
258Q8×C151—22no—
259Q8×C151—22no—
260Q8×C151—22no—
261Q8×C151—41no—
262Q8×C151—41no—
263Q8×C151—41no—
264Q8×C151—41no—
265D4×C151—44no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—22no—
271C2×C4×C151—21no—
272C2×C4×C151—22no—
273C2×C4×C151—22no—
274C2×C4×C151—21no—
275C2×C4×C151—22no—
276C2×C4×C151—22no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—48no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151#12012yes—
310C2×C4×C151#12012yes—
311C2×C4×C151C22×D411yescharacteristic
312C2×C4×C151C22×D411yescharacteristic
313C2×C4×C151C2×#4111yescharacteristic
314C2×C4×C151C2×#4111yescharacteristic
315C2×C4×C151H(5,𝔽2)11yescharacteristic
316C2×C4×C1512−1+411yescharacteristic
317C8×C151—22no—
318C8×C151—41no—
319C8×C151—41no—
320C8×C151—41no—
321C22×C151—22no—
322C22×C151—22no—
323C22×C151—22no—
324C22×C151—41no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—41no—
334C22×C151—41no—
335C22×C151C2×#12011yescharacteristic
336C22×C151#54611yescharacteristic
337C22×C151#54711yescharacteristic
338C22×C151C2×#13511yescharacteristic
339C22×C151#57511yescharacteristic
340C22×C151#57811yescharacteristic
341C22×C151#57811yescharacteristic
342C4×C151—22no—
343C4×C151—22no—
344C4×C151—41no—
345C4×C151—41no—
346C4×C151—42no—
347C4×C151—42no—
348C4×C151—42no—
349C4×C151—42no—
350C4×C151—42no—
351C4×C151—81no—
352C4×C151—81no—
353C4×C151—81no—
354C4×C151#52511yescharacteristic
355C4×C151#53711yescharacteristic
356C4×C151#54811yescharacteristic
357C4×C151#55011yescharacteristic
358C2×C151—42no—
359C2×C151—81no—
360C2×C151#240711yescharacteristic
361C2×C151#300211yescharacteristic
362C2×C151#301111yescharacteristic
363C2×C151#330011yescharacteristic
364C2×C151#332711yescharacteristic
365C2×C151#333611yescharacteristic
366C2×C151#335211yescharacteristic
367#24127C15111yesmaximal, characteristic, direct product factor, Sylow
368C151#2412711yescharacteristic, direct product factor, Sylow
369C2×#552C2×C15111yescharacteristic
370C2×#479C2×C15111yescharacteristic, complemented
371C2×C4×Q16C2×C15111yescharacteristic, complemented
372#2536C2×C15111yescharacteristic
373#2036C2×C15111yescharacteristic, complemented
374#2035C2×C15111yescharacteristic, complemented
375#2001C2×C15111yescharacteristic, complemented
376#2001C2×C15111yescharacteristic, complemented
377#1991C2×C15111yescharacteristic, complemented
378#1954C2×C15111yescharacteristic
379#1873C2×C15111yescharacteristic, complemented
380#1872C2×C15111yescharacteristic, complemented
381#1854C2×C15111yescharacteristic, complemented
382#1852C2×C15111yescharacteristic, complemented
383#1805C2×C15111yescharacteristic, complemented
384C22×Q16C22×C15111yescharacteristic
385#552—24no—
386#552—24no—
387C2×#126—21no—
388C2×#125—21no—
389C2×#125C22×C15111yescharacteristic
390C2×#123—21no—
391C2×C22⋊Q8C22×C15111yescharacteristic
392C2×C22⋊Q8C22×C15111yescharacteristic
393C2×C22⋊Q8C22×C15111yescharacteristic
394C2×C22⋊Q8C22×C15111yescharacteristic
395C2×C4×Q8C22×C15111yescharacteristic
396C2×C4×Q8C22×C15111yescharacteristic
397C2×C4×D4C22×C15111yescharacteristic
398C2×#117—21no—
399C2×#117C22×C15111yescharacteristic
400C22×C4⋊C4C22×C15111yescharacteristic
401#479—24no—
402C4×Q16—24no—
403C2×#107C22×C15111yescharacteristic
404C2×#107C22×C15111yescharacteristic
405C2×#106C22×C15111yescharacteristic
406C2×C4⋊C8C22×C15111yescharacteristic
407C2×#103C22×C15111yescharacteristic
408C2×#103C22×C15111yescharacteristic
409C2×#103C22×C15111yescharacteristic
410C2×#103C22×C15111yescharacteristic
411C2×#103C22×C15111yescharacteristic
412C2×#103C22×C15111yescharacteristic
413C2×C22⋊C8C22×C15111yescharacteristic
414C2×C22⋊C8C22×C15111yescharacteristic
415C2×C22⋊C8C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×C4×C8C22×C15111yescharacteristic
418#398—21no—
419#394—21no—
420#388—21no—
421#388—21no—
422#382C22×C15111yescharacteristic
423#380C22×C15111yescharacteristic
424#380C22×C15111yescharacteristic
425#340C22×C15111yescharacteristic
426#340C22×C15111yescharacteristic
427#340C22×C15111yescharacteristic
428#340C22×C15111yescharacteristic
429#340C22×C15111yescharacteristic
430#340C22×C15111yescharacteristic
431C22×Q8C23×C15111yescharacteristic
432C22×Q8C23×C15111yescharacteristic
433C22×D4D4×C15111yescharacteristic
434C23×C4—21no—
435C23×C4C23×C15111yescharacteristic
436C23×C4C23×C15111yescharacteristic
437C2×Q16—22no—
438C2×Q16—22no—
439C2×Q16—22no—
440C22×C8C23×C15111yescharacteristic
441C22×C8C23×C15111yescharacteristic
442C22×C8C23×C15111yescharacteristic
443C22×C8C23×C15111yescharacteristic
444#126—28no—
445#125—28no—
446#125—22no—
447#125D4×C15114yes—
448#123—28no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—41no—
456C22⋊Q8—41no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8D4×C15114yes—
461C4×D4—22no—
462C4×D4—22no—
463#117—28no—
464#117—22no—
465#117—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4D4×C15111yescharacteristic
478C2×C4⋊C4C23×C15111yescharacteristic
479C2×C4⋊C4C23×C15111yescharacteristic
480C2×C4⋊C4C23×C15111yescharacteristic
481C2×C4⋊C4C23×C15111yescharacteristic
482C2×C4⋊C4C23×C15111yescharacteristic
483C2×C4⋊C4C23×C15111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4D4×C15111yescharacteristic
492C2×C22⋊C4D4×C15111yescharacteristic
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42C23×C15111yescharacteristic
497#107—22no—
498#107—22no—
499#106—22no—
500C4⋊C8—22no—
501#103—22no—
502#103—22no—
503#103—22no—
504#103—22no—
505#103—41no—
506#103—41no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—41no—
510C22⋊C8—41no—
511C4×C8—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24C2×D4×C15111yescharacteristic
517C24C2×D4×C15111yescharacteristic
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×D4×C15112yes—
529C2×Q8#41×C15112yes—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—41no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4C2×D4×C15111yescharacteristic
557C22×C4C2×D4×C15111yescharacteristic
558C22×C4C2×D4×C15111yescharacteristic
559C22×C4C2×D4×C15111yescharacteristic
560C22×C4C24×C15111yescharacteristic
561Q16—28no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8#41×C15112yes—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4C2×D4×C15112yes—
594C4⋊C4C2×D4×C15112yes—
595C4⋊C4C2×D4×C15112yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C42—24no—
606C42—24no—
607C42—42no—
608C42C2×D4×C15112yes—
609C42C2×D4×C15112yes—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23#135×C15112yes—
624C23C22×D4×C15111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—44no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4#120×C15112yes—
678C2×C4#120×C15112yes—
679C2×C4C22×D4×C15111yescharacteristic
680C2×C4C22×D4×C15111yescharacteristic
681C2×C4C2×#41×C15111yescharacteristic
682C2×C4C2×#41×C15111yescharacteristic
683C2×C4H(5,𝔽2)×C15111yescharacteristic
684C2×C42−1+4×C15111yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×#120×C15111yescharacteristic
704C22#546×C15111yescharacteristic
705C22#547×C15111yescharacteristic
706C22C2×#135×C15111yescharacteristic
707C22#575×C15111yescharacteristic
708C22#578×C15111yescharacteristic
709C22#578×C15111yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4#525×C15111yescharacteristic
723C4#537×C15111yescharacteristic
724C4#548×C15111yescharacteristic
725C4#550×C15111yescharacteristic
726C2—42no—
727C2—81no—
728C2#2407×C15111yescharacteristic
729C2#3002×C15111yescharacteristic
730C2#3011×C15111yescharacteristic
731C2#3300×C15111yescharacteristic
732C2#3327×C15111yescharacteristic
733C2#3336×C15111yescharacteristic
734C2#3352×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#479×C151C2semidirect
3. C2×C4×Q16×C151C2semidirect
5. #2036×C151C2semidirect
6. #2035×C151C2semidirect
7. #2001×C151C2semidirect
8. #2001×C151C2semidirect
9. #1991×C151C2semidirect
11. #1873×C151C2semidirect
12. #1872×C151C2semidirect
13. #1854×C151C2semidirect
14. #1852×C151C2semidirect
15. #1805×C151C2semidirect
367. #24127C151direct (N × H)
368. C151#24127direct (N × H)
370. C2×#479C2×C151semidirect
371. C2×C4×Q16C2×C151semidirect
373. #2036C2×C151semidirect
374. #2035C2×C151semidirect
375. #2001C2×C151semidirect
376. #2001C2×C151semidirect
377. #1991C2×C151semidirect
379. #1873C2×C151semidirect
380. #1872C2×C151semidirect
381. #1854C2×C151semidirect
382. #1852C2×C151semidirect
383. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#552×C1512
C2×#479×C1512
C2×C4×Q16×C1512
#2536×C1512
#2036×C1512
#2035×C1512
#2001×C1512
#1991×C1512
#1954×C1512
#1873×C1512
#1872×C1512
#1854×C1512
#1852×C1512
#1805×C1512
#24127151