Finite Group Databasebeta

← C151×#23971 #50328896

Subgroups — C151×#23971 #50328896

Order 38656.

1274 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C151C211yesmaximal, characteristic, complemented
2C2×#452×C151C211yesmaximal, characteristic, complemented
3C2×#416×C151C211yesmaximal, characteristic, complemented
4#2407×C151C211yesmaximal, characteristic
5#2026×C151C211yesmaximal, characteristic, complemented
6#2025×C151C211yesmaximal, characteristic, complemented
7#2001×C151C211yesmaximal, characteristic, complemented
8#2000×C151C211yesmaximal, characteristic, complemented
9#1892×C151C211yesmaximal, characteristic, complemented
10#1880×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1872×C151C211yesmaximal, characteristic, complemented
14#1869×C151C211yesmaximal, characteristic, complemented
15#1825×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20#552×C151—24no—
21#552×C151—24no—
22C2×#126×C151—21no—
23C2×#125×C151—21no—
24C2×#125×C151C2211yescharacteristic
25C2×#123×C151—21no—
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×C4×Q8×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151—21no—
33C2×#117×C151C2211yescharacteristic
34C22×C4⋊C4×C151C2211yescharacteristic
35#452×C151—24no—
36#416×C151—24no—
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48#394×C151—21no—
49#392×C151—21no—
50#391×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
52#386×C151—21no—
53#385×C151—21no—
54#380×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—41no—
68C2×#41×C151—41no—
69C22×Q8×C151C2311yescharacteristic
70C22×Q8×C151C2311yescharacteristic
71C22×D4×C151—21no—
72C22×D4×C151—21no—
73C22×D4×C151D411yescharacteristic
74C22×D4×C151C2311yescharacteristic
75C23×C4×C151—21no—
76C23×C4×C151—21no—
77C23×C4×C151C2311yescharacteristic
78C23×C4×C151C2311yescharacteristic
79C2×Q16×C151—22no—
80C2×Q16×C151—22no—
81C2×Q16×C151—41no—
82C2×SD16×C151—22no—
83C2×SD16×C151—22no—
84C2×SD16×C151—41no—
85C22×C8×C151—22no—
86C22×C8×C151—41no—
87C22×C8×C151—41no—
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91C22×C8×C151C2311yescharacteristic
92#126×C151—28no—
93#125×C151—28no—
94#125×C151—22no—
95#125×C151—22no—
96#123×C151—28no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151—22no—
99C22⋊Q8×C151—22no—
100C22⋊Q8×C151—22no—
101C22⋊Q8×C151—41no—
102C22⋊Q8×C151D414yescomplemented
103#121×C151—22no—
104#121×C151—41no—
105C4×Q8×C151—22no—
106C4×Q8×C151—22no—
107C4×D4×C151—22no—
108C4×D4×C151—22no—
109#117×C151—28no—
110#117×C151—22no—
111#117×C151D414yescomplemented
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151—22no—
119C2×C4⋊C4×C151—22no—
120C2×C4⋊C4×C151—21no—
121C2×C4⋊C4×C151D411yescharacteristic
122C2×C4⋊C4×C151C2311yescharacteristic
123C2×C4⋊C4×C151C2311yescharacteristic
124C2×C4⋊C4×C151C2311yescharacteristic
125C2×C4⋊C4×C151C2311yescharacteristic
126C2×C4⋊C4×C151C2311yescharacteristic
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151D411yescharacteristic
136C2×C22⋊C4×C151D411yescharacteristic
137C2×C42×C151—21no—
138C2×C42×C151—21no—
139C2×C42×C151C2311yescharacteristic
140#103×C151—22no—
141#103×C151—22no—
142#103×C151—22no—
143#103×C151—41no—
144#103×C151—41no—
145#102×C151—22no—
146#102×C151—22no—
147#102×C151—22no—
148C22⋊C8×C151—22no—
149C22⋊C8×C151—41no—
150C22⋊C8×C151—41no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—21no—
154C24×C151—21no—
155C24×C151C2×D411yescharacteristic
156C24×C151C2×D411yescharacteristic
157#41×C151—28no—
158#41×C151—44no—
159#41×C151—44no—
160#41×C151—44no—
161C2×Q8×C151—21no—
162C2×Q8×C151—21no—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151—21no—
167C2×Q8×C151—21no—
168C2×Q8×C151—21no—
169C2×Q8×C151—21no—
170C2×Q8×C151—21no—
171C2×Q8×C151C2×D412yes—
172C2×Q8×C151#4112yes—
173C2×D4×C151—22no—
174C2×D4×C151—22no—
175C2×D4×C151—21no—
176C2×D4×C151—21no—
177C2×D4×C151—21no—
178C2×D4×C151—21no—
179C2×D4×C151—21no—
180C2×D4×C151—41no—
181C2×D4×C151—42no—
182C2×D4×C151—42no—
183C2×D4×C151—42no—
184C2×D4×C151—42no—
185C2×D4×C151—42no—
186C2×D4×C151—81no—
187C2×D4×C151#4112yes—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—24no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—42no—
207C22×C4×C151—42no—
208C22×C4×C151—42no—
209C22×C4×C151—42no—
210C22×C4×C151—42no—
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151C2×D412yes—
216C22×C4×C151C2×D412yes—
217C22×C4×C151C2411yescharacteristic
218Q16×C151—44no—
219SD16×C151—44no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—44no—
233C4⋊C4×C151—24no—
234C4⋊C4×C151—24no—
235C4⋊C4×C151—24no—
236C4⋊C4×C151—24no—
237C4⋊C4×C151—24no—
238C4⋊C4×C151—24no—
239C4⋊C4×C151—22no—
240C4⋊C4×C151—21no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—42no—
248C4⋊C4×C151C2×D412yes—
249C4⋊C4×C151C2×D412yes—
250C4⋊C4×C151C2×D412yes—
251C22⋊C4×C151—24no—
252C22⋊C4×C151—24no—
253C22⋊C4×C151—24no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—42no—
257C22⋊C4×C151—42no—
258C22⋊C4×C151—42no—
259C22⋊C4×C151—81no—
260C22⋊C4×C151—81no—
261C42×C151—24no—
262C42×C151—24no—
263C42×C151—21no—
264C42×C151—21no—
265C23×C151—21no—
266C23×C151—21no—
267C23×C151—21no—
268C23×C151—21no—
269C23×C151—21no—
270C23×C151—21no—
271C23×C151—21no—
272C23×C151—21no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—22no—
278C23×C151—41no—
279C23×C151—41no—
280C23×C151—41no—
281C23×C151—41no—
282C23×C151—41no—
283C23×C151—41no—
284C23×C151#12012yes—
285C23×C151#13512yes—
286C23×C151C22×D411yescharacteristic
287Q8×C151—22no—
288Q8×C151—22no—
289Q8×C151—22no—
290Q8×C151—22no—
291Q8×C151—41no—
292Q8×C151—41no—
293Q8×C151—41no—
294Q8×C151—41no—
295D4×C151—22no—
296D4×C151—22no—
297D4×C151—44no—
298D4×C151—48no—
299D4×C151—41no—
300D4×C151—41no—
301D4×C151—84no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—22no—
307C2×C4×C151—22no—
308C2×C4×C151—22no—
309C2×C4×C151—21no—
310C2×C4×C151—22no—
311C2×C4×C151—22no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—22no—
315C2×C4×C151—22no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—48no—
323C2×C4×C151—48no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—41no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151#12012yes—
345C2×C4×C151C22×D411yescharacteristic
346C2×C4×C151C22×D411yescharacteristic
347C2×C4×C151C2×#4111yescharacteristic
348C2×C4×C151C2×#4111yescharacteristic
349C2×C4×C151H(5,𝔽2)11yescharacteristic
350C2×C4×C151H(5,𝔽2)11yescharacteristic
351C8×C151—41no—
352C8×C151—41no—
353C8×C151—41no—
354C8×C151—41no—
355C22×C151—22no—
356C22×C151—22no—
357C22×C151—22no—
358C22×C151—22no—
359C22×C151—22no—
360C22×C151—22no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—41no—
366C22×C151—41no—
367C22×C151—41no—
368C22×C151—41no—
369C22×C151—42no—
370C22×C151—42no—
371C22×C151—42no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151C2×#12011yescharacteristic
377C22×C151#54611yescharacteristic
378C22×C151#54611yescharacteristic
379C22×C151C2×#13511yescharacteristic
380C22×C151#57511yescharacteristic
381C22×C151#57711yescharacteristic
382C22×C151#57811yescharacteristic
383C4×C151—22no—
384C4×C151—41no—
385C4×C151—42no—
386C4×C151—42no—
387C4×C151—41no—
388C4×C151—42no—
389C4×C151—42no—
390C4×C151—41no—
391C4×C151—42no—
392C4×C151—81no—
393C4×C151—81no—
394C4×C151#52511yescharacteristic
395C4×C151#53511yescharacteristic
396C4×C151#54611yescharacteristic
397C4×C151#54611yescharacteristic
398C2×C151—42no—
399C2×C151—42no—
400C2×C151—82no—
401C2×C151#240411yescharacteristic
402C2×C151#300211yescharacteristic
403C2×C151#301311yescharacteristic
404C2×C151#329611yescharacteristic
405C2×C151#330011yescharacteristic
406C2×C151#331511yescharacteristic
407C2×C151#331711yescharacteristic
408#23971C15111yesmaximal, characteristic, direct product factor, Sylow
409C151#2397111yescharacteristic, direct product factor, Sylow
410C2×#552C2×C15111yescharacteristic, complemented
411C2×#452C2×C15111yescharacteristic, complemented
412C2×#416C2×C15111yescharacteristic, complemented
413#2407C2×C15111yescharacteristic
414#2026C2×C15111yescharacteristic, complemented
415#2025C2×C15111yescharacteristic, complemented
416#2001C2×C15111yescharacteristic, complemented
417#2000C2×C15111yescharacteristic, complemented
418#1892C2×C15111yescharacteristic, complemented
419#1880C2×C15111yescharacteristic, complemented
420#1878C2×C15111yescharacteristic, complemented
421#1874C2×C15111yescharacteristic, complemented
422#1872C2×C15111yescharacteristic, complemented
423#1869C2×C15111yescharacteristic, complemented
424#1825C2×C15111yescharacteristic, complemented
425C22×#41C22×C15111yescharacteristic
426C22×Q16C22×C15111yescharacteristic
427C22×SD16C22×C15111yescharacteristic
428C23×C8C22×C15111yescharacteristic
429#552—24no—
430#552—24no—
431C2×#126—21no—
432C2×#125—21no—
433C2×#125C22×C15111yescharacteristic
434C2×#123—21no—
435C2×C22⋊Q8C22×C15111yescharacteristic
436C2×C22⋊Q8C22×C15111yescharacteristic
437C2×C22⋊Q8C22×C15111yescharacteristic
438C2×#121C22×C15111yescharacteristic
439C2×C4×Q8C22×C15111yescharacteristic
440C2×C4×D4C22×C15111yescharacteristic
441C2×#117—21no—
442C2×#117C22×C15111yescharacteristic
443C22×C4⋊C4C22×C15111yescharacteristic
444#452—24no—
445#416—24no—
446C2×#103C22×C15111yescharacteristic
447C2×#103C22×C15111yescharacteristic
448C2×#103C22×C15111yescharacteristic
449C2×#103C22×C15111yescharacteristic
450C2×#103C22×C15111yescharacteristic
451C2×#102C22×C15111yescharacteristic
452C2×#102C22×C15111yescharacteristic
453C2×#102C22×C15111yescharacteristic
454C2×C22⋊C8C22×C15111yescharacteristic
455C2×C22⋊C8C22×C15111yescharacteristic
456C2×C22⋊C8C22×C15111yescharacteristic
457#394—21no—
458#392—21no—
459#391C22×C15111yescharacteristic
460#390C22×C15111yescharacteristic
461#386—21no—
462#385—21no—
463#380C22×C15111yescharacteristic
464#340C22×C15111yescharacteristic
465#340C22×C15111yescharacteristic
466#340C22×C15111yescharacteristic
467#340C22×C15111yescharacteristic
468#340C22×C15111yescharacteristic
469#340C22×C15111yescharacteristic
470#336C22×C15111yescharacteristic
471#336C22×C15111yescharacteristic
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C22×Q8C23×C15111yescharacteristic
479C22×Q8C23×C15111yescharacteristic
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C15111yescharacteristic
483C22×D4C23×C15111yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4C23×C15111yescharacteristic
487C23×C4C23×C15111yescharacteristic
488C2×Q16—22no—
489C2×Q16—22no—
490C2×Q16—41no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C22×C8—22no—
495C22×C8—41no—
496C22×C8—41no—
497C22×C8C23×C15111yescharacteristic
498C22×C8C23×C15111yescharacteristic
499C22×C8C23×C15111yescharacteristic
500C22×C8C23×C15111yescharacteristic
501#126—28no—
502#125—28no—
503#125—22no—
504#125—22no—
505#123—28no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8D4×C15114yescomplemented
512#121—22no—
513#121—41no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×D4—22no—
517C4×D4—22no—
518#117—28no—
519#117—22no—
520#117D4×C15114yescomplemented
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C15111yescharacteristic
531C2×C4⋊C4C23×C15111yescharacteristic
532C2×C4⋊C4C23×C15111yescharacteristic
533C2×C4⋊C4C23×C15111yescharacteristic
534C2×C4⋊C4C23×C15111yescharacteristic
535C2×C4⋊C4C23×C15111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4D4×C15111yescharacteristic
545C2×C22⋊C4D4×C15111yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C15111yescharacteristic
549#103—22no—
550#103—22no—
551#103—22no—
552#103—41no—
553#103—41no—
554#102—22no—
555#102—22no—
556#102—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559C22⋊C8—41no—
560#95—21no—
561#95—21no—
562#95—21no—
563C24—21no—
564C24C2×D4×C15111yescharacteristic
565C24C2×D4×C15111yescharacteristic
566#41—28no—
567#41—44no—
568#41—44no—
569#41—44no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8C2×D4×C15112yes—
581C2×Q8#41×C15112yes—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—81no—
596C2×D4#41×C15112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4C2×D4×C15111yescharacteristic
621C22×C4C2×D4×C15111yescharacteristic
622C22×C4C2×D4×C15111yescharacteristic
623C22×C4C2×D4×C15111yescharacteristic
624C22×C4C2×D4×C15112yes—
625C22×C4C2×D4×C15112yes—
626C22×C4C24×C15111yescharacteristic
627Q16—44no—
628SD16—44no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—44no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C15112yes—
658C4⋊C4C2×D4×C15112yes—
659C4⋊C4C2×D4×C15112yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C42—24no—
671C42—24no—
672C42—21no—
673C42—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23#120×C15112yes—
694C23#135×C15112yes—
695C23C22×D4×C15111yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—22no—
706D4—44no—
707D4—48no—
708D4—41no—
709D4—41no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4#120×C15112yes—
754C2×C4C22×D4×C15111yescharacteristic
755C2×C4C22×D4×C15111yescharacteristic
756C2×C4C2×#41×C15111yescharacteristic
757C2×C4C2×#41×C15111yescharacteristic
758C2×C4H(5,𝔽2)×C15111yescharacteristic
759C2×C4H(5,𝔽2)×C15111yescharacteristic
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#120×C15111yescharacteristic
786C22#546×C15111yescharacteristic
787C22#546×C15111yescharacteristic
788C22C2×#135×C15111yescharacteristic
789C22#575×C15111yescharacteristic
790C22#577×C15111yescharacteristic
791C22#578×C15111yescharacteristic
792C4—22no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—42no—
799C4—41no—
800C4—42no—
801C4—81no—
802C4—81no—
803C4#525×C15111yescharacteristic
804C4#535×C15111yescharacteristic
805C4#546×C15111yescharacteristic
806C4#546×C15111yescharacteristic
807C2—42no—
808C2—42no—
809C2—82no—
810C2#2404×C15111yescharacteristic
811C2#3002×C15111yescharacteristic
812C2#3013×C15111yescharacteristic
813C2#3296×C15111yescharacteristic
814C2#3300×C15111yescharacteristic
815C2#3315×C15111yescharacteristic
816C2#3317×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2407×C151C2
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
1. C2×#552×C151C2semidirect
2. C2×#452×C151C2semidirect
3. C2×#416×C151C2semidirect
5. #2026×C151C2semidirect
6. #2025×C151C2semidirect
7. #2001×C151C2semidirect
8. #2000×C151C2semidirect
9. #1892×C151C2semidirect
10. #1880×C151C2semidirect
11. #1878×C151C2semidirect
12. #1874×C151C2semidirect
13. #1872×C151C2semidirect
14. #1869×C151C2semidirect
15. #1825×C151C2semidirect
102. C22⋊Q8×C151D4semidirect
111. #117×C151D4semidirect
408. #23971C151direct (N × H)
409. C151#23971direct (N × H)
410. C2×#552C2×C151semidirect
411. C2×#452C2×C151semidirect
412. C2×#416C2×C151semidirect
414. #2026C2×C151semidirect
415. #2025C2×C151semidirect
416. #2001C2×C151semidirect
417. #2000C2×C151semidirect
418. #1892C2×C151semidirect
419. #1880C2×C151semidirect
420. #1878C2×C151semidirect
421. #1874C2×C151semidirect
422. #1872C2×C151semidirect
423. #1869C2×C151semidirect
424. #1825C2×C151semidirect
511. C22⋊Q8D4×C151semidirect
520. #117D4×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×#452×C1512
C2×#416×C1512
#2407×C1512
#2026×C1512
#2025×C1512
#2001×C1512
#2000×C1512
#1892×C1512
#1880×C1512
#1878×C1512
#1874×C1512
#1872×C1512
#1869×C1512
#1825×C1512
#23971151