Finite Group Databasebeta

← C151×#23981 #50328906

Subgroups — C151×#23981 #50328906

Order 38656.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic, complemented
2C2×#452×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2407×C151C211yesmaximal, characteristic
5#2024×C151C211yesmaximal, characteristic, complemented
6#2023×C151C211yesmaximal, characteristic, complemented
7#2001×C151C211yesmaximal, characteristic, complemented
8#2000×C151C211yesmaximal, characteristic, complemented
9#1894×C151C211yesmaximal, characteristic, complemented
10#1880×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1872×C151C211yesmaximal, characteristic, complemented
14#1870×C151C211yesmaximal, characteristic, complemented
15#1823×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20#554×C151—24no—
21#554×C151—24no—
22C2×C4⋊Q8×C151C2211yescharacteristic
23C2×#125×C151—21no—
24C2×C22⋊Q8×C151—21no—
25C2×C22⋊Q8×C151—21no—
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×C4×Q8×C151C2211yescharacteristic
31C2×C4×D4×C151—21no—
32C2×C4×D4×C151C2211yescharacteristic
33C22×C4⋊C4×C151C2211yescharacteristic
34C22×C4⋊C4×C151C2211yescharacteristic
35#452×C151—24no—
36#417×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×C151—21no—
70C22×Q8×C151C2311yescharacteristic
71C22×Q8×C151C2311yescharacteristic
72C22×D4×C151—21no—
73C22×D4×C151—21no—
74C22×D4×C151D411yescharacteristic
75C22×D4×C151C2311yescharacteristic
76C23×C4×C151—21no—
77C23×C4×C151—21no—
78C23×C4×C151—21no—
79C23×C4×C151C2311yescharacteristic
80C23×C4×C151C2311yescharacteristic
81C2×Q16×C151—22no—
82C2×Q16×C151—22no—
83C2×Q16×C151—41no—
84C2×SD16×C151—22no—
85C2×SD16×C151—22no—
86C2×SD16×C151—41no—
87C2×M16×C151—22no—
88C2×M16×C151—41no—
89C2×M16×C151—41no—
90C22×C8×C151C2311yescharacteristic
91C22×C8×C151C2311yescharacteristic
92C22×C8×C151C2311yescharacteristic
93C22×C8×C151C2311yescharacteristic
94C4⋊Q8×C151—22no—
95C4⋊Q8×C151—22no—
96#125×C151—28no—
97C22⋊Q8×C151—28no—
98C22⋊Q8×C151—28no—
99C22⋊Q8×C151—22no—
100C22⋊Q8×C151—22no—
101C22⋊Q8×C151—22no—
102C22⋊Q8×C151—22no—
103C22⋊Q8×C151—41no—
104C22⋊Q8×C151D414yescomplemented
105#121×C151—22no—
106#121×C151—41no—
107C4×Q8×C151—22no—
108C4×Q8×C151—22no—
109C4×D4×C151—28no—
110C4×D4×C151—22no—
111C4×D4×C151—22no—
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—22no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151—21no—
119C2×C4⋊C4×C151—22no—
120C2×C4⋊C4×C151—22no—
121C2×C4⋊C4×C151—21no—
122C2×C4⋊C4×C151D411yescharacteristic
123C2×C4⋊C4×C151D414yescomplemented
124C2×C4⋊C4×C151C2311yescharacteristic
125C2×C4⋊C4×C151C2311yescharacteristic
126C2×C4⋊C4×C151C2311yescharacteristic
127C2×C4⋊C4×C151C2311yescharacteristic
128C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
136C2×C22⋊C4×C151D411yescharacteristic
137C2×C22⋊C4×C151D411yescharacteristic
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—24no—
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×C151—21no—
172C2×Q8×C151—81no—
173C2×Q8×C151—81no—
174C2×Q8×C151C2×D412yes—
175C2×Q8×C151#4112yes—
176C2×D4×C151—22no—
177C2×D4×C151—22no—
178C2×D4×C151—22no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—42no—
185C2×D4×C151—42no—
186C2×D4×C151—42no—
187C2×D4×C151—42no—
188C2×D4×C151—42no—
189C2×D4×C151—81no—
190C2×D4×C151#4112yes—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
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—24no—
201C22×C4×C151—24no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—42no—
211C22×C4×C151—42no—
212C22×C4×C151—42no—
213C22×C4×C151—81no—
214C22×C4×C151—81no—
215C22×C4×C151—81no—
216C22×C4×C151—81no—
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220C22×C4×C151C2×D412yes—
221C22×C4×C151C2×D412yes—
222C22×C4×C151C2×D411yescharacteristic
223C22×C4×C151C2411yescharacteristic
224Q16×C151—44no—
225SD16×C151—44no—
226M16×C151—44no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C4⋊C4×C151—24no—
240C4⋊C4×C151—24no—
241C4⋊C4×C151—24no—
242C4⋊C4×C151—24no—
243C4⋊C4×C151—24no—
244C4⋊C4×C151—24no—
245C4⋊C4×C151—22no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—42no—
254C4⋊C4×C151C2×D412yes—
255C4⋊C4×C151C2×D412yes—
256C4⋊C4×C151C2×D412yes—
257C22⋊C4×C151—24no—
258C22⋊C4×C151—24no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—42no—
262C22⋊C4×C151—42no—
263C22⋊C4×C151—42no—
264C22⋊C4×C151—81no—
265C22⋊C4×C151—81no—
266C42×C151—24no—
267C42×C151—21no—
268C42×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—21no—
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—22no—
282C23×C151—41no—
283C23×C151—41no—
284C23×C151—41no—
285C23×C151—41no—
286C23×C151—41no—
287C23×C151—41no—
288C23×C151#12012yes—
289C23×C151#13712yes—
290C23×C151C22×D411yescharacteristic
291Q8×C151—22no—
292Q8×C151—22no—
293Q8×C151—22no—
294Q8×C151—22no—
295Q8×C151—41no—
296Q8×C151—41no—
297Q8×C151—41no—
298Q8×C151—41no—
299Q8×C151—84no—
300D4×C151—28no—
301D4×C151—22no—
302D4×C151—22no—
303D4×C151—48no—
304D4×C151—41no—
305D4×C151—41no—
306D4×C151—84no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—22no—
312C2×C4×C151—22no—
313C2×C4×C151—22no—
314C2×C4×C151—22no—
315C2×C4×C151—21no—
316C2×C4×C151—22no—
317C2×C4×C151—22no—
318C2×C4×C151—22no—
319C2×C4×C151—22no—
320C2×C4×C151—21no—
321C2×C4×C151—22no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—48no—
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—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—84no—
348C2×C4×C151—84no—
349C2×C4×C151#12012yes—
350C2×C4×C151#13712yes—
351C2×C4×C151C22×D411yescharacteristic
352C2×C4×C151C22×D411yescharacteristic
353C2×C4×C151C2×#4111yescharacteristic
354C2×C4×C151C2×#4111yescharacteristic
355C2×C4×C151H(5,𝔽2)11yescharacteristic
356C2×C4×C151H(5,𝔽2)11yescharacteristic
357C8×C151—41no—
358C8×C151—41no—
359C8×C151—41no—
360C8×C151—41no—
361C22×C151—22no—
362C22×C151—22no—
363C22×C151—22no—
364C22×C151—22no—
365C22×C151—22no—
366C22×C151—22no—
367C22×C151—41no—
368C22×C151—41no—
369C22×C151—41no—
370C22×C151—41no—
371C22×C151—41no—
372C22×C151—41no—
373C22×C151—41no—
374C22×C151—41no—
375C22×C151—42no—
376C22×C151—42no—
377C22×C151—42no—
378C22×C151—81no—
379C22×C151—81no—
380C22×C151—81no—
381C22×C151—81no—
382C22×C151C2×#12011yescharacteristic
383C22×C151#54611yescharacteristic
384C22×C151#54611yescharacteristic
385C22×C151C2×#13711yescharacteristic
386C22×C151C2×#13711yescharacteristic
387C22×C151#57611yescharacteristic
388C22×C151#57711yescharacteristic
389C4×C151—22no—
390C4×C151—22no—
391C4×C151—41no—
392C4×C151—42no—
393C4×C151—42no—
394C4×C151—41no—
395C4×C151—42no—
396C4×C151—42no—
397C4×C151—42no—
398C4×C151—81no—
399C4×C151—81no—
400C4×C151#52511yescharacteristic
401C4×C151#53511yescharacteristic
402C4×C151#54611yescharacteristic
403C4×C151#54611yescharacteristic
404C2×C151—42no—
405C2×C151—42no—
406C2×C151—82no—
407C2×C151#240411yescharacteristic
408C2×C151#300411yescharacteristic
409C2×C151#301211yescharacteristic
410C2×C151#331411yescharacteristic
411C2×C151#331611yescharacteristic
412C2×C151#333111yescharacteristic
413C2×C151#333311yescharacteristic
414#23981C15111yesmaximal, characteristic, direct product factor, Sylow
415C151#2398111yescharacteristic, direct product factor, Sylow
416C2×#554C2×C15111yescharacteristic, complemented
417C2×#452C2×C15111yescharacteristic, complemented
418C2×#417C2×C15111yescharacteristic, complemented
419#2407C2×C15111yescharacteristic
420#2024C2×C15111yescharacteristic, complemented
421#2023C2×C15111yescharacteristic, complemented
422#2001C2×C15111yescharacteristic, complemented
423#2000C2×C15111yescharacteristic, complemented
424#1894C2×C15111yescharacteristic, complemented
425#1880C2×C15111yescharacteristic, complemented
426#1878C2×C15111yescharacteristic, complemented
427#1874C2×C15111yescharacteristic, complemented
428#1872C2×C15111yescharacteristic, complemented
429#1870C2×C15111yescharacteristic, complemented
430#1823C2×C15111yescharacteristic, complemented
431C22×#41C22×C15111yescharacteristic
432C22×Q16C22×C15111yescharacteristic
433C22×SD16C22×C15111yescharacteristic
434C22×M16C22×C15111yescharacteristic
435#554—24no—
436#554—24no—
437C2×C4⋊Q8C22×C15111yescharacteristic
438C2×#125—21no—
439C2×C22⋊Q8—21no—
440C2×C22⋊Q8—21no—
441C2×C22⋊Q8C22×C15111yescharacteristic
442C2×C22⋊Q8C22×C15111yescharacteristic
443C2×C22⋊Q8C22×C15111yescharacteristic
444C2×#121C22×C15111yescharacteristic
445C2×C4×Q8C22×C15111yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4C22×C15111yescharacteristic
448C22×C4⋊C4C22×C15111yescharacteristic
449C22×C4⋊C4C22×C15111yescharacteristic
450#452—24no—
451#417—24no—
452C2×#103C22×C15111yescharacteristic
453C2×#103C22×C15111yescharacteristic
454C2×#103C22×C15111yescharacteristic
455C2×#103C22×C15111yescharacteristic
456C2×#103C22×C15111yescharacteristic
457C2×#102C22×C15111yescharacteristic
458C2×#102C22×C15111yescharacteristic
459C2×#102C22×C15111yescharacteristic
460C2×C22⋊C8C22×C15111yescharacteristic
461C2×C22⋊C8C22×C15111yescharacteristic
462C2×C22⋊C8C22×C15111yescharacteristic
463#394—21no—
464#392—21no—
465#391C22×C15111yescharacteristic
466#390C22×C15111yescharacteristic
467#386—21no—
468#385—21no—
469#380C22×C15111yescharacteristic
470#340C22×C15111yescharacteristic
471#340C22×C15111yescharacteristic
472#340C22×C15111yescharacteristic
473#340C22×C15111yescharacteristic
474#340C22×C15111yescharacteristic
475#340C22×C15111yescharacteristic
476#336C22×C15111yescharacteristic
477#336C22×C15111yescharacteristic
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C22×Q8—21no—
485C22×Q8C23×C15111yescharacteristic
486C22×Q8C23×C15111yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4D4×C15111yescharacteristic
490C22×D4C23×C15111yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C15111yescharacteristic
495C23×C4C23×C15111yescharacteristic
496C2×Q16—22no—
497C2×Q16—22no—
498C2×Q16—41no—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—41no—
502C2×M16—22no—
503C2×M16—41no—
504C2×M16—41no—
505C22×C8C23×C15111yescharacteristic
506C22×C8C23×C15111yescharacteristic
507C22×C8C23×C15111yescharacteristic
508C22×C8C23×C15111yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511#125—28no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—22no—
518C22⋊Q8—41no—
519C22⋊Q8D4×C15114yescomplemented
520#121—22no—
521#121—41no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×D4—28no—
525C4×D4—22no—
526C4×D4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4D4×C15111yescharacteristic
538C2×C4⋊C4D4×C15114yescomplemented
539C2×C4⋊C4C23×C15111yescharacteristic
540C2×C4⋊C4C23×C15111yescharacteristic
541C2×C4⋊C4C23×C15111yescharacteristic
542C2×C4⋊C4C23×C15111yescharacteristic
543C2×C4⋊C4C23×C15111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4D4×C15111yescharacteristic
552C2×C22⋊C4D4×C15111yescharacteristic
553C2×C42—21no—
554C2×C42C23×C15111yescharacteristic
555#103—22no—
556#103—22no—
557#103—22no—
558#103—41no—
559#103—41no—
560#102—22no—
561#102—22no—
562#102—22no—
563C22⋊C8—22no—
564C22⋊C8—41no—
565C22⋊C8—41no—
566#95—21no—
567#95—21no—
568#95—21no—
569C24—21no—
570C24C2×D4×C15111yescharacteristic
571C24C2×D4×C15111yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—24no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—81no—
588C2×Q8—81no—
589C2×Q8C2×D4×C15112yes—
590C2×Q8#41×C15112yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4#41×C15112yes—
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—24no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C15111yescharacteristic
633C22×C4C2×D4×C15111yescharacteristic
634C22×C4C2×D4×C15111yescharacteristic
635C22×C4C2×D4×C15112yes—
636C22×C4C2×D4×C15112yes—
637C22×C4C2×D4×C15111yescharacteristic
638C22×C4C24×C15111yescharacteristic
639Q16—44no—
640SD16—44no—
641M16—44no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4C2×D4×C15112yes—
670C4⋊C4C2×D4×C15112yes—
671C4⋊C4C2×D4×C15112yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C42—24no—
682C42—21no—
683C42—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23#120×C15112yes—
704C23#137×C15112yes—
705C23C22×D4×C15111yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714Q8—84no—
715D4—28no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—41no—
720D4—41no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—48no—
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—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4#120×C15112yes—
765C2×C4#137×C15112yes—
766C2×C4C22×D4×C15111yescharacteristic
767C2×C4C22×D4×C15111yescharacteristic
768C2×C4C2×#41×C15111yescharacteristic
769C2×C4C2×#41×C15111yescharacteristic
770C2×C4H(5,𝔽2)×C15111yescharacteristic
771C2×C4H(5,𝔽2)×C15111yescharacteristic
772C8—41no—
773C8—41no—
774C8—41no—
775C8—41no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22C2×#120×C15111yescharacteristic
798C22#546×C15111yescharacteristic
799C22#546×C15111yescharacteristic
800C22C2×#137×C15111yescharacteristic
801C22C2×#137×C15111yescharacteristic
802C22#576×C15111yescharacteristic
803C22#577×C15111yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4#525×C15111yescharacteristic
816C4#535×C15111yescharacteristic
817C4#546×C15111yescharacteristic
818C4#546×C15111yescharacteristic
819C2—42no—
820C2—42no—
821C2—82no—
822C2#2404×C15111yescharacteristic
823C2#3004×C15111yescharacteristic
824C2#3012×C15111yescharacteristic
825C2#3314×C15111yescharacteristic
826C2#3316×C15111yescharacteristic
827C2#3331×C15111yescharacteristic
828C2#3333×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×#554×C151C2semidirect
2. C2×#452×C151C2semidirect
3. C2×#417×C151C2semidirect
5. #2024×C151C2semidirect
6. #2023×C151C2semidirect
7. #2001×C151C2semidirect
8. #2000×C151C2semidirect
9. #1894×C151C2semidirect
10. #1880×C151C2semidirect
11. #1878×C151C2semidirect
12. #1874×C151C2semidirect
13. #1872×C151C2semidirect
14. #1870×C151C2semidirect
15. #1823×C151C2semidirect
104. C22⋊Q8×C151D4semidirect
123. C2×C4⋊C4×C151D4semidirect
414. #23981C151direct (N × H)
415. C151#23981direct (N × H)
416. C2×#554C2×C151semidirect
417. C2×#452C2×C151semidirect
418. C2×#417C2×C151semidirect
420. #2024C2×C151semidirect
421. #2023C2×C151semidirect
422. #2001C2×C151semidirect
423. #2000C2×C151semidirect
424. #1894C2×C151semidirect
425. #1880C2×C151semidirect
426. #1878C2×C151semidirect
427. #1874C2×C151semidirect
428. #1872C2×C151semidirect
429. #1870C2×C151semidirect
430. #1823C2×C151semidirect
519. C22⋊Q8D4×C151semidirect
538. C2×C4⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#452×C1512
C2×#417×C1512
#2407×C1512
#2024×C1512
#2023×C1512
#2001×C1512
#2000×C1512
#1894×C1512
#1880×C1512
#1878×C1512
#1874×C1512
#1872×C1512
#1870×C1512
#1823×C1512
#23981151