Finite Group Databasebeta

← C151×#23854 #50328779

Subgroups — C151×#23854 #50328779

Order 38656.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C151C211yesmaximal, characteristic, complemented
2C2×#548×C151C211yesmaximal, characteristic, complemented
3C2×#452×C151C211yesmaximal, characteristic, complemented
4C2×#451×C151C211yesmaximal, characteristic, complemented
5C2×#448×C151C211yesmaximal, characteristic, complemented
6#2407×C151C211yesmaximal, characteristic, complemented
7#2015×C151C211yesmaximal, characteristic, complemented
8#2012×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1892×C151C211yesmaximal, characteristic, complemented
12#1880×C151C211yesmaximal, characteristic, complemented
13#1878×C151C211yesmaximal, characteristic, complemented
14#1869×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C23×Q8×C151C2211yescharacteristic
19C2×#135×C151—24no—
20C2×#135×C151—24no—
21C2×#135×C151—24no—
22C22×Q16×C151C2211yescharacteristic
23C22×Q16×C151C2211yescharacteristic
24C22×SD16×C151C2211yescharacteristic
25C22×SD16×C151C2211yescharacteristic
26C22×SD16×C151C2211yescharacteristic
27C22×D8×C151C2211yescharacteristic
28C23×C8×C151C2211yescharacteristic
29#548×C151—24no—
30#548×C151—24no—
31C2×#124×C151—21no—
32C2×#124×C151C2211yescharacteristic
33C2×C22⋊Q8×C151—21no—
34C2×C22⋊Q8×C151C2211yescharacteristic
35C2×C22⋊Q8×C151C2211yescharacteristic
36C2×#121×C151—21no—
37C2×#121×C151C2211yescharacteristic
38C2×#121×C151C2211yescharacteristic
39C2×C4×Q8×C151C2211yescharacteristic
40C2×C4×D4×C151—21no—
41C2×C4×D4×C151C2211yescharacteristic
42#452×C151—24no—
43#451×C151—24no—
44#448×C151—24no—
45C2×#103×C151C2211yescharacteristic
46C2×#103×C151C2211yescharacteristic
47C2×#103×C151C2211yescharacteristic
48C2×#103×C151C2211yescharacteristic
49C2×#103×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×#102×C151C2211yescharacteristic
52C2×#102×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55C2×C22⋊C8×C151C2211yescharacteristic
56#394×C151—21no—
57#392×C151—21no—
58#391×C151C2211yescharacteristic
59#390×C151C2211yescharacteristic
60#386×C151—21no—
61#385×C151—21no—
62#380×C151C2211yescharacteristic
63#340×C151C2211yescharacteristic
64#340×C151C2211yescharacteristic
65#336×C151C2211yescharacteristic
66#336×C151C2211yescharacteristic
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—22no—
71C2×#41×C151—22no—
72C2×#41×C151—22no—
73C2×#41×C151—22no—
74C2×#41×C151—41no—
75C2×#41×C151—41no—
76C2×#41×C151—41no—
77C2×#41×C151—41no—
78C2×#41×C151D414yescomplemented
79C22×Q8×C151—21no—
80C22×Q8×C151—22no—
81C22×Q8×C151—22no—
82C22×Q8×C151—22no—
83C22×Q8×C151—22no—
84C22×Q8×C151—41no—
85C22×Q8×C151—41no—
86C22×Q8×C151C2311yescharacteristic
87C22×Q8×C151C2311yescharacteristic
88C22×Q8×C151C2311yescharacteristic
89C22×D4×C151—21no—
90C22×D4×C151—21no—
91C22×D4×C151—21no—
92C22×D4×C151—21no—
93C22×D4×C151D411yescharacteristic
94C22×D4×C151C2311yescharacteristic
95C22×D4×C151C2311yescharacteristic
96C23×C4×C151—21no—
97C23×C4×C151—21no—
98C23×C4×C151—21no—
99C23×C4×C151C2311yescharacteristic
100C23×C4×C151C2311yescharacteristic
101#135×C151—232no—
102C2×Q16×C151—22no—
103C2×Q16×C151—22no—
104C2×Q16×C151—22no—
105C2×Q16×C151—22no—
106C2×Q16×C151—41no—
107C2×Q16×C151D414yescomplemented
108C2×SD16×C151—22no—
109C2×SD16×C151—22no—
110C2×SD16×C151—22no—
111C2×SD16×C151—22no—
112C2×SD16×C151—22no—
113C2×SD16×C151—22no—
114C2×SD16×C151—22no—
115C2×SD16×C151—41no—
116C2×SD16×C151D414yescomplemented
117C2×D8×C151—22no—
118C2×D8×C151—22no—
119C2×D8×C151—22no—
120C22×C8×C151—22no—
121C22×C8×C151—22no—
122C22×C8×C151—22no—
123C22×C8×C151C2311yescharacteristic
124C22×C8×C151C2311yescharacteristic
125C22×C8×C151C2311yescharacteristic
126C22×C8×C151C2311yescharacteristic
127#124×C151—28no—
128#124×C151—22no—
129#124×C151—22no—
130C22⋊Q8×C151—28no—
131C22⋊Q8×C151—22no—
132C22⋊Q8×C151—22no—
133C22⋊Q8×C151—41no—
134C22⋊Q8×C151D414yescomplemented
135#121×C151—28no—
136#121×C151—22no—
137#121×C151—22no—
138#121×C151—22no—
139#121×C151—41no—
140C4×Q8×C151—22no—
141C4×Q8×C151—22no—
142C4×D4×C151—28no—
143C4×D4×C151—22no—
144C4×D4×C151—22no—
145C2×C4⋊C4×C151—21no—
146C2×C4⋊C4×C151—21no—
147C2×C4⋊C4×C151—21no—
148C2×C4⋊C4×C151D411yescharacteristic
149C2×C4⋊C4×C151C2311yescharacteristic
150C2×C4⋊C4×C151C2311yescharacteristic
151C2×C4⋊C4×C151C2311yescharacteristic
152C2×C22⋊C4×C151—21no—
153C2×C22⋊C4×C151—21no—
154C2×C22⋊C4×C151—21no—
155C2×C22⋊C4×C151—21no—
156C2×C22⋊C4×C151—21no—
157C2×C22⋊C4×C151—21no—
158C2×C22⋊C4×C151—21no—
159C2×C22⋊C4×C151—21no—
160C2×C22⋊C4×C151—21no—
161C2×C22⋊C4×C151D411yescharacteristic
162C2×C22⋊C4×C151D411yescharacteristic
163C2×C42×C151—21no—
164C2×C42×C151C2311yescharacteristic
165#103×C151—22no—
166#103×C151—22no—
167#103×C151—22no—
168#103×C151—22no—
169#103×C151—22no—
170#102×C151—22no—
171#102×C151—41no—
172#102×C151—41no—
173C22⋊C8×C151—22no—
174C22⋊C8×C151—22no—
175C22⋊C8×C151—22no—
176#95×C151—21no—
177#95×C151—21no—
178#95×C151—21no—
179C24×C151—21no—
180C24×C151—21no—
181C24×C151C2×D411yescharacteristic
182C24×C151C2×D411yescharacteristic
183#41×C151—28no—
184#41×C151—28no—
185#41×C151—44no—
186#41×C151—44no—
187#41×C151—44no—
188#41×C151—44no—
189#41×C151—44no—
190#41×C151—44no—
191C2×Q8×C151—24no—
192C2×Q8×C151—21no—
193C2×Q8×C151—21no—
194C2×Q8×C151—21no—
195C2×Q8×C151—21no—
196C2×Q8×C151—21no—
197C2×Q8×C151—21no—
198C2×Q8×C151—21no—
199C2×Q8×C151—21no—
200C2×Q8×C151—21no—
201C2×Q8×C151—21no—
202C2×Q8×C151—21no—
203C2×Q8×C151—21no—
204C2×Q8×C151—21no—
205C2×Q8×C151—42no—
206C2×Q8×C151—42no—
207C2×Q8×C151—44no—
208C2×Q8×C151—44no—
209C2×Q8×C151—44no—
210C2×Q8×C151—44no—
211C2×Q8×C151C2×D412yes—
212C2×Q8×C151C2×D412yes—
213C2×Q8×C151C2×D412yes—
214C2×Q8×C151C2×D412yes—
215C2×Q8×C151C2×D412yes—
216C2×D4×C151—24no—
217C2×D4×C151—22no—
218C2×D4×C151—24no—
219C2×D4×C151—22no—
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—21no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—21no—
230C2×D4×C151—41no—
231C2×D4×C151—42no—
232C2×D4×C151—42no—
233C2×D4×C151—42no—
234C2×D4×C151—42no—
235C2×D4×C151—42no—
236C2×D4×C151—42no—
237C2×D4×C151—42no—
238C2×D4×C151—42no—
239C2×D4×C151—42no—
240C2×D4×C151—81no—
241C2×D4×C151C2×D412yes—
242C2×D4×C151C2×D412yes—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—24no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—24no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—42no—
262C22×C4×C151—42no—
263C22×C4×C151—42no—
264C22×C4×C151—42no—
265C22×C4×C151—42no—
266C22×C4×C151—42no—
267C22×C4×C151—42no—
268C22×C4×C151C2×D411yescharacteristic
269C22×C4×C151C2×D411yescharacteristic
270C22×C4×C151C2×D411yescharacteristic
271C22×C4×C151C2×D411yescharacteristic
272C22×C4×C151C2×D412yes—
273C22×C4×C151C2×D412yes—
274C22×C4×C151C2411yescharacteristic
275Q16×C151—28no—
276Q16×C151—44no—
277SD16×C151—28no—
278SD16×C151—28no—
279SD16×C151—44no—
280D8×C151—28no—
281C2×C8×C151—28no—
282C2×C8×C151—21no—
283C2×C8×C151—21no—
284C2×C8×C151—21no—
285C2×C8×C151—21no—
286C2×C8×C151—21no—
287C2×C8×C151—21no—
288C2×C8×C151—21no—
289C2×C8×C151—21no—
290C2×C8×C151—21no—
291C2×C8×C151—21no—
292C2×C8×C151C2×D412yes—
293C2×C8×C151C2×D412yes—
294C4⋊C4×C151—24no—
295C4⋊C4×C151—24no—
296C4⋊C4×C151—22no—
297C4⋊C4×C151—21no—
298C4⋊C4×C151—21no—
299C4⋊C4×C151—21no—
300C4⋊C4×C151—21no—
301C4⋊C4×C151—21no—
302C4⋊C4×C151—42no—
303C4⋊C4×C151C2×D412yes—
304C22⋊C4×C151—24no—
305C22⋊C4×C151—24no—
306C22⋊C4×C151—24no—
307C22⋊C4×C151—24no—
308C22⋊C4×C151—22no—
309C22⋊C4×C151—22no—
310C22⋊C4×C151—42no—
311C22⋊C4×C151—42no—
312C22⋊C4×C151—42no—
313C22⋊C4×C151—81no—
314C22⋊C4×C151—81no—
315C42×C151—24no—
316C42×C151—21no—
317C42×C151—21no—
318C23×C151—21no—
319C23×C151—21no—
320C23×C151—21no—
321C23×C151—21no—
322C23×C151—21no—
323C23×C151—21no—
324C23×C151—21no—
325C23×C151—21no—
326C23×C151—21no—
327C23×C151—21no—
328C23×C151—21no—
329C23×C151—21no—
330C23×C151—22no—
331C23×C151—22no—
332C23×C151—41no—
333C23×C151—41no—
334C23×C151—41no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151#12012yes—
345C23×C151#13512yescomplemented
346C23×C151C22×D411yescharacteristic
347Q8×C151—22no—
348Q8×C151—22no—
349Q8×C151—22no—
350Q8×C151—22no—
351Q8×C151—22no—
352Q8×C151—22no—
353Q8×C151—22no—
354Q8×C151—48no—
355Q8×C151—41no—
356Q8×C151—41no—
357Q8×C151—41no—
358Q8×C151—41no—
359Q8×C151#12014yes—
360D4×C151—22no—
361D4×C151—22no—
362D4×C151—22no—
363D4×C151—22no—
364D4×C151—48no—
365D4×C151—44no—
366D4×C151—48no—
367D4×C151—48no—
368D4×C151—41no—
369D4×C151—41no—
370D4×C151—41no—
371D4×C151—41no—
372D4×C151—84no—
373C2×C4×C151—22no—
374C2×C4×C151—22no—
375C2×C4×C151—22no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—22no—
379C2×C4×C151—22no—
380C2×C4×C151—22no—
381C2×C4×C151—22no—
382C2×C4×C151—21no—
383C2×C4×C151—22no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—22no—
387C2×C4×C151—22no—
388C2×C4×C151—21no—
389C2×C4×C151—21no—
390C2×C4×C151—21no—
391C2×C4×C151—21no—
392C2×C4×C151—21no—
393C2×C4×C151—21no—
394C2×C4×C151—48no—
395C2×C4×C151—48no—
396C2×C4×C151—48no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—41no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—41no—
405C2×C4×C151—41no—
406C2×C4×C151—41no—
407C2×C4×C151—41no—
408C2×C4×C151—41no—
409C2×C4×C151—41no—
410C2×C4×C151—41no—
411C2×C4×C151—41no—
412C2×C4×C151—41no—
413C2×C4×C151#12012yes—
414C2×C4×C151C22×D411yescharacteristic
415C2×C4×C151C22×D411yescharacteristic
416C2×C4×C151C22×D411yescharacteristic
417C2×C4×C151C22×D411yescharacteristic
418C2×C4×C151H(5,𝔽2)11yescharacteristic
419C2×C4×C151H(5,𝔽2)11yescharacteristic
420C8×C151—22no—
421C8×C151—22no—
422C8×C151—41no—
423C8×C151—41no—
424C22×C151—22no—
425C22×C151—22no—
426C22×C151—22no—
427C22×C151—22no—
428C22×C151—22no—
429C22×C151—22no—
430C22×C151—41no—
431C22×C151—41no—
432C22×C151—41no—
433C22×C151—41no—
434C22×C151—41no—
435C22×C151—41no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—42no—
439C22×C151—42no—
440C22×C151—42no—
441C22×C151—42no—
442C22×C151—42no—
443C22×C151—42no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151—81no—
447C22×C151—81no—
448C22×C151—81no—
449C22×C151—81no—
450C22×C151—81no—
451C22×C151—81no—
452C22×C151C2×#12011yescharacteristic
453C22×C151D4211yescharacteristic
454C22×C151D4211yescharacteristic
455C22×C151C2×#13511yescharacteristic
456C22×C151#57511yescharacteristic
457C22×C151#57711yescharacteristic
458C22×C151#57811yescharacteristic
459C4×C151—22no—
460C4×C151—24no—
461C4×C151—41no—
462C4×C151—42no—
463C4×C151—42no—
464C4×C151—41no—
465C4×C151—42no—
466C4×C151—41no—
467C4×C151—81no—
468C4×C151—81no—
469C4×C151C2×#12011yescharacteristic
470C4×C151#53411yescharacteristic
471C4×C151D4211yescharacteristic
472C4×C151D4211yescharacteristic
473C2×C151—42no—
474C2×C151—42no—
475C2×C151—82no—
476C2×C151—82no—
477C2×C151#240311yescharacteristic
478C2×C151#300211yescharacteristic
479C2×C151#301311yescharacteristic
480C2×C151#326911yescharacteristic
481C2×C151#327111yescharacteristic
482C2×C151#328211yescharacteristic
483C2×C151#328511yescharacteristic
484#23854C15111yesmaximal, characteristic, direct product factor, Sylow
485C151#2385411yescharacteristic, direct product factor, Sylow
486C22×#135C2×C15111yescharacteristic, complemented
487C2×#548C2×C15111yescharacteristic, complemented
488C2×#452C2×C15111yescharacteristic, complemented
489C2×#451C2×C15111yescharacteristic, complemented
490C2×#448C2×C15111yescharacteristic, complemented
491#2407C2×C15111yescharacteristic, complemented
492#2015C2×C15111yescharacteristic, complemented
493#2012C2×C15111yescharacteristic, complemented
494#2000C2×C15111yescharacteristic, complemented
495#1999C2×C15111yescharacteristic, complemented
496#1892C2×C15111yescharacteristic, complemented
497#1880C2×C15111yescharacteristic, complemented
498#1878C2×C15111yescharacteristic, complemented
499#1869C2×C15111yescharacteristic, complemented
500#1788C2×C15111yescharacteristic, complemented
501C22×#41C22×C15111yescharacteristic
502C22×#41C22×C15111yescharacteristic
503C23×Q8C22×C15111yescharacteristic
504C2×#135—24no—
505C2×#135—24no—
506C2×#135—24no—
507C22×Q16C22×C15111yescharacteristic
508C22×Q16C22×C15111yescharacteristic
509C22×SD16C22×C15111yescharacteristic
510C22×SD16C22×C15111yescharacteristic
511C22×SD16C22×C15111yescharacteristic
512C22×D8C22×C15111yescharacteristic
513C23×C8C22×C15111yescharacteristic
514#548—24no—
515#548—24no—
516C2×#124—21no—
517C2×#124C22×C15111yescharacteristic
518C2×C22⋊Q8—21no—
519C2×C22⋊Q8C22×C15111yescharacteristic
520C2×C22⋊Q8C22×C15111yescharacteristic
521C2×#121—21no—
522C2×#121C22×C15111yescharacteristic
523C2×#121C22×C15111yescharacteristic
524C2×C4×Q8C22×C15111yescharacteristic
525C2×C4×D4—21no—
526C2×C4×D4C22×C15111yescharacteristic
527#452—24no—
528#451—24no—
529#448—24no—
530C2×#103C22×C15111yescharacteristic
531C2×#103C22×C15111yescharacteristic
532C2×#103C22×C15111yescharacteristic
533C2×#103C22×C15111yescharacteristic
534C2×#103C22×C15111yescharacteristic
535C2×#102C22×C15111yescharacteristic
536C2×#102C22×C15111yescharacteristic
537C2×#102C22×C15111yescharacteristic
538C2×C22⋊C8C22×C15111yescharacteristic
539C2×C22⋊C8C22×C15111yescharacteristic
540C2×C22⋊C8C22×C15111yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C15111yescharacteristic
544#390C22×C15111yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C15111yescharacteristic
548#340C22×C15111yescharacteristic
549#340C22×C15111yescharacteristic
550#336C22×C15111yescharacteristic
551#336C22×C15111yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—41no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41—41no—
563C2×#41D4×C15114yescomplemented
564C22×Q8—22no—
565C22×Q8—22no—
566C22×Q8—21no—
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—41no—
570C22×Q8—41no—
571C22×Q8C23×C15111yescharacteristic
572C22×Q8C23×C15111yescharacteristic
573C22×Q8C23×C15111yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C15111yescharacteristic
579C22×D4C23×C15111yescharacteristic
580C22×D4C23×C15111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C15111yescharacteristic
585C23×C4C23×C15111yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—41no—
592C2×Q16D4×C15114yescomplemented
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C15114yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—22no—
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C15111yescharacteristic
609C22×C8C23×C15111yescharacteristic
610C22×C8C23×C15111yescharacteristic
611C22×C8C23×C15111yescharacteristic
612#124—28no—
613#124—22no—
614#124—22no—
615C22⋊Q8—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—41no—
619C22⋊Q8D4×C15114yescomplemented
620#121—28no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—41no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×D4—28no—
628C4×D4—22no—
629C4×D4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C15111yescharacteristic
634C2×C4⋊C4C23×C15111yescharacteristic
635C2×C4⋊C4C23×C15111yescharacteristic
636C2×C4⋊C4C23×C15111yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C15111yescharacteristic
647C2×C22⋊C4D4×C15111yescharacteristic
648C2×C42—21no—
649C2×C42C23×C15111yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#102—22no—
656#102—41no—
657#102—41no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C15111yescharacteristic
667C24C2×D4×C15111yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8C2×D4×C15112yes—
697C2×Q8C2×D4×C15112yes—
698C2×Q8C2×D4×C15112yes—
699C2×Q8C2×D4×C15112yes—
700C2×Q8C2×D4×C15112yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—81no—
726C2×D4C2×D4×C15112yes—
727C2×D4C2×D4×C15112yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—24no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C15111yescharacteristic
754C22×C4C2×D4×C15111yescharacteristic
755C22×C4C2×D4×C15111yescharacteristic
756C22×C4C2×D4×C15111yescharacteristic
757C22×C4C2×D4×C15112yes—
758C22×C4C2×D4×C15112yes—
759C22×C4C24×C15111yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C15112yes—
778C2×C8C2×D4×C15112yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—42no—
788C4⋊C4C2×D4×C15112yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—22no—
816C23—22no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23#120×C15112yes—
830C23#135×C15112yescomplemented
831C23C22×D4×C15111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—22no—
839Q8—48no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8#120×C15114yes—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—48no—
850D4—44no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—84no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4#120×C15112yes—
899C2×C4C22×D4×C15111yescharacteristic
900C2×C4C22×D4×C15111yescharacteristic
901C2×C4C22×D4×C15111yescharacteristic
902C2×C4C22×D4×C15111yescharacteristic
903C2×C4H(5,𝔽2)×C15111yescharacteristic
904C2×C4H(5,𝔽2)×C15111yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C15111yescharacteristic
938C22D42×C15111yescharacteristic
939C22D42×C15111yescharacteristic
940C22C2×#135×C15111yescharacteristic
941C22#575×C15111yescharacteristic
942C22#577×C15111yescharacteristic
943C22#578×C15111yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C15111yescharacteristic
955C4#534×C15111yescharacteristic
956C4D42×C15111yescharacteristic
957C4D42×C15111yescharacteristic
958C2—42no—
959C2—42no—
960C2—82no—
961C2—82no—
962C2#2403×C15111yescharacteristic
963C2#3002×C15111yescharacteristic
964C2#3013×C15111yescharacteristic
965C2#3269×C15111yescharacteristic
966C2#3271×C15111yescharacteristic
967C2#3282×C15111yescharacteristic
968C2#3285×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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. C22×#135×C151C2semidirect
2. C2×#548×C151C2semidirect
3. C2×#452×C151C2semidirect
4. C2×#451×C151C2semidirect
5. C2×#448×C151C2semidirect
6. #2407×C151C2semidirect
7. #2015×C151C2semidirect
8. #2012×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1892×C151C2semidirect
12. #1880×C151C2semidirect
13. #1878×C151C2semidirect
14. #1869×C151C2semidirect
15. #1788×C151C2semidirect
78. C2×#41×C151D4semidirect
107. C2×Q16×C151D4semidirect
116. C2×SD16×C151D4semidirect
134. C22⋊Q8×C151D4semidirect
345. C23×C151#135semidirect
484. #23854C151direct (N × H)
485. C151#23854direct (N × H)
486. C22×#135C2×C151semidirect
487. C2×#548C2×C151semidirect
488. C2×#452C2×C151semidirect
489. C2×#451C2×C151semidirect
490. C2×#448C2×C151semidirect
491. #2407C2×C151semidirect
492. #2015C2×C151semidirect
493. #2012C2×C151semidirect
494. #2000C2×C151semidirect
495. #1999C2×C151semidirect
496. #1892C2×C151semidirect
497. #1880C2×C151semidirect
498. #1878C2×C151semidirect
499. #1869C2×C151semidirect
500. #1788C2×C151semidirect
563. C2×#41D4×C151semidirect
592. C2×Q16D4×C151semidirect
601. C2×SD16D4×C151semidirect
619. C22⋊Q8D4×C151semidirect
830. C23#135×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1512
C2×#548×C1512
C2×#452×C1512
C2×#451×C1512
C2×#448×C1512
#2407×C1512
#2015×C1512
#2012×C1512
#2000×C1512
#1999×C1512
#1892×C1512
#1880×C1512
#1878×C1512
#1869×C1512
#1788×C1512
#23854151