Finite Group Databasebeta

← C151×#24443 #50329368

Subgroups — C151×#24443 #50329368

Order 38656.

1510 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic
2C2×#468×C151C211yesmaximal, characteristic, complemented
3C2×#452×C151C211yesmaximal, characteristic, complemented
4C2×#452×C151C211yesmaximal, characteristic, complemented
5C2×#417×C151C211yesmaximal, characteristic, complemented
6#2417×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#2014×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1870×C151C211yesmaximal, characteristic, complemented
14#1863×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C22×SD16×C151C2211yescharacteristic
20C22×SD16×C151C2211yescharacteristic
21C22×M16×C151C2211yescharacteristic
22#550×C151—24no—
23#550×C151—24no—
24C2×#127×C151—21no—
25C2×#127×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×#121×C151—21no—
29C2×#121×C151—21no—
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic
32C2×C4×Q8×C151C2211yescharacteristic
33C2×C4×D4×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35C22×C4⋊C4×C151C2211yescharacteristic
36#468×C151—24no—
37#452×C151—24no—
38#452×C151—24no—
39C2×#107×C151C2211yescharacteristic
40#417×C151—24no—
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54#398×C151—21no—
55#396×C151—21no—
56#391×C151C2211yescharacteristic
57#389×C151C2211yescharacteristic
58#386×C151—21no—
59#380×C151—21no—
60#380×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63#336×C151C2211yescharacteristic
64#336×C151C2211yescharacteristic
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—22no—
71C2×#41×C151—22no—
72C2×#41×C151—41no—
73C2×#41×C151—41no—
74C2×#41×C151—41no—
75C2×#41×C151—41no—
76C2×#41×C151D414yes—
77C22×Q8×C151C2311yescharacteristic
78C22×Q8×C151C2311yescharacteristic
79C22×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151—21no—
85C22×D4×C151D411yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C23×C4×C151—21no—
89C23×C4×C151—21no—
90C23×C4×C151—21no—
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C2×Q16×C151—22no—
94C2×Q16×C151—22no—
95C2×Q16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—22no—
99C2×SD16×C151—41no—
100C2×SD16×C151—41no—
101C2×SD16×C151—41no—
102C2×M16×C151—22no—
103C2×M16×C151—22no—
104C2×M16×C151—41no—
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107C22×C8×C151C2311yescharacteristic
108C22×C8×C151C2311yescharacteristic
109#127×C151—28no—
110#127×C151—22no—
111#127×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—41no—
116#121×C151—28no—
117#121×C151—28no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151D414yes—
122C4×Q8×C151—22no—
123C4×Q8×C151—22no—
124C4×D4×C151—28no—
125C4×D4×C151—22no—
126C4×D4×C151—22no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—22no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151—21no—
133C2×C4⋊C4×C151—41no—
134C2×C4⋊C4×C151D411yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C4⋊C4×C151C2311yescharacteristic
138C2×C4⋊C4×C151C2311yescharacteristic
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—21no—
142C2×C22⋊C4×C151—21no—
143C2×C22⋊C4×C151—21no—
144C2×C22⋊C4×C151D411yescharacteristic
145C2×C22⋊C4×C151D411yescharacteristic
146C2×C42×C151—21no—
147C2×C42×C151C2311yescharacteristic
148#107×C151—22no—
149#103×C151—22no—
150#103×C151—22no—
151#103×C151—22no—
152#103×C151D414yescomplemented
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—41no—
159C22⋊C8×C151—22no—
160C22⋊C8×C151—22no—
161C22⋊C8×C151—41no—
162#95×C151—21no—
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—21no—
167C24×C151—21no—
168C24×C151C2×D411yescharacteristic
169C24×C151C2×D411yescharacteristic
170#41×C151—28no—
171#41×C151—44no—
172#41×C151—44no—
173#41×C151—44no—
174#41×C151—44no—
175#41×C151—44no—
176#41×C151—44no—
177#41×C151—44no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151C2×D412yes—
188C2×Q8×C151C2×D412yes—
189C2×Q8×C151#4112yes—
190C2×D4×C151—24no—
191C2×D4×C151—24no—
192C2×D4×C151—22no—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—24no—
196C2×D4×C151—24no—
197C2×D4×C151—22no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—41no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—42no—
215C2×D4×C151—81no—
216C2×D4×C151—81no—
217C2×D4×C151—81no—
218C2×D4×C151—81no—
219C2×D4×C151—81no—
220C2×D4×C151—81no—
221C2×D4×C151C2×D412yes—
222C2×D4×C151C2×D412yes—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—24no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—24no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—42no—
242C22×C4×C151—42no—
243C22×C4×C151—42no—
244C22×C4×C151—42no—
245C22×C4×C151—42no—
246C22×C4×C151—42no—
247C22×C4×C151—81no—
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2×D412yes—
252C22×C4×C151C2×D412yes—
253C22×C4×C151C2×D411yescharacteristic
254C22×C4×C151C2411yescharacteristic
255Q16×C151—44no—
256SD16×C151—44no—
257SD16×C151—44no—
258M16×C151—44no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—21no—
270C2×C8×C151C2×D412yes—
271C4⋊C4×C151—24no—
272C4⋊C4×C151—22no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—42no—
280C4⋊C4×C151—42no—
281C4⋊C4×C151—42no—
282C4⋊C4×C151—81no—
283C4⋊C4×C151C2×D412yes—
284C4⋊C4×C151C2×D412yes—
285C22⋊C4×C151—24no—
286C22⋊C4×C151—22no—
287C22⋊C4×C151—24no—
288C22⋊C4×C151—22no—
289C22⋊C4×C151—42no—
290C22⋊C4×C151—42no—
291C22⋊C4×C151—81no—
292C42×C151—24no—
293C42×C151—21no—
294C42×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—22no—
302C23×C151—22no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—41no—
311C23×C151—41no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151—41no—
321C23×C151—41no—
322C23×C151#12012yes—
323C23×C151C22×D411yescharacteristic
324Q8×C151—22no—
325Q8×C151—22no—
326Q8×C151—22no—
327Q8×C151—41no—
328Q8×C151—41no—
329Q8×C151—41no—
330Q8×C151—41no—
331Q8×C151#12114yes—
332D4×C151—22no—
333D4×C151—22no—
334D4×C151—22no—
335D4×C151—22no—
336D4×C151—48no—
337D4×C151—44no—
338D4×C151—48no—
339D4×C151—48no—
340D4×C151—41no—
341D4×C151—41no—
342D4×C151—41no—
343D4×C151—41no—
344D4×C151—84no—
345D4×C151—84no—
346D4×C151—84no—
347C2×C4×C151—22no—
348C2×C4×C151—21no—
349C2×C4×C151—22no—
350C2×C4×C151—21no—
351C2×C4×C151—22no—
352C2×C4×C151—21no—
353C2×C4×C151—21no—
354C2×C4×C151—22no—
355C2×C4×C151—22no—
356C2×C4×C151—22no—
357C2×C4×C151—22no—
358C2×C4×C151—21no—
359C2×C4×C151—22no—
360C2×C4×C151—21no—
361C2×C4×C151—22no—
362C2×C4×C151—21no—
363C2×C4×C151—21no—
364C2×C4×C151—21no—
365C2×C4×C151—21no—
366C2×C4×C151—48no—
367C2×C4×C151—48no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—41no—
378C2×C4×C151—41no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—41no—
384C2×C4×C151—41no—
385C2×C4×C151—84no—
386C2×C4×C151#12012yes—
387C2×C4×C151#13712yes—
388C2×C4×C151C22×D411yescharacteristic
389C2×C4×C151C22×D411yescharacteristic
390C2×C4×C151C22×D411yescharacteristic
391C2×C4×C151C2×#4111yescharacteristic
392C2×C4×C151H(5,𝔽2)11yescharacteristic
393C2×C4×C151H(5,𝔽2)11yescharacteristic
394C8×C151—22no—
395C8×C151—41no—
396C8×C151—41no—
397C8×C151—41no—
398C22×C151—22no—
399C22×C151—22no—
400C22×C151—22no—
401C22×C151—41no—
402C22×C151—41no—
403C22×C151—41no—
404C22×C151—41no—
405C22×C151—41no—
406C22×C151—42no—
407C22×C151—42no—
408C22×C151—41no—
409C22×C151—41no—
410C22×C151—42no—
411C22×C151—42no—
412C22×C151—41no—
413C22×C151—42no—
414C22×C151—42no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—81no—
419C22×C151—81no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151—81no—
423C22×C151—81no—
424C22×C151—81no—
425C22×C151—81no—
426C22×C151C2×#12011yescharacteristic
427C22×C151D4211yescharacteristic
428C22×C151#54611yescharacteristic
429C22×C151C2×#13711yescharacteristic
430C22×C151#57511yescharacteristic
431C22×C151#57611yescharacteristic
432C22×C151#57711yescharacteristic
433C4×C151—22no—
434C4×C151—24no—
435C4×C151—22no—
436C4×C151—41no—
437C4×C151—41no—
438C4×C151—42no—
439C4×C151—42no—
440C4×C151—81no—
441C4×C151—81no—
442C4×C151—81no—
443C4×C151C2×#12111yescharacteristic
444C4×C151#53411yescharacteristic
445C4×C151D4211yescharacteristic
446C4×C151#54611yescharacteristic
447C2×C151—42no—
448C2×C151—81no—
449C2×C151—82no—
450C2×C151—82no—
451C2×C151#241011yescharacteristic
452C2×C151#300711yescharacteristic
453C2×C151#301211yescharacteristic
454C2×C151#326811yescharacteristic
455C2×C151#327811yescharacteristic
456C2×C151#331711yescharacteristic
457C2×C151#333311yescharacteristic
458#24443C15111yesmaximal, characteristic, direct product factor, Sylow
459C151#2444311yescharacteristic, direct product factor, Sylow
460C2×#550C2×C15111yescharacteristic
461C2×#468C2×C15111yescharacteristic, complemented
462C2×#452C2×C15111yescharacteristic, complemented
463C2×#452C2×C15111yescharacteristic, complemented
464C2×#417C2×C15111yescharacteristic, complemented
465#2417C2×C15111yescharacteristic, complemented
466#2041C2×C15111yescharacteristic, complemented
467#2033C2×C15111yescharacteristic, complemented
468#2014C2×C15111yescharacteristic, complemented
469#2000C2×C15111yescharacteristic, complemented
470#1878C2×C15111yescharacteristic, complemented
471#1874C2×C15111yescharacteristic, complemented
472#1870C2×C15111yescharacteristic, complemented
473#1863C2×C15111yescharacteristic, complemented
474#1788C2×C15111yescharacteristic, complemented
475C22×#41C22×C15111yescharacteristic
476C22×#41C22×C15111yescharacteristic
477C22×Q16C22×C15111yescharacteristic
478C22×SD16C22×C15111yescharacteristic
479C22×SD16C22×C15111yescharacteristic
480C22×M16C22×C15111yescharacteristic
481#550—24no—
482#550—24no—
483C2×#127—21no—
484C2×#127C22×C15111yescharacteristic
485C2×C22⋊Q8C22×C15111yescharacteristic
486C2×C22⋊Q8C22×C15111yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C15111yescharacteristic
490C2×#121C22×C15111yescharacteristic
491C2×C4×Q8C22×C15111yescharacteristic
492C2×C4×D4—21no—
493C2×C4×D4C22×C15111yescharacteristic
494C22×C4⋊C4C22×C15111yescharacteristic
495#468—24no—
496#452—24no—
497#452—24no—
498C2×#107C22×C15111yescharacteristic
499#417—24no—
500C2×#103C22×C15111yescharacteristic
501C2×#103C22×C15111yescharacteristic
502C2×#103C22×C15111yescharacteristic
503C2×#103C22×C15111yescharacteristic
504C2×#102C22×C15111yescharacteristic
505C2×#102C22×C15111yescharacteristic
506C2×#102C22×C15111yescharacteristic
507C2×#102C22×C15111yescharacteristic
508C2×#102C22×C15111yescharacteristic
509C2×#102C22×C15111yescharacteristic
510C2×C22⋊C8C22×C15111yescharacteristic
511C2×C22⋊C8C22×C15111yescharacteristic
512C2×C22⋊C8C22×C15111yescharacteristic
513#398—21no—
514#396—21no—
515#391C22×C15111yescharacteristic
516#389C22×C15111yescharacteristic
517#386—21no—
518#380—21no—
519#380C22×C15111yescharacteristic
520#340C22×C15111yescharacteristic
521#340C22×C15111yescharacteristic
522#336C22×C15111yescharacteristic
523#336C22×C15111yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C15114yes—
536C22×Q8C23×C15111yescharacteristic
537C22×Q8C23×C15111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4D4×C15111yescharacteristic
545C22×D4C23×C15111yescharacteristic
546C22×D4C23×C15111yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C15111yescharacteristic
551C23×C4C23×C15111yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C22×C8C23×C15111yescharacteristic
565C22×C8C23×C15111yescharacteristic
566C22×C8C23×C15111yescharacteristic
567C22×C8C23×C15111yescharacteristic
568#127—28no—
569#127—22no—
570#127—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575#121—28no—
576#121—28no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121D4×C15114yes—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4D4×C15111yescharacteristic
594C2×C4⋊C4C23×C15111yescharacteristic
595C2×C4⋊C4C23×C15111yescharacteristic
596C2×C4⋊C4C23×C15111yescharacteristic
597C2×C4⋊C4C23×C15111yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4D4×C15111yescharacteristic
604C2×C22⋊C4D4×C15111yescharacteristic
605C2×C42—21no—
606C2×C42C23×C15111yescharacteristic
607#107—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C15114yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C15111yescharacteristic
628C24C2×D4×C15111yescharacteristic
629#41—28no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8C2×D4×C15112yes—
647C2×Q8C2×D4×C15112yes—
648C2×Q8#41×C15112yes—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4C2×D4×C15112yes—
681C2×D4C2×D4×C15112yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—81no—
707C22×C4C2×D4×C15111yescharacteristic
708C22×C4C2×D4×C15111yescharacteristic
709C22×C4C2×D4×C15111yescharacteristic
710C22×C4C2×D4×C15112yes—
711C22×C4C2×D4×C15112yes—
712C22×C4C2×D4×C15111yescharacteristic
713C22×C4C24×C15111yescharacteristic
714Q16—44no—
715SD16—44no—
716SD16—44no—
717M16—44no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8C2×D4×C15112yes—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C15112yes—
743C4⋊C4C2×D4×C15112yes—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—81no—
751C42—24no—
752C42—21no—
753C42—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C15112yes—
782C23C22×D4×C15111yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8#121×C15114yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—48no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—84no—
804D4—84no—
805D4—84no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C15112yes—
846C2×C4#137×C15112yes—
847C2×C4C22×D4×C15111yescharacteristic
848C2×C4C22×D4×C15111yescharacteristic
849C2×C4C22×D4×C15111yescharacteristic
850C2×C4C2×#41×C15111yescharacteristic
851C2×C4H(5,𝔽2)×C15111yescharacteristic
852C2×C4H(5,𝔽2)×C15111yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C15111yescharacteristic
886C22D42×C15111yescharacteristic
887C22#546×C15111yescharacteristic
888C22C2×#137×C15111yescharacteristic
889C22#575×C15111yescharacteristic
890C22#576×C15111yescharacteristic
891C22#577×C15111yescharacteristic
892C4—22no—
893C4—24no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4C2×#121×C15111yescharacteristic
903C4#534×C15111yescharacteristic
904C4D42×C15111yescharacteristic
905C4#546×C15111yescharacteristic
906C2—42no—
907C2—81no—
908C2—82no—
909C2—82no—
910C2#2410×C15111yescharacteristic
911C2#3007×C15111yescharacteristic
912C2#3012×C15111yescharacteristic
913C2#3268×C15111yescharacteristic
914C2#3278×C15111yescharacteristic
915C2#3317×C15111yescharacteristic
916C2#3333×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#550×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
2. C2×#468×C151C2semidirect
3. C2×#452×C151C2semidirect
4. C2×#452×C151C2semidirect
5. C2×#417×C151C2semidirect
6. #2417×C151C2semidirect
7. #2041×C151C2semidirect
8. #2033×C151C2semidirect
9. #2014×C151C2semidirect
10. #2000×C151C2semidirect
11. #1878×C151C2semidirect
12. #1874×C151C2semidirect
13. #1870×C151C2semidirect
14. #1863×C151C2semidirect
15. #1788×C151C2semidirect
152. #103×C151D4semidirect
458. #24443C151direct (N × H)
459. C151#24443direct (N × H)
461. C2×#468C2×C151semidirect
462. C2×#452C2×C151semidirect
463. C2×#452C2×C151semidirect
464. C2×#417C2×C151semidirect
465. #2417C2×C151semidirect
466. #2041C2×C151semidirect
467. #2033C2×C151semidirect
468. #2014C2×C151semidirect
469. #2000C2×C151semidirect
470. #1878C2×C151semidirect
471. #1874C2×C151semidirect
472. #1870C2×C151semidirect
473. #1863C2×C151semidirect
474. #1788C2×C151semidirect
611. #103D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1512
C2×#468×C1512
C2×#452×C1512
C2×#417×C1512
#2417×C1512
#2041×C1512
#2033×C1512
#2014×C1512
#2000×C1512
#1878×C1512
#1874×C1512
#1870×C1512
#1863×C1512
#1788×C1512
#24443151