Finite Group Databasebeta

← C151×#24431 #50329356

Subgroups — C151×#24431 #50329356

Order 38656.

1464 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C151C211yesmaximal, characteristic
2C2×#465×C151C211yesmaximal, characteristic, complemented
3C2×#452×C151C211yesmaximal, characteristic, complemented
4C2×#451×C151C211yesmaximal, characteristic, complemented
5C22×#103×C151C211yesmaximal, characteristic, complemented
6#2417×C151C211yesmaximal, characteristic, complemented
7#2042×C151C211yesmaximal, characteristic, complemented
8#2035×C151C211yesmaximal, characteristic, complemented
9#2015×C151C211yesmaximal, characteristic, complemented
10#2001×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1869×C151C211yesmaximal, characteristic, complemented
14#1865×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×Q8×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C22×Q16×C151C2211yescharacteristic
20C22×SD16×C151C2211yescharacteristic
21C23×C8×C151C2211yescharacteristic
22#548×C151—24no—
23#548×C151—24no—
24C2×#124×C151—21no—
25C2×#124×C151C2211yescharacteristic
26C2×C22⋊Q8×C151—21no—
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×C22⋊Q8×C151C2211yescharacteristic
30C2×#121×C151—21no—
31C2×#121×C151C2211yescharacteristic
32C2×C4×Q8×C151C2211yescharacteristic
33C2×C4×D4×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35C22×C4⋊C4×C151C2211yescharacteristic
36#465×C151—24no—
37#452×C151—24no—
38#451×C151—24no—
39C2×#106×C151C2211yescharacteristic
40C2×#103×C151—24no—
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#103×C151C2211yescharacteristic
47C2×#103×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—41no—
70C2×#41×C151—41no—
71C22×Q8×C151—22no—
72C22×Q8×C151—22no—
73C22×Q8×C151—21no—
74C22×Q8×C151—22no—
75C22×Q8×C151—41no—
76C22×Q8×C151—41no—
77C22×Q8×C151D414yes—
78C22×Q8×C151C2311yescharacteristic
79C22×Q8×C151C2311yescharacteristic
80C22×Q8×C151C2311yescharacteristic
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151D411yescharacteristic
84C22×D4×C151C2311yescharacteristic
85C23×C4×C151—21no—
86C23×C4×C151—21no—
87C23×C4×C151—21no—
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C2×Q16×C151—22no—
91C2×Q16×C151—22no—
92C2×Q16×C151—22no—
93C2×Q16×C151—22no—
94C2×Q16×C151—41no—
95C2×Q16×C151—41no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—41no—
99C22×C8×C151—22no—
100C22×C8×C151—22no—
101C22×C8×C151—41no—
102C22×C8×C151C2311yescharacteristic
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106#124×C151—28no—
107#124×C151—22no—
108#124×C151—22no—
109C22⋊Q8×C151—28no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×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—22no—
118#121×C151D414yes—
119C4×Q8×C151—22no—
120C4×Q8×C151—22no—
121C4×D4×C151—28no—
122C4×D4×C151—22no—
123C4×D4×C151—22no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—22no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—41no—
132C2×C4⋊C4×C151D411yescharacteristic
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C4⋊C4×C151C2311yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
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#106×C151—22no—
149#103×C151—22no—
150#103×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151—22no—
154#103×C151—22no—
155#103×C151D414yescomplemented
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×C151C2×D411yescharacteristic
168C24×C151C2×D411yescharacteristic
169#41×C151—44no—
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—44no—
173C2×Q8×C151—24no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—28no—
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×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151—42no—
190C2×Q8×C151—42no—
191C2×Q8×C151—44no—
192C2×Q8×C151—44no—
193C2×Q8×C151—44no—
194C2×Q8×C151C2×D412yes—
195C2×Q8×C151C2×D412yes—
196C2×Q8×C151C2×D412yes—
197C2×Q8×C151#4112yes—
198C2×D4×C151—24no—
199C2×D4×C151—22no—
200C2×D4×C151—24no—
201C2×D4×C151—22no—
202C2×D4×C151—22no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151C2×D412yes—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—24no—
219C22×C4×C151—24no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—42no—
233C22×C4×C151—42no—
234C22×C4×C151—42no—
235C22×C4×C151—42no—
236C22×C4×C151—42no—
237C22×C4×C151—42no—
238C22×C4×C151—81no—
239C22×C4×C151C2×D411yescharacteristic
240C22×C4×C151C2×D411yescharacteristic
241C22×C4×C151C2×D411yescharacteristic
242C22×C4×C151C2×D411yescharacteristic
243C22×C4×C151C2×D412yes—
244C22×C4×C151C2×D412yes—
245C22×C4×C151C2411yescharacteristic
246Q16×C151—44no—
247Q16×C151—44no—
248SD16×C151—44no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—44no—
261C2×C8×C151C2×D412yes—
262C4⋊C4×C151—24no—
263C4⋊C4×C151—24no—
264C4⋊C4×C151—22no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—42no—
272C4⋊C4×C151—42no—
273C4⋊C4×C151—42no—
274C4⋊C4×C151—81no—
275C4⋊C4×C151C2×D412yes—
276C4⋊C4×C151C2×D412yes—
277C22⋊C4×C151—24no—
278C22⋊C4×C151—24no—
279C22⋊C4×C151—24no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—24no—
282C22⋊C4×C151—22no—
283C22⋊C4×C151—42no—
284C22⋊C4×C151—42no—
285C22⋊C4×C151—81no—
286C42×C151—24no—
287C42×C151—21no—
288C42×C151—21no—
289C23×C151—21no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—22no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151#12012yes—
308C23×C151#13512yes—
309C23×C151#13712yes—
310C23×C151C22×D411yescharacteristic
311Q8×C151—22no—
312Q8×C151—22no—
313Q8×C151—22no—
314Q8×C151—22no—
315Q8×C151—22no—
316Q8×C151—48no—
317Q8×C151—41no—
318Q8×C151—41no—
319Q8×C151—41no—
320Q8×C151—41no—
321Q8×C151—41no—
322Q8×C151—41no—
323Q8×C151#12114yes—
324D4×C151—22no—
325D4×C151—22no—
326D4×C151—48no—
327D4×C151—44no—
328D4×C151—48no—
329D4×C151—41no—
330D4×C151—41no—
331C2×C4×C151—22no—
332C2×C4×C151—22no—
333C2×C4×C151—21no—
334C2×C4×C151—22no—
335C2×C4×C151—21no—
336C2×C4×C151—22no—
337C2×C4×C151—22no—
338C2×C4×C151—22no—
339C2×C4×C151—22no—
340C2×C4×C151—22no—
341C2×C4×C151—21no—
342C2×C4×C151—21no—
343C2×C4×C151—22no—
344C2×C4×C151—21no—
345C2×C4×C151—22no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—21no—
352C2×C4×C151—48no—
353C2×C4×C151—48no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—84no—
374C2×C4×C151#12012yes—
375C2×C4×C151C22×D411yescharacteristic
376C2×C4×C151C22×D411yescharacteristic
377C2×C4×C151C22×D411yescharacteristic
378C2×C4×C151C2×#4111yescharacteristic
379C2×C4×C151H(5,𝔽2)11yescharacteristic
380C2×C4×C151H(5,𝔽2)11yescharacteristic
381C8×C151—22no—
382C8×C151—41no—
383C8×C151—41no—
384C8×C151—41no—
385C22×C151—22no—
386C22×C151—22no—
387C22×C151—22no—
388C22×C151—22no—
389C22×C151—22no—
390C22×C151—22no—
391C22×C151—42no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—42no—
395C22×C151—41no—
396C22×C151—42no—
397C22×C151—41no—
398C22×C151—41no—
399C22×C151—41no—
400C22×C151—41no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151—81no—
404C22×C151—81no—
405C22×C151#45214yescomplemented
406C22×C151C2×#12011yescharacteristic
407C22×C151D4211yescharacteristic
408C22×C151#54611yescharacteristic
409C22×C151C2×#13511yescharacteristic
410C22×C151C2×#13711yescharacteristic
411C22×C151#57711yescharacteristic
412C22×C151#57811yescharacteristic
413C4×C151—22no—
414C4×C151—24no—
415C4×C151—41no—
416C4×C151—42no—
417C4×C151—41no—
418C4×C151—42no—
419C4×C151—41no—
420C4×C151—42no—
421C4×C151—81no—
422C4×C151—81no—
423C4×C151—81no—
424C4×C151C2×#12111yescharacteristic
425C4×C151#53411yescharacteristic
426C4×C151D4211yescharacteristic
427C4×C151#54611yescharacteristic
428C2×C151—24no—
429C2×C151—81no—
430C2×C151—82no—
431C2×C151#241011yescharacteristic
432C2×C151C2×#45211yescharacteristic
433C2×C151#301311yescharacteristic
434C2×C151#327011yescharacteristic
435C2×C151#328211yescharacteristic
436C2×C151#330011yescharacteristic
437C2×C151#331611yescharacteristic
438#24431C15111yesmaximal, characteristic, direct product factor, Sylow
439C151#2443111yescharacteristic, direct product factor, Sylow
440C2×#548C2×C15111yescharacteristic
441C2×#465C2×C15111yescharacteristic, complemented
442C2×#452C2×C15111yescharacteristic, complemented
443C2×#451C2×C15111yescharacteristic, complemented
444C22×#103C2×C15111yescharacteristic, complemented
445#2417C2×C15111yescharacteristic, complemented
446#2042C2×C15111yescharacteristic, complemented
447#2035C2×C15111yescharacteristic, complemented
448#2015C2×C15111yescharacteristic, complemented
449#2001C2×C15111yescharacteristic, complemented
450#1878C2×C15111yescharacteristic, complemented
451#1874C2×C15111yescharacteristic, complemented
452#1869C2×C15111yescharacteristic, complemented
453#1865C2×C15111yescharacteristic, complemented
454#1788C2×C15111yescharacteristic, complemented
455C22×#41C22×C15111yescharacteristic
456C23×Q8C22×C15111yescharacteristic
457C22×Q16C22×C15111yescharacteristic
458C22×Q16C22×C15111yescharacteristic
459C22×SD16C22×C15111yescharacteristic
460C23×C8C22×C15111yescharacteristic
461#548—24no—
462#548—24no—
463C2×#124—21no—
464C2×#124C22×C15111yescharacteristic
465C2×C22⋊Q8—21no—
466C2×C22⋊Q8C22×C15111yescharacteristic
467C2×C22⋊Q8C22×C15111yescharacteristic
468C2×C22⋊Q8C22×C15111yescharacteristic
469C2×#121—21no—
470C2×#121C22×C15111yescharacteristic
471C2×C4×Q8C22×C15111yescharacteristic
472C2×C4×D4—21no—
473C2×C4×D4C22×C15111yescharacteristic
474C22×C4⋊C4C22×C15111yescharacteristic
475#465—24no—
476#452—24no—
477#451—24no—
478C2×#106C22×C15111yescharacteristic
479C2×#103—24no—
480C2×#103C22×C15111yescharacteristic
481C2×#103C22×C15111yescharacteristic
482C2×#103C22×C15111yescharacteristic
483C2×#103C22×C15111yescharacteristic
484C2×#103C22×C15111yescharacteristic
485C2×#103C22×C15111yescharacteristic
486C2×#103C22×C15111yescharacteristic
487C2×#102C22×C15111yescharacteristic
488C2×#102C22×C15111yescharacteristic
489C2×#102C22×C15111yescharacteristic
490C2×C22⋊C8C22×C15111yescharacteristic
491C2×C22⋊C8C22×C15111yescharacteristic
492C2×C22⋊C8C22×C15111yescharacteristic
493#398—21no—
494#396—21no—
495#391C22×C15111yescharacteristic
496#389C22×C15111yescharacteristic
497#386—21no—
498#380—21no—
499#380C22×C15111yescharacteristic
500#340C22×C15111yescharacteristic
501#340C22×C15111yescharacteristic
502#336C22×C15111yescharacteristic
503#336C22×C15111yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8D4×C15114yes—
517C22×Q8C23×C15111yescharacteristic
518C22×Q8C23×C15111yescharacteristic
519C22×Q8C23×C15111yescharacteristic
520C22×D4—21no—
521C22×D4—21no—
522C22×D4D4×C15111yescharacteristic
523C22×D4C23×C15111yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C23×C15111yescharacteristic
528C23×C4C23×C15111yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—41no—
541C22×C8C23×C15111yescharacteristic
542C22×C8C23×C15111yescharacteristic
543C22×C8C23×C15111yescharacteristic
544C22×C8C23×C15111yescharacteristic
545#124—28no—
546#124—22no—
547#124—22no—
548C22⋊Q8—28no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—41no—
555#121—28no—
556#121—22no—
557#121D4×C15114yes—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×D4—28no—
561C4×D4—22no—
562C4×D4—22no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4D4×C15111yescharacteristic
572C2×C4⋊C4C23×C15111yescharacteristic
573C2×C4⋊C4C23×C15111yescharacteristic
574C2×C4⋊C4C23×C15111yescharacteristic
575C2×C4⋊C4C23×C15111yescharacteristic
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4D4×C15111yescharacteristic
584C2×C22⋊C4D4×C15111yescharacteristic
585C2×C42—21no—
586C2×C42C23×C15111yescharacteristic
587#106—22no—
588#103—22no—
589#103—22no—
590#103—22no—
591#103—22no—
592#103—22no—
593#103—22no—
594#103D4×C15114yescomplemented
595#102—22no—
596#102—22no—
597#102—41no—
598C22⋊C8—22no—
599C22⋊C8—22no—
600C22⋊C8—41no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—21no—
606C24C2×D4×C15111yescharacteristic
607C24C2×D4×C15111yescharacteristic
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—24no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—28no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—42no—
629C2×Q8—42no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8C2×D4×C15112yes—
634C2×Q8C2×D4×C15112yes—
635C2×Q8C2×D4×C15112yes—
636C2×Q8#41×C15112yes—
637C2×D4—24no—
638C2×D4—22no—
639C2×D4—24no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4C2×D4×C15112yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4C2×D4×C15111yescharacteristic
679C22×C4C2×D4×C15111yescharacteristic
680C22×C4C2×D4×C15111yescharacteristic
681C22×C4C2×D4×C15111yescharacteristic
682C22×C4C2×D4×C15112yes—
683C22×C4C2×D4×C15112yes—
684C22×C4C24×C15111yescharacteristic
685Q16—44no—
686Q16—44no—
687SD16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—44no—
700C2×C8C2×D4×C15112yes—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—22no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—42no—
713C4⋊C4—81no—
714C4⋊C4C2×D4×C15112yes—
715C4⋊C4C2×D4×C15112yes—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—22no—
720C22⋊C4—24no—
721C22⋊C4—22no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—81no—
725C42—24no—
726C42—21no—
727C42—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23#120×C15112yes—
747C23#135×C15112yes—
748C23#137×C15112yes—
749C23C22×D4×C15111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—48no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—41no—
762Q8#121×C15114yes—
763D4—22no—
764D4—22no—
765D4—48no—
766D4—44no—
767D4—48no—
768D4—41no—
769D4—41no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—48no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—84no—
813C2×C4#120×C15112yes—
814C2×C4C22×D4×C15111yescharacteristic
815C2×C4C22×D4×C15111yescharacteristic
816C2×C4C22×D4×C15111yescharacteristic
817C2×C4C2×#41×C15111yescharacteristic
818C2×C4H(5,𝔽2)×C15111yescharacteristic
819C2×C4H(5,𝔽2)×C15111yescharacteristic
820C8—22no—
821C8—41no—
822C8—41no—
823C8—41no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22#452×C15114yescomplemented
845C22C2×#120×C15111yescharacteristic
846C22D42×C15111yescharacteristic
847C22#546×C15111yescharacteristic
848C22C2×#135×C15111yescharacteristic
849C22C2×#137×C15111yescharacteristic
850C22#577×C15111yescharacteristic
851C22#578×C15111yescharacteristic
852C4—22no—
853C4—24no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—42no—
858C4—41no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4C2×#121×C15111yescharacteristic
864C4#534×C15111yescharacteristic
865C4D42×C15111yescharacteristic
866C4#546×C15111yescharacteristic
867C2—24no—
868C2—81no—
869C2—82no—
870C2#2410×C15111yescharacteristic
871C2C2×#452×C15111yescharacteristic
872C2#3013×C15111yescharacteristic
873C2#3270×C15111yescharacteristic
874C2#3282×C15111yescharacteristic
875C2#3300×C15111yescharacteristic
876C2#3316×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#548×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×#465×C151C2semidirect
3. C2×#452×C151C2semidirect
4. C2×#451×C151C2semidirect
5. C22×#103×C151C2semidirect
6. #2417×C151C2semidirect
7. #2042×C151C2semidirect
8. #2035×C151C2semidirect
9. #2015×C151C2semidirect
10. #2001×C151C2semidirect
11. #1878×C151C2semidirect
12. #1874×C151C2semidirect
13. #1869×C151C2semidirect
14. #1865×C151C2semidirect
15. #1788×C151C2semidirect
155. #103×C151D4semidirect
405. C22×C151#452semidirect
438. #24431C151direct (N × H)
439. C151#24431direct (N × H)
441. C2×#465C2×C151semidirect
442. C2×#452C2×C151semidirect
443. C2×#451C2×C151semidirect
444. C22×#103C2×C151semidirect
445. #2417C2×C151semidirect
446. #2042C2×C151semidirect
447. #2035C2×C151semidirect
448. #2015C2×C151semidirect
449. #2001C2×C151semidirect
450. #1878C2×C151semidirect
451. #1874C2×C151semidirect
452. #1869C2×C151semidirect
453. #1865C2×C151semidirect
454. #1788C2×C151semidirect
594. #103D4×C151semidirect
844. C22#452×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1512
C2×#465×C1512
C2×#452×C1512
C2×#451×C1512
C22×#103×C1512
#2417×C1512
#2042×C1512
#2035×C1512
#2015×C1512
#2001×C1512
#1878×C1512
#1874×C1512
#1869×C1512
#1865×C1512
#1788×C1512
#24431151