Finite Group Databasebeta

← C151×#24427 #50329352

Subgroups — C151×#24427 #50329352

Order 38656.

1500 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic
2C2×#465×C151C211yesmaximal, characteristic, complemented
3C2×#452×C151C211yesmaximal, characteristic, complemented
4C2×#452×C151C211yesmaximal, characteristic, complemented
5C2×#416×C151C211yesmaximal, characteristic, complemented
6#2415×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2014×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1875×C151C211yesmaximal, characteristic, complemented
13#1869×C151C211yesmaximal, characteristic, complemented
14#1865×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C22×SD16×C151C2211yescharacteristic
20C22×SD16×C151C2211yescharacteristic
21C23×C8×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
35C2×#117×C151C2211yescharacteristic
36#465×C151—24no—
37#452×C151—24no—
38#452×C151—24no—
39C2×#106×C151C2211yescharacteristic
40#416×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#397×C151—21no—
55#394×C151—21no—
56#391×C151C2211yescharacteristic
57#389×C151—21no—
58#389×C151C2211yescharacteristic
59#388×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×C151C2311yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C2×Q16×C151—22no—
93C2×Q16×C151—22no—
94C2×Q16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—41no—
99C2×SD16×C151—41no—
100C2×SD16×C151—41no—
101C22×C8×C151—22no—
102C22×C8×C151—22no—
103C22×C8×C151—41no—
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107C22×C8×C151C2311yescharacteristic
108#127×C151—28no—
109#127×C151—22no—
110#127×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—41no—
115#121×C151—28no—
116#121×C151—28no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151D414yes—
121C4×Q8×C151—22no—
122C4×Q8×C151—22no—
123C4×D4×C151—28no—
124C4×D4×C151—22no—
125C4×D4×C151—22no—
126#117×C151—22no—
127#117×C151—41no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—21no—
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×C151D411yescharacteristic
144C2×C22⋊C4×C151D411yescharacteristic
145C2×C42×C151—21no—
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×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×C151C2×D411yescharacteristic
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151C2×D411yescharacteristic
248C22×C4×C151C2×D412yes—
249C22×C4×C151C2×D412yes—
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2411yescharacteristic
252Q16×C151—44no—
253SD16×C151—44no—
254SD16×C151—44no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
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—44no—
267C2×C8×C151C2×D412yes—
268C4⋊C4×C151—24no—
269C4⋊C4×C151—22no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—42no—
277C4⋊C4×C151—42no—
278C4⋊C4×C151—42no—
279C4⋊C4×C151C2×D412yes—
280C4⋊C4×C151C2×D412yes—
281C22⋊C4×C151—24no—
282C22⋊C4×C151—22no—
283C22⋊C4×C151—24no—
284C22⋊C4×C151—22no—
285C22⋊C4×C151—42no—
286C22⋊C4×C151—42no—
287C22⋊C4×C151—42no—
288C22⋊C4×C151—42no—
289C42×C151—24no—
290C42×C151—21no—
291C42×C151—21no—
292C42×C151—42no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—22no—
300C23×C151—22no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—41no—
309C23×C151—41no—
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#12012yes—
321C23×C151C22×D411yescharacteristic
322Q8×C151—22no—
323Q8×C151—22no—
324Q8×C151—22no—
325Q8×C151—41no—
326Q8×C151—41no—
327Q8×C151—41no—
328Q8×C151—41no—
329Q8×C151#12114yes—
330D4×C151—22no—
331D4×C151—22no—
332D4×C151—22no—
333D4×C151—22no—
334D4×C151—48no—
335D4×C151—44no—
336D4×C151—48no—
337D4×C151—48no—
338D4×C151—41no—
339D4×C151—41no—
340D4×C151—41no—
341D4×C151—41no—
342D4×C151—84no—
343D4×C151—84no—
344D4×C151—84no—
345C2×C4×C151—22no—
346C2×C4×C151—21no—
347C2×C4×C151—22no—
348C2×C4×C151—21no—
349C2×C4×C151—22no—
350C2×C4×C151—21no—
351C2×C4×C151—21no—
352C2×C4×C151—22no—
353C2×C4×C151—22no—
354C2×C4×C151—22no—
355C2×C4×C151—22no—
356C2×C4×C151—21no—
357C2×C4×C151—22no—
358C2×C4×C151—21no—
359C2×C4×C151—22no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—21no—
363C2×C4×C151—21no—
364C2×C4×C151—48no—
365C2×C4×C151—48no—
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—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#12012yes—
384C2×C4×C151#13512yes—
385C2×C4×C151C22×D411yescharacteristic
386C2×C4×C151C22×D411yescharacteristic
387C2×C4×C151C22×D411yescharacteristic
388C2×C4×C151C2×#4111yescharacteristic
389C2×C4×C151H(5,𝔽2)11yescharacteristic
390C2×C4×C151H(5,𝔽2)11yescharacteristic
391C8×C151—22no—
392C8×C151—41no—
393C8×C151—41no—
394C8×C151—41no—
395C22×C151—22no—
396C22×C151—22no—
397C22×C151—22no—
398C22×C151—41no—
399C22×C151—41no—
400C22×C151—41no—
401C22×C151—41no—
402C22×C151—42no—
403C22×C151—42no—
404C22×C151—41no—
405C22×C151—41no—
406C22×C151—42no—
407C22×C151—42no—
408C22×C151—41no—
409C22×C151—42no—
410C22×C151—42no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—81no—
416C22×C151—81no—
417C22×C151—81no—
418C22×C151—81no—
419C22×C151—81no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151—81no—
423C22×C151C2×#12011yescharacteristic
424C22×C151D4211yescharacteristic
425C22×C151#54611yescharacteristic
426C22×C151C2×#13511yescharacteristic
427C22×C151#57511yescharacteristic
428C22×C151#57711yescharacteristic
429C22×C151#57711yescharacteristic
430C4×C151—22no—
431C4×C151—24no—
432C4×C151—22no—
433C4×C151—41no—
434C4×C151—41no—
435C4×C151—42no—
436C4×C151—42no—
437C4×C151—81no—
438C4×C151—81no—
439C4×C151—81no—
440C4×C151C2×#12111yescharacteristic
441C4×C151#53411yescharacteristic
442C4×C151D4211yescharacteristic
443C4×C151#54611yescharacteristic
444C2×C151—42no—
445C2×C151—81no—
446C2×C151—82no—
447C2×C151—82no—
448C2×C151#241011yescharacteristic
449C2×C151#300211yescharacteristic
450C2×C151#300911yescharacteristic
451C2×C151#327111yescharacteristic
452C2×C151#328411yescharacteristic
453C2×C151#330411yescharacteristic
454C2×C151#331711yescharacteristic
455#24427C15111yesmaximal, characteristic, direct product factor, Sylow
456C151#2442711yescharacteristic, direct product factor, Sylow
457C2×#550C2×C15111yescharacteristic
458C2×#465C2×C15111yescharacteristic, complemented
459C2×#452C2×C15111yescharacteristic, complemented
460C2×#452C2×C15111yescharacteristic, complemented
461C2×#416C2×C15111yescharacteristic, complemented
462#2415C2×C15111yescharacteristic, complemented
463#2041C2×C15111yescharacteristic, complemented
464#2034C2×C15111yescharacteristic, complemented
465#2014C2×C15111yescharacteristic, complemented
466#2000C2×C15111yescharacteristic, complemented
467#1878C2×C15111yescharacteristic, complemented
468#1875C2×C15111yescharacteristic, complemented
469#1869C2×C15111yescharacteristic, complemented
470#1865C2×C15111yescharacteristic, complemented
471#1788C2×C15111yescharacteristic, complemented
472C22×#41C22×C15111yescharacteristic
473C22×#41C22×C15111yescharacteristic
474C22×Q16C22×C15111yescharacteristic
475C22×SD16C22×C15111yescharacteristic
476C22×SD16C22×C15111yescharacteristic
477C23×C8C22×C15111yescharacteristic
478#550—24no—
479#550—24no—
480C2×#127—21no—
481C2×#127C22×C15111yescharacteristic
482C2×C22⋊Q8C22×C15111yescharacteristic
483C2×C22⋊Q8C22×C15111yescharacteristic
484C2×#121—21no—
485C2×#121—21no—
486C2×#121C22×C15111yescharacteristic
487C2×#121C22×C15111yescharacteristic
488C2×C4×Q8C22×C15111yescharacteristic
489C2×C4×D4—21no—
490C2×C4×D4C22×C15111yescharacteristic
491C2×#117C22×C15111yescharacteristic
492#465—24no—
493#452—24no—
494#452—24no—
495C2×#106C22×C15111yescharacteristic
496#416—24no—
497C2×#103C22×C15111yescharacteristic
498C2×#103C22×C15111yescharacteristic
499C2×#103C22×C15111yescharacteristic
500C2×#103C22×C15111yescharacteristic
501C2×#102C22×C15111yescharacteristic
502C2×#102C22×C15111yescharacteristic
503C2×#102C22×C15111yescharacteristic
504C2×#102C22×C15111yescharacteristic
505C2×#102C22×C15111yescharacteristic
506C2×#102C22×C15111yescharacteristic
507C2×C22⋊C8C22×C15111yescharacteristic
508C2×C22⋊C8C22×C15111yescharacteristic
509C2×C22⋊C8C22×C15111yescharacteristic
510#397—21no—
511#394—21no—
512#391C22×C15111yescharacteristic
513#389—21no—
514#389C22×C15111yescharacteristic
515#388—21no—
516#380C22×C15111yescharacteristic
517#340C22×C15111yescharacteristic
518#340C22×C15111yescharacteristic
519#336C22×C15111yescharacteristic
520#336C22×C15111yescharacteristic
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C15114yes—
533C22×Q8C23×C15111yescharacteristic
534C22×Q8C23×C15111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C15111yescharacteristic
542C22×D4C23×C15111yescharacteristic
543C22×D4C23×C15111yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C15111yescharacteristic
547C23×C4C23×C15111yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C23×C15111yescharacteristic
561C22×C8C23×C15111yescharacteristic
562C22×C8C23×C15111yescharacteristic
563C22×C8C23×C15111yescharacteristic
564#127—28no—
565#127—22no—
566#127—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571#121—28no—
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121D4×C15114yes—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582#117—22no—
583#117—41no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C15111yescharacteristic
589C2×C4⋊C4C23×C15111yescharacteristic
590C2×C4⋊C4C23×C15111yescharacteristic
591C2×C4⋊C4C23×C15111yescharacteristic
592C2×C4⋊C4C23×C15111yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4D4×C15111yescharacteristic
600C2×C22⋊C4D4×C15111yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C23×C15111yescharacteristic
604#106—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608#103D4×C15114yescomplemented
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616C22⋊C8—22no—
617C22⋊C8—41no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622C24—21no—
623C24—21no—
624C24C2×D4×C15111yescharacteristic
625C24C2×D4×C15111yescharacteristic
626#41—28no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C15112yes—
644C2×Q8C2×D4×C15112yes—
645C2×Q8#41×C15112yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C15112yes—
678C2×D4C2×D4×C15112yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4C2×D4×C15111yescharacteristic
702C22×C4C2×D4×C15111yescharacteristic
703C22×C4C2×D4×C15111yescharacteristic
704C22×C4C2×D4×C15112yes—
705C22×C4C2×D4×C15112yes—
706C22×C4C2×D4×C15111yescharacteristic
707C22×C4C24×C15111yescharacteristic
708Q16—44no—
709SD16—44no—
710SD16—44no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C15112yes—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4C2×D4×C15112yes—
736C4⋊C4C2×D4×C15112yes—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C42—24no—
746C42—21no—
747C42—21no—
748C42—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23#120×C15112yes—
777C23C22×D4×C15111yescharacteristic
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8#121×C15114yes—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—84no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
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#120×C15112yes—
840C2×C4#135×C15112yes—
841C2×C4C22×D4×C15111yescharacteristic
842C2×C4C22×D4×C15111yescharacteristic
843C2×C4C22×D4×C15111yescharacteristic
844C2×C4C2×#41×C15111yescharacteristic
845C2×C4H(5,𝔽2)×C15111yescharacteristic
846C2×C4H(5,𝔽2)×C15111yescharacteristic
847C8—22no—
848C8—41no—
849C8—41no—
850C8—41no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×#120×C15111yescharacteristic
880C22D42×C15111yescharacteristic
881C22#546×C15111yescharacteristic
882C22C2×#135×C15111yescharacteristic
883C22#575×C15111yescharacteristic
884C22#577×C15111yescharacteristic
885C22#577×C15111yescharacteristic
886C4—22no—
887C4—24no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4C2×#121×C15111yescharacteristic
897C4#534×C15111yescharacteristic
898C4D42×C15111yescharacteristic
899C4#546×C15111yescharacteristic
900C2—42no—
901C2—81no—
902C2—82no—
903C2—82no—
904C2#2410×C15111yescharacteristic
905C2#3002×C15111yescharacteristic
906C2#3009×C15111yescharacteristic
907C2#3271×C15111yescharacteristic
908C2#3284×C15111yescharacteristic
909C2#3304×C15111yescharacteristic
910C2#3317×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×#465×C151C2semidirect
3. C2×#452×C151C2semidirect
4. C2×#452×C151C2semidirect
5. C2×#416×C151C2semidirect
6. #2415×C151C2semidirect
7. #2041×C151C2semidirect
8. #2034×C151C2semidirect
9. #2014×C151C2semidirect
10. #2000×C151C2semidirect
11. #1878×C151C2semidirect
12. #1875×C151C2semidirect
13. #1869×C151C2semidirect
14. #1865×C151C2semidirect
15. #1788×C151C2semidirect
152. #103×C151D4semidirect
455. #24427C151direct (N × H)
456. C151#24427direct (N × H)
458. C2×#465C2×C151semidirect
459. C2×#452C2×C151semidirect
460. C2×#452C2×C151semidirect
461. C2×#416C2×C151semidirect
462. #2415C2×C151semidirect
463. #2041C2×C151semidirect
464. #2034C2×C151semidirect
465. #2014C2×C151semidirect
466. #2000C2×C151semidirect
467. #1878C2×C151semidirect
468. #1875C2×C151semidirect
469. #1869C2×C151semidirect
470. #1865C2×C151semidirect
471. #1788C2×C151semidirect
608. #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×#465×C1512
C2×#452×C1512
C2×#416×C1512
#2415×C1512
#2041×C1512
#2034×C1512
#2014×C1512
#2000×C1512
#1878×C1512
#1875×C1512
#1869×C1512
#1865×C1512
#1788×C1512
#24427151