Finite Group Databasebeta

← C151×#14520 #50319445

Subgroups — C151×#14520 #50319445

Order 38656.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C151C211yesmaximal, characteristic
2C2×#390×C151C211yesmaximal, characteristic, complemented
3C2×#388×C151C211yesmaximal, characteristic, complemented
4C2×#386×C151C211yesmaximal, characteristic, complemented
5C2×#386×C151C211yesmaximal, characteristic, complemented
6#1442×C151C211yesmaximal, characteristic, complemented
7#1440×C151C211yesmaximal, characteristic, complemented
8#1438×C151C211yesmaximal, characteristic, complemented
9#1438×C151C211yesmaximal, characteristic, complemented
10#1438×C151C211yesmaximal, characteristic, complemented
11#1437×C151C211yesmaximal, characteristic, complemented
12#1437×C151C211yesmaximal, characteristic, complemented
13#1437×C151C211yesmaximal, characteristic, complemented
14#1434×C151C211yesmaximal, characteristic, complemented
15C22⋊#95×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C24×C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C22⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151C2211yescharacteristic
23C22×C22⋊C4×C151C2211yescharacteristic
24C22×C22⋊C4×C151C2211yescharacteristic
25C22×C22⋊C4×C151C2211yescharacteristic
26C22×C22⋊C4×C151C2211yescharacteristic
27C22×C22⋊C4×C151C2211yescharacteristic
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C22×C22⋊C4×C151C2211yescharacteristic
31C22×C22⋊C4×C151C2211yescharacteristic
32C22×C22⋊C4×C151C2211yescharacteristic
33C22×C22⋊C4×C151C2211yescharacteristic
34C22×C22⋊C4×C151C2211yescharacteristic
35C22×C42×C151C2211yescharacteristic
36C22×C42×C151C2211yescharacteristic
37#392×C151C418yescomplemented
38#390×C151—24no—
39#388×C151—24no—
40#386×C151—24no—
41#386×C151—24no—
42C2×#95×C151C2211yescharacteristic
43C2×#95×C151C2211yescharacteristic
44C2×#95×C151C2211yescharacteristic
45C2×#95×C151C2211yescharacteristic
46C2×#95×C151C2211yescharacteristic
47C2×#95×C151C2211yescharacteristic
48C2×#95×C151C2211yescharacteristic
49C2×#95×C151C2211yescharacteristic
50C2×#95×C151C2211yescharacteristic
51C2×#95×C151C2211yescharacteristic
52C2×#95×C151C2211yescharacteristic
53C2×#95×C151C2211yescharacteristic
54C2×#95×C151C2211yescharacteristic
55C2×#95×C151C2211yescharacteristic
56C25×C151C2311yescharacteristic
57C25×C151C2311yescharacteristic
58C25×C151C2311yescharacteristic
59C22×D4×C151—22no—
60C22×D4×C151—22no—
61C22×D4×C151—22no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—41no—
66C22×D4×C151—41no—
67C22×D4×C151—41no—
68C22×D4×C151—41no—
69C22×D4×C151—41no—
70C22×D4×C151—41no—
71C22×D4×C151—41no—
72C22×D4×C151—41no—
73C22×D4×C151—41no—
74C22×D4×C151—41no—
75C22×D4×C151—41no—
76C22×D4×C151—41no—
77C22×D4×C151C2×C414yes—
78C22×D4×C151C2×C414yes—
79C22×D4×C151C2×C414yescomplemented
80C23×C4×C151—22no—
81C23×C4×C151—22no—
82C23×C4×C151—22no—
83C23×C4×C151—41no—
84C23×C4×C151—41no—
85C23×C4×C151—41no—
86C23×C4×C151—41no—
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C23×C4×C151C2311yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C23×C4×C151C2311yescharacteristic
94C23×C4×C151C2311yescharacteristic
95C23×C4×C151C2311yescharacteristic
96C23×C4×C151C2311yescharacteristic
97C23×C4×C151C2311yescharacteristic
98C23×C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151—22no—
100C2×C4⋊C4×C151—22no—
101C2×C4⋊C4×C151—41no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151—22no—
104C2×C22⋊C4×C151—22no—
105C2×C22⋊C4×C151—22no—
106C2×C22⋊C4×C151—22no—
107C2×C22⋊C4×C151—22no—
108C2×C22⋊C4×C151—22no—
109C2×C22⋊C4×C151—22no—
110C2×C22⋊C4×C151—22no—
111C2×C22⋊C4×C151—22no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151—22no—
114C2×C22⋊C4×C151—22no—
115C2×C22⋊C4×C151—22no—
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151—22no—
118C2×C22⋊C4×C151—22no—
119C2×C22⋊C4×C151—22no—
120C2×C22⋊C4×C151—41no—
121C2×C22⋊C4×C151—41no—
122C2×C22⋊C4×C151—41no—
123C2×C22⋊C4×C151—41no—
124C2×C22⋊C4×C151—41no—
125C2×C22⋊C4×C151—41no—
126C2×C22⋊C4×C151—41no—
127C2×C22⋊C4×C151—41no—
128C2×C22⋊C4×C151—41no—
129C2×C22⋊C4×C151—41no—
130C2×C22⋊C4×C151—41no—
131C2×C22⋊C4×C151—41no—
132C2×C22⋊C4×C151—41no—
133C2×C22⋊C4×C151—41no—
134C2×C22⋊C4×C151—41no—
135C2×C22⋊C4×C151—41no—
136C2×C22⋊C4×C151—41no—
137C2×C22⋊C4×C151—41no—
138C2×C22⋊C4×C151—41no—
139C2×C22⋊C4×C151—41no—
140C2×C22⋊C4×C151C2×C414yes—
141C2×C22⋊C4×C151C2×C414yescomplemented
142C2×C22⋊C4×C151C2×C414yescomplemented
143C2×C22⋊C4×C151D414yescomplemented
144C2×C42×C151—22no—
145C2×C42×C151—22no—
146C2×C42×C151—22no—
147C2×C42×C151—41no—
148C2×C42×C151—41no—
149C2×C42×C151—41no—
150#95×C151—22no—
151#95×C151—22no—
152#95×C151—22no—
153#95×C151—22no—
154#95×C151—41no—
155#95×C151—41no—
156#95×C151—41no—
157#95×C151—41no—
158#95×C151—41no—
159#95×C151—41no—
160#95×C151—41no—
161#95×C151—41no—
162#95×C151C2×C414yescomplemented
163#95×C151D414yescomplemented
164C24×C151—21no—
165C24×C151—21no—
166C24×C151—21no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151—21no—
170C24×C151—21no—
171C24×C151—21no—
172C24×C151—21no—
173C24×C151—21no—
174C24×C151—21no—
175C24×C151—21no—
176C24×C151—21no—
177C24×C151—21no—
178C24×C151—21no—
179C24×C151—21no—
180C24×C151—21no—
181C24×C151—21no—
182C24×C151—21no—
183C24×C151—21no—
184C24×C151—21no—
185C24×C151—21no—
186C24×C151—21no—
187C24×C151—21no—
188C24×C151—21no—
189C24×C151—21no—
190C24×C151—21no—
191C24×C151—21no—
192C24×C151—21no—
193C24×C151—21no—
194C24×C151—21no—
195C24×C151—21no—
196C24×C151—21no—
197C24×C151—21no—
198C24×C151—21no—
199C24×C151—21no—
200C24×C151—21no—
201C24×C151—21no—
202C24×C151—21no—
203C24×C151—21no—
204C24×C151C22×C412yes—
205C24×C151C22×C412yes—
206C24×C151C22×C412yes—
207C24×C151C2×D412yes—
208C24×C151#4112yes—
209C24×C151C2411yescharacteristic
210C2×D4×C151—28no—
211C2×D4×C151—28no—
212C2×D4×C151—28no—
213C2×D4×C151—44no—
214C2×D4×C151—44no—
215C2×D4×C151—44no—
216C2×D4×C151—44no—
217C2×D4×C151—44no—
218C2×D4×C151—44no—
219C2×D4×C151—44no—
220C2×D4×C151—44no—
221C2×D4×C151—44no—
222C2×D4×C151—44no—
223C2×D4×C151—44no—
224C2×D4×C151—44no—
225C2×D4×C151—44no—
226C2×D4×C151—44no—
227C2×D4×C151—44no—
228C2×D4×C151—44no—
229C2×D4×C151—44no—
230C2×D4×C151—44no—
231C22×C4×C151—21no—
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—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
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—21no—
262C22×C4×C151—21no—
263C22×C4×C151—21no—
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—21no—
268C22×C4×C151—21no—
269C22×C4×C151—21no—
270C22×C4×C151—21no—
271C22×C4×C151—21no—
272C22×C4×C151—21no—
273C22×C4×C151—21no—
274C22×C4×C151—21no—
275C22×C4×C151—21no—
276C22×C4×C151—21no—
277C22×C4×C151—21no—
278C22×C4×C151—21no—
279C22×C4×C151—21no—
280C22×C4×C151—21no—
281C22×C4×C151—21no—
282C22×C4×C151—21no—
283C22×C4×C151—21no—
284C22×C4×C151—21no—
285C22×C4×C151—21no—
286C22×C4×C151—21no—
287C22×C4×C151—21no—
288C22×C4×C151—21no—
289C22×C4×C151—21no—
290C22×C4×C151—21no—
291C22×C4×C151—21no—
292C22×C4×C151—21no—
293C22×C4×C151—21no—
294C22×C4×C151—21no—
295C22×C4×C151—21no—
296C22×C4×C151—21no—
297C22×C4×C151—21no—
298C22×C4×C151—21no—
299C22×C4×C151—21no—
300C22×C4×C151—21no—
301C22×C4×C151—21no—
302C22×C4×C151—21no—
303C22×C4×C151—44no—
304C22×C4×C151—44no—
305C22×C4×C151—44no—
306C22×C4×C151—44no—
307C22×C4×C151—44no—
308C22×C4×C151—44no—
309C22×C4×C151—44no—
310C22×C4×C151C22×C412yes—
311C22×C4×C151C22×C412yes—
312C22×C4×C151C22×C412yes—
313C22×C4×C151C22×C412yes—
314C22×C4×C151C2×D412yes—
315C22×C4×C151C2×D412yes—
316C22×C4×C151C2×D412yes—
317C22×C4×C151C2×D412yes—
318C22×C4×C151C2×D412yes—
319C22×C4×C151#4112yes—
320C22×C4×C151#4112yes—
321C22×C4×C151#4112yes—
322C4⋊C4×C151—44no—
323C22⋊C4×C151—28no—
324C22⋊C4×C151—44no—
325C22⋊C4×C151—44no—
326C22⋊C4×C151—44no—
327C22⋊C4×C151—44no—
328C22⋊C4×C151—44no—
329C22⋊C4×C151—44no—
330C22⋊C4×C151—44no—
331C22⋊C4×C151—44no—
332C22⋊C4×C151—44no—
333C22⋊C4×C151—44no—
334C22⋊C4×C151—44no—
335C22⋊C4×C151—44no—
336C22⋊C4×C151—44no—
337C42×C151—44no—
338C42×C151—44no—
339C23×C151—22no—
340C23×C151—22no—
341C23×C151—22no—
342C23×C151—22no—
343C23×C151—22no—
344C23×C151—22no—
345C23×C151—22no—
346C23×C151—22no—
347C23×C151—22no—
348C23×C151—22no—
349C23×C151—22no—
350C23×C151—22no—
351C23×C151—22no—
352C23×C151—22no—
353C23×C151—22no—
354C23×C151—22no—
355C23×C151—22no—
356C23×C151—22no—
357C23×C151—22no—
358C23×C151—22no—
359C23×C151—22no—
360C23×C151—22no—
361C23×C151—22no—
362C23×C151—22no—
363C23×C151—22no—
364C23×C151—22no—
365C23×C151—22no—
366C23×C151—22no—
367C23×C151—22no—
368C23×C151—22no—
369C23×C151—22no—
370C23×C151—22no—
371C23×C151—41no—
372C23×C151—41no—
373C23×C151—41no—
374C23×C151—41no—
375C23×C151—41no—
376C23×C151—41no—
377C23×C151—41no—
378C23×C151—41no—
379C23×C151—41no—
380C23×C151—41no—
381C23×C151—41no—
382C23×C151—41no—
383C23×C151—41no—
384C23×C151—41no—
385C23×C151—41no—
386C23×C151—41no—
387C23×C151—41no—
388C23×C151—41no—
389C23×C151—41no—
390C23×C151—41no—
391C23×C151—41no—
392C23×C151—41no—
393C23×C151—41no—
394C23×C151—41no—
395C23×C151—41no—
396C23×C151—41no—
397C23×C151—41no—
398C23×C151—41no—
399C23×C151—41no—
400C23×C151—41no—
401C23×C151—41no—
402C23×C151—41no—
403C23×C151—41no—
404C23×C151—41no—
405C23×C151—41no—
406C23×C151—41no—
407C23×C151—41no—
408C23×C151—41no—
409C23×C151—41no—
410C23×C151—41no—
411C23×C151—41no—
412C23×C151—41no—
413C23×C151—41no—
414C23×C151—41no—
415C23×C151—41no—
416C23×C151—41no—
417C23×C151—41no—
418C23×C151—41no—
419C23×C151—41no—
420C23×C151—41no—
421C23×C151—41no—
422C23×C151—41no—
423C23×C151—41no—
424C23×C151—41no—
425C23×C151—41no—
426C23×C151—41no—
427C23×C151—41no—
428C23×C151—41no—
429C23×C151—41no—
430C23×C151—41no—
431C23×C151—41no—
432C23×C151—41no—
433C23×C151—41no—
434C23×C151—41no—
435C23×C151—41no—
436C23×C151—41no—
437C23×C151—41no—
438C23×C151—41no—
439C23×C151—41no—
440C23×C151—41no—
441C23×C151—41no—
442C23×C151—41no—
443C23×C151C4×D414yes—
444C23×C151C23×C411yescharacteristic
445C23×C151C22×D411yescharacteristic
446C23×C151C22×D411yescharacteristic
447C23×C151C2×#4111yescharacteristic
448C23×C151C2×#4111yescharacteristic
449C23×C151C2×#4111yescharacteristic
450C23×C151C2×#4111yescharacteristic
451C23×C151H(5,𝔽2)11yescharacteristic
452C23×C151H(5,𝔽2)11yescharacteristic
453C23×C151H(5,𝔽2)11yescharacteristic
454C23×C151H(5,𝔽2)11yescharacteristic
455C23×C151H(5,𝔽2)11yescharacteristic
456C23×C151H(5,𝔽2)11yescharacteristic
457C23×C151H(5,𝔽2)11yescharacteristic
458C23×C151H(5,𝔽2)11yescharacteristic
459D4×C151—416no—
460D4×C151—416no—
461D4×C151—416no—
462C2×C4×C151—22no—
463C2×C4×C151—22no—
464C2×C4×C151—22no—
465C2×C4×C151—22no—
466C2×C4×C151—22no—
467C2×C4×C151—22no—
468C2×C4×C151—22no—
469C2×C4×C151—22no—
470C2×C4×C151—22no—
471C2×C4×C151—22no—
472C2×C4×C151—22no—
473C2×C4×C151—22no—
474C2×C4×C151—22no—
475C2×C4×C151—22no—
476C2×C4×C151—22no—
477C2×C4×C151—22no—
478C2×C4×C151—22no—
479C2×C4×C151—22no—
480C2×C4×C151—22no—
481C2×C4×C151—22no—
482C2×C4×C151—22no—
483C2×C4×C151—22no—
484C2×C4×C151—22no—
485C2×C4×C151—22no—
486C2×C4×C151—22no—
487C2×C4×C151—22no—
488C2×C4×C151—22no—
489C2×C4×C151—22no—
490C2×C4×C151—22no—
491C2×C4×C151—22no—
492C2×C4×C151—22no—
493C2×C4×C151—22no—
494C2×C4×C151—22no—
495C2×C4×C151—416no—
496C2×C4×C151—41no—
497C2×C4×C151—41no—
498C2×C4×C151—41no—
499C2×C4×C151—41no—
500C2×C4×C151—41no—
501C2×C4×C151—41no—
502C2×C4×C151—41no—
503C2×C4×C151—41no—
504C2×C4×C151—41no—
505C2×C4×C151—41no—
506C2×C4×C151—41no—
507C2×C4×C151—41no—
508C2×C4×C151—41no—
509C2×C4×C151—41no—
510C2×C4×C151—41no—
511C2×C4×C151—41no—
512C2×C4×C151—41no—
513C2×C4×C151—41no—
514C2×C4×C151—41no—
515C2×C4×C151—41no—
516C2×C4×C151—41no—
517C2×C4×C151—41no—
518C2×C4×C151—41no—
519C2×C4×C151—41no—
520C2×C4×C151—41no—
521C2×C4×C151—41no—
522C2×C4×C151—41no—
523C2×C4×C151—41no—
524C2×C4×C151—41no—
525C2×C4×C151—41no—
526C2×C4×C151—41no—
527C2×C4×C151—41no—
528C2×C4×C151—41no—
529C2×C4×C151—41no—
530C2×C4×C151—41no—
531C2×C4×C151—41no—
532C2×C4×C151—41no—
533C2×C4×C151—41no—
534C2×C4×C151—41no—
535C2×C4×C151—41no—
536C2×C4×C151—41no—
537C2×C4×C151—41no—
538C2×C4×C151—41no—
539C2×C4×C151—41no—
540C2×C4×C151—41no—
541C2×C4×C151—41no—
542C2×C4×C151—41no—
543C2×C4×C151—41no—
544C2×C4×C151—41no—
545C2×C4×C151—41no—
546C2×C4×C151C4×D414yes—
547C22×C151—24no—
548C22×C151—24no—
549C22×C151—24no—
550C22×C151—42no—
551C22×C151—42no—
552C22×C151—42no—
553C22×C151—42no—
554C22×C151—42no—
555C22×C151—42no—
556C22×C151—42no—
557C22×C151—42no—
558C22×C151—42no—
559C22×C151—42no—
560C22×C151—42no—
561C22×C151—42no—
562C22×C151—42no—
563C22×C151—42no—
564C22×C151—42no—
565C22×C151—42no—
566C22×C151—42no—
567C22×C151—42no—
568C22×C151—42no—
569C22×C151—42no—
570C22×C151—42no—
571C22×C151—42no—
572C22×C151—42no—
573C22×C151—42no—
574C22×C151—42no—
575C22×C151—42no—
576C22×C151—81no—
577C22×C151—81no—
578C22×C151—81no—
579C22×C151—81no—
580C22×C151—81no—
581C22×C151—81no—
582C22×C151—81no—
583C22×C151—81no—
584C22×C151—81no—
585C22×C151—81no—
586C22×C151—81no—
587C22×C151—81no—
588C22×C151—81no—
589C22×C151—81no—
590C22×C151—81no—
591C22×C151—81no—
592C22×C151C2×C4×D411yescharacteristic
593C22×C151C2×C4×D411yescharacteristic
594C22×C151C4×#4111yescharacteristic
595C22×C151#51811yescharacteristic
596C22×C151#51811yescharacteristic
597C22×C151#51811yescharacteristic
598C22×C151#51811yescharacteristic
599C22×C151#53411yescharacteristic
600C22×C151#53511yescharacteristic
601C22×C151#53511yescharacteristic
602C22×C151#53511yescharacteristic
603C22×C151#53811yescharacteristic
604C22×C151#53811yescharacteristic
605C22×C151#53811yescharacteristic
606C22×C151#53811yescharacteristic
607C22×C151#54011yescharacteristic
608C22×C151#54011yescharacteristic
609C22×C151#54011yescharacteristic
610C22×C151#54011yescharacteristic
611C22×C151D4211yescharacteristic
612C22×C151#54611yescharacteristic
613C22×C151#54611yescharacteristic
614C22×C151#54611yescharacteristic
615C22×C151#54611yescharacteristic
616C22×C151#54611yescharacteristic
617C22×C151#55011yescharacteristic
618C22×C151#55111yescharacteristic
619C22×C151#55311yescharacteristic
620C22×C151#55311yescharacteristic
621C22×C151#55311yescharacteristic
622C22×C151#55511yescharacteristic
623C22×C151#56011yescharacteristic
624C22×C151#56011yescharacteristic
625C22×C151#56011yescharacteristic
626C22×C151H(3,𝔽4)11yescharacteristic
627C4×C151—24no—
628C4×C151—42no—
629C4×C151—42no—
630C4×C151—42no—
631C4×C151—42no—
632C4×C151—42no—
633C4×C151—42no—
634C4×C151—42no—
635C4×C151—42no—
636C4×C151—42no—
637C4×C151—81no—
638C4×C151—81no—
639C2×C151—44no—
640C2×C151—82no—
641C2×C151—82no—
642C2×C151#232111yescharacteristic
643C2×C151#232811yescharacteristic
644C2×C151#233311yescharacteristic
645C2×C151#235811yescharacteristic
646C2×C151#236311yescharacteristic
647C2×C151#236411yescharacteristic
648C2×C151#237511yescharacteristic
649C2×C151#267011yescharacteristic
650C2×C151#267311yescharacteristic
651C2×C151#269911yescharacteristic
652C2×C151#270311yescharacteristic
653C2×C151#270311yescharacteristic
654C2×C151#271411yescharacteristic
655C2×C151#275311yescharacteristic
656C2×C151#275611yescharacteristic
657#14520C15111yesmaximal, characteristic, direct product factor, Sylow
658C151#1452011yescharacteristic, direct product factor, Sylow
659C2×#392C2×C15111yescharacteristic
660C2×#390C2×C15111yescharacteristic, complemented
661C2×#388C2×C15111yescharacteristic, complemented
662C2×#386C2×C15111yescharacteristic, complemented
663C2×#386C2×C15111yescharacteristic, complemented
664#1442C2×C15111yescharacteristic, complemented
665#1440C2×C15111yescharacteristic, complemented
666#1438C2×C15111yescharacteristic, complemented
667#1438C2×C15111yescharacteristic, complemented
668#1438C2×C15111yescharacteristic, complemented
669#1437C2×C15111yescharacteristic, complemented
670#1437C2×C15111yescharacteristic, complemented
671#1437C2×C15111yescharacteristic, complemented
672#1434C2×C15111yescharacteristic, complemented
673C22⋊#95C2×C15111yescharacteristic, complemented
674C23×D4C22×C15111yescharacteristic
675C23×D4C22×C15111yescharacteristic
676C23×D4C22×C15111yescharacteristic
677C24×C4C22×C15111yescharacteristic
678C22×C4⋊C4C22×C15111yescharacteristic
679C22×C22⋊C4C22×C15111yescharacteristic
680C22×C22⋊C4C22×C15111yescharacteristic
681C22×C22⋊C4C22×C15111yescharacteristic
682C22×C22⋊C4C22×C15111yescharacteristic
683C22×C22⋊C4C22×C15111yescharacteristic
684C22×C22⋊C4C22×C15111yescharacteristic
685C22×C22⋊C4C22×C15111yescharacteristic
686C22×C22⋊C4C22×C15111yescharacteristic
687C22×C22⋊C4C22×C15111yescharacteristic
688C22×C22⋊C4C22×C15111yescharacteristic
689C22×C22⋊C4C22×C15111yescharacteristic
690C22×C22⋊C4C22×C15111yescharacteristic
691C22×C22⋊C4C22×C15111yescharacteristic
692C22×C22⋊C4C22×C15111yescharacteristic
693C22×C42C22×C15111yescharacteristic
694C22×C42C22×C15111yescharacteristic
695#392C4×C15118yescomplemented
696#390—24no—
697#388—24no—
698#386—24no—
699#386—24no—
700C2×#95C22×C15111yescharacteristic
701C2×#95C22×C15111yescharacteristic
702C2×#95C22×C15111yescharacteristic
703C2×#95C22×C15111yescharacteristic
704C2×#95C22×C15111yescharacteristic
705C2×#95C22×C15111yescharacteristic
706C2×#95C22×C15111yescharacteristic
707C2×#95C22×C15111yescharacteristic
708C2×#95C22×C15111yescharacteristic
709C2×#95C22×C15111yescharacteristic
710C2×#95C22×C15111yescharacteristic
711C2×#95C22×C15111yescharacteristic
712C2×#95C22×C15111yescharacteristic
713C2×#95C22×C15111yescharacteristic
714C25C23×C15111yescharacteristic
715C25C23×C15111yescharacteristic
716C25C23×C15111yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4C2×C4×C15114yes—
736C22×D4C2×C4×C15114yes—
737C22×D4C2×C4×C15114yescomplemented
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4C23×C15111yescharacteristic
746C23×C4C23×C15111yescharacteristic
747C23×C4C23×C15111yescharacteristic
748C23×C4C23×C15111yescharacteristic
749C23×C4C23×C15111yescharacteristic
750C23×C4C23×C15111yescharacteristic
751C23×C4C23×C15111yescharacteristic
752C23×C4C23×C15111yescharacteristic
753C23×C4C23×C15111yescharacteristic
754C23×C4C23×C15111yescharacteristic
755C23×C4C23×C15111yescharacteristic
756C23×C4C23×C15111yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—41no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4C2×C4×C15114yes—
799C2×C22⋊C4C2×C4×C15114yescomplemented
800C2×C22⋊C4C2×C4×C15114yescomplemented
801C2×C22⋊C4D4×C15114yescomplemented
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807C2×C42—41no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95—41no—
819#95—41no—
820#95C2×C4×C15114yescomplemented
821#95D4×C15114yescomplemented
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24C22×C4×C15112yes—
863C24C22×C4×C15112yes—
864C24C22×C4×C15112yes—
865C24C2×D4×C15112yes—
866C24#41×C15112yes—
867C24C24×C15111yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4C22×C4×C15112yes—
969C22×C4C22×C4×C15112yes—
970C22×C4C22×C4×C15112yes—
971C22×C4C22×C4×C15112yes—
972C22×C4C2×D4×C15112yes—
973C22×C4C2×D4×C15112yes—
974C22×C4C2×D4×C15112yes—
975C22×C4C2×D4×C15112yes—
976C22×C4C2×D4×C15112yes—
977C22×C4#41×C15112yes—
978C22×C4#41×C15112yes—
979C22×C4#41×C15112yes—
980C4⋊C4—44no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C42—44no—
996C42—44no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23C4×D4×C15114yes—
1102C23C23×C4×C15111yescharacteristic
1103C23C22×D4×C15111yescharacteristic
1104C23C22×D4×C15111yescharacteristic
1105C23C2×#41×C15111yescharacteristic
1106C23C2×#41×C15111yescharacteristic
1107C23C2×#41×C15111yescharacteristic
1108C23C2×#41×C15111yescharacteristic
1109C23H(5,𝔽2)×C15111yescharacteristic
1110C23H(5,𝔽2)×C15111yescharacteristic
1111C23H(5,𝔽2)×C15111yescharacteristic
1112C23H(5,𝔽2)×C15111yescharacteristic
1113C23H(5,𝔽2)×C15111yescharacteristic
1114C23H(5,𝔽2)×C15111yescharacteristic
1115C23H(5,𝔽2)×C15111yescharacteristic
1116C23H(5,𝔽2)×C15111yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—416no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4C4×D4×C15114yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×C4×D4×C15111yescharacteristic
1251C22C2×C4×D4×C15111yescharacteristic
1252C22C4×#41×C15111yescharacteristic
1253C22#518×C15111yescharacteristic
1254C22#518×C15111yescharacteristic
1255C22#518×C15111yescharacteristic
1256C22#518×C15111yescharacteristic
1257C22#534×C15111yescharacteristic
1258C22#535×C15111yescharacteristic
1259C22#535×C15111yescharacteristic
1260C22#535×C15111yescharacteristic
1261C22#538×C15111yescharacteristic
1262C22#538×C15111yescharacteristic
1263C22#538×C15111yescharacteristic
1264C22#538×C15111yescharacteristic
1265C22#540×C15111yescharacteristic
1266C22#540×C15111yescharacteristic
1267C22#540×C15111yescharacteristic
1268C22#540×C15111yescharacteristic
1269C22D42×C15111yescharacteristic
1270C22#546×C15111yescharacteristic
1271C22#546×C15111yescharacteristic
1272C22#546×C15111yescharacteristic
1273C22#546×C15111yescharacteristic
1274C22#546×C15111yescharacteristic
1275C22#550×C15111yescharacteristic
1276C22#551×C15111yescharacteristic
1277C22#553×C15111yescharacteristic
1278C22#553×C15111yescharacteristic
1279C22#553×C15111yescharacteristic
1280C22#555×C15111yescharacteristic
1281C22#560×C15111yescharacteristic
1282C22#560×C15111yescharacteristic
1283C22#560×C15111yescharacteristic
1284C22H(3,𝔽4)×C15111yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2#2321×C15111yescharacteristic
1301C2#2328×C15111yescharacteristic
1302C2#2333×C15111yescharacteristic
1303C2#2358×C15111yescharacteristic
1304C2#2363×C15111yescharacteristic
1305C2#2364×C15111yescharacteristic
1306C2#2375×C15111yescharacteristic
1307C2#2670×C15111yescharacteristic
1308C2#2673×C15111yescharacteristic
1309C2#2699×C15111yescharacteristic
1310C2#2703×C15111yescharacteristic
1311C2#2703×C15111yescharacteristic
1312C2#2714×C15111yescharacteristic
1313C2#2753×C15111yescharacteristic
1314C2#2756×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC2×#392×C151C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#390×C151C2semidirect
3. C2×#388×C151C2semidirect
4. C2×#386×C151C2semidirect
5. C2×#386×C151C2semidirect
6. #1442×C151C2semidirect
7. #1440×C151C2semidirect
8. #1438×C151C2semidirect
9. #1438×C151C2semidirect
10. #1438×C151C2semidirect
11. #1437×C151C2semidirect
12. #1437×C151C2semidirect
13. #1437×C151C2semidirect
14. #1434×C151C2semidirect
15. C22⋊#95×C151C2semidirect
37. #392×C151C4semidirect
79. C22×D4×C151C2×C4semidirect
141. C2×C22⋊C4×C151C2×C4semidirect
142. C2×C22⋊C4×C151C2×C4semidirect
143. C2×C22⋊C4×C151D4semidirect
162. #95×C151C2×C4semidirect
163. #95×C151D4semidirect
657. #14520C151direct (N × H)
658. C151#14520direct (N × H)
660. C2×#390C2×C151semidirect
661. C2×#388C2×C151semidirect
662. C2×#386C2×C151semidirect
663. C2×#386C2×C151semidirect
664. #1442C2×C151semidirect
665. #1440C2×C151semidirect
666. #1438C2×C151semidirect
667. #1438C2×C151semidirect
668. #1438C2×C151semidirect
669. #1437C2×C151semidirect
670. #1437C2×C151semidirect
671. #1437C2×C151semidirect
672. #1434C2×C151semidirect
673. C22⋊#95C2×C151semidirect
695. #392C4×C151semidirect
737. C22×D4C2×C4×C151semidirect
799. C2×C22⋊C4C2×C4×C151semidirect
800. C2×C22⋊C4C2×C4×C151semidirect
801. C2×C22⋊C4D4×C151semidirect
820. #95C2×C4×C151semidirect
821. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C1512
C2×#390×C1512
C2×#388×C1512
C2×#386×C1512
#1442×C1512
#1440×C1512
#1438×C1512
#1437×C1512
#1434×C1512
C22⋊#95×C1512
#14520151