Finite Group Databasebeta

← C151×#14817 #50319742

Subgroups — C151×#14817 #50319742

Order 38656.

1942 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C151C211yesmaximal, characteristic
2C2×#393×C151C211yesmaximal, characteristic, complemented
3C2×#393×C151C211yesmaximal, characteristic, complemented
4C2×#391×C151C211yesmaximal, characteristic, complemented
5C2×#386×C151C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
7#1443×C151C211yesmaximal, characteristic, complemented
8#1442×C151C211yesmaximal, characteristic, complemented
9#1440×C151C211yesmaximal, characteristic, complemented
10#1440×C151C211yesmaximal, characteristic, complemented
11#1438×C151C211yesmaximal, characteristic
12#1437×C151C211yesmaximal, characteristic, complemented
13#1437×C151C211yesmaximal, characteristic, complemented
14#1434×C151C211yesmaximal, characteristic, complemented
15C22⋊#95×C151C211yesmaximal, characteristic, complemented
16C23×Q8×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C24×C4×C151C2211yescharacteristic
19C22×C4⋊C4×C151C2211yescharacteristic
20C22×C22⋊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×C42×C151C2211yescharacteristic
32C22×C42×C151C2211yescharacteristic
33#394×C151—24no—
34#393×C151—24no—
35#393×C151—24no—
36#391×C151—24no—
37#386×C151—24no—
38C4×C22⋊C4×C151—24no—
39C2×#95×C151C2211yescharacteristic
40C2×#95×C151C2211yescharacteristic
41C2×#95×C151C2211yescharacteristic
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
56C2×#95×C151C2211yescharacteristic
57C25×C151C2311yescharacteristic
58C25×C151C2311yescharacteristic
59C22×Q8×C151—22no—
60C22×Q8×C151—22no—
61C22×Q8×C151—22no—
62C22×Q8×C151—22no—
63C22×Q8×C151—22no—
64C22×Q8×C151—41no—
65C22×Q8×C151—41no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—41no—
72C22×D4×C151—41no—
73C23×C4×C151—22no—
74C23×C4×C151—22no—
75C23×C4×C151—22no—
76C23×C4×C151—22no—
77C23×C4×C151—22no—
78C23×C4×C151—41no—
79C23×C4×C151—41no—
80C23×C4×C151C2311yescharacteristic
81C23×C4×C151C2311yescharacteristic
82C23×C4×C151C2311yescharacteristic
83C23×C4×C151C2311yescharacteristic
84C23×C4×C151C2311yescharacteristic
85C23×C4×C151C2311yescharacteristic
86C23×C4×C151C2311yescharacteristic
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C23×C4×C151C2311yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C2×C4⋊C4×C151—22no—
94C2×C4⋊C4×C151—22no—
95C2×C4⋊C4×C151—41no—
96C2×C22⋊C4×C151—22no—
97C2×C22⋊C4×C151—22no—
98C2×C22⋊C4×C151—22no—
99C2×C22⋊C4×C151—22no—
100C2×C22⋊C4×C151—22no—
101C2×C22⋊C4×C151—22no—
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—22no—
121C2×C22⋊C4×C151—22no—
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×C151D414yes—
129C2×C42×C151—22no—
130C2×C42×C151—22no—
131C2×C42×C151—22no—
132C2×C42×C151—22no—
133C2×C42×C151—41no—
134C2×C42×C151—41no—
135#95×C151—22no—
136#95×C151—22no—
137#95×C151—22no—
138#95×C151—22no—
139#95×C151—22no—
140#95×C151—22no—
141#95×C151—22no—
142#95×C151—22no—
143#95×C151—22no—
144#95×C151—22no—
145#95×C151—22no—
146#95×C151—22no—
147#95×C151—22no—
148#95×C151—41no—
149#95×C151—41no—
150#95×C151—41no—
151#95×C151D414yes—
152#95×C151D414yescomplemented
153C24×C151—21no—
154C24×C151—21no—
155C24×C151—21no—
156C24×C151—21no—
157C24×C151—21no—
158C24×C151—21no—
159C24×C151—21no—
160C24×C151—21no—
161C24×C151—21no—
162C24×C151—21no—
163C24×C151—21no—
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×C151C2×D412yes—
180C24×C151#4112yes—
181C24×C151#4112yes—
182C24×C151#4112yes—
183C24×C151C2411yescharacteristic
184C2×Q8×C151—28no—
185C2×Q8×C151—44no—
186C2×Q8×C151—44no—
187C2×Q8×C151—44no—
188C2×Q8×C151—44no—
189C2×Q8×C151—44no—
190C2×Q8×C151—44no—
191C2×D4×C151—28no—
192C2×D4×C151—44no—
193C2×D4×C151—44no—
194C2×D4×C151—44no—
195C2×D4×C151—44no—
196C2×D4×C151—44no—
197C2×D4×C151—44no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—28no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
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—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—44no—
278C22×C4×C151—44no—
279C22×C4×C151—44no—
280C22×C4×C151—44no—
281C22×C4×C151—44no—
282C22×C4×C151—44no—
283C22×C4×C151C2×D412yes—
284C22×C4×C151C2×D412yes—
285C22×C4×C151C2×D412yes—
286C22×C4×C151C2×D412yes—
287C22×C4×C151C2×D412yes—
288C22×C4×C151C2×D412yes—
289C22×C4×C151C2×D412yes—
290C22×C4×C151C2×D412yes—
291C22×C4×C151#4112yes—
292C22×C4×C151#4112yes—
293C22×C4×C151#4112yes—
294C22×C4×C151#4112yes—
295C22×C4×C151#4112yes—
296C4⋊C4×C151—44no—
297C22⋊C4×C151—28no—
298C22⋊C4×C151—28no—
299C22⋊C4×C151—44no—
300C22⋊C4×C151—44no—
301C22⋊C4×C151—44no—
302C22⋊C4×C151—44no—
303C22⋊C4×C151—44no—
304C22⋊C4×C151—44no—
305C22⋊C4×C151—44no—
306C22⋊C4×C151—44no—
307C22⋊C4×C151—44no—
308C42×C151—44no—
309C42×C151—44no—
310C23×C151—22no—
311C23×C151—22no—
312C23×C151—22no—
313C23×C151—22no—
314C23×C151—22no—
315C23×C151—22no—
316C23×C151—22no—
317C23×C151—22no—
318C23×C151—22no—
319C23×C151—22no—
320C23×C151—22no—
321C23×C151—22no—
322C23×C151—22no—
323C23×C151—22no—
324C23×C151—22no—
325C23×C151—22no—
326C23×C151—22no—
327C23×C151—22no—
328C23×C151—22no—
329C23×C151—22no—
330C23×C151—22no—
331C23×C151—22no—
332C23×C151—22no—
333C23×C151—22no—
334C23×C151—22no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151—41no—
349C23×C151—41no—
350C23×C151—41no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—41no—
354C23×C151—41no—
355C23×C151—41no—
356C23×C151—41no—
357C23×C151—41no—
358C23×C151—41no—
359C23×C151—41no—
360C23×C151—41no—
361C23×C151—41no—
362C23×C151—41no—
363C23×C151—41no—
364C23×C151—41no—
365C23×C151—41no—
366C23×C151—41no—
367C23×C151—41no—
368C23×C151—41no—
369C23×C151—41no—
370C23×C151—41no—
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#12414yes—
380C23×C151C22×D411yescharacteristic
381C23×C151C22×D411yescharacteristic
382C23×C151C22×D411yescharacteristic
383C23×C151C2×#4111yescharacteristic
384C23×C151C2×#4111yescharacteristic
385C23×C151C2×#4111yescharacteristic
386C23×C151C2×#4111yescharacteristic
387C23×C151C2×#4111yescharacteristic
388C23×C151C2×#4111yescharacteristic
389C23×C151C2×#4111yescharacteristic
390C23×C151C2×#4111yescharacteristic
391C23×C151H(5,𝔽2)11yescharacteristic
392C23×C151H(5,𝔽2)11yescharacteristic
393C23×C151H(5,𝔽2)11yescharacteristic
394C23×C1512−1+411yescharacteristic
395Q8×C151—416no—
396D4×C151—416no—
397C2×C4×C151—22no—
398C2×C4×C151—22no—
399C2×C4×C151—22no—
400C2×C4×C151—22no—
401C2×C4×C151—22no—
402C2×C4×C151—22no—
403C2×C4×C151—22no—
404C2×C4×C151—22no—
405C2×C4×C151—22no—
406C2×C4×C151—22no—
407C2×C4×C151—22no—
408C2×C4×C151—22no—
409C2×C4×C151—22no—
410C2×C4×C151—22no—
411C2×C4×C151—22no—
412C2×C4×C151—22no—
413C2×C4×C151—22no—
414C2×C4×C151—22no—
415C2×C4×C151—22no—
416C2×C4×C151—22no—
417C2×C4×C151—22no—
418C2×C4×C151—22no—
419C2×C4×C151—22no—
420C2×C4×C151—22no—
421C2×C4×C151—22no—
422C2×C4×C151—22no—
423C2×C4×C151—22no—
424C2×C4×C151—22no—
425C2×C4×C151—22no—
426C2×C4×C151—22no—
427C2×C4×C151—22no—
428C2×C4×C151—22no—
429C2×C4×C151—22no—
430C2×C4×C151—416no—
431C2×C4×C151—41no—
432C2×C4×C151—41no—
433C2×C4×C151—41no—
434C2×C4×C151—41no—
435C2×C4×C151—41no—
436C2×C4×C151—41no—
437C2×C4×C151—41no—
438C2×C4×C151—41no—
439C2×C4×C151—41no—
440C2×C4×C151—41no—
441C2×C4×C151—41no—
442C2×C4×C151—41no—
443C2×C4×C151—41no—
444C2×C4×C151—41no—
445C2×C4×C151—41no—
446C2×C4×C151—41no—
447C2×C4×C151—41no—
448C2×C4×C151—41no—
449C2×C4×C151—41no—
450C2×C4×C151—41no—
451C2×C4×C151—41no—
452C2×C4×C151—41no—
453C2×C4×C151—41no—
454C2×C4×C151—41no—
455C2×C4×C151—41no—
456C2×C4×C151—41no—
457C2×C4×C151—41no—
458C2×C4×C151—41no—
459C2×C4×C151—41no—
460C2×C4×C151—41no—
461C2×C4×C151—41no—
462C2×C4×C151—41no—
463C2×C4×C151—41no—
464C2×C4×C151—41no—
465C2×C4×C151—41no—
466C2×C4×C151—41no—
467C2×C4×C151—41no—
468C2×C4×C151—41no—
469C2×C4×C151—41no—
470C2×C4×C151—41no—
471C2×C4×C151—41no—
472C2×C4×C151—41no—
473C2×C4×C151—41no—
474C2×C4×C151—41no—
475C2×C4×C151—41no—
476C2×C4×C151—41no—
477C2×C4×C151—41no—
478C2×C4×C151—41no—
479C2×C4×C151—41no—
480C2×C4×C151—41no—
481C2×C4×C151—41no—
482C2×C4×C151—41no—
483C2×C4×C151—41no—
484C2×C4×C151—41no—
485C2×C4×C151—41no—
486C2×C4×C151—41no—
487C2×C4×C151#12114yes—
488C2×C4×C151#12414yes—
489C22×C151—24no—
490C22×C151—24no—
491C22×C151—24no—
492C22×C151—42no—
493C22×C151—42no—
494C22×C151—42no—
495C22×C151—42no—
496C22×C151—42no—
497C22×C151—42no—
498C22×C151—42no—
499C22×C151—42no—
500C22×C151—42no—
501C22×C151—42no—
502C22×C151—42no—
503C22×C151—42no—
504C22×C151—42no—
505C22×C151—42no—
506C22×C151—42no—
507C22×C151—42no—
508C22×C151—42no—
509C22×C151—42no—
510C22×C151—42no—
511C22×C151—81no—
512C22×C151—81no—
513C22×C151—81no—
514C22×C151—81no—
515C22×C151—81no—
516C22×C151—81no—
517C22×C151—81no—
518C22×C151—81no—
519C22×C151C2×#12111yescharacteristic
520C22×C151#52511yescharacteristic
521C22×C151#52511yescharacteristic
522C22×C151#52511yescharacteristic
523C22×C151#52511yescharacteristic
524C22×C151C2×#12411yescharacteristic
525C22×C151C2×#12411yescharacteristic
526C22×C151#52911yescharacteristic
527C22×C151#52911yescharacteristic
528C22×C151#52911yescharacteristic
529C22×C151#52911yescharacteristic
530C22×C151#52911yescharacteristic
531C22×C151#53211yescharacteristic
532C22×C151#53811yescharacteristic
533C22×C151#53811yescharacteristic
534C22×C151#53811yescharacteristic
535C22×C151#53911yescharacteristic
536C22×C151#54211yescharacteristic
537C22×C151#54211yescharacteristic
538C22×C151D4211yescharacteristic
539C22×C151D4211yescharacteristic
540C22×C151#54611yescharacteristic
541C22×C151#54611yescharacteristic
542C22×C151#54611yescharacteristic
543C22×C151#54611yescharacteristic
544C22×C151#54611yescharacteristic
545C22×C151#54711yescharacteristic
546C22×C151#54811yescharacteristic
547C22×C151#54811yescharacteristic
548C22×C151#55111yescharacteristic
549C22×C151#55111yescharacteristic
550C22×C151#55111yescharacteristic
551C22×C151#55211yescharacteristic
552C22×C151#55511yescharacteristic
553C22×C151#55911yescharacteristic
554C4×C151—24no—
555C4×C151—24no—
556C4×C151—42no—
557C4×C151—42no—
558C4×C151—42no—
559C4×C151—42no—
560C4×C151—42no—
561C4×C151—42no—
562C4×C151—42no—
563C4×C151—81no—
564C4×C151—81no—
565C4×C151—81no—
566C4×C151—81no—
567C2×C151—44no—
568C2×C151—82no—
569C2×C151#239811yescharacteristic
570C2×C151#242411yescharacteristic
571C2×C151#242711yescharacteristic
572C2×C151#245811yescharacteristic
573C2×C151#245911yescharacteristic
574C2×C151#246311yescharacteristic
575C2×C151#247211yescharacteristic
576C2×C151#247211yescharacteristic
577C2×C151#247711yescharacteristic
578C2×C151#248811yescharacteristic
579C2×C151#249111yescharacteristic
580C2×C151#255711yescharacteristic
581C2×C151#257211yescharacteristic
582C2×C151#265311yescharacteristic
583C2×C151#285011yescharacteristic
584#14817C15111yesmaximal, characteristic, direct product factor, Sylow
585C151#1481711yescharacteristic, direct product factor, Sylow
586C2×#394C2×C15111yescharacteristic
587C2×#393C2×C15111yescharacteristic, complemented
588C2×#393C2×C15111yescharacteristic, complemented
589C2×#391C2×C15111yescharacteristic, complemented
590C2×#386C2×C15111yescharacteristic
591C2×C4×C22⋊C4C2×C15111yescharacteristic, complemented
592#1443C2×C15111yescharacteristic, complemented
593#1442C2×C15111yescharacteristic, complemented
594#1440C2×C15111yescharacteristic, complemented
595#1440C2×C15111yescharacteristic, complemented
596#1438C2×C15111yescharacteristic
597#1437C2×C15111yescharacteristic, complemented
598#1437C2×C15111yescharacteristic, complemented
599#1434C2×C15111yescharacteristic, complemented
600C22⋊#95C2×C15111yescharacteristic, complemented
601C23×Q8C22×C15111yescharacteristic
602C23×D4C22×C15111yescharacteristic
603C24×C4C22×C15111yescharacteristic
604C22×C4⋊C4C22×C15111yescharacteristic
605C22×C22⋊C4C22×C15111yescharacteristic
606C22×C22⋊C4C22×C15111yescharacteristic
607C22×C22⋊C4C22×C15111yescharacteristic
608C22×C22⋊C4C22×C15111yescharacteristic
609C22×C22⋊C4C22×C15111yescharacteristic
610C22×C22⋊C4C22×C15111yescharacteristic
611C22×C22⋊C4C22×C15111yescharacteristic
612C22×C22⋊C4C22×C15111yescharacteristic
613C22×C22⋊C4C22×C15111yescharacteristic
614C22×C22⋊C4C22×C15111yescharacteristic
615C22×C22⋊C4C22×C15111yescharacteristic
616C22×C42C22×C15111yescharacteristic
617C22×C42C22×C15111yescharacteristic
618#394—24no—
619#393—24no—
620#393—24no—
621#391—24no—
622#386—24no—
623C4×C22⋊C4—24no—
624C2×#95C22×C15111yescharacteristic
625C2×#95C22×C15111yescharacteristic
626C2×#95C22×C15111yescharacteristic
627C2×#95C22×C15111yescharacteristic
628C2×#95C22×C15111yescharacteristic
629C2×#95C22×C15111yescharacteristic
630C2×#95C22×C15111yescharacteristic
631C2×#95C22×C15111yescharacteristic
632C2×#95C22×C15111yescharacteristic
633C2×#95C22×C15111yescharacteristic
634C2×#95C22×C15111yescharacteristic
635C2×#95C22×C15111yescharacteristic
636C2×#95C22×C15111yescharacteristic
637C2×#95C22×C15111yescharacteristic
638C2×#95C22×C15111yescharacteristic
639C2×#95C22×C15111yescharacteristic
640C2×#95C22×C15111yescharacteristic
641C2×#95C22×C15111yescharacteristic
642C25C23×C15111yescharacteristic
643C25C23×C15111yescharacteristic
644C22×Q8—22no—
645C22×Q8—22no—
646C22×Q8—22no—
647C22×Q8—22no—
648C22×Q8—22no—
649C22×Q8—41no—
650C22×Q8—41no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—41no—
657C22×D4—41no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4C23×C15111yescharacteristic
666C23×C4C23×C15111yescharacteristic
667C23×C4C23×C15111yescharacteristic
668C23×C4C23×C15111yescharacteristic
669C23×C4C23×C15111yescharacteristic
670C23×C4C23×C15111yescharacteristic
671C23×C4C23×C15111yescharacteristic
672C23×C4C23×C15111yescharacteristic
673C23×C4C23×C15111yescharacteristic
674C23×C4C23×C15111yescharacteristic
675C23×C4C23×C15111yescharacteristic
676C23×C4C23×C15111yescharacteristic
677C23×C4C23×C15111yescharacteristic
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—41no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4D4×C15114yes—
714C2×C42—22no—
715C2×C42—22no—
716C2×C42—22no—
717C2×C42—22no—
718C2×C42—41no—
719C2×C42—41no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—41no—
734#95—41no—
735#95—41no—
736#95D4×C15114yes—
737#95D4×C15114yescomplemented
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24C2×D4×C15112yes—
765C24#41×C15112yes—
766C24#41×C15112yes—
767C24#41×C15112yes—
768C24C24×C15111yescharacteristic
769C2×Q8—28no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×D4—28no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—28no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4C2×D4×C15112yes—
869C22×C4C2×D4×C15112yes—
870C22×C4C2×D4×C15112yes—
871C22×C4C2×D4×C15112yes—
872C22×C4C2×D4×C15112yes—
873C22×C4C2×D4×C15112yes—
874C22×C4C2×D4×C15112yes—
875C22×C4C2×D4×C15112yes—
876C22×C4#41×C15112yes—
877C22×C4#41×C15112yes—
878C22×C4#41×C15112yes—
879C22×C4#41×C15112yes—
880C22×C4#41×C15112yes—
881C4⋊C4—44no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C42—44no—
894C42—44no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23#124×C15114yes—
965C23C22×D4×C15111yescharacteristic
966C23C22×D4×C15111yescharacteristic
967C23C22×D4×C15111yescharacteristic
968C23C2×#41×C15111yescharacteristic
969C23C2×#41×C15111yescharacteristic
970C23C2×#41×C15111yescharacteristic
971C23C2×#41×C15111yescharacteristic
972C23C2×#41×C15111yescharacteristic
973C23C2×#41×C15111yescharacteristic
974C23C2×#41×C15111yescharacteristic
975C23C2×#41×C15111yescharacteristic
976C23H(5,𝔽2)×C15111yescharacteristic
977C23H(5,𝔽2)×C15111yescharacteristic
978C23H(5,𝔽2)×C15111yescharacteristic
979C232−1+4×C15111yescharacteristic
980Q8—416no—
981D4—416no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—416no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4#121×C15114yes—
1073C2×C4#124×C15114yes—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22C2×#121×C15111yescharacteristic
1105C22#525×C15111yescharacteristic
1106C22#525×C15111yescharacteristic
1107C22#525×C15111yescharacteristic
1108C22#525×C15111yescharacteristic
1109C22C2×#124×C15111yescharacteristic
1110C22C2×#124×C15111yescharacteristic
1111C22#529×C15111yescharacteristic
1112C22#529×C15111yescharacteristic
1113C22#529×C15111yescharacteristic
1114C22#529×C15111yescharacteristic
1115C22#529×C15111yescharacteristic
1116C22#532×C15111yescharacteristic
1117C22#538×C15111yescharacteristic
1118C22#538×C15111yescharacteristic
1119C22#538×C15111yescharacteristic
1120C22#539×C15111yescharacteristic
1121C22#542×C15111yescharacteristic
1122C22#542×C15111yescharacteristic
1123C22D42×C15111yescharacteristic
1124C22D42×C15111yescharacteristic
1125C22#546×C15111yescharacteristic
1126C22#546×C15111yescharacteristic
1127C22#546×C15111yescharacteristic
1128C22#546×C15111yescharacteristic
1129C22#546×C15111yescharacteristic
1130C22#547×C15111yescharacteristic
1131C22#548×C15111yescharacteristic
1132C22#548×C15111yescharacteristic
1133C22#551×C15111yescharacteristic
1134C22#551×C15111yescharacteristic
1135C22#551×C15111yescharacteristic
1136C22#552×C15111yescharacteristic
1137C22#555×C15111yescharacteristic
1138C22#559×C15111yescharacteristic
1139C4—24no—
1140C4—24no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C2—44no—
1153C2—82no—
1154C2#2398×C15111yescharacteristic
1155C2#2424×C15111yescharacteristic
1156C2#2427×C15111yescharacteristic
1157C2#2458×C15111yescharacteristic
1158C2#2459×C15111yescharacteristic
1159C2#2463×C15111yescharacteristic
1160C2#2472×C15111yescharacteristic
1161C2#2472×C15111yescharacteristic
1162C2#2477×C15111yescharacteristic
1163C2#2488×C15111yescharacteristic
1164C2#2491×C15111yescharacteristic
1165C2#2557×C15111yescharacteristic
1166C2#2572×C15111yescharacteristic
1167C2#2653×C15111yescharacteristic
1168C2#2850×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#393×C151C2semidirect
3. C2×#393×C151C2semidirect
4. C2×#391×C151C2semidirect
6. C2×C4×C22⋊C4×C151C2semidirect
7. #1443×C151C2semidirect
8. #1442×C151C2semidirect
9. #1440×C151C2semidirect
10. #1440×C151C2semidirect
12. #1437×C151C2semidirect
13. #1437×C151C2semidirect
14. #1434×C151C2semidirect
15. C22⋊#95×C151C2semidirect
152. #95×C151D4semidirect
584. #14817C151direct (N × H)
585. C151#14817direct (N × H)
587. C2×#393C2×C151semidirect
588. C2×#393C2×C151semidirect
589. C2×#391C2×C151semidirect
591. C2×C4×C22⋊C4C2×C151semidirect
592. #1443C2×C151semidirect
593. #1442C2×C151semidirect
594. #1440C2×C151semidirect
595. #1440C2×C151semidirect
597. #1437C2×C151semidirect
598. #1437C2×C151semidirect
599. #1434C2×C151semidirect
600. C22⋊#95C2×C151semidirect
737. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C1512
C2×#393×C1512
C2×#391×C1512
C2×#386×C1512
C2×C4×C22⋊C4×C1512
#1443×C1512
#1442×C1512
#1440×C1512
#1438×C1512
#1437×C1512
#1434×C1512
C22⋊#95×C1512
#14817151