Finite Group Databasebeta

← C151×#15498 #50320423

Subgroups — C151×#15498 #50320423

Order 38656.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C151C211yesmaximal, characteristic, complemented
2C2×#394×C151C211yesmaximal, characteristic, complemented
3C2×#394×C151C211yesmaximal, characteristic, complemented
4C2×#392×C151C211yesmaximal, characteristic
5C2×#390×C151C211yesmaximal, characteristic, complemented
6C2×#386×C151C211yesmaximal, characteristic, complemented
7C2×#386×C151C211yesmaximal, characteristic, complemented
8C2×#385×C151C211yesmaximal, characteristic, complemented
9#1441×C151C211yesmaximal, characteristic, complemented
10#1440×C151C211yesmaximal, characteristic, complemented
11#1440×C151C211yesmaximal, characteristic, complemented
12#1439×C151C211yesmaximal, characteristic, complemented
13#1439×C151C211yesmaximal, characteristic, complemented
14#1437×C151C211yesmaximal, characteristic, complemented
15C4⋊#95×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C24×C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C22×C4⋊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×C22⋊C4×C151C2211yescharacteristic
36C22×C22⋊C4×C151C2211yescharacteristic
37C22×C22⋊C4×C151C2211yescharacteristic
38C22×C42×C151C2211yescharacteristic
39#394×C151—24no—
40#394×C151—24no—
41#394×C151—24no—
42#392×C151—24no—
43#390×C151—24no—
44#386×C151—24no—
45#386×C151—24no—
46#385×C151—24no—
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
57C2×#95×C151C2211yescharacteristic
58C2×#95×C151C2211yescharacteristic
59C25×C151C2311yescharacteristic
60C25×C151C2311yescharacteristic
61C25×C151C2311yescharacteristic
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—22no—
74C22×D4×C151—41no—
75C22×D4×C151—41no—
76C22×D4×C151—41no—
77C22×D4×C151—41no—
78C22×D4×C151—41no—
79C22×D4×C151—41no—
80C22×D4×C151—41no—
81C22×D4×C151—41no—
82C22×D4×C151D414yes—
83C23×C4×C151—22no—
84C23×C4×C151—22no—
85C23×C4×C151—22no—
86C23×C4×C151—41no—
87C23×C4×C151—41no—
88C23×C4×C151—41no—
89C23×C4×C151—41no—
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
99C23×C4×C151C2311yescharacteristic
100C23×C4×C151C2311yescharacteristic
101C23×C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151—22no—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151—22no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151—22no—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—41no—
109C2×C4⋊C4×C151—41no—
110C2×C4⋊C4×C151—41no—
111C2×C4⋊C4×C151—41no—
112C2×C4⋊C4×C151—41no—
113C2×C4⋊C4×C151D414yescomplemented
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—22no—
123C2×C22⋊C4×C151—22no—
124C2×C22⋊C4×C151—22no—
125C2×C22⋊C4×C151—22no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—22no—
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—22no—
130C2×C22⋊C4×C151—22no—
131C2×C22⋊C4×C151—22no—
132C2×C22⋊C4×C151—22no—
133C2×C22⋊C4×C151—22no—
134C2×C22⋊C4×C151—22no—
135C2×C22⋊C4×C151—22no—
136C2×C22⋊C4×C151—22no—
137C2×C22⋊C4×C151—22no—
138C2×C22⋊C4×C151—22no—
139C2×C22⋊C4×C151—22no—
140C2×C22⋊C4×C151—22no—
141C2×C22⋊C4×C151—22no—
142C2×C22⋊C4×C151—22no—
143C2×C22⋊C4×C151—22no—
144C2×C22⋊C4×C151—41no—
145C2×C22⋊C4×C151—41no—
146C2×C22⋊C4×C151—41no—
147C2×C22⋊C4×C151—41no—
148C2×C22⋊C4×C151—41no—
149C2×C22⋊C4×C151—41no—
150C2×C22⋊C4×C151—41no—
151C2×C22⋊C4×C151—41no—
152C2×C22⋊C4×C151—41no—
153C2×C22⋊C4×C151—41no—
154C2×C22⋊C4×C151D414yescomplemented
155C2×C22⋊C4×C151D414yescomplemented
156C2×C42×C151—22no—
157C2×C42×C151—22no—
158C2×C42×C151—41no—
159#95×C151—22no—
160#95×C151—22no—
161#95×C151—22no—
162#95×C151—22no—
163#95×C151—22no—
164#95×C151—22no—
165#95×C151—22no—
166#95×C151—22no—
167#95×C151—22no—
168#95×C151—22no—
169#95×C151—41no—
170#95×C151—41no—
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×C151—21no—
205C24×C151—21no—
206C24×C151—21no—
207C24×C151—21no—
208C24×C151—21no—
209C24×C151—21no—
210C24×C151—21no—
211C24×C151C2×D412yes—
212C24×C151C2×D412yes—
213C24×C151C2×D412yes—
214C24×C151C2×D412yes—
215C24×C151#4112yes—
216C24×C151C2411yescharacteristic
217C2×D4×C151—28no—
218C2×D4×C151—28no—
219C2×D4×C151—28no—
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—
231C2×D4×C151—44no—
232C2×D4×C151—44no—
233C2×D4×C151—44no—
234C2×D4×C151—44no—
235C2×D4×C151—44no—
236C2×D4×C151—44no—
237C2×D4×C151—44no—
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—21no—
304C22×C4×C151—21no—
305C22×C4×C151—21no—
306C22×C4×C151—21no—
307C22×C4×C151—21no—
308C22×C4×C151—21no—
309C22×C4×C151—21no—
310C22×C4×C151—44no—
311C22×C4×C151—44no—
312C22×C4×C151—44no—
313C22×C4×C151—44no—
314C22×C4×C151—44no—
315C22×C4×C151—44no—
316C22×C4×C151—44no—
317C22×C4×C151C2×D412yes—
318C22×C4×C151C2×D412yes—
319C22×C4×C151C2×D412yes—
320C22×C4×C151C2×D412yes—
321C22×C4×C151C2×D412yes—
322C22×C4×C151C2×D412yes—
323C22×C4×C151C2×D412yes—
324C22×C4×C151C2×D412yes—
325C22×C4×C151#4112yes—
326C22×C4×C151#4112yes—
327C22×C4×C151#4112yes—
328C22×C4×C151#4112yes—
329C4⋊C4×C151—44no—
330C4⋊C4×C151—44no—
331C4⋊C4×C151—44no—
332C4⋊C4×C151—44no—
333C22⋊C4×C151—28no—
334C22⋊C4×C151—44no—
335C22⋊C4×C151—44no—
336C22⋊C4×C151—44no—
337C22⋊C4×C151—44no—
338C22⋊C4×C151—44no—
339C22⋊C4×C151—44no—
340C22⋊C4×C151—44no—
341C22⋊C4×C151—44no—
342C22⋊C4×C151—44no—
343C22⋊C4×C151—44no—
344C22⋊C4×C151—44no—
345C22⋊C4×C151—44no—
346C22⋊C4×C151—44no—
347C42×C151—44no—
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—22no—
372C23×C151—22no—
373C23×C151—22no—
374C23×C151—22no—
375C23×C151—22no—
376C23×C151—22no—
377C23×C151—22no—
378C23×C151—22no—
379C23×C151—22no—
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×C151—41no—
444C23×C151—41no—
445C23×C151—41no—
446C23×C151—41no—
447C23×C151—41no—
448C23×C151—41no—
449C23×C151—41no—
450C23×C151—41no—
451C23×C151—41no—
452C23×C151#12114yes—
453C23×C151C22×D411yescharacteristic
454C23×C151C22×D411yescharacteristic
455C23×C151C22×D411yescharacteristic
456C23×C151C22×D411yescharacteristic
457C23×C151C2×#4111yescharacteristic
458C23×C151C2×#4111yescharacteristic
459C23×C151C2×#4111yescharacteristic
460C23×C151C2×#4111yescharacteristic
461C23×C151C2×#4111yescharacteristic
462C23×C151H(5,𝔽2)11yescharacteristic
463C23×C151H(5,𝔽2)11yescharacteristic
464C23×C151H(5,𝔽2)11yescharacteristic
465C23×C151H(5,𝔽2)11yescharacteristic
466C23×C151H(5,𝔽2)11yescharacteristic
467C23×C1512−1+411yescharacteristic
468D4×C151—416no—
469D4×C151—416no—
470D4×C151—416no—
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—22no—
496C2×C4×C151—22no—
497C2×C4×C151—22no—
498C2×C4×C151—22no—
499C2×C4×C151—22no—
500C2×C4×C151—22no—
501C2×C4×C151—416no—
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×C151—41no—
547C2×C4×C151—41no—
548C2×C4×C151—41no—
549C2×C4×C151—41no—
550C2×C4×C151—41no—
551C2×C4×C151—41no—
552C2×C4×C151—41no—
553C2×C4×C151—41no—
554C2×C4×C151#12114yes—
555C2×C4×C151#12314yes—
556C22×C151—24no—
557C22×C151—24no—
558C22×C151—24no—
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—42no—
577C22×C151—42no—
578C22×C151—42no—
579C22×C151—42no—
580C22×C151—42no—
581C22×C151—42no—
582C22×C151—42no—
583C22×C151—42no—
584C22×C151—42no—
585C22×C151—81no—
586C22×C151—81no—
587C22×C151—81no—
588C22×C151—81no—
589C22×C151—81no—
590C22×C151—81no—
591C22×C151—81no—
592C22×C151—81no—
593C22×C151—81no—
594C22×C151—81no—
595C22×C151—81no—
596C22×C151—81no—
597C22×C151—81no—
598C22×C151—81no—
599C22×C151—81no—
600C22×C151—81no—
601C22×C151C2×#12111yescharacteristic
602C22×C151C2×#12111yescharacteristic
603C22×C151C2×#12311yescharacteristic
604C22×C151#52511yescharacteristic
605C22×C151#53211yescharacteristic
606C22×C151#53211yescharacteristic
607C22×C151#53411yescharacteristic
608C22×C151#53411yescharacteristic
609C22×C151#53411yescharacteristic
610C22×C151#53711yescharacteristic
611C22×C151#53811yescharacteristic
612C22×C151#54011yescharacteristic
613C22×C151#54011yescharacteristic
614C22×C151#54211yescharacteristic
615C22×C151#54211yescharacteristic
616C22×C151D4211yescharacteristic
617C22×C151D4211yescharacteristic
618C22×C151D4211yescharacteristic
619C22×C151D4211yescharacteristic
620C22×C151#54611yescharacteristic
621C22×C151#54611yescharacteristic
622C22×C151#54611yescharacteristic
623C22×C151#54611yescharacteristic
624C22×C151#54711yescharacteristic
625C22×C151#54711yescharacteristic
626C22×C151#54811yescharacteristic
627C22×C151#55011yescharacteristic
628C22×C151#55111yescharacteristic
629C22×C151#55111yescharacteristic
630C22×C151#55311yescharacteristic
631C22×C151#55311yescharacteristic
632C22×C151#55311yescharacteristic
633C22×C151#55911yescharacteristic
634C22×C151H(3,𝔽4)11yescharacteristic
635C22×C151#56211yescharacteristic
636C4×C151—24no—
637C4×C151—24no—
638C4×C151—42no—
639C4×C151—42no—
640C4×C151—42no—
641C4×C151—42no—
642C4×C151—42no—
643C4×C151—42no—
644C4×C151—81no—
645C4×C151—81no—
646C4×C151—81no—
647C4×C151—81no—
648C2×C151—44no—
649C2×C151—82no—
650C2×C151—82no—
651C2×C151#241211yescharacteristic
652C2×C151#241611yescharacteristic
653C2×C151#242211yescharacteristic
654C2×C151#242411yescharacteristic
655C2×C151#242811yescharacteristic
656C2×C151#244511yescharacteristic
657C2×C151#246111yescharacteristic
658C2×C151#254311yescharacteristic
659C2×C151#260211yescharacteristic
660C2×C151#267111yescharacteristic
661C2×C151#267911yescharacteristic
662C2×C151#270111yescharacteristic
663C2×C151#271211yescharacteristic
664C2×C151#273011yescharacteristic
665C2×C151#275311yescharacteristic
666#15498C15111yesmaximal, characteristic, direct product factor, Sylow
667C151#1549811yescharacteristic, direct product factor, Sylow
668C2×#394C2×C15111yescharacteristic, complemented
669C2×#394C2×C15111yescharacteristic, complemented
670C2×#394C2×C15111yescharacteristic, complemented
671C2×#392C2×C15111yescharacteristic
672C2×#390C2×C15111yescharacteristic, complemented
673C2×#386C2×C15111yescharacteristic, complemented
674C2×#386C2×C15111yescharacteristic, complemented
675C2×#385C2×C15111yescharacteristic, complemented
676#1441C2×C15111yescharacteristic, complemented
677#1440C2×C15111yescharacteristic, complemented
678#1440C2×C15111yescharacteristic, complemented
679#1439C2×C15111yescharacteristic, complemented
680#1439C2×C15111yescharacteristic, complemented
681#1437C2×C15111yescharacteristic, complemented
682C4⋊#95C2×C15111yescharacteristic, complemented
683C23×D4C22×C15111yescharacteristic
684C23×D4C22×C15111yescharacteristic
685C23×D4C22×C15111yescharacteristic
686C24×C4C22×C15111yescharacteristic
687C22×C4⋊C4C22×C15111yescharacteristic
688C22×C4⋊C4C22×C15111yescharacteristic
689C22×C4⋊C4C22×C15111yescharacteristic
690C22×C4⋊C4C22×C15111yescharacteristic
691C22×C22⋊C4C22×C15111yescharacteristic
692C22×C22⋊C4C22×C15111yescharacteristic
693C22×C22⋊C4C22×C15111yescharacteristic
694C22×C22⋊C4C22×C15111yescharacteristic
695C22×C22⋊C4C22×C15111yescharacteristic
696C22×C22⋊C4C22×C15111yescharacteristic
697C22×C22⋊C4C22×C15111yescharacteristic
698C22×C22⋊C4C22×C15111yescharacteristic
699C22×C22⋊C4C22×C15111yescharacteristic
700C22×C22⋊C4C22×C15111yescharacteristic
701C22×C22⋊C4C22×C15111yescharacteristic
702C22×C22⋊C4C22×C15111yescharacteristic
703C22×C22⋊C4C22×C15111yescharacteristic
704C22×C22⋊C4C22×C15111yescharacteristic
705C22×C42C22×C15111yescharacteristic
706#394—24no—
707#394—24no—
708#394—24no—
709#392—24no—
710#390—24no—
711#386—24no—
712#386—24no—
713#385—24no—
714C2×#95C22×C15111yescharacteristic
715C2×#95C22×C15111yescharacteristic
716C2×#95C22×C15111yescharacteristic
717C2×#95C22×C15111yescharacteristic
718C2×#95C22×C15111yescharacteristic
719C2×#95C22×C15111yescharacteristic
720C2×#95C22×C15111yescharacteristic
721C2×#95C22×C15111yescharacteristic
722C2×#95C22×C15111yescharacteristic
723C2×#95C22×C15111yescharacteristic
724C2×#95C22×C15111yescharacteristic
725C2×#95C22×C15111yescharacteristic
726C25C23×C15111yescharacteristic
727C25C23×C15111yescharacteristic
728C25C23×C15111yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4D4×C15114yes—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4C23×C15111yescharacteristic
758C23×C4C23×C15111yescharacteristic
759C23×C4C23×C15111yescharacteristic
760C23×C4C23×C15111yescharacteristic
761C23×C4C23×C15111yescharacteristic
762C23×C4C23×C15111yescharacteristic
763C23×C4C23×C15111yescharacteristic
764C23×C4C23×C15111yescharacteristic
765C23×C4C23×C15111yescharacteristic
766C23×C4C23×C15111yescharacteristic
767C23×C4C23×C15111yescharacteristic
768C23×C4C23×C15111yescharacteristic
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4—41no—
780C2×C4⋊C4D4×C15114yescomplemented
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4D4×C15114yescomplemented
822C2×C22⋊C4D4×C15114yescomplemented
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
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—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24C2×D4×C15112yes—
879C24C2×D4×C15112yes—
880C24C2×D4×C15112yes—
881C24C2×D4×C15112yes—
882C24#41×C15112yes—
883C24C24×C15111yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
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—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4C2×D4×C15112yes—
985C22×C4C2×D4×C15112yes—
986C22×C4C2×D4×C15112yes—
987C22×C4C2×D4×C15112yes—
988C22×C4C2×D4×C15112yes—
989C22×C4C2×D4×C15112yes—
990C22×C4C2×D4×C15112yes—
991C22×C4C2×D4×C15112yes—
992C22×C4#41×C15112yes—
993C22×C4#41×C15112yes—
994C22×C4#41×C15112yes—
995C22×C4#41×C15112yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—28no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C42—44no—
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—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
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—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23#121×C15114yes—
1120C23C22×D4×C15111yescharacteristic
1121C23C22×D4×C15111yescharacteristic
1122C23C22×D4×C15111yescharacteristic
1123C23C22×D4×C15111yescharacteristic
1124C23C2×#41×C15111yescharacteristic
1125C23C2×#41×C15111yescharacteristic
1126C23C2×#41×C15111yescharacteristic
1127C23C2×#41×C15111yescharacteristic
1128C23C2×#41×C15111yescharacteristic
1129C23H(5,𝔽2)×C15111yescharacteristic
1130C23H(5,𝔽2)×C15111yescharacteristic
1131C23H(5,𝔽2)×C15111yescharacteristic
1132C23H(5,𝔽2)×C15111yescharacteristic
1133C23H(5,𝔽2)×C15111yescharacteristic
1134C232−1+4×C15111yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
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—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—416no—
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×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4#121×C15114yes—
1222C2×C4#123×C15114yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×#121×C15111yescharacteristic
1269C22C2×#121×C15111yescharacteristic
1270C22C2×#123×C15111yescharacteristic
1271C22#525×C15111yescharacteristic
1272C22#532×C15111yescharacteristic
1273C22#532×C15111yescharacteristic
1274C22#534×C15111yescharacteristic
1275C22#534×C15111yescharacteristic
1276C22#534×C15111yescharacteristic
1277C22#537×C15111yescharacteristic
1278C22#538×C15111yescharacteristic
1279C22#540×C15111yescharacteristic
1280C22#540×C15111yescharacteristic
1281C22#542×C15111yescharacteristic
1282C22#542×C15111yescharacteristic
1283C22D42×C15111yescharacteristic
1284C22D42×C15111yescharacteristic
1285C22D42×C15111yescharacteristic
1286C22D42×C15111yescharacteristic
1287C22#546×C15111yescharacteristic
1288C22#546×C15111yescharacteristic
1289C22#546×C15111yescharacteristic
1290C22#546×C15111yescharacteristic
1291C22#547×C15111yescharacteristic
1292C22#547×C15111yescharacteristic
1293C22#548×C15111yescharacteristic
1294C22#550×C15111yescharacteristic
1295C22#551×C15111yescharacteristic
1296C22#551×C15111yescharacteristic
1297C22#553×C15111yescharacteristic
1298C22#553×C15111yescharacteristic
1299C22#553×C15111yescharacteristic
1300C22#559×C15111yescharacteristic
1301C22H(3,𝔽4)×C15111yescharacteristic
1302C22#562×C15111yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2#2412×C15111yescharacteristic
1319C2#2416×C15111yescharacteristic
1320C2#2422×C15111yescharacteristic
1321C2#2424×C15111yescharacteristic
1322C2#2428×C15111yescharacteristic
1323C2#2445×C15111yescharacteristic
1324C2#2461×C15111yescharacteristic
1325C2#2543×C15111yescharacteristic
1326C2#2602×C15111yescharacteristic
1327C2#2671×C15111yescharacteristic
1328C2#2679×C15111yescharacteristic
1329C2#2701×C15111yescharacteristic
1330C2#2712×C15111yescharacteristic
1331C2#2730×C15111yescharacteristic
1332C2#2753×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC2×#392×C151C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#394×C151C2semidirect
2. C2×#394×C151C2semidirect
3. C2×#394×C151C2semidirect
5. C2×#390×C151C2semidirect
6. C2×#386×C151C2semidirect
7. C2×#386×C151C2semidirect
8. C2×#385×C151C2semidirect
9. #1441×C151C2semidirect
10. #1440×C151C2semidirect
11. #1440×C151C2semidirect
12. #1439×C151C2semidirect
13. #1439×C151C2semidirect
14. #1437×C151C2semidirect
15. C4⋊#95×C151C2semidirect
113. C2×C4⋊C4×C151D4semidirect
154. C2×C22⋊C4×C151D4semidirect
155. C2×C22⋊C4×C151D4semidirect
666. #15498C151direct (N × H)
667. C151#15498direct (N × H)
668. C2×#394C2×C151semidirect
669. C2×#394C2×C151semidirect
670. C2×#394C2×C151semidirect
672. C2×#390C2×C151semidirect
673. C2×#386C2×C151semidirect
674. C2×#386C2×C151semidirect
675. C2×#385C2×C151semidirect
676. #1441C2×C151semidirect
677. #1440C2×C151semidirect
678. #1440C2×C151semidirect
679. #1439C2×C151semidirect
680. #1439C2×C151semidirect
681. #1437C2×C151semidirect
682. C4⋊#95C2×C151semidirect
780. C2×C4⋊C4D4×C151semidirect
821. C2×C22⋊C4D4×C151semidirect
822. C2×C22⋊C4D4×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×#392×C1512
C2×#390×C1512
C2×#386×C1512
C2×#385×C1512
#1441×C1512
#1440×C1512
#1439×C1512
#1437×C1512
C4⋊#95×C1512
#15498151