Finite Group Databasebeta

← C151×#24539 #50329464

Subgroups — C151×#24539 #50329464

Order 38656.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic
2C2×#418×C151C211yesmaximal, characteristic, complemented
3#2500×C151C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
5#2073×C151C211yesmaximal, characteristic, complemented
6#2071×C151C211yesmaximal, characteristic, complemented
7#2054×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1851×C151C211yesmaximal, characteristic, complemented
13#1825×C151C211yesmaximal, characteristic, complemented
14#1804×C151C211yesmaximal, characteristic, complemented
15#1802×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24C22×C22⋊C4×C151—21no—
25#447×C151—24no—
26C2×C4⋊C8×C151C2211yescharacteristic, complemented
27C2×C4⋊C8×C151C2211yescharacteristic, complemented
28#418×C151—24no—
29C2×#102×C151C2211yescharacteristic
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic, complemented
36C2×#102×C151C2211yescharacteristic, complemented
37C2×C22⋊C8×C151C2211yescharacteristic
38#394×C151—21no—
39#394×C151—21no—
40#390×C151C2211yescharacteristic
41#390×C151C2211yescharacteristic
42#390×C151C2211yescharacteristic, complemented
43#390×C151C2211yescharacteristic, complemented
44#388×C151—21no—
45#388×C151—21no—
46#386×C151—21no—
47#386×C151—21no—
48#384×C151C2211yescharacteristic, complemented
49#382×C151C2211yescharacteristic, complemented
50#380×C151C2211yescharacteristic
51#379×C151—21no—
52C4×C22⋊C4×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic, complemented
54#340×C151C2211yescharacteristic, complemented
55#340×C151C2211yescharacteristic, complemented
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#336×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61C25×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151—22no—
64C22×D4×C151—21no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—41no—
68C22×D4×C151—41no—
69C22×D4×C151D414yes—
70C22×D4×C151C2311yescharacteristic
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151—21no—
74C23×C4×C151—21no—
75C23×C4×C151C2311yescharacteristic
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C2×D8×C151—22no—
79C2×D8×C151—22no—
80C2×D8×C151—41no—
81C2×D8×C151—41no—
82C2×M16×C151—22no—
83C2×M16×C151—41no—
84C2×M16×C151—41no—
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89#121×C151—22no—
90#121×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—41no—
94C4×D4×C151—41no—
95#117×C151—22no—
96#117×C151—22no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—44no—
118C2×C22⋊C4×C151D411yescharacteristic
119C2×C22⋊C4×C151D411yescharacteristic
120C2×C42×C151—21no—
121C2×C42×C151C2311yescharacteristic
122C2×C42×C151C2311yescharacteristic
123C4⋊C8×C151—41no—
124C4⋊C8×C151—41no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—22no—
130#102×C151—22no—
131#102×C151—41no—
132#102×C151—41no—
133C22⋊C8×C151—22no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151D411yescharacteristic
138#95×C151D411yescharacteristic
139C24×C151—21no—
140C24×C151—21no—
141C24×C151—24no—
142C24×C151—21no—
143C24×C151—42no—
144C24×C151—42no—
145C24×C151—42no—
146C24×C151—42no—
147C24×C151—81no—
148C24×C151—81no—
149C24×C151C2×D411yescharacteristic
150C2×D4×C151—28no—
151C2×D4×C151—24no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—44no—
167C2×D4×C151—44no—
168C2×D4×C151—44no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—81no—
173C2×D4×C151—81no—
174C2×D4×C151C2×D412yes—
175C2×D4×C151C2×D412yes—
176C2×D4×C151#4112yes—
177C2×D4×C151#4112yes—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—42no—
188C22×C4×C151—42no—
189C22×C4×C151—42no—
190C22×C4×C151—42no—
191C22×C4×C151—81no—
192C22×C4×C151—81no—
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2×D411yescharacteristic
196C22×C4×C151C2×D411yescharacteristic
197C22×C4×C151C2×D412yes—
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151#4112yes—
200C22×C4×C151C2411yescharacteristic
201D8×C151—44no—
202D8×C151—44no—
203M16×C151—44no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—81no—
227C4⋊C4×C151—81no—
228C22⋊C4×C151—22no—
229C22⋊C4×C151—41no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—42no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—81no—
240C22⋊C4×C151—81no—
241C22⋊C4×C151—81no—
242C22⋊C4×C151—81no—
243C42×C151—21no—
244C42×C151—21no—
245C42×C151—21no—
246C42×C151—21no—
247C42×C151—42no—
248C23×C151—22no—
249C23×C151—22no—
250C23×C151—22no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—22no—
258C23×C151—48no—
259C23×C151—48no—
260C23×C151—41no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151—41no—
277C23×C151—84no—
278C23×C151—84no—
279C23×C151—84no—
280C23×C151—84no—
281C23×C151—84no—
282C23×C151#12112yes—
283C23×C151C22×D411yescharacteristic
284D4×C151—22no—
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—22no—
288D4×C151—22no—
289D4×C151—48no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—84no—
297D4×C151#12314yes—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—22no—
303C2×C4×C151—22no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—84no—
331C2×C4×C151—84no—
332C2×C4×C151#12112yes—
333C2×C4×C151AGL(1,ℤ/8)12yes—
334C2×C4×C151C22×D411yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C2×C4×C151C2×#4111yescharacteristic
337C2×C4×C151C2×#4111yescharacteristic
338C2×C4×C151H(5,𝔽2)11yescharacteristic
339C2×C4×C151H(5,𝔽2)11yescharacteristic
340C8×C151—41no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C22×C151—22no—
345C22×C151—24no—
346C22×C151—22no—
347C22×C151—22no—
348C22×C151—42no—
349C22×C151—42no—
350C22×C151—42no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—42no—
354C22×C151—41no—
355C22×C151—42no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—42no—
359C22×C151—42no—
360C22×C151—42no—
361C22×C151—816no—
362C22×C151—81no—
363C22×C151—81no—
364C22×C151—81no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151—81no—
368C22×C151—81no—
369C22×C151—81no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151C2×#12111yescharacteristic
374C22×C151#54611yescharacteristic
375C22×C151#54611yescharacteristic
376C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C151#57511yescharacteristic
378C22×C151#57611yescharacteristic
379C22×C151#57611yescharacteristic
380C4×C151—22no—
381C4×C151—22no—
382C4×C151—41no—
383C4×C151—41no—
384C4×C151—41no—
385C4×C151—81no—
386C4×C151—81no—
387C4×C151—81no—
388C4×C151—81no—
389C4×C151—81no—
390C4×C151C2×#12311yescharacteristic
391C4×C151#53411yescharacteristic
392C4×C151#55111yescharacteristic
393C4×C151#55111yescharacteristic
394C2×C151—42no—
395C2×C151—44no—
396C2×C151—82no—
397C2×C151—161no—
398C2×C151#241211yescharacteristic
399C2×C151#303611yescharacteristic
400C2×C151#304111yescharacteristic
401C2×C151#331811yescharacteristic
402C2×C151#331911yescharacteristic
403C2×C151#332211yescharacteristic
404C2×C151#332511yescharacteristic
405#24539C15111yesmaximal, characteristic, direct product factor, Sylow
406C151#2453911yescharacteristic, direct product factor, Sylow
407C2×#447C2×C15111yescharacteristic
408C2×#418C2×C15111yescharacteristic, complemented
409#2500C2×C15111yescharacteristic, complemented
410D4×C22⋊C4C2×C15111yescharacteristic, complemented
411#2073C2×C15111yescharacteristic, complemented
412#2071C2×C15111yescharacteristic, complemented
413#2054C2×C15111yescharacteristic, complemented
414#2054C2×C15111yescharacteristic, complemented
415#1895C2×C15111yescharacteristic, complemented
416#1879C2×C15111yescharacteristic, complemented
417#1879C2×C15111yescharacteristic, complemented
418#1851C2×C15111yescharacteristic, complemented
419#1825C2×C15111yescharacteristic, complemented
420#1804C2×C15111yescharacteristic, complemented
421#1802C2×C15111yescharacteristic, complemented
422C23×D4C22×C15111yescharacteristic
423C22×D8C22×C15111yescharacteristic
424C22×D8C22×C15111yescharacteristic
425C22×M16C22×C15111yescharacteristic
426C2×#121C22×C15111yescharacteristic
427C2×C4×D4C22×C15111yescharacteristic
428C2×C4×D4C22×C15111yescharacteristic
429C2×#117C22×C15111yescharacteristic
430C22×C22⋊C4—21no—
431#447—24no—
432C2×C4⋊C8C22×C15111yescharacteristic, complemented
433C2×C4⋊C8C22×C15111yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C15111yescharacteristic
436C2×#102C22×C15111yescharacteristic
437C2×#102C22×C15111yescharacteristic
438C2×#102C22×C15111yescharacteristic
439C2×#102C22×C15111yescharacteristic
440C2×#102C22×C15111yescharacteristic
441C2×#102C22×C15111yescharacteristic, complemented
442C2×#102C22×C15111yescharacteristic, complemented
443C2×C22⋊C8C22×C15111yescharacteristic
444#394—21no—
445#394—21no—
446#390C22×C15111yescharacteristic
447#390C22×C15111yescharacteristic
448#390C22×C15111yescharacteristic, complemented
449#390C22×C15111yescharacteristic, complemented
450#388—21no—
451#388—21no—
452#386—21no—
453#386—21no—
454#384C22×C15111yescharacteristic, complemented
455#382C22×C15111yescharacteristic, complemented
456#380C22×C15111yescharacteristic
457#379—21no—
458C4×C22⋊C4C22×C15111yescharacteristic
459#340C22×C15111yescharacteristic, complemented
460#340C22×C15111yescharacteristic, complemented
461#340C22×C15111yescharacteristic, complemented
462#340C22×C15111yescharacteristic, complemented
463#340C22×C15111yescharacteristic, complemented
464#340C22×C15111yescharacteristic, complemented
465#336C22×C15111yescharacteristic, complemented
466#336C22×C15111yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4D4×C15114yes—
476C22×D4C23×C15111yescharacteristic
477C22×D4C23×C15111yescharacteristic
478C22×D4C23×C15111yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C15111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—41no—
487C2×D8—41no—
488C2×M16—22no—
489C2×M16—41no—
490C2×M16—41no—
491C22×C8C23×C15111yescharacteristic
492C22×C8C23×C15111yescharacteristic
493C22×C8C23×C15111yescharacteristic
494C22×C8C23×C15111yescharacteristic
495#121—22no—
496#121—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—41no—
500C4×D4—41no—
501#117—22no—
502#117—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C4⋊C4C23×C15111yescharacteristic
507C2×C4⋊C4C23×C15111yescharacteristic
508C2×C4⋊C4C23×C15111yescharacteristic
509C2×C4⋊C4C23×C15111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—44no—
524C2×C22⋊C4D4×C15111yescharacteristic
525C2×C22⋊C4D4×C15111yescharacteristic
526C2×C42—21no—
527C2×C42C23×C15111yescharacteristic
528C2×C42C23×C15111yescharacteristic
529C4⋊C8—41no—
530C4⋊C8—41no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539C22⋊C8—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C15111yescharacteristic
544#95D4×C15111yescharacteristic
545C24—21no—
546C24—21no—
547C24—24no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C15111yescharacteristic
556C2×D4—28no—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C15112yes—
581C2×D4C2×D4×C15112yes—
582C2×D4#41×C15112yes—
583C2×D4#41×C15112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4C2×D4×C15111yescharacteristic
600C22×C4C2×D4×C15111yescharacteristic
601C22×C4C2×D4×C15111yescharacteristic
602C22×C4C2×D4×C15111yescharacteristic
603C22×C4C2×D4×C15112yes—
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4#41×C15112yes—
606C22×C4C24×C15111yescharacteristic
607D8—44no—
608D8—44no—
609M16—44no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—81no—
633C4⋊C4—81no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—42no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23#121×C15112yes—
689C23C22×D4×C15111yescharacteristic
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4#123×C15114yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4#121×C15112yes—
739C2×C4AGL(1,ℤ/8)×C15112yes—
740C2×C4C22×D4×C15111yescharacteristic
741C2×C4C2×#41×C15111yescharacteristic
742C2×C4C2×#41×C15111yescharacteristic
743C2×C4C2×#41×C15111yescharacteristic
744C2×C4H(5,𝔽2)×C15111yescharacteristic
745C2×C4H(5,𝔽2)×C15111yescharacteristic
746C8—41no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—816no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#121×C15111yescharacteristic
780C22#546×C15111yescharacteristic
781C22#546×C15111yescharacteristic
782C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
783C22#575×C15111yescharacteristic
784C22#576×C15111yescharacteristic
785C22#576×C15111yescharacteristic
786C4—22no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C15111yescharacteristic
797C4#534×C15111yescharacteristic
798C4#551×C15111yescharacteristic
799C4#551×C15111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—161no—
804C2#2412×C15111yescharacteristic
805C2#3036×C15111yescharacteristic
806C2#3041×C15111yescharacteristic
807C2#3318×C15111yescharacteristic
808C2#3319×C15111yescharacteristic
809C2#3322×C15111yescharacteristic
810C2#3325×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#418×C151C2semidirect
3. #2500×C151C2semidirect
4. D4×C22⋊C4×C151C2semidirect
5. #2073×C151C2semidirect
6. #2071×C151C2semidirect
7. #2054×C151C2semidirect
8. #2054×C151C2semidirect
9. #1895×C151C2semidirect
10. #1879×C151C2semidirect
11. #1879×C151C2semidirect
12. #1851×C151C2semidirect
13. #1825×C151C2semidirect
14. #1804×C151C2semidirect
15. #1802×C151C2semidirect
26. C2×C4⋊C8×C151C22semidirect
27. C2×C4⋊C8×C151C22semidirect
35. C2×#102×C151C22semidirect
36. C2×#102×C151C22semidirect
42. #390×C151C22semidirect
43. #390×C151C22semidirect
48. #384×C151C22semidirect
49. #382×C151C22semidirect
53. #340×C151C22semidirect
54. #340×C151C22semidirect
55. #340×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #336×C151C22semidirect
60. #336×C151C22semidirect
405. #24539C151direct (N × H)
406. C151#24539direct (N × H)
408. C2×#418C2×C151semidirect
409. #2500C2×C151semidirect
410. D4×C22⋊C4C2×C151semidirect
411. #2073C2×C151semidirect
412. #2071C2×C151semidirect
413. #2054C2×C151semidirect
414. #2054C2×C151semidirect
415. #1895C2×C151semidirect
416. #1879C2×C151semidirect
417. #1879C2×C151semidirect
418. #1851C2×C151semidirect
419. #1825C2×C151semidirect
420. #1804C2×C151semidirect
421. #1802C2×C151semidirect
432. C2×C4⋊C8C22×C151semidirect
433. C2×C4⋊C8C22×C151semidirect
441. C2×#102C22×C151semidirect
442. C2×#102C22×C151semidirect
448. #390C22×C151semidirect
449. #390C22×C151semidirect
454. #384C22×C151semidirect
455. #382C22×C151semidirect
459. #340C22×C151semidirect
460. #340C22×C151semidirect
461. #340C22×C151semidirect
462. #340C22×C151semidirect
463. #340C22×C151semidirect
464. #340C22×C151semidirect
465. #336C22×C151semidirect
466. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
C2×#418×C1512
#2500×C1512
D4×C22⋊C4×C1512
#2073×C1512
#2071×C1512
#2054×C1512
#1895×C1512
#1879×C1512
#1851×C1512
#1825×C1512
#1804×C1512
#1802×C1512
#24539151