Finite Group Databasebeta

← C151×#24555 #50329480

Subgroups — C151×#24555 #50329480

Order 38656.

1194 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C151C211yesmaximal, characteristic, complemented
2C22×C22⋊C8×C151C211yesmaximal, characteristic, complemented
3#2847×C151C211yesmaximal, characteristic
4#2280×C151C211yesmaximal, characteristic, complemented
5#2077×C151C211yesmaximal, characteristic, complemented
6#2076×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1893×C151C211yesmaximal, characteristic, complemented
10#1893×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic, complemented
12#1854×C151C211yesmaximal, characteristic, complemented
13#1825×C151C211yesmaximal, characteristic, complemented
14#1808×C151C211yesmaximal, characteristic, complemented
15#1807×C151C211yesmaximal, characteristic, complemented
16C24×C4×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×#120×C151—21no—
23C2×#117×C151C2211yescharacteristic
24C2×#117×C151C2211yescharacteristic
25#482×C151—24no—
26C2×#107×C151C2211yescharacteristic, complemented
27C2×#107×C151C2211yescharacteristic, complemented
28C2×#106×C151C2211yescharacteristic, complemented
29C2×#106×C151C2211yescharacteristic, complemented
30C2×#102×C151C2211yescharacteristic, complemented
31C2×#102×C151C2211yescharacteristic, complemented
32C2×#102×C151C2211yescharacteristic, complemented
33C2×#102×C151C2211yescharacteristic, complemented
34C2×C22⋊C8×C151—24no—
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39#386×C151—21no—
40#386×C151—21no—
41#386×C151—21no—
42#381×C151—21no—
43#380×C151C2211yescharacteristic
44#380×C151C2211yescharacteristic
45#380×C151C2211yescharacteristic
46#380×C151C2211yescharacteristic
47#380×C151C2211yescharacteristic
48#380×C151C2211yescharacteristic
49#380×C151C2211yescharacteristic
50#379×C151—21no—
51C4×C22⋊C4×C151—21no—
52C4×C22⋊C4×C151—21no—
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#340×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61C25×C151D411yescharacteristic
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151C2311yescharacteristic
66C23×C4×C151—22no—
67C23×C4×C151—22no—
68C23×C4×C151—22no—
69C23×C4×C151—22no—
70C23×C4×C151—41no—
71C23×C4×C151—41no—
72C23×C4×C151D411yescharacteristic
73C23×C4×C151D411yescharacteristic
74C23×C4×C151D411yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C23×C4×C151C2311yescharacteristic
77C23×C4×C151C2311yescharacteristic
78C22×C8×C151—22no—
79C22×C8×C151—22no—
80C22×C8×C151—22no—
81C22×C8×C151—22no—
82C22×C8×C151—41no—
83C22×C8×C151—41no—
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—41no—
93#121×C151—41no—
94#120×C151—44no—
95#117×C151—22no—
96#117×C151—22no—
97#117×C151—41no—
98#117×C151—41no—
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
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—21no—
118C2×C42×C151—21no—
119C2×C42×C151—21no—
120#107×C151—22no—
121#107×C151—41no—
122#106×C151—22no—
123#106×C151—41no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—41no—
127#102×C151—41no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151—22no—
131C22⋊C8×C151D414yescomplemented
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139C24×C151—22no—
140C24×C151—22no—
141C24×C151—22no—
142C24×C151—22no—
143C24×C151—22no—
144C24×C151—21no—
145C24×C151—41no—
146C24×C151—41no—
147C24×C151C2×D411yescharacteristic
148C24×C151C2×D411yescharacteristic
149C24×C151C2×D411yescharacteristic
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—42no—
157C2×D4×C151—42no—
158C2×D4×C151—42no—
159C2×D4×C151—42no—
160C2×D4×C151—42no—
161C2×D4×C151—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—22no—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—22no—
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—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—41no—
193C22×C4×C151—41no—
194C22×C4×C151—41no—
195C22×C4×C151—44no—
196C22×C4×C151—44no—
197C22×C4×C151—44no—
198C22×C4×C151—44no—
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D412yes—
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151#4112yes—
204C22×C4×C151#4112yes—
205C22×C4×C151#4112yes—
206C22×C4×C151C2411yescharacteristic
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—
216C2×C8×C151—21no—
217C2×C8×C151—44no—
218C2×C8×C151—44no—
219C2×C8×C151C2×D412yes—
220C2×C8×C151C2×D412yes—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151—21no—
234C4⋊C4×C151—21no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—42no—
240C22⋊C4×C151—42no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—42no—
243C22⋊C4×C151—42no—
244C22⋊C4×C151—42no—
245C22⋊C4×C151—42no—
246C22⋊C4×C151—42no—
247C42×C151—42no—
248C42×C151—42no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—28no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—21no—
264C23×C151—21no—
265C23×C151—21no—
266C23×C151—44no—
267C23×C151—44no—
268C23×C151—44no—
269C23×C151—44no—
270C23×C151—44no—
271C23×C151—44no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151—41no—
277C23×C151—41no—
278C23×C151—41no—
279C23×C151#12112yes—
280C23×C151#12312yes—
281C23×C151#13512yes—
282C23×C151#13512yes—
283C23×C151AGL(1,ℤ/8)12yes—
284C23×C151C22×D411yescharacteristic
285D4×C151—41no—
286D4×C151—41no—
287D4×C151—41no—
288D4×C151—41no—
289D4×C151—84no—
290D4×C151—84no—
291D4×C151—84no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—22no—
297C2×C4×C151—22no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—22no—
302C2×C4×C151—22no—
303C2×C4×C151—22no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—44no—
308C2×C4×C151—44no—
309C2×C4×C151—44no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
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—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151#12112yes—
336C2×C4×C151#12312yes—
337C2×C4×C151C22×D411yescharacteristic
338C2×C4×C151C2×#4111yescharacteristic
339C2×C4×C151C2×#4111yescharacteristic
340C2×C4×C151C2×#4111yescharacteristic
341C2×C4×C151H(5,𝔽2)11yescharacteristic
342C2×C4×C151H(5,𝔽2)11yescharacteristic
343C8×C151—22no—
344C8×C151—22no—
345C8×C151—41no—
346C8×C151—41no—
347C22×C151—22no—
348C22×C151—22no—
349C22×C151—22no—
350C22×C151—22no—
351C22×C151—22no—
352C22×C151—22no—
353C22×C151—22no—
354C22×C151—22no—
355C22×C151—22no—
356C22×C151—22no—
357C22×C151—22no—
358C22×C151—22no—
359C22×C151—416no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—41no—
366C22×C151—41no—
367C22×C151—41no—
368C22×C151—81no—
369C22×C151—81no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151#48214yescomplemented
376C22×C151C2×#12111yescharacteristic
377C22×C151C2×#12311yescharacteristic
378C22×C151#53411yescharacteristic
379C22×C151C2×#13511yescharacteristic
380C22×C151C2×#13511yescharacteristic
381C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C151#57511yescharacteristic
383C4×C151—22no—
384C4×C151—22no—
385C4×C151—41no—
386C4×C151—81no—
387C4×C151—81no—
388C4×C151—81no—
389C4×C151—81no—
390C4×C151—81no—
391C4×C151—81no—
392C4×C151—81no—
393C4×C151#54611yescharacteristic
394C4×C151#54611yescharacteristic
395C4×C151#55111yescharacteristic
396C4×C151#55111yescharacteristic
397C2×C151—24no—
398C2×C151—42no—
399C2×C151—42no—
400C2×C151—161no—
401C2×C151#241211yescharacteristic
402C2×C151#305011yescharacteristic
403C2×C151#305511yescharacteristic
404C2×C151C2×#48211yescharacteristic
405C2×C151#309111yescharacteristic
406C2×C151#318811yescharacteristic
407C2×C151#319111yescharacteristic
408#24555C15111yesmaximal, characteristic, direct product factor, Sylow
409C151#2455511yescharacteristic, direct product factor, Sylow
410C2×#482C2×C15111yescharacteristic, complemented
411C22×C22⋊C8C2×C15111yescharacteristic, complemented
412#2847C2×C15111yescharacteristic
413#2280C2×C15111yescharacteristic, complemented
414#2077C2×C15111yescharacteristic, complemented
415#2076C2×C15111yescharacteristic, complemented
416#2034C2×C15111yescharacteristic, complemented
417#2033C2×C15111yescharacteristic, complemented
418#1893C2×C15111yescharacteristic, complemented
419#1893C2×C15111yescharacteristic, complemented
420#1875C2×C15111yescharacteristic, complemented
421#1854C2×C15111yescharacteristic, complemented
422#1825C2×C15111yescharacteristic, complemented
423#1808C2×C15111yescharacteristic, complemented
424#1807C2×C15111yescharacteristic, complemented
425C24×C4C22×C15111yescharacteristic
426C23×C8C22×C15111yescharacteristic
427C23×C8C22×C15111yescharacteristic
428C2×#121C22×C15111yescharacteristic
429C2×#121C22×C15111yescharacteristic
430C2×#121C22×C15111yescharacteristic
431C2×#120—21no—
432C2×#117C22×C15111yescharacteristic
433C2×#117C22×C15111yescharacteristic
434#482—24no—
435C2×#107C22×C15111yescharacteristic, complemented
436C2×#107C22×C15111yescharacteristic, complemented
437C2×#106C22×C15111yescharacteristic, complemented
438C2×#106C22×C15111yescharacteristic, complemented
439C2×#102C22×C15111yescharacteristic, complemented
440C2×#102C22×C15111yescharacteristic, complemented
441C2×#102C22×C15111yescharacteristic, complemented
442C2×#102C22×C15111yescharacteristic, complemented
443C2×C22⋊C8—24no—
444C2×C22⋊C8C22×C15111yescharacteristic
445C2×C22⋊C8C22×C15111yescharacteristic
446C2×C22⋊C8C22×C15111yescharacteristic
447C2×C22⋊C8C22×C15111yescharacteristic
448#386—21no—
449#386—21no—
450#386—21no—
451#381—21no—
452#380C22×C15111yescharacteristic
453#380C22×C15111yescharacteristic
454#380C22×C15111yescharacteristic
455#380C22×C15111yescharacteristic
456#380C22×C15111yescharacteristic
457#380C22×C15111yescharacteristic
458#380C22×C15111yescharacteristic
459#379—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462#340C22×C15111yescharacteristic, complemented
463#340C22×C15111yescharacteristic, complemented
464#340C22×C15111yescharacteristic, complemented
465#340C22×C15111yescharacteristic, complemented
466#340C22×C15111yescharacteristic, complemented
467#340C22×C15111yescharacteristic, complemented
468#340C22×C15111yescharacteristic, complemented
469#340C22×C15111yescharacteristic, complemented
470C25D4×C15111yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C23×C15111yescharacteristic
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—41no—
480C23×C4—41no—
481C23×C4D4×C15111yescharacteristic
482C23×C4D4×C15111yescharacteristic
483C23×C4D4×C15111yescharacteristic
484C23×C4C23×C15111yescharacteristic
485C23×C4C23×C15111yescharacteristic
486C23×C4C23×C15111yescharacteristic
487C22×C8—22no—
488C22×C8—22no—
489C22×C8—22no—
490C22×C8—22no—
491C22×C8—41no—
492C22×C8—41no—
493C22×C8C23×C15111yescharacteristic
494C22×C8C23×C15111yescharacteristic
495C22×C8C23×C15111yescharacteristic
496C22×C8C23×C15111yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503#120—44no—
504#117—22no—
505#117—22no—
506#117—41no—
507#117—41no—
508C2×C4⋊C4C23×C15111yescharacteristic
509C2×C4⋊C4C23×C15111yescharacteristic
510C2×C4⋊C4C23×C15111yescharacteristic
511C2×C4⋊C4C23×C15111yescharacteristic
512C2×C4⋊C4C23×C15111yescharacteristic
513C2×C4⋊C4C23×C15111yescharacteristic
514C2×C4⋊C4C23×C15111yescharacteristic
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—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C42—21no—
528C2×C42—21no—
529#107—22no—
530#107—41no—
531#106—22no—
532#106—41no—
533#102—22no—
534#102—22no—
535#102—41no—
536#102—41no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8D4×C15114yescomplemented
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—41no—
555C24—41no—
556C24C2×D4×C15111yescharacteristic
557C24C2×D4×C15111yescharacteristic
558C24C2×D4×C15111yescharacteristic
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C2×D4×C15111yescharacteristic
610C22×C4C2×D4×C15112yes—
611C22×C4C2×D4×C15111yescharacteristic
612C22×C4#41×C15112yes—
613C22×C4#41×C15112yes—
614C22×C4#41×C15112yes—
615C22×C4C24×C15111yescharacteristic
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—44no—
627C2×C8—44no—
628C2×C8C2×D4×C15112yes—
629C2×C8C2×D4×C15112yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C42—42no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—28no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23#121×C15112yes—
689C23#123×C15112yes—
690C23#135×C15112yes—
691C23#135×C15112yes—
692C23AGL(1,ℤ/8)×C15112yes—
693C23C22×D4×C15111yescharacteristic
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
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—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4#121×C15112yes—
745C2×C4#123×C15112yes—
746C2×C4C22×D4×C15111yescharacteristic
747C2×C4C2×#41×C15111yescharacteristic
748C2×C4C2×#41×C15111yescharacteristic
749C2×C4C2×#41×C15111yescharacteristic
750C2×C4H(5,𝔽2)×C15111yescharacteristic
751C2×C4H(5,𝔽2)×C15111yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—416no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22#482×C15114yescomplemented
785C22C2×#121×C15111yescharacteristic
786C22C2×#123×C15111yescharacteristic
787C22#534×C15111yescharacteristic
788C22C2×#135×C15111yescharacteristic
789C22C2×#135×C15111yescharacteristic
790C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
791C22#575×C15111yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4#546×C15111yescharacteristic
803C4#546×C15111yescharacteristic
804C4#551×C15111yescharacteristic
805C4#551×C15111yescharacteristic
806C2—24no—
807C2—42no—
808C2—42no—
809C2—161no—
810C2#2412×C15111yescharacteristic
811C2#3050×C15111yescharacteristic
812C2#3055×C15111yescharacteristic
813C2C2×#482×C15111yescharacteristic
814C2#3091×C15111yescharacteristic
815C2#3188×C15111yescharacteristic
816C2#3191×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2847×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C151C2semidirect
2. C22×C22⋊C8×C151C2semidirect
4. #2280×C151C2semidirect
5. #2077×C151C2semidirect
6. #2076×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1893×C151C2semidirect
10. #1893×C151C2semidirect
11. #1875×C151C2semidirect
12. #1854×C151C2semidirect
13. #1825×C151C2semidirect
14. #1808×C151C2semidirect
15. #1807×C151C2semidirect
26. C2×#107×C151C22semidirect
27. C2×#107×C151C22semidirect
28. C2×#106×C151C22semidirect
29. C2×#106×C151C22semidirect
30. C2×#102×C151C22semidirect
31. C2×#102×C151C22semidirect
32. C2×#102×C151C22semidirect
33. C2×#102×C151C22semidirect
53. #340×C151C22semidirect
54. #340×C151C22semidirect
55. #340×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #340×C151C22semidirect
60. #340×C151C22semidirect
131. C22⋊C8×C151D4semidirect
375. C22×C151#482semidirect
408. #24555C151direct (N × H)
409. C151#24555direct (N × H)
410. C2×#482C2×C151semidirect
411. C22×C22⋊C8C2×C151semidirect
413. #2280C2×C151semidirect
414. #2077C2×C151semidirect
415. #2076C2×C151semidirect
416. #2034C2×C151semidirect
417. #2033C2×C151semidirect
418. #1893C2×C151semidirect
419. #1893C2×C151semidirect
420. #1875C2×C151semidirect
421. #1854C2×C151semidirect
422. #1825C2×C151semidirect
423. #1808C2×C151semidirect
424. #1807C2×C151semidirect
435. C2×#107C22×C151semidirect
436. C2×#107C22×C151semidirect
437. C2×#106C22×C151semidirect
438. C2×#106C22×C151semidirect
439. C2×#102C22×C151semidirect
440. C2×#102C22×C151semidirect
441. C2×#102C22×C151semidirect
442. C2×#102C22×C151semidirect
462. #340C22×C151semidirect
463. #340C22×C151semidirect
464. #340C22×C151semidirect
465. #340C22×C151semidirect
466. #340C22×C151semidirect
467. #340C22×C151semidirect
468. #340C22×C151semidirect
469. #340C22×C151semidirect
540. C22⋊C8D4×C151semidirect
784. C22#482×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1512
C22×C22⋊C8×C1512
#2847×C1512
#2280×C1512
#2077×C1512
#2076×C1512
#2034×C1512
#2033×C1512
#1893×C1512
#1875×C1512
#1854×C1512
#1825×C1512
#1808×C1512
#1807×C1512
#24555151