Finite Group Databasebeta

← C151×#24124 #50329049

Subgroups — C151×#24124 #50329049

Order 38656.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C151C211yesmaximal, characteristic, complemented
2C2×#478×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic, complemented
4#2535×C151C211yesmaximal, characteristic, complemented
5#2034×C151C211yesmaximal, characteristic, complemented
6#2033×C151C211yesmaximal, characteristic, complemented
7#1999×C151C211yesmaximal, characteristic, complemented
8#1999×C151C211yesmaximal, characteristic, complemented
9#1991×C151C211yesmaximal, characteristic, complemented
10#1954×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1852×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×D8×C151C2211yescharacteristic
17#553×C151—24no—
18#553×C151—24no—
19C2×#126×C151—21no—
20C2×#125×C151C2211yescharacteristic
21C2×#123×C151—21no—
22C2×#121×C151—21no—
23C2×#121×C151C2211yescharacteristic
24C2×#121×C151C2211yescharacteristic
25C2×#121×C151C2211yescharacteristic
26C2×#121×C151C2211yescharacteristic
27C2×C4×D4×C151—21no—
28C2×C4×D4×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31C2×#117×C151C2211yescharacteristic
32C22×C4⋊C4×C151C2211yescharacteristic
33#478×C151—24no—
34C4×D8×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×#107×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×C4⋊C8×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic
49C2×C4×C8×C151C2211yescharacteristic
50#397×C151—21no—
51#392×C151—21no—
52#386×C151—21no—
53#386×C151—21no—
54#382×C151C2211yescharacteristic
55#380×C151C2211yescharacteristic
56#380×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C22×D4×C151D411yescharacteristic
68C22×D4×C151C2311yescharacteristic
69C22×D4×C151C2311yescharacteristic
70C23×C4×C151—21no—
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C2×D8×C151—22no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82#126×C151—28no—
83#125×C151—22no—
84#125×C151D414yescomplemented
85#123×C151—28no—
86#121×C151—28no—
87#121×C151—22no—
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93#121×C151—41no—
94#121×C151—41no—
95C4×D4×C151—28no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151D414yescomplemented
102#117×C151—22no—
103#117×C151—22no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151D411yescharacteristic
126C2×C22⋊C4×C151D411yescharacteristic
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#107×C151—22no—
130#107×C151—22no—
131#106×C151—22no—
132C4⋊C8×C151—22no—
133#102×C151—22no—
134#102×C151—22no—
135#102×C151—22no—
136#102×C151—22no—
137#102×C151—41no—
138#102×C151—41no—
139C22⋊C8×C151—22no—
140C22⋊C8×C151—22no—
141C22⋊C8×C151—41no—
142C22⋊C8×C151—41no—
143C4×C8×C151—22no—
144#95×C151—21no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151—21no—
149C24×C151—21no—
150C24×C151C2×D411yescharacteristic
151C24×C151C2×D411yescharacteristic
152C2×D4×C151—24no—
153C2×D4×C151—22no—
154C2×D4×C151—24no—
155C2×D4×C151—22no—
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—41no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151—81no—
174C2×D4×C151—81no—
175C2×D4×C151—81no—
176C2×D4×C151—81no—
177C2×D4×C151C2×D412yes—
178C2×D4×C151#4112yes—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—24no—
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—21no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—24no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—42no—
200C22×C4×C151—81no—
201C22×C4×C151—81no—
202C22×C4×C151—81no—
203C22×C4×C151—81no—
204C22×C4×C151—81no—
205C22×C4×C151—81no—
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2411yescharacteristic
211D8×C151—28no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151#4112yes—
224C4⋊C4×C151—24no—
225C4⋊C4×C151—24no—
226C4⋊C4×C151—24no—
227C4⋊C4×C151—22no—
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—
235C4⋊C4×C151—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151C2×D412yes—
238C4⋊C4×C151C2×D412yes—
239C4⋊C4×C151C2×D412yes—
240C22⋊C4×C151—24no—
241C22⋊C4×C151—24no—
242C22⋊C4×C151—24no—
243C22⋊C4×C151—24no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—42no—
247C22⋊C4×C151—42no—
248C22⋊C4×C151—42no—
249C22⋊C4×C151—81no—
250C22⋊C4×C151—81no—
251C42×C151—24no—
252C42×C151C2×D412yes—
253C42×C151C2×D412yes—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—22no—
261C23×C151—21no—
262C23×C151—22no—
263C23×C151—21no—
264C23×C151—21no—
265C23×C151—21no—
266C23×C151—21no—
267C23×C151—21no—
268C23×C151—21no—
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—41no—
278C23×C151—41no—
279C23×C151—41no—
280C23×C151—41no—
281C23×C151#13512yes—
282C23×C151C22×D411yescharacteristic
283D4×C151—22no—
284D4×C151—22no—
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—44no—
288D4×C151—48no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—84no—
294D4×C151—84no—
295D4×C151—84no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—22no—
302C2×C4×C151—22no—
303C2×C4×C151—21no—
304C2×C4×C151—22no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—41no—
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—84no—
333C2×C4×C151—84no—
334C2×C4×C151—84no—
335C2×C4×C151#12012yes—
336C2×C4×C151#12012yes—
337C2×C4×C151C22×D411yescharacteristic
338C2×C4×C151C22×D411yescharacteristic
339C2×C4×C151C2×#4111yescharacteristic
340C2×C4×C151C2×#4111yescharacteristic
341C2×C4×C151H(5,𝔽2)11yescharacteristic
342C2×C4×C1512−1+411yescharacteristic
343C8×C151—22no—
344C8×C151—41no—
345C8×C151—41no—
346C8×C151—41no—
347C22×C151—22no—
348C22×C151—22no—
349C22×C151—22no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—41no—
356C22×C151—41no—
357C22×C151—42no—
358C22×C151—42no—
359C22×C151—41no—
360C22×C151—42no—
361C22×C151—42no—
362C22×C151—41no—
363C22×C151—42no—
364C22×C151—41no—
365C22×C151—41no—
366C22×C151—42no—
367C22×C151—81no—
368C22×C151—81no—
369C22×C151—81no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151C2×#12011yescharacteristic
376C22×C151#54611yescharacteristic
377C22×C151#54711yescharacteristic
378C22×C151C2×#13511yescharacteristic
379C22×C151#57511yescharacteristic
380C22×C151#57611yescharacteristic
381C22×C151#57611yescharacteristic
382C4×C151—22no—
383C4×C151—22no—
384C4×C151—41no—
385C4×C151—41no—
386C4×C151—42no—
387C4×C151—42no—
388C4×C151—42no—
389C4×C151—81no—
390C4×C151—81no—
391C4×C151—81no—
392C4×C151#52511yescharacteristic
393C4×C151#53711yescharacteristic
394C4×C151#54811yescharacteristic
395C4×C151#55011yescharacteristic
396C2×C151—42no—
397C2×C151—81no—
398C2×C151—82no—
399C2×C151—82no—
400C2×C151#240711yescharacteristic
401C2×C151#300211yescharacteristic
402C2×C151#300811yescharacteristic
403C2×C151#329711yescharacteristic
404C2×C151#332211yescharacteristic
405C2×C151#333911yescharacteristic
406C2×C151#335511yescharacteristic
407#24124C15111yesmaximal, characteristic, direct product factor, Sylow
408C151#2412411yescharacteristic, direct product factor, Sylow
409C2×#553C2×C15111yescharacteristic, complemented
410C2×#478C2×C15111yescharacteristic, complemented
411C2×C4×D8C2×C15111yescharacteristic, complemented
412#2535C2×C15111yescharacteristic, complemented
413#2034C2×C15111yescharacteristic, complemented
414#2033C2×C15111yescharacteristic, complemented
415#1999C2×C15111yescharacteristic, complemented
416#1999C2×C15111yescharacteristic, complemented
417#1991C2×C15111yescharacteristic, complemented
418#1954C2×C15111yescharacteristic, complemented
419#1875C2×C15111yescharacteristic, complemented
420#1874C2×C15111yescharacteristic, complemented
421#1854C2×C15111yescharacteristic, complemented
422#1852C2×C15111yescharacteristic, complemented
423#1804C2×C15111yescharacteristic, complemented
424C22×D8C22×C15111yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C15111yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C15111yescharacteristic
432C2×#121C22×C15111yescharacteristic
433C2×#121C22×C15111yescharacteristic
434C2×#121C22×C15111yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C15111yescharacteristic
437C2×C4×D4C22×C15111yescharacteristic
438C2×C4×D4C22×C15111yescharacteristic
439C2×#117C22×C15111yescharacteristic
440C22×C4⋊C4C22×C15111yescharacteristic
441#478—24no—
442C4×D8—24no—
443C2×#107C22×C15111yescharacteristic
444C2×#107C22×C15111yescharacteristic
445C2×#106C22×C15111yescharacteristic
446C2×C4⋊C8C22×C15111yescharacteristic
447C2×#102C22×C15111yescharacteristic
448C2×#102C22×C15111yescharacteristic
449C2×#102C22×C15111yescharacteristic
450C2×#102C22×C15111yescharacteristic
451C2×#102C22×C15111yescharacteristic
452C2×#102C22×C15111yescharacteristic
453C2×C22⋊C8C22×C15111yescharacteristic
454C2×C22⋊C8C22×C15111yescharacteristic
455C2×C22⋊C8C22×C15111yescharacteristic
456C2×C22⋊C8C22×C15111yescharacteristic
457C2×C4×C8C22×C15111yescharacteristic
458#397—21no—
459#392—21no—
460#386—21no—
461#386—21no—
462#382C22×C15111yescharacteristic
463#380C22×C15111yescharacteristic
464#380C22×C15111yescharacteristic
465#340C22×C15111yescharacteristic
466#340C22×C15111yescharacteristic
467#340C22×C15111yescharacteristic
468#340C22×C15111yescharacteristic
469#340C22×C15111yescharacteristic
470#340C22×C15111yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C15111yescharacteristic
476C22×D4C23×C15111yescharacteristic
477C22×D4C23×C15111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C15111yescharacteristic
482C23×C4C23×C15111yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C15111yescharacteristic
487C22×C8C23×C15111yescharacteristic
488C22×C8C23×C15111yescharacteristic
489C22×C8C23×C15111yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C15114yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C15114yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C15111yescharacteristic
518C2×C4⋊C4C23×C15111yescharacteristic
519C2×C4⋊C4C23×C15111yescharacteristic
520C2×C4⋊C4C23×C15111yescharacteristic
521C2×C4⋊C4C23×C15111yescharacteristic
522C2×C4⋊C4C23×C15111yescharacteristic
523C2×C4⋊C4C23×C15111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C15111yescharacteristic
534C2×C22⋊C4D4×C15111yescharacteristic
535C2×C42—21no—
536C2×C42C23×C15111yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C15111yescharacteristic
559C24C2×D4×C15111yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
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—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C15112yes—
586C2×D4#41×C15112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
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—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C15111yescharacteristic
615C22×C4C2×D4×C15111yescharacteristic
616C22×C4C2×D4×C15111yescharacteristic
617C22×C4C2×D4×C15111yescharacteristic
618C22×C4C24×C15111yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C15112yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C15112yes—
646C4⋊C4C2×D4×C15112yes—
647C4⋊C4C2×D4×C15112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C15112yes—
661C42C2×D4×C15112yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C15112yes—
690C23C22×D4×C15111yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
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—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C15112yes—
744C2×C4#120×C15112yes—
745C2×C4C22×D4×C15111yescharacteristic
746C2×C4C22×D4×C15111yescharacteristic
747C2×C4C2×#41×C15111yescharacteristic
748C2×C4C2×#41×C15111yescharacteristic
749C2×C4H(5,𝔽2)×C15111yescharacteristic
750C2×C42−1+4×C15111yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C15111yescharacteristic
784C22#546×C15111yescharacteristic
785C22#547×C15111yescharacteristic
786C22C2×#135×C15111yescharacteristic
787C22#575×C15111yescharacteristic
788C22#576×C15111yescharacteristic
789C22#576×C15111yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4#525×C15111yescharacteristic
801C4#537×C15111yescharacteristic
802C4#548×C15111yescharacteristic
803C4#550×C15111yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2#2407×C15111yescharacteristic
809C2#3002×C15111yescharacteristic
810C2#3008×C15111yescharacteristic
811C2#3297×C15111yescharacteristic
812C2#3322×C15111yescharacteristic
813C2#3339×C15111yescharacteristic
814C2#3355×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#553×C151C2semidirect
2. C2×#478×C151C2semidirect
3. C2×C4×D8×C151C2semidirect
4. #2535×C151C2semidirect
5. #2034×C151C2semidirect
6. #2033×C151C2semidirect
7. #1999×C151C2semidirect
8. #1999×C151C2semidirect
9. #1991×C151C2semidirect
10. #1954×C151C2semidirect
11. #1875×C151C2semidirect
12. #1874×C151C2semidirect
13. #1854×C151C2semidirect
14. #1852×C151C2semidirect
15. #1804×C151C2semidirect
84. #125×C151D4semidirect
101. C4×D4×C151D4semidirect
407. #24124C151direct (N × H)
408. C151#24124direct (N × H)
409. C2×#553C2×C151semidirect
410. C2×#478C2×C151semidirect
411. C2×C4×D8C2×C151semidirect
412. #2535C2×C151semidirect
413. #2034C2×C151semidirect
414. #2033C2×C151semidirect
415. #1999C2×C151semidirect
416. #1999C2×C151semidirect
417. #1991C2×C151semidirect
418. #1954C2×C151semidirect
419. #1875C2×C151semidirect
420. #1874C2×C151semidirect
421. #1854C2×C151semidirect
422. #1852C2×C151semidirect
423. #1804C2×C151semidirect
492. #125D4×C151semidirect
509. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1512
C2×#478×C1512
C2×C4×D8×C1512
#2535×C1512
#2034×C1512
#2033×C1512
#1999×C1512
#1991×C1512
#1954×C1512
#1875×C1512
#1874×C1512
#1854×C1512
#1852×C1512
#1804×C1512
#24124151