Finite Group Databasebeta

← #529×D151 #34082368

Subgroups — #529×D151 #34082368

Order 19328.

1232 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752749C211yesmaximal, characteristic, complemented
2#23752748C211yesmaximal, characteristic, complemented
3#23752747C211yesmaximal, characteristic, complemented
4#23752746C211yesmaximal, characteristic, complemented
5#23752745C212yesmaximal, complemented
6#23752744C211yesmaximal, characteristic, complemented
7#23752743C211yesmaximal, characteristic, complemented
8#23752742C212yesmaximal, complemented
9#23752741C211yesmaximal, characteristic, complemented
10#23752740C212yesmaximal, complemented
11#23752739C212yesmaximal, complemented
12#126×D151C212yesmaximal, complemented
13#125×D151C211yesmaximal, characteristic, complemented
14#124×D151C211yesmaximal, characteristic, complemented
15#123×D151C212yesmaximal, complemented
16C22⋊Q8×D151C211yesmaximal, characteristic, complemented
17#121×D151C211yesmaximal, characteristic
18C4×Q8×D151C211yesmaximal, characteristic, complemented
19C4×D4×D151C211yesmaximal, characteristic, complemented
20C4×D4×D151C212yesmaximal, complemented
21#117×D151C212yesmaximal, complemented
22C2×C42×D151C211yesmaximal, characteristic, complemented
23#529×C151C211yesmaximal, characteristic, complemented
24C2×Q8×D151C2211yescharacteristic
25C2×D4×D151C2212yes—
26C2×D4×D151C2211yescharacteristic
27C22×C4×D151C2211yescharacteristic
28C22×C4×D151C2211yescharacteristic
29C22×C4×D151C2211yescharacteristic
30C22×C4×D151C2212yes—
31#18012734C2212yescomplemented
32#18012734C2212yescomplemented
33#18012734C2212yescomplemented
34#18012733C2212yescomplemented
35#18012732C2212yescomplemented
36#18012732C2212yescomplemented
37#18012732C2212yescomplemented
38#18012731C2211yescharacteristic, complemented
39#18012730C2211yescharacteristic, complemented
40#18012730C2211yescharacteristic, complemented
41#18012729C2212yescomplemented
42#18012729C2212yescomplemented
43#18012728C2211yescharacteristic, complemented
44#18012727C2211yescharacteristic, complemented
45#18012726C2211yescharacteristic, complemented
46#18012725C2212yescomplemented
47#18012725C2212yescomplemented
48#18012724C2212yescomplemented
49#18012724C2212yescomplemented
50#18012723C2212yescomplemented
51#18012722C2212yescomplemented
52#18012721C2212yescomplemented
53#18012721C2212yescomplemented
54#18012720C2212yescomplemented
55#18012719C2211yescharacteristic, complemented
56#18012718C2211yescharacteristic, complemented
57#18012717C2212yescomplemented
58#18012716C2212yescomplemented
59#18012715C2211yescharacteristic, complemented
60#18012714C2211yescharacteristic
61#18012713C2211yescharacteristic
62#18012712C2212yes—
63#18012711C2212yes—
64#18012710C2211yescharacteristic
65Q8×Dic151C2211yescharacteristic, complemented
66C4×Dic302C2212yescomplemented
67C4×Dic302C2211yescharacteristic, complemented
68#18012704C2212yescomplemented
69#18012704C2211yescharacteristic, complemented
70C4×D604C2212yescomplemented
71C4×D604C2211yescharacteristic, complemented
72D4×Dic151C2212yescomplemented
73D4×Dic151C2211yescharacteristic, complemented
74#18012701C2212yescomplemented
75#18012701C2211yescharacteristic, complemented
76C4×C22⋊D151C2212yescomplemented
77C4×C22⋊D151C2212yescomplemented
78C4×C22⋊D151C2212yescomplemented
79(C22⋊D151)⋊C4C2212yescomplemented
80(C22⋊D151)⋊C4C2212yescomplemented
81(C22⋊D151)⋊C4C2212yescomplemented
82#18012698C2212yescomplemented
83#18012697C2212yescomplemented
84#18012697C2212yescomplemented
85#18012696C2212yescomplemented
86#18012696C2212yescomplemented
87#18012695C2212yescomplemented
88#18012695C2212yescomplemented
89C4⋊C4×D151C2211yescharacteristic
90C4⋊C4×D151C2212yes—
91C4⋊C4×D151C2212yes—
92C4⋊C4×D151C2212yes—
93C4⋊C4×D151C2212yes—
94C4⋊C4×D151C2211yescharacteristic
95C22⋊C4×D151C2212yes—
96C22⋊C4×D151C2212yes—
97C22⋊C4×D151C2212yes—
98C22⋊C4×D151C2212yes—
99C22⋊C4×D151C2212yes—
100C2×C4×Dic151C2211yescharacteristic, complemented
101C2×C4×Dic151C2211yescharacteristic, complemented
102C2×C4×Dic151C2211yescharacteristic, complemented
103C42×D151C2211yescharacteristic
104C42×D151C2211yescharacteristic
105C42×D151C2211yescharacteristic
106C42×D151C2211yescharacteristic
107C42×D151C2212yes—
108C42×D151C2211yescharacteristic, complemented
109C42×D151C2211yescharacteristic, complemented
110C42×D151C2211yescharacteristic, complemented
111C42×D151C2211yescharacteristic, complemented
112#126×C151C2212yescomplemented
113#125×C151C2211yescharacteristic, complemented
114#124×C151C2211yescharacteristic, complemented
115#123×C151C2212yescomplemented
116C22⋊Q8×C151C2211yescharacteristic, complemented
117#121×C151C2211yescharacteristic
118C4×Q8×C151C2211yescharacteristic, complemented
119C4×D4×C151C2212yescomplemented
120C4×D4×C151C2211yescharacteristic, complemented
121#117×C151C2212yescomplemented
122C2×C42×C151C2211yescharacteristic, complemented
123C23×D151C2312yes—
124C23×D151C2311yescharacteristic
125C2×Dic302C2312yes—
126C2×Dic302C2311yescharacteristic
127Q8×D151—24no—
128C2×D604C2312yes—
129C2×D604C2311yescharacteristic
130C2×C22⋊D151C2312yes—
131C2×C22⋊D151C2312yes—
132C2×C22⋊D151C2312yes—
133D4×D151—28no—
134D4×D151—24no—
135C22×Dic151C2311yescharacteristic
136C22×Dic151C2311yescharacteristic
137C22×Dic151C2311yescharacteristic
138C22×Dic151C2312yes—
139C2×C4×D151—24no—
140C2×C4×D151—24no—
141C2×C4×D151—28no—
142C2×C4×D151—24no—
143C2×C4×D151C2311yescharacteristic
144C2×C4×D151C2311yescharacteristic
145C2×C4×D151C2311yescharacteristic
146C2×C4×D151C2311yescharacteristic
147C2×C4×D151C2312yes—
148C2×C4×D151C2312yes—
149C2×C4×D151C2311yescharacteristic
150C2×C4×D151C2311yescharacteristic
151C2×C4×D151C2311yescharacteristic
152C2×C4×D151C2311yescharacteristic
153C2×C4×D151C2311yescharacteristic
154C2×C4×D151C2311yescharacteristic
155C2×C4×D151C2312yes—
156C2×C4×D151C2312yes—
157C2×C4×D151C2312yes—
158C2×C4×D151C2311yescharacteristic
159C2×C4×D151C2311yescharacteristic
160C4⋊Dic151C2312yes—
161C4⋊Dic151C2312yes—
162C4⋊Dic151C2311yescharacteristic
163C4⋊Dic151C2312yes—
164C4⋊Dic151C2311yescharacteristic
165C4⋊Dic151C2312yes—
166Dic151⋊C4C2312yes—
167Dic151⋊C4C2312yes—
168Dic151⋊C4C2312yes—
169Dic151⋊C4C2312yes—
170Dic151⋊C4C2312yes—
171Dic151⋊C4C2312yes—
172Dic151⋊C4C2312yes—
173Dic151⋊C4C2312yes—
174Dic151⋊C4C2312yes—
175Dic151⋊C4C2312yes—
176C22⋊Dic151C2312yes—
177C22⋊Dic151C2312yes—
178C22⋊Dic151C2312yes—
179C22⋊Dic151C2312yes—
180C22⋊Dic151C2312yes—
181(C2×D151)⋊C4C2312yes—
182(C2×D151)⋊C4C2312yes—
183(C2×D151)⋊C4C2312yes—
184(C2×D151)⋊C4C2312yes—
185(C2×D151)⋊C4C2312yes—
186(C2×D151)⋊C4C2312yes—
187(C2×D151)⋊C4C2312yes—
188(C2×D151)⋊C4C2312yes—
189(C2×D151)⋊C4C2312yes—
190(C2×D151)⋊C4C2312yes—
191C4×Dic151C2311yescharacteristic
192C4×Dic151C2311yescharacteristic
193C4×Dic151C2311yescharacteristic
194C4×Dic151C2311yescharacteristic
195C4×Dic151C2311yescharacteristic
196C4×Dic151C2311yescharacteristic
197C4×Dic151C2311yescharacteristic
198C4×Dic151C2311yescharacteristic
199C4×Dic151C2311yescharacteristic
200C4×Dic151C2311yescharacteristic
201C4×Dic151C2311yescharacteristic
202C4×Dic151C2311yescharacteristic
203C4×Dic151C2312yes—
204C4×Dic151C2312yes—
205C4×Dic151C2312yes—
206C2×Q8×C151C2311yescharacteristic
207C2×D4×C151C2311yescharacteristic
208C2×D4×C151C2312yes—
209C22×C4×C151C2311yescharacteristic
210C22×C4×C151C2311yescharacteristic
211C22×C4×C151C2311yescharacteristic
212C22×C4×C151C2312yes—
213C4⋊C4×C151C2312yes—
214C4⋊C4×C151C2312yes—
215C4⋊C4×C151C2311yescharacteristic
216C4⋊C4×C151C2312yes—
217C4⋊C4×C151C2311yescharacteristic
218C4⋊C4×C151C2312yes—
219C22⋊C4×C151C2312yes—
220C22⋊C4×C151C2312yes—
221C22⋊C4×C151C2312yes—
222C22⋊C4×C151C2312yes—
223C22⋊C4×C151C2312yes—
224C42×C151C2311yescharacteristic
225C42×C151C2311yescharacteristic
226C42×C151C2311yescharacteristic
227C42×C151C2311yescharacteristic
228C42×C151C2312yes—
229C22×D151—22no—
230C22×D151—22no—
231C22×D151—24no—
232C22×D151—24no—
233C22×D151—24no—
234C22×D151#4114yes—
235C22×D151C2412yes—
236C22×D151C2411yescharacteristic
237C22×D151C2411yescharacteristic
238Dic302—22no—
239Dic302—24no—
240D604—24no—
241D604—22no—
242C22⋊D151—24no—
243C22⋊D151—24no—
244C22⋊D151—24no—
245C2×Dic151—22no—
246C2×Dic151—22no—
247C2×Dic151—24no—
248C2×Dic151—22no—
249C2×Dic151C2411yescharacteristic
250C2×Dic151C2411yescharacteristic
251C2×Dic151C2411yescharacteristic
252C2×Dic151C2411yescharacteristic
253C2×Dic151C2412yes—
254C2×Dic151C2412yes—
255C2×Dic151C2412yes—
256C2×Dic151C2411yescharacteristic
257C2×Dic151C2411yescharacteristic
258C4×D151—22no—
259C4×D151—22no—
260C4×D151—22no—
261C4×D151—22no—
262C4×D151—22no—
263C4×D151—22no—
264C4×D151—24no—
265C4×D151—24no—
266C4×D151—24no—
267C4×D151—22no—
268C4×D151—24no—
269C4×D151—22no—
270C4×D151—22no—
271C4×D151—24no—
272C4×D151—22no—
273C4×D151#4114yes—
274C4×D151#4114yes—
275C23×C151C2412yes—
276C23×C151C2411yescharacteristic
277Q8×C151—22no—
278D4×C151—24no—
279D4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—24no—
283C2×C4×C151—22no—
284C2×C4×C151C2412yes—
285C2×C4×C151C2411yescharacteristic
286C2×C4×C151C2411yescharacteristic
287C2×C4×C151C2411yescharacteristic
288C2×C4×C151C2411yescharacteristic
289C2×C4×C151C2412yes—
290C2×C4×C151C2412yes—
291C2×C4×C151C2411yescharacteristic
292C2×C4×C151C2411yescharacteristic
293C22×C151—21no—
294C22×C151—21no—
295C22×C151—22no—
296C22×C151—22no—
297C22×C151—22no—
298C22×C151C2×#4112yes—
299C22×C151C2511yescharacteristic
300C2×D151—21no—
301C2×D151—21no—
302C2×D151—28no—
303C2×D151—22no—
304C2×D151—22no—
305C2×D151—22no—
306C2×D151—48no—
307C2×D151C2×#4112yes—
308C2×D151C2×#4112yes—
309C2×D151C2×#4112yes—
310C2×D151C2×#4112yes—
311C4×C151—21no—
312C4×C151—21no—
313C4×C151—21no—
314C4×C151—21no—
315C4×C151—22no—
316C4×C151—22no—
317C4×C151—22no—
318C4×C151C2×#4112yes—
319C4×C151C2×#4112yes—
320Dic151—21no—
321Dic151—21no—
322Dic151—21no—
323Dic151—21no—
324Dic151—22no—
325Dic151—22no—
326Dic151—22no—
327Dic151C2×#4112yes—
328Dic151C2×#4112yes—
329C2×C151—22no—
330C2×C151—42no—
331C2×C151C22×#4111yescharacteristic
332C2×C151C22×#4111yescharacteristic
333C2×C151C22×#4111yescharacteristic
334D151—22no—
335D151—42no—
336D151#52914yesdirect product factor
337C151C2×#52911yescharacteristic, complemented, Sylow
338C2×#529—1511nomaximal, Sylow
339#529—1512no—
340#529—1511no—
341#529—1511no—
342#529—1512no—
343#529—1511no—
344#529—1511no—
345#529—1511no—
346#529—1512no—
347#529—1511no—
348#529—1512no—
349#529—1511no—
350#529D15111yescharacteristic, direct product factor
351C2×#126—1512no—
352C2×#125—1511no—
353C2×#124—1511no—
354C2×#123—1512no—
355C2×C22⋊Q8—1511no—
356C2×#121—1511no—
357C2×C4×Q8—1511no—
358C2×C4×D4—1512no—
359C2×C4×D4—1511no—
360C2×#117—1512no—
361C22×C42—1511no—
362C22×Q8—1511no—
363C22×D4—1512no—
364C22×D4—1511no—
365C23×C4—1512no—
366C23×C4—1511no—
367C23×C4—1511no—
368C23×C4—1511no—
369#126—1512no—
370#126—1512no—
371#126—1512no—
372#126—1512no—
373#126—1512no—
374#126—1512no—
375#126—1512no—
376#126C2×D15112yescomplemented
377#125—1512no—
378#125—1512no—
379#125—1511no—
380#125—1511no—
381#125—1511no—
382#125C2×D15111yescharacteristic, complemented
383#124—1511no—
384#124—1511no—
385#124—1512no—
386#124—1512no—
387#124—1511no—
388#124C2×D15111yescharacteristic, complemented
389#123—1512no—
390#123—1512no—
391#123—1512no—
392#123—1512no—
393#123—1512no—
394#123—1512no—
395#123—1512no—
396#123C2×D15112yescomplemented
397C22⋊Q8—1511no—
398C22⋊Q8—1511no—
399C22⋊Q8—1512no—
400C22⋊Q8—1511no—
401C22⋊Q8—1512no—
402C22⋊Q8C2×D15111yescharacteristic, complemented
403#121—1511no—
404#121—1512no—
405#121—1511no—
406#121—1511no—
407#121—1512no—
408#121C2×D15111yescharacteristic
409C4×Q8—1511no—
410C4×Q8—1512no—
411C4×Q8—1511no—
412C4×Q8—1512no—
413C4×Q8—1511no—
414C4×Q8C2×D15111yescharacteristic, complemented
415C4×D4—1511no—
416C4×D4—1512no—
417C4×D4—1512no—
418C4×D4—1512no—
419C4×D4—1512no—
420C4×D4—1511no—
421C4×D4—1512no—
422C4×D4—1512no—
423C4×D4—1512no—
424C4×D4—1512no—
425C4×D4—1511no—
426C4×D4—1512no—
427C4×D4C2×D15111yescharacteristic, complemented
428C4×D4C2×D15112yescomplemented
429#117—1512no—
430#117—1512no—
431#117—1512no—
432#117—1512no—
433#117—1512no—
434#117—1512no—
435#117—1512no—
436#117C2×D15112yescomplemented
437C2×C4⋊C4—1512no—
438C2×C4⋊C4—1512no—
439C2×C4⋊C4—1511no—
440C2×C4⋊C4—1512no—
441C2×C4⋊C4—1511no—
442C2×C4⋊C4—1512no—
443C2×C22⋊C4—1512no—
444C2×C22⋊C4—1512no—
445C2×C22⋊C4—1512no—
446C2×C22⋊C4—1512no—
447C2×C22⋊C4—1512no—
448C2×C42—1511no—
449C2×C42—1511no—
450C2×C42—1511no—
451C2×C42—1511no—
452C2×C42—1512no—
453C2×C42—1511no—
454C2×C42—1511no—
455C2×C42—1511no—
456C2×C42—1511no—
457C2×C42—1511no—
458C2×C42—1511no—
459C2×C42—1511no—
460C2×C42C2×D15111yescharacteristic, complemented
461C24—1512no—
462C24—1511no—
463C2×Q8—3024no—
464C2×Q8—1511no—
465C2×Q8—1512no—
466C2×Q8C22×D15111yescharacteristic
467C2×D4—3028no—
468C2×D4—3024no—
469C2×D4—1512no—
470C2×D4—1512no—
471C2×D4—1512no—
472C2×D4—1512no—
473C2×D4—1511no—
474C2×D4C22×D15112yes—
475C2×D4C22×D15111yescharacteristic
476C22×C4—3024no—
477C22×C4—3024no—
478C22×C4—3028no—
479C22×C4—3024no—
480C22×C4—1511no—
481C22×C4—1511no—
482C22×C4—1511no—
483C22×C4—1512no—
484C22×C4—1511no—
485C22×C4—1511no—
486C22×C4—1511no—
487C22×C4—1511no—
488C22×C4—1511no—
489C22×C4—1511no—
490C22×C4—1511no—
491C22×C4—1511no—
492C22×C4—1511no—
493C22×C4—1512no—
494C22×C4—1512no—
495C22×C4—1512no—
496C22×C4—1512no—
497C22×C4—1511no—
498C22×C4—1512no—
499C22×C4—1511no—
500C22×C4—1511no—
501C22×C4C22×D15111yescharacteristic
502C22×C4C22×D15111yescharacteristic
503C22×C4C22×D15111yescharacteristic
504C22×C4C22×D15112yes—
505C4⋊C4—1512no—
506C4⋊C4—1512no—
507C4⋊C4—1512no—
508C4⋊C4—1512no—
509C4⋊C4—1512no—
510C4⋊C4—1512no—
511C4⋊C4—1512no—
512C4⋊C4—1512no—
513C4⋊C4—1512no—
514C4⋊C4—1512no—
515C4⋊C4—1512no—
516C4⋊C4—1512no—
517C4⋊C4—1511no—
518C4⋊C4—1512no—
519C4⋊C4—1511no—
520C4⋊C4—1512no—
521C4⋊C4C22×D15112yes—
522C4⋊C4C22×D15112yes—
523C4⋊C4C22×D15111yescharacteristic
524C4⋊C4C22×D15112yes—
525C4⋊C4C22×D15111yescharacteristic
526C4⋊C4C22×D15112yes—
527C22⋊C4—1512no—
528C22⋊C4—1512no—
529C22⋊C4—1512no—
530C22⋊C4—1512no—
531C22⋊C4—1512no—
532C22⋊C4—1512no—
533C22⋊C4—1512no—
534C22⋊C4—1512no—
535C22⋊C4—1512no—
536C22⋊C4—1512no—
537C22⋊C4—1512no—
538C22⋊C4—1512no—
539C22⋊C4—1512no—
540C22⋊C4—1512no—
541C22⋊C4—1512no—
542C22⋊C4C22×D15112yes—
543C22⋊C4C22×D15112yes—
544C22⋊C4C22×D15112yes—
545C22⋊C4C22×D15112yes—
546C22⋊C4C22×D15112yes—
547C42—1511no—
548C42—1511no—
549C42—1511no—
550C42—1511no—
551C42—1511no—
552C42—1511no—
553C42—1511no—
554C42—1511no—
555C42—1511no—
556C42—1511no—
557C42—1512no—
558C42—1512no—
559C42—1511no—
560C42—1511no—
561C42—1512no—
562C42C22×D15111yescharacteristic
563C42C22×D15111yescharacteristic
564C42C22×D15111yescharacteristic
565C42C22×D15111yescharacteristic
566C42C22×D15112yes—
567C23—3022no—
568C23—3022no—
569C23—3024no—
570C23—3024no—
571C23—3024no—
572C23—1512no—
573C23—1514no—
574C23—1511no—
575C23—1511no—
576C23C23×D15112yes—
577C23C23×D15111yescharacteristic
578Q8—22no—
579Q8—3024no—
580Q8—3022no—
581D4—24no—
582D4—22no—
583D4—3024no—
584D4—3024no—
585D4—3024no—
586D4—3024no—
587D4—3022no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—3022no—
593C2×C4—3022no—
594C2×C4—3022no—
595C2×C4—3022no—
596C2×C4—3022no—
597C2×C4—3022no—
598C2×C4—3024no—
599C2×C4—3024no—
600C2×C4—3024no—
601C2×C4—3022no—
602C2×C4—3024no—
603C2×C4—3022no—
604C2×C4—3022no—
605C2×C4—3022no—
606C2×C4—3024no—
607C2×C4—3022no—
608C2×C4—3022no—
609C2×C4—3024no—
610C2×C4—3022no—
611C2×C4—1511no—
612C2×C4—1511no—
613C2×C4—1511no—
614C2×C4—1511no—
615C2×C4—1512no—
616C2×C4—1512no—
617C2×C4—1512no—
618C2×C4—1511no—
619C2×C4—1511no—
620C2×C4—1514no—
621C2×C4—1514no—
622C2×C4C23×D15111yescharacteristic
623C2×C4C23×D15111yescharacteristic
624C2×C4C23×D15111yescharacteristic
625C2×C4C23×D15111yescharacteristic
626C2×C4C23×D15112yes—
627C2×C4C23×D15112yes—
628C2×C4C23×D15112yes—
629C2×C4C23×D15111yescharacteristic
630C2×C4C23×D15111yescharacteristic
631C22—21no—
632C22—21no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—3028no—
637C22—3021no—
638C22—3021no—
639C22—3022no—
640C22—3022no—
641C22—3022no—
642C22—6048no—
643C22—1512no—
644C22—1512no—
645C22—1512no—
646C22—1512no—
647C22#41×D15112yes—
648C22C24×D15111yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—3021no—
657C4—3021no—
658C4—3021no—
659C4—3021no—
660C4—3022no—
661C4—3022no—
662C4—3022no—
663C4—1512no—
664C4—1512no—
665C4#41×D15112yes—
666C4#41×D15112yes—
667C2—22no—
668C2—42no—
669C2—3022no—
670C2—6042no—
671C2—1514no—
672C2C2×#41×D15111yescharacteristic
673C2C2×#41×D15111yescharacteristic
674C2C2×#41×D15111yescharacteristic
subgroupG/H
centerC2×C4C23×D151
commutator, socle, cosocleC22×C151C25
FrattiniC22C24×D151
Fitting#529×C151C2
prime radical#121×D151C2
hypercenter#529D151
hypocenterC151C2×#529
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #23752749C2semidirect
2. #23752748C2semidirect
3. #23752747C2semidirect
4. #23752746C2semidirect
5. #23752745C2semidirect
6. #23752744C2semidirect
7. #23752743C2semidirect
8. #23752742C2semidirect
9. #23752741C2semidirect
10. #23752740C2semidirect
11. #23752739C2semidirect
12. #126×D151C2semidirect
13. #125×D151C2semidirect
14. #124×D151C2semidirect
15. #123×D151C2semidirect
16. C22⋊Q8×D151C2semidirect
18. C4×Q8×D151C2semidirect
19. C4×D4×D151C2semidirect
20. C4×D4×D151C2semidirect
21. #117×D151C2semidirect
22. C2×C42×D151C2semidirect
23. #529×C151C2semidirect
31. #18012734C22semidirect
32. #18012734C22semidirect
33. #18012734C22semidirect
34. #18012733C22semidirect
35. #18012732C22semidirect
36. #18012732C22semidirect
37. #18012732C22semidirect
38. #18012731C22semidirect
39. #18012730C22semidirect
40. #18012730C22semidirect
41. #18012729C22semidirect
42. #18012729C22semidirect
43. #18012728C22semidirect
44. #18012727C22semidirect
45. #18012726C22semidirect
46. #18012725C22semidirect
47. #18012725C22semidirect
48. #18012724C22semidirect
49. #18012724C22semidirect
50. #18012723C22semidirect
51. #18012722C22semidirect
52. #18012721C22semidirect
53. #18012721C22semidirect
54. #18012720C22semidirect
55. #18012719C22semidirect
56. #18012718C22semidirect
57. #18012717C22semidirect
58. #18012716C22semidirect
59. #18012715C22semidirect
65. Q8×Dic151C22semidirect
66. C4×Dic302C22semidirect
67. C4×Dic302C22semidirect
68. #18012704C22semidirect
69. #18012704C22semidirect
70. C4×D604C22semidirect
71. C4×D604C22semidirect
72. D4×Dic151C22semidirect
73. D4×Dic151C22semidirect
74. #18012701C22semidirect
75. #18012701C22semidirect
76. C4×C22⋊D151C22semidirect
77. C4×C22⋊D151C22semidirect
78. C4×C22⋊D151C22semidirect
79. (C22⋊D151)⋊C4C22semidirect
80. (C22⋊D151)⋊C4C22semidirect
81. (C22⋊D151)⋊C4C22semidirect
82. #18012698C22semidirect
83. #18012697C22semidirect
84. #18012697C22semidirect
85. #18012696C22semidirect
86. #18012696C22semidirect
87. #18012695C22semidirect
88. #18012695C22semidirect
100. C2×C4×Dic151C22semidirect
101. C2×C4×Dic151C22semidirect
102. C2×C4×Dic151C22semidirect
108. C42×D151C22semidirect
109. C42×D151C22semidirect
110. C42×D151C22semidirect
111. C42×D151C22semidirect
112. #126×C151C22semidirect
113. #125×C151C22semidirect
114. #124×C151C22semidirect
115. #123×C151C22semidirect
116. C22⋊Q8×C151C22semidirect
118. C4×Q8×C151C22semidirect
119. C4×D4×C151C22semidirect
120. C4×D4×C151C22semidirect
121. #117×C151C22semidirect
122. C2×C42×C151C22semidirect
336. D151#529direct (N × H)
337. C151C2×#529semidirect
350. #529D151direct (N × H)
376. #126C2×D151semidirect
382. #125C2×D151semidirect
388. #124C2×D151semidirect
396. #123C2×D151semidirect
402. C22⋊Q8C2×D151semidirect
414. C4×Q8C2×D151semidirect
427. C4×D4C2×D151semidirect
428. C4×D4C2×D151semidirect
436. #117C2×D151semidirect
460. C2×C42C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527492
#237527482
#237527472
#237527462
#237527452
#237527442
#237527432
#237527422
#237527412
#237527402
#237527392
#126×D1512
#125×D1512
#124×D1512
#123×D1512
C22⋊Q8×D1512
#121×D1512
C4×Q8×D1512
C4×D4×D1512
#117×D1512
C2×C42×D1512
#529×C1512
C2×#529151