Finite Group Databasebeta

← C151×#24192 #50329117

Subgroups — C151×#24192 #50329117

Order 38656.

1186 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic, complemented
4#2580×C151C211yesmaximal, characteristic, complemented
5#2042×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic, complemented
7#2012×C151C211yesmaximal, characteristic, complemented
8#2011×C151C211yesmaximal, characteristic
9#1984×C151C211yesmaximal, characteristic, complemented
10#1958×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1863×C151C211yesmaximal, characteristic, complemented
14#1862×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19#559×C151—24no—
20#559×C151—24no—
21C2×#127×C151C2211yescharacteristic
22C2×#124×C151—21no—
23C2×#124×C151C2211yescharacteristic
24C2×#124×C151C2211yescharacteristic
25C2×#123×C151—21no—
26C2×#123×C151—21no—
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×D4×C151—21no—
30C2×C4×D4×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33#463×C151—24no—
34C4×D8×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×C4×C8×C151C2211yescharacteristic
48#399×C151—21no—
49#393×C151—21no—
50#390×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
52#389×C151C2211yescharacteristic
53#389×C151C2211yescharacteristic
54#385×C151—21no—
55#385×C151—21no—
56#382×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151D411yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C22×D4×C151C2311yescharacteristic
68C22×D4×C151C2311yescharacteristic
69C22×D4×C151C2311yescharacteristic
70C23×C4×C151—21no—
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—41no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C2×D8×C151—22no—
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C2×D8×C151—41no—
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86#127×C151—22no—
87#127×C151—22no—
88#124×C151—28no—
89#124×C151—22no—
90#124×C151—22no—
91#124×C151—22no—
92#124×C151D414yes—
93#123×C151—28no—
94#123×C151—28no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151—22no—
98C4×Q8×C151—22no—
99C4×D4×C151—28no—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102C4×D4×C151—22no—
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151D414yes—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151D411yescharacteristic
111C2×C4⋊C4×C151D411yescharacteristic
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×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129C2×C42×C151C2311yescharacteristic
130C2×C42×C151C2311yescharacteristic
131#107×C151—22no—
132C4⋊C8×C151—22no—
133#103×C151—22no—
134#103×C151—22no—
135#103×C151—41no—
136#102×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—41no—
141#102×C151—41no—
142#102×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×C151—21no—
151C2×Q8×C151—22no—
152C2×Q8×C151—22no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—41no—
159C2×Q8×C151C2×D412yes—
160C2×D4×C151—24no—
161C2×D4×C151—24no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151—21no—
176C2×D4×C151—21no—
177C2×D4×C151—42no—
178C2×D4×C151—42no—
179C2×D4×C151—81no—
180C2×D4×C151—81no—
181C2×D4×C151C2×D412yes—
182C2×D4×C151C2×D412yes—
183C2×D4×C151#4112yes—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—24no—
187C22×C4×C151—24no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—42no—
192C22×C4×C151—81no—
193C22×C4×C151—81no—
194C22×C4×C151—81no—
195C22×C4×C151—81no—
196C22×C4×C151—81no—
197C22×C4×C151—81no—
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2411yescharacteristic
205SD16×C151—44no—
206D8×C151—28no—
207D8×C151—44no—
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—21no—
218C2×C8×C151—21no—
219C2×C8×C151#4112yes—
220C4⋊C4×C151—24no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
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—81no—
232C4⋊C4×C151—81no—
233C4⋊C4×C151C2×D412yes—
234C22⋊C4×C151—24no—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—24no—
237C22⋊C4×C151—24no—
238C22⋊C4×C151—24no—
239C22⋊C4×C151—24no—
240C22⋊C4×C151—42no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—42no—
243C22⋊C4×C151—81no—
244C22⋊C4×C151—81no—
245C42×C151—24no—
246C42×C151—21no—
247C42×C151—21no—
248C42×C151—21no—
249C42×C151—21no—
250C42×C151C2×D412yes—
251C42×C151C2×D412yes—
252C23×C151—22no—
253C23×C151—22no—
254C23×C151—22no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—41no—
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×C151C22×D411yescharacteristic
274Q8×C151—22no—
275Q8×C151—22no—
276Q8×C151—44no—
277Q8×C151—41no—
278Q8×C151—41no—
279D4×C151—22no—
280D4×C151—22no—
281D4×C151—22no—
282D4×C151—22no—
283D4×C151—22no—
284D4×C151—22no—
285D4×C151—48no—
286D4×C151—41no—
287D4×C151—41no—
288D4×C151—41no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—84no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—22no—
301C2×C4×C151—21no—
302C2×C4×C151—22no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
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—84no—
324C2×C4×C151—84no—
325C2×C4×C151—84no—
326C2×C4×C151#12012yes—
327C2×C4×C151#12012yes—
328C2×C4×C151#13512yes—
329C2×C4×C151C22×D411yescharacteristic
330C2×C4×C151C22×D411yescharacteristic
331C2×C4×C151C2×#4111yescharacteristic
332C2×C4×C151C2×#4111yescharacteristic
333C2×C4×C151H(5,𝔽2)11yescharacteristic
334C2×C4×C1512−1+411yescharacteristic
335C8×C151—22no—
336C8×C151—41no—
337C8×C151—41no—
338C8×C151—41no—
339C22×C151—42no—
340C22×C151—42no—
341C22×C151—42no—
342C22×C151—42no—
343C22×C151—42no—
344C22×C151—42no—
345C22×C151—42no—
346C22×C151—42no—
347C22×C151—42no—
348C22×C151—81no—
349C22×C151—81no—
350C22×C151—81no—
351C22×C151—81no—
352C22×C151—81no—
353C22×C151—81no—
354C22×C151—81no—
355C22×C151—81no—
356C22×C151—81no—
357C22×C151—81no—
358C22×C151—81no—
359C22×C151—81no—
360C22×C151C2×#12011yescharacteristic
361C22×C151#54811yescharacteristic
362C22×C151#55011yescharacteristic
363C22×C151C2×#13511yescharacteristic
364C22×C151#57511yescharacteristic
365C22×C151#57611yescharacteristic
366C22×C151#57611yescharacteristic
367C4×C151—22no—
368C4×C151—22no—
369C4×C151—22no—
370C4×C151—42no—
371C4×C151—41no—
372C4×C151—41no—
373C4×C151—41no—
374C4×C151—42no—
375C4×C151—81no—
376C4×C151—81no—
377C4×C151—81no—
378C4×C151#52511yescharacteristic
379C4×C151#53711yescharacteristic
380C4×C151#54611yescharacteristic
381C4×C151#54711yescharacteristic
382C2×C151—82no—
383C2×C151—82no—
384C2×C151—82no—
385C2×C151#240711yescharacteristic
386C2×C151#300211yescharacteristic
387C2×C151#300811yescharacteristic
388C2×C151#336111yescharacteristic
389C2×C151#337011yescharacteristic
390C2×C151#339611yescharacteristic
391C2×C151#340311yescharacteristic
392#24192C15111yesmaximal, characteristic, direct product factor, Sylow
393C151#2419211yescharacteristic, direct product factor, Sylow
394C2×#559C2×C15111yescharacteristic, complemented
395C2×#463C2×C15111yescharacteristic, complemented
396C2×C4×D8C2×C15111yescharacteristic, complemented
397#2580C2×C15111yescharacteristic, complemented
398#2042C2×C15111yescharacteristic, complemented
399#2041C2×C15111yescharacteristic, complemented
400#2012C2×C15111yescharacteristic, complemented
401#2011C2×C15111yescharacteristic
402#1984C2×C15111yescharacteristic, complemented
403#1958C2×C15111yescharacteristic, complemented
404#1880C2×C15111yescharacteristic, complemented
405#1879C2×C15111yescharacteristic, complemented
406#1863C2×C15111yescharacteristic, complemented
407#1862C2×C15111yescharacteristic, complemented
408#1804C2×C15111yescharacteristic, complemented
409C22×SD16C22×C15111yescharacteristic
410C22×D8C22×C15111yescharacteristic
411C22×D8C22×C15111yescharacteristic
412#559—24no—
413#559—24no—
414C2×#127C22×C15111yescharacteristic
415C2×#124—21no—
416C2×#124C22×C15111yescharacteristic
417C2×#124C22×C15111yescharacteristic
418C2×#123—21no—
419C2×#123—21no—
420C2×C4×Q8C22×C15111yescharacteristic
421C2×C4×Q8C22×C15111yescharacteristic
422C2×C4×D4—21no—
423C2×C4×D4C22×C15111yescharacteristic
424C2×C4×D4C22×C15111yescharacteristic
425C2×C4×D4C22×C15111yescharacteristic
426#463—24no—
427C4×D8—24no—
428C2×#107C22×C15111yescharacteristic
429C2×C4⋊C8C22×C15111yescharacteristic
430C2×#103C22×C15111yescharacteristic
431C2×#103C22×C15111yescharacteristic
432C2×#103C22×C15111yescharacteristic
433C2×#102C22×C15111yescharacteristic
434C2×#102C22×C15111yescharacteristic
435C2×#102C22×C15111yescharacteristic
436C2×#102C22×C15111yescharacteristic
437C2×#102C22×C15111yescharacteristic
438C2×#102C22×C15111yescharacteristic
439C2×#102C22×C15111yescharacteristic
440C2×C4×C8C22×C15111yescharacteristic
441#399—21no—
442#393—21no—
443#390C22×C15111yescharacteristic
444#390C22×C15111yescharacteristic
445#389C22×C15111yescharacteristic
446#389C22×C15111yescharacteristic
447#385—21no—
448#385—21no—
449#382C22×C15111yescharacteristic
450#340C22×C15111yescharacteristic
451#340C22×C15111yescharacteristic
452#336C22×C15111yescharacteristic
453#336C22×C15111yescharacteristic
454#336C22×C15111yescharacteristic
455#336C22×C15111yescharacteristic
456C22×Q8D4×C15111yescharacteristic
457C22×Q8C23×C15111yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C23×C15111yescharacteristic
461C22×D4C23×C15111yescharacteristic
462C22×D4C23×C15111yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—21no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—41no—
475C22×C8C23×C15111yescharacteristic
476C22×C8C23×C15111yescharacteristic
477C22×C8C23×C15111yescharacteristic
478C22×C8C23×C15111yescharacteristic
479#127—22no—
480#127—22no—
481#124—28no—
482#124—22no—
483#124—22no—
484#124—22no—
485#124D4×C15114yes—
486#123—28no—
487#123—28no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×D4—28no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4D4×C15114yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4D4×C15111yescharacteristic
503C2×C4⋊C4D4×C15111yescharacteristic
504C2×C4⋊C4D4×C15111yescharacteristic
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C4⋊C4C23×C15111yescharacteristic
507C2×C4⋊C4C23×C15111yescharacteristic
508C2×C4⋊C4C23×C15111yescharacteristic
509C2×C22⋊C4—21no—
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×C42—21no—
521C2×C42C23×C15111yescharacteristic
522C2×C42C23×C15111yescharacteristic
523C2×C42C23×C15111yescharacteristic
524#107—22no—
525C4⋊C8—22no—
526#103—22no—
527#103—22no—
528#103—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535#102—41no—
536C4×C8—22no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—41no—
552C2×Q8C2×D4×C15112yes—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
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—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4C2×D4×C15112yes—
575C2×D4C2×D4×C15112yes—
576C2×D4#41×C15112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4C2×D4×C15111yescharacteristic
592C22×C4C2×D4×C15111yescharacteristic
593C22×C4C2×D4×C15111yescharacteristic
594C22×C4C2×D4×C15111yescharacteristic
595C22×C4C2×D4×C15111yescharacteristic
596C22×C4C2×D4×C15111yescharacteristic
597C22×C4C24×C15111yescharacteristic
598SD16—44no—
599D8—28no—
600D8—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8#41×C15112yes—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—81no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C15112yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C42—24no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×D4×C15112yes—
644C42C2×D4×C15112yes—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23C22×D4×C15111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—44no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4#120×C15112yes—
720C2×C4#120×C15112yes—
721C2×C4#135×C15112yes—
722C2×C4C22×D4×C15111yescharacteristic
723C2×C4C22×D4×C15111yescharacteristic
724C2×C4C2×#41×C15111yescharacteristic
725C2×C4C2×#41×C15111yescharacteristic
726C2×C4H(5,𝔽2)×C15111yescharacteristic
727C2×C42−1+4×C15111yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22C2×#120×C15111yescharacteristic
754C22#548×C15111yescharacteristic
755C22#550×C15111yescharacteristic
756C22C2×#135×C15111yescharacteristic
757C22#575×C15111yescharacteristic
758C22#576×C15111yescharacteristic
759C22#576×C15111yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4#525×C15111yescharacteristic
772C4#537×C15111yescharacteristic
773C4#546×C15111yescharacteristic
774C4#547×C15111yescharacteristic
775C2—82no—
776C2—82no—
777C2—82no—
778C2#2407×C15111yescharacteristic
779C2#3002×C15111yescharacteristic
780C2#3008×C15111yescharacteristic
781C2#3361×C15111yescharacteristic
782C2#3370×C15111yescharacteristic
783C2#3396×C15111yescharacteristic
784C2#3403×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2011×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#559×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×C4×D8×C151C2semidirect
4. #2580×C151C2semidirect
5. #2042×C151C2semidirect
6. #2041×C151C2semidirect
7. #2012×C151C2semidirect
9. #1984×C151C2semidirect
10. #1958×C151C2semidirect
11. #1880×C151C2semidirect
12. #1879×C151C2semidirect
13. #1863×C151C2semidirect
14. #1862×C151C2semidirect
15. #1804×C151C2semidirect
392. #24192C151direct (N × H)
393. C151#24192direct (N × H)
394. C2×#559C2×C151semidirect
395. C2×#463C2×C151semidirect
396. C2×C4×D8C2×C151semidirect
397. #2580C2×C151semidirect
398. #2042C2×C151semidirect
399. #2041C2×C151semidirect
400. #2012C2×C151semidirect
402. #1984C2×C151semidirect
403. #1958C2×C151semidirect
404. #1880C2×C151semidirect
405. #1879C2×C151semidirect
406. #1863C2×C151semidirect
407. #1862C2×C151semidirect
408. #1804C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1512
C2×#463×C1512
C2×C4×D8×C1512
#2580×C1512
#2042×C1512
#2041×C1512
#2012×C1512
#2011×C1512
#1984×C1512
#1958×C1512
#1880×C1512
#1879×C1512
#1863×C1512
#1862×C1512
#1804×C1512
#24192151