Finite Group Databasebeta

← C151×#22878 #50327803

Subgroups — C151×#22878 #50327803

Order 38656.

1218 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C151C211yesmaximal, characteristic
2C2×C4×D8×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2361×C151C211yesmaximal, characteristic, complemented
5#2339×C151C211yesmaximal, characteristic, complemented
6#1973×C151C211yesmaximal, characteristic, complemented
7#1933×C151C211yesmaximal, characteristic, complemented
8#1928×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1862×C151C211yesmaximal, characteristic, complemented
13#1852×C151C211yesmaximal, characteristic, complemented
14#1762×C151C211yesmaximal, characteristic, complemented
15#1753×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×C4×D4×C151—21no—
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25C22×C4⋊C4×C151C2211yescharacteristic
26#449×C151C418yescomplemented
27C4×D8×C151—24no—
28C2×#107×C151C2211yescharacteristic
29C2×#107×C151C2211yescharacteristic
30#417×C151—24no—
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41C2×C4×C8×C151C2211yescharacteristic
42#391×C151C2211yescharacteristic
43#391×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#389×C151C2211yescharacteristic
46#388×C151—21no—
47#386×C151—21no—
48#386×C151—21no—
49#386×C151—21no—
50#385×C151—21no—
51#381×C151—21no—
52#380×C151C2211yescharacteristic
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C22⋊C4×C151C2211yescharacteristic
55C2×#95×C151—21no—
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C2×#41×C151C2×C414yescomplemented
68C22×Q8×C151C2311yescharacteristic
69C22×D4×C151—21no—
70C22×D4×C151—21no—
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151—21no—
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151—21no—
77C23×C4×C151—21no—
78C23×C4×C151C2311yescharacteristic
79C2×SD16×C151—41no—
80C2×SD16×C151—41no—
81C2×SD16×C151C2×C414yescomplemented
82C2×D8×C151—22no—
83C2×D8×C151—22no—
84C2×D8×C151C2×C414yescomplemented
85C2×M16×C151—22no—
86C2×M16×C151—22no—
87C2×M16×C151—41no—
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91C22×C8×C151C2311yescharacteristic
92#121×C151—22no—
93#121×C151C2×C414yescomplemented
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—41no—
98C4×D4×C151—41no—
99C4×D4×C151—41no—
100C4×D4×C151—44no—
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—41no—
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
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×C151D411yescharacteristic
118C2×C22⋊C4×C151D411yescharacteristic
119C2×C42×C151—21no—
120C2×C42×C151C2311yescharacteristic
121C2×C42×C151C2311yescharacteristic
122#107×C151—22no—
123#107×C151—41no—
124#103×C151—22no—
125#103×C151—22no—
126#103×C151C2×C414yescomplemented
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—41no—
130#102×C151C2×C414yescomplemented
131#102×C151D414yescomplemented
132C22⋊C8×C151C2×C414yescomplemented
133#97×C151—41no—
134C4×C8×C151—22no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151—21no—
142#95×C151D411yescharacteristic
143#95×C151D411yescharacteristic
144C24×C151—21no—
145C24×C151—21no—
146C24×C151C2×D411yescharacteristic
147#41×C151—28no—
148#41×C151—44no—
149#41×C151—44no—
150#41×C151—44no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151C22×C412yes—
157C2×D4×C151—24no—
158C2×D4×C151—24no—
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—21no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151C22×C412yes—
172C2×D4×C151C22×C412yes—
173C2×D4×C151C2×D412yes—
174C2×D4×C151#4112yes—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
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—42no—
187C22×C4×C151—42no—
188C22×C4×C151—42no—
189C22×C4×C151—42no—
190C22×C4×C151—42no—
191C22×C4×C151—42no—
192C22×C4×C151—42no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—42no—
196C22×C4×C151—81no—
197C22×C4×C151—81no—
198C22×C4×C151—81no—
199C22×C4×C151—81no—
200C22×C4×C151C22×C412yes—
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151#4112yes—
207C22×C4×C151C2411yescharacteristic
208SD16×C151—44no—
209D8×C151—28no—
210M16×C151—44no—
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—21no—
220C2×C8×C151C22×C412yes—
221C2×C8×C151C22×C412yes—
222C2×C8×C151C2×D412yes—
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—42no—
232C4⋊C4×C151—42no—
233C4⋊C4×C151C22×C412yes—
234C4⋊C4×C151C2×D412yes—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—41no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—42no—
240C22⋊C4×C151—42no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—81no—
243C22⋊C4×C151—81no—
244C42×C151—21no—
245C42×C151—21no—
246C42×C151—21no—
247C42×C151—21no—
248C42×C151—42no—
249C23×C151—22no—
250C23×C151—22no—
251C23×C151—21no—
252C23×C151—22no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—22no—
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×C151C4×D412yes—
270C23×C151C22×D411yescharacteristic
271Q8×C151—22no—
272Q8×C151—22no—
273Q8×C151—41no—
274Q8×C151—41no—
275D4×C151—22no—
276D4×C151—22no—
277D4×C151—22no—
278D4×C151—22no—
279D4×C151—22no—
280D4×C151—48no—
281D4×C151—48no—
282D4×C151—41no—
283D4×C151—41no—
284D4×C151C4×D414yescomplemented
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—22no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—22no—
293C2×C4×C151—22no—
294C2×C4×C151—22no—
295C2×C4×C151—21no—
296C2×C4×C151—22no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—48no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
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—84no—
322C2×C4×C151—84no—
323C2×C4×C151—84no—
324C2×C4×C151—84no—
325C2×C4×C151C4×D412yes—
326C2×C4×C151AGL(1,ℤ/8)12yes—
327C2×C4×C151C23×C411yescharacteristic
328C2×C4×C151C22×D411yescharacteristic
329C2×C4×C151C2×#4111yescharacteristic
330C2×C4×C151C2×#4111yescharacteristic
331C2×C4×C151H(5,𝔽2)11yescharacteristic
332C2×C4×C151H(5,𝔽2)11yescharacteristic
333C8×C151—22no—
334C8×C151—22no—
335C8×C151—22no—
336C8×C151—41no—
337C22×C151—22no—
338C22×C151—24no—
339C22×C151—22no—
340C22×C151—22no—
341C22×C151—41no—
342C22×C151—42no—
343C22×C151—42no—
344C22×C151—42no—
345C22×C151—41no—
346C22×C151—42no—
347C22×C151—41no—
348C22×C151—42no—
349C22×C151—42no—
350C22×C151—41no—
351C22×C151—42no—
352C22×C151—42no—
353C22×C151—42no—
354C22×C151—81no—
355C22×C151—81no—
356C22×C151—81no—
357C22×C151—81no—
358C22×C151C2×C4×D411yescharacteristic
359C22×C151D4211yescharacteristic
360C22×C151#54611yescharacteristic
361C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C151#57511yescharacteristic
363C22×C151#57611yescharacteristic
364C22×C151#57811yescharacteristic
365C4×C151—22no—
366C4×C151—22no—
367C4×C151—41no—
368C4×C151—42no—
369C4×C151—42no—
370C4×C151—42no—
371C4×C151—41no—
372C4×C151—41no—
373C4×C151—81no—
374C4×C151—81no—
375C4×C151—81no—
376C4×C151C2×C4×D411yescharacteristic
377C4×C151#51811yescharacteristic
378C4×C151#54611yescharacteristic
379C4×C151#55111yescharacteristic
380C2×C151—42no—
381C2×C151—44no—
382C2×C151—82no—
383C2×C151#235811yescharacteristic
384C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
385C2×C151#295111yescharacteristic
386C2×C151#326411yescharacteristic
387C2×C151#326911yescharacteristic
388C2×C151#332211yescharacteristic
389C2×C151#333011yescharacteristic
390#22878C15111yesmaximal, characteristic, direct product factor, Sylow
391C151#2287811yescharacteristic, direct product factor, Sylow
392C2×#449C2×C15111yescharacteristic
393C2×C4×D8C2×C15111yescharacteristic, complemented
394C2×#417C2×C15111yescharacteristic, complemented
395#2361C2×C15111yescharacteristic, complemented
396#2339C2×C15111yescharacteristic, complemented
397#1973C2×C15111yescharacteristic, complemented
398#1933C2×C15111yescharacteristic, complemented
399#1928C2×C15111yescharacteristic, complemented
400#1895C2×C15111yescharacteristic, complemented
401#1879C2×C15111yescharacteristic, complemented
402#1877C2×C15111yescharacteristic, complemented
403#1862C2×C15111yescharacteristic, complemented
404#1852C2×C15111yescharacteristic, complemented
405#1762C2×C15111yescharacteristic, complemented
406#1753C2×C15111yescharacteristic, complemented
407C22×#41C22×C15111yescharacteristic
408C22×SD16C22×C15111yescharacteristic
409C22×D8C22×C15111yescharacteristic
410C22×M16C22×C15111yescharacteristic
411C2×#121C22×C15111yescharacteristic
412C2×C4×D4—21no—
413C2×C4×D4C22×C15111yescharacteristic
414C2×C4×D4C22×C15111yescharacteristic
415C2×C4×D4C22×C15111yescharacteristic
416C22×C4⋊C4C22×C15111yescharacteristic
417#449C4×C15118yescomplemented
418C4×D8—24no—
419C2×#107C22×C15111yescharacteristic
420C2×#107C22×C15111yescharacteristic
421#417—24no—
422C2×#103C22×C15111yescharacteristic
423C2×#103C22×C15111yescharacteristic
424C2×#103C22×C15111yescharacteristic
425C2×#102C22×C15111yescharacteristic
426C2×#102C22×C15111yescharacteristic
427C2×#102C22×C15111yescharacteristic
428C2×#102C22×C15111yescharacteristic
429C2×#102C22×C15111yescharacteristic
430C2×C22⋊C8C22×C15111yescharacteristic
431C2×#97C22×C15111yescharacteristic
432C2×C4×C8C22×C15111yescharacteristic
433#391C22×C15111yescharacteristic
434#391C22×C15111yescharacteristic
435#390C22×C15111yescharacteristic
436#389C22×C15111yescharacteristic
437#388—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#381—21no—
443#380C22×C15111yescharacteristic
444C4×C4⋊C4C22×C15111yescharacteristic
445C4×C22⋊C4C22×C15111yescharacteristic
446C2×#95—21no—
447#340C22×C15111yescharacteristic
448#340C22×C15111yescharacteristic
449#340C22×C15111yescharacteristic
450#340C22×C15111yescharacteristic
451#336C22×C15111yescharacteristic
452#336C22×C15111yescharacteristic
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—41no—
457C2×#41—41no—
458C2×#41C2×C4×C15114yescomplemented
459C22×Q8C23×C15111yescharacteristic
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C15111yescharacteristic
463C22×D4C23×C15111yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C15111yescharacteristic
470C2×SD16—41no—
471C2×SD16—41no—
472C2×SD16C2×C4×C15114yescomplemented
473C2×D8—22no—
474C2×D8—22no—
475C2×D8C2×C4×C15114yescomplemented
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C15111yescharacteristic
480C22×C8C23×C15111yescharacteristic
481C22×C8C23×C15111yescharacteristic
482C22×C8C23×C15111yescharacteristic
483#121—22no—
484#121C2×C4×C15114yescomplemented
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—41no—
489C4×D4—41no—
490C4×D4—41no—
491C4×D4—44no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4C23×C15111yescharacteristic
497C2×C4⋊C4C23×C15111yescharacteristic
498C2×C4⋊C4C23×C15111yescharacteristic
499C2×C4⋊C4C23×C15111yescharacteristic
500C2×C4⋊C4C23×C15111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4D4×C15111yescharacteristic
509C2×C22⋊C4D4×C15111yescharacteristic
510C2×C42—21no—
511C2×C42C23×C15111yescharacteristic
512C2×C42C23×C15111yescharacteristic
513#107—22no—
514#107—41no—
515#103—22no—
516#103—22no—
517#103C2×C4×C15114yescomplemented
518#102—22no—
519#102—22no—
520#102—41no—
521#102C2×C4×C15114yescomplemented
522#102D4×C15114yescomplemented
523C22⋊C8C2×C4×C15114yescomplemented
524#97—41no—
525C4×C8—22no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C15111yescharacteristic
534#95D4×C15111yescharacteristic
535C24—21no—
536C24—21no—
537C24C2×D4×C15111yescharacteristic
538#41—28no—
539#41—44no—
540#41—44no—
541#41—44no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C22×C4×C15112yes—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4C22×C4×C15112yes—
563C2×D4C22×C4×C15112yes—
564C2×D4C2×D4×C15112yes—
565C2×D4#41×C15112yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4C22×C4×C15112yes—
592C22×C4C2×D4×C15111yescharacteristic
593C22×C4C2×D4×C15111yescharacteristic
594C22×C4C2×D4×C15111yescharacteristic
595C22×C4C2×D4×C15111yescharacteristic
596C22×C4C2×D4×C15111yescharacteristic
597C22×C4#41×C15112yes—
598C22×C4C24×C15111yescharacteristic
599SD16—44no—
600D8—28no—
601M16—44no—
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×C8C22×C4×C15112yes—
612C2×C8C22×C4×C15112yes—
613C2×C8C2×D4×C15112yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4C22×C4×C15112yes—
625C4⋊C4C2×D4×C15112yes—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—41no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—42no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—22no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C4×D4×C15112yes—
661C23C22×D4×C15111yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—22no—
671D4—48no—
672D4—48no—
673D4—41no—
674D4—41no—
675D4C4×D4×C15114yescomplemented
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
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—84no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4C4×D4×C15112yes—
717C2×C4AGL(1,ℤ/8)×C15112yes—
718C2×C4C23×C4×C15111yescharacteristic
719C2×C4C22×D4×C15111yescharacteristic
720C2×C4C2×#41×C15111yescharacteristic
721C2×C4C2×#41×C15111yescharacteristic
722C2×C4H(5,𝔽2)×C15111yescharacteristic
723C2×C4H(5,𝔽2)×C15111yescharacteristic
724C8—22no—
725C8—22no—
726C8—22no—
727C8—41no—
728C22—22no—
729C22—24no—
730C22—22no—
731C22—22no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C2×C4×D4×C15111yescharacteristic
750C22D42×C15111yescharacteristic
751C22#546×C15111yescharacteristic
752C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
753C22#575×C15111yescharacteristic
754C22#576×C15111yescharacteristic
755C22#578×C15111yescharacteristic
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4C2×C4×D4×C15111yescharacteristic
768C4#518×C15111yescharacteristic
769C4#546×C15111yescharacteristic
770C4#551×C15111yescharacteristic
771C2—42no—
772C2—44no—
773C2—82no—
774C2#2358×C15111yescharacteristic
775C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
776C2#2951×C15111yescharacteristic
777C2#3264×C15111yescharacteristic
778C2#3269×C15111yescharacteristic
779C2#3322×C15111yescharacteristic
780C2#3330×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×C151C2
LCSG ▷ C2×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×C4×D8×C151C2semidirect
3. C2×#417×C151C2semidirect
4. #2361×C151C2semidirect
5. #2339×C151C2semidirect
6. #1973×C151C2semidirect
7. #1933×C151C2semidirect
8. #1928×C151C2semidirect
9. #1895×C151C2semidirect
10. #1879×C151C2semidirect
11. #1877×C151C2semidirect
12. #1862×C151C2semidirect
13. #1852×C151C2semidirect
14. #1762×C151C2semidirect
15. #1753×C151C2semidirect
26. #449×C151C4semidirect
67. C2×#41×C151C2×C4semidirect
81. C2×SD16×C151C2×C4semidirect
84. C2×D8×C151C2×C4semidirect
93. #121×C151C2×C4semidirect
126. #103×C151C2×C4semidirect
130. #102×C151C2×C4semidirect
131. #102×C151D4semidirect
132. C22⋊C8×C151C2×C4semidirect
284. D4×C151C4×D4semidirect
390. #22878C151direct (N × H)
391. C151#22878direct (N × H)
393. C2×C4×D8C2×C151semidirect
394. C2×#417C2×C151semidirect
395. #2361C2×C151semidirect
396. #2339C2×C151semidirect
397. #1973C2×C151semidirect
398. #1933C2×C151semidirect
399. #1928C2×C151semidirect
400. #1895C2×C151semidirect
401. #1879C2×C151semidirect
402. #1877C2×C151semidirect
403. #1862C2×C151semidirect
404. #1852C2×C151semidirect
405. #1762C2×C151semidirect
406. #1753C2×C151semidirect
417. #449C4×C151semidirect
458. C2×#41C2×C4×C151semidirect
472. C2×SD16C2×C4×C151semidirect
475. C2×D8C2×C4×C151semidirect
484. #121C2×C4×C151semidirect
517. #103C2×C4×C151semidirect
521. #102C2×C4×C151semidirect
522. #102D4×C151semidirect
523. C22⋊C8C2×C4×C151semidirect
675. D4C4×D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1512
C2×C4×D8×C1512
C2×#417×C1512
#2361×C1512
#2339×C1512
#1973×C1512
#1933×C1512
#1928×C1512
#1895×C1512
#1879×C1512
#1877×C1512
#1862×C1512
#1852×C1512
#1762×C1512
#1753×C1512
#22878151