Finite Group Databasebeta

← C151×#22859 #50327784

Subgroups — C151×#22859 #50327784

Order 38656.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#451×C151C211yesmaximal, characteristic
2C2×#441×C151C211yesmaximal, characteristic, complemented
3C22×#103×C151C211yesmaximal, characteristic
4#2360×C151C211yesmaximal, characteristic
5Q8×C22⋊C4×C151C211yesmaximal, characteristic
6#1971×C151C211yesmaximal, characteristic, complemented
7#1935×C151C211yesmaximal, characteristic, complemented
8#1927×C151C211yesmaximal, characteristic, complemented
9#1892×C151C211yesmaximal, characteristic
10#1878×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1865×C151C211yesmaximal, characteristic, complemented
13#1853×C151C211yesmaximal, characteristic
14#1763×C151C211yesmaximal, characteristic, complemented
15#1752×C151C211yesmaximal, characteristic
16C23×Q8×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic
25#451×C151C418yescomplemented
26#441×C151—24no—
27C2×#106×C151C2211yescharacteristic
28C2×#106×C151C2211yescharacteristic
29C2×#103×C151—24no—
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#103×C151C2211yescharacteristic
36C2×#103×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41#391×C151—21no—
42#391×C151—21no—
43#391×C151C2211yescharacteristic
44#391×C151C2211yescharacteristic
45#391×C151C2211yescharacteristic
46#389×C151—21no—
47#389×C151C2211yescharacteristic
48#387×C151—21no—
49#385×C151—21no—
50#380×C151—21no—
51#380×C151C2211yescharacteristic
52C4×C4⋊C4×C151C2211yescharacteristic
53C4×C22⋊C4×C151—21no—
54C4×C22⋊C4×C151—21no—
55C4×C22⋊C4×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62C22×Q8×C151—22no—
63C22×Q8×C151—22no—
64C22×Q8×C151—21no—
65C22×Q8×C151—22no—
66C22×Q8×C151—41no—
67C22×Q8×C151—41no—
68C22×Q8×C151C2×C414yes—
69C22×Q8×C151C2311yescharacteristic
70C22×Q8×C151C2311yescharacteristic
71C22×Q8×C151C2311yescharacteristic
72C23×C4×C151—21no—
73C23×C4×C151—21no—
74C23×C4×C151C2311yescharacteristic
75C2×Q16×C151—22no—
76C2×Q16×C151—22no—
77C2×Q16×C151—41no—
78C2×Q16×C151—41no—
79C2×Q16×C151C2×C414yescomplemented
80C2×Q16×C151C2×C414yescomplemented
81C22×C8×C151—22no—
82C22×C8×C151—22no—
83C22×C8×C151—41no—
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151C2×C414yes—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151—41no—
94C4×Q8×C151—41no—
95C4×Q8×C151—41no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—22no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—41no—
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151D411yescharacteristic
112C2×C22⋊C4×C151D411yescharacteristic
113C2×C42×C151—21no—
114C2×C42×C151—21no—
115C2×C42×C151—21no—
116C2×C42×C151—21no—
117C2×C42×C151C2311yescharacteristic
118C2×C42×C151C2311yescharacteristic
119#106×C151—22no—
120#106×C151—41no—
121#103×C151—22no—
122#103×C151—22no—
123#103×C151—22no—
124#103×C151—22no—
125#103×C151—41no—
126#103×C151C2×C414yescomplemented
127#103×C151C2×C414yescomplemented
128#103×C151D414yes—
129C22⋊C8×C151C2×C414yes—
130#97×C151—22no—
131#97×C151—41no—
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—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151D411yescharacteristic
142#95×C151D411yescharacteristic
143C24×C151C2×D411yescharacteristic
144C2×Q8×C151—24no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—28no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151—42no—
160C2×Q8×C151—42no—
161C2×Q8×C151—44no—
162C2×Q8×C151—44no—
163C2×Q8×C151—44no—
164C2×Q8×C151C22×C412yes—
165C2×Q8×C151C22×C412yes—
166C2×Q8×C151C22×C412yes—
167C2×Q8×C151C2×D412yes—
168C2×Q8×C151#4112yes—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—24no—
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—42no—
183C22×C4×C151—42no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151—81no—
187C22×C4×C151C22×C412yes—
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151#4112yes—
194C22×C4×C151C2411yescharacteristic
195Q16×C151—28no—
196Q16×C151—44no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—44no—
207C2×C8×C151C22×C412yes—
208C2×C8×C151C22×C412yes—
209C2×C8×C151C2×D412yes—
210C4⋊C4×C151—24no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—42no—
220C4⋊C4×C151—42no—
221C4⋊C4×C151—42no—
222C4⋊C4×C151—42no—
223C4⋊C4×C151—81no—
224C4⋊C4×C151C22×C412yes—
225C4⋊C4×C151C2×D412yes—
226C22⋊C4×C151—24no—
227C22⋊C4×C151—22no—
228C22⋊C4×C151—22no—
229C22⋊C4×C151—42no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—42no—
235C42×C151—42no—
236C42×C151—42no—
237C42×C151—81no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151C4×D412yes—
243C23×C151#13712yes—
244C23×C151#13712yes—
245C23×C151C22×D411yescharacteristic
246Q8×C151—22no—
247Q8×C151—22no—
248Q8×C151—22no—
249Q8×C151—22no—
250Q8×C151—22no—
251Q8×C151—22no—
252Q8×C151—22no—
253Q8×C151—48no—
254Q8×C151—41no—
255Q8×C151—41no—
256Q8×C151—41no—
257Q8×C151—41no—
258Q8×C151C4×D414yes—
259C2×C4×C151—22no—
260C2×C4×C151—22no—
261C2×C4×C151—21no—
262C2×C4×C151—22no—
263C2×C4×C151—21no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—22no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—48no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—84no—
303C2×C4×C151C4×D412yes—
304C2×C4×C151C23×C411yescharacteristic
305C2×C4×C151C22×D411yescharacteristic
306C2×C4×C151C2×#4111yescharacteristic
307C2×C4×C151C2×#4111yescharacteristic
308C2×C4×C151H(5,𝔽2)11yescharacteristic
309C2×C4×C151H(5,𝔽2)11yescharacteristic
310C8×C151—22no—
311C8×C151—22no—
312C8×C151—22no—
313C8×C151—41no—
314C22×C151—22no—
315C22×C151—22no—
316C22×C151—22no—
317C22×C151—22no—
318C22×C151—22no—
319C22×C151—22no—
320C22×C151#44114yescomplemented
321C22×C151C2×C4×D411yescharacteristic
322C22×C151D4211yescharacteristic
323C22×C151#54611yescharacteristic
324C22×C151C2×#13711yescharacteristic
325C22×C151C2×#13711yescharacteristic
326C22×C151#57711yescharacteristic
327C22×C151#57811yescharacteristic
328C4×C151—22no—
329C4×C151—24no—
330C4×C151—42no—
331C4×C151—42no—
332C4×C151—42no—
333C4×C151—41no—
334C4×C151—42no—
335C4×C151—41no—
336C4×C151—41no—
337C4×C151—41no—
338C4×C151—81no—
339C4×C151—81no—
340C4×C151—81no—
341C4×C151C2×C4×D411yescharacteristic
342C4×C151#51811yescharacteristic
343C4×C151#54611yescharacteristic
344C4×C151#55111yescharacteristic
345C2×C151—24no—
346C2×C151#235811yescharacteristic
347C2×C151C2×#44111yescharacteristic
348C2×C151#294711yescharacteristic
349C2×C151#326611yescharacteristic
350C2×C151#327011yescharacteristic
351C2×C151#331211yescharacteristic
352C2×C151#331611yescharacteristic
353#22859C15111yesmaximal, characteristic, direct product factor, Sylow
354C151#2285911yescharacteristic, direct product factor, Sylow
355C2×#451C2×C15111yescharacteristic
356C2×#441C2×C15111yescharacteristic, complemented
357C22×#103C2×C15111yescharacteristic
358#2360C2×C15111yescharacteristic
359Q8×C22⋊C4C2×C15111yescharacteristic
360#1971C2×C15111yescharacteristic, complemented
361#1935C2×C15111yescharacteristic, complemented
362#1927C2×C15111yescharacteristic, complemented
363#1892C2×C15111yescharacteristic
364#1878C2×C15111yescharacteristic, complemented
365#1878C2×C15111yescharacteristic, complemented
366#1865C2×C15111yescharacteristic, complemented
367#1853C2×C15111yescharacteristic
368#1763C2×C15111yescharacteristic, complemented
369#1752C2×C15111yescharacteristic
370C23×Q8C22×C15111yescharacteristic
371C22×Q16C22×C15111yescharacteristic
372C22×Q16C22×C15111yescharacteristic
373C23×C8C22×C15111yescharacteristic
374C2×C22⋊Q8C22×C15111yescharacteristic
375C2×C4×Q8C22×C15111yescharacteristic
376C2×C4×Q8C22×C15111yescharacteristic
377C2×C4×Q8C22×C15111yescharacteristic
378C22×C4⋊C4C22×C15111yescharacteristic
379#451C4×C15118yescomplemented
380#441—24no—
381C2×#106C22×C15111yescharacteristic
382C2×#106C22×C15111yescharacteristic
383C2×#103—24no—
384C2×#103C22×C15111yescharacteristic
385C2×#103C22×C15111yescharacteristic
386C2×#103C22×C15111yescharacteristic
387C2×#103C22×C15111yescharacteristic
388C2×#103C22×C15111yescharacteristic
389C2×#103C22×C15111yescharacteristic
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×C22⋊C8C22×C15111yescharacteristic
393C2×#97C22×C15111yescharacteristic
394C2×#97C22×C15111yescharacteristic
395#391—21no—
396#391—21no—
397#391C22×C15111yescharacteristic
398#391C22×C15111yescharacteristic
399#391C22×C15111yescharacteristic
400#389—21no—
401#389C22×C15111yescharacteristic
402#387—21no—
403#385—21no—
404#380—21no—
405#380C22×C15111yescharacteristic
406C4×C4⋊C4C22×C15111yescharacteristic
407C4×C22⋊C4—21no—
408C4×C22⋊C4—21no—
409C4×C22⋊C4C22×C15111yescharacteristic
410#340C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#336C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416C22×Q8—22no—
417C22×Q8—21no—
418C22×Q8—22no—
419C22×Q8—22no—
420C22×Q8—41no—
421C22×Q8—41no—
422C22×Q8C2×C4×C15114yes—
423C22×Q8C23×C15111yescharacteristic
424C22×Q8C23×C15111yescharacteristic
425C22×Q8C23×C15111yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4C23×C15111yescharacteristic
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—41no—
432C2×Q16—41no—
433C2×Q16C2×C4×C15114yescomplemented
434C2×Q16C2×C4×C15114yescomplemented
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8C23×C15111yescharacteristic
439C22×C8C23×C15111yescharacteristic
440C22×C8C23×C15111yescharacteristic
441C22×C8C23×C15111yescharacteristic
442C22⋊Q8—22no—
443C22⋊Q8C2×C4×C15114yes—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—41no—
448C4×Q8—41no—
449C4×Q8—41no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4C23×C15111yescharacteristic
459C2×C4⋊C4C23×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15111yescharacteristic
462C2×C4⋊C4C23×C15111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C15111yescharacteristic
466C2×C22⋊C4D4×C15111yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C15111yescharacteristic
472C2×C42C23×C15111yescharacteristic
473#106—22no—
474#106—41no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—41no—
480#103C2×C4×C15114yescomplemented
481#103C2×C4×C15114yescomplemented
482#103D4×C15114yes—
483C22⋊C8C2×C4×C15114yes—
484#97—22no—
485#97—41no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95D4×C15111yescharacteristic
496#95D4×C15111yescharacteristic
497C24C2×D4×C15111yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—28no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8C22×C4×C15112yes—
519C2×Q8C22×C4×C15112yes—
520C2×Q8C22×C4×C15112yes—
521C2×Q8C2×D4×C15112yes—
522C2×Q8#41×C15112yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4C22×C4×C15112yes—
542C22×C4C2×D4×C15111yescharacteristic
543C22×C4C2×D4×C15111yescharacteristic
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4#41×C15112yes—
548C22×C4C24×C15111yescharacteristic
549Q16—28no—
550Q16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—44no—
561C2×C8C22×C4×C15112yes—
562C2×C8C22×C4×C15112yes—
563C2×C8C2×D4×C15112yes—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4C22×C4×C15112yes—
579C4⋊C4C2×D4×C15112yes—
580C22⋊C4—24no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—42no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—42no—
590C42—42no—
591C42—81no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C4×D4×C15112yes—
597C23#137×C15112yes—
598C23#137×C15112yes—
599C23C22×D4×C15111yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—22no—
607Q8—48no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8C4×D4×C15114yes—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—48no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4C4×D4×C15112yes—
658C2×C4C23×C4×C15111yescharacteristic
659C2×C4C22×D4×C15111yescharacteristic
660C2×C4C2×#41×C15111yescharacteristic
661C2×C4C2×#41×C15111yescharacteristic
662C2×C4H(5,𝔽2)×C15111yescharacteristic
663C2×C4H(5,𝔽2)×C15111yescharacteristic
664C8—22no—
665C8—22no—
666C8—22no—
667C8—41no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22#441×C15114yescomplemented
675C22C2×C4×D4×C15111yescharacteristic
676C22D42×C15111yescharacteristic
677C22#546×C15111yescharacteristic
678C22C2×#137×C15111yescharacteristic
679C22C2×#137×C15111yescharacteristic
680C22#577×C15111yescharacteristic
681C22#578×C15111yescharacteristic
682C4—22no—
683C4—24no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4C2×C4×D4×C15111yescharacteristic
696C4#518×C15111yescharacteristic
697C4#546×C15111yescharacteristic
698C4#551×C15111yescharacteristic
699C2—24no—
700C2#2358×C15111yescharacteristic
701C2C2×#441×C15111yescharacteristic
702C2#2947×C15111yescharacteristic
703C2#3266×C15111yescharacteristic
704C2#3270×C15111yescharacteristic
705C2#3312×C15111yescharacteristic
706C2#3316×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
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×#441×C151C2semidirect
6. #1971×C151C2semidirect
7. #1935×C151C2semidirect
8. #1927×C151C2semidirect
10. #1878×C151C2semidirect
11. #1878×C151C2semidirect
12. #1865×C151C2semidirect
14. #1763×C151C2semidirect
25. #451×C151C4semidirect
79. C2×Q16×C151C2×C4semidirect
80. C2×Q16×C151C2×C4semidirect
126. #103×C151C2×C4semidirect
127. #103×C151C2×C4semidirect
320. C22×C151#441semidirect
353. #22859C151direct (N × H)
354. C151#22859direct (N × H)
356. C2×#441C2×C151semidirect
360. #1971C2×C151semidirect
361. #1935C2×C151semidirect
362. #1927C2×C151semidirect
364. #1878C2×C151semidirect
365. #1878C2×C151semidirect
366. #1865C2×C151semidirect
368. #1763C2×C151semidirect
379. #451C4×C151semidirect
433. C2×Q16C2×C4×C151semidirect
434. C2×Q16C2×C4×C151semidirect
480. #103C2×C4×C151semidirect
481. #103C2×C4×C151semidirect
674. C22#441×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#451×C1512
C2×#441×C1512
C22×#103×C1512
#2360×C1512
Q8×C22⋊C4×C1512
#1971×C1512
#1935×C1512
#1927×C1512
#1892×C1512
#1878×C1512
#1865×C1512
#1853×C1512
#1763×C1512
#1752×C1512
#22859151