Finite Group Databasebeta

← C151×#24924 #50329849

Subgroups — C151×#24924 #50329849

Order 38656.

960 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#452×C151C211yesmaximal, characteristic
2C2×#441×C151C211yesmaximal, characteristic, complemented
3#2423×C151C211yesmaximal, characteristic, complemented
4#2341×C151C211yesmaximal, characteristic
5#2094×C151C211yesmaximal, characteristic, complemented
6#2077×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2035×C151C211yesmaximal, characteristic, complemented
9#1936×C151C211yesmaximal, characteristic, complemented
10#1924×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1878×C151C211yesmaximal, characteristic, complemented
13#1865×C151C211yesmaximal, characteristic, complemented
14#1803×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic
16C22×#41×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23#452×C151—24no—
24#441×C151—24no—
25C2×#106×C151C2211yescharacteristic
26C2×#106×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic
39#399×C151—21no—
40#398×C151—21no—
41#391×C151C2211yescharacteristic
42#390×C151—21no—
43#390×C151—21no—
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#388×C151—21no—
48#387×C151—21no—
49#384×C151C2211yescharacteristic
50#380×C151—21no—
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53C4×C22⋊C4×C151—21no—
54C4×C22⋊C4×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151C2311yescharacteristic
68C22×Q8×C151C2311yescharacteristic
69C22×D4×C151—21no—
70C22×D4×C151C2311yescharacteristic
71C23×C4×C151—21no—
72C23×C4×C151C2311yescharacteristic
73C2×Q16×C151—22no—
74C2×Q16×C151—22no—
75C2×Q16×C151D414yes—
76C2×SD16×C151—22no—
77C2×SD16×C151—22no—
78C2×SD16×C151—41no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—41no—
85C4×Q8×C151—22no—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C4×Q8×C151—41no—
89C4×Q8×C151—41no—
90C4×Q8×C151—41no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151D411yescharacteristic
111C2×C22⋊C4×C151D411yescharacteristic
112C2×C42×C151—21no—
113C2×C42×C151—21no—
114C2×C42×C151—21no—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117#106×C151—22no—
118#106×C151—41no—
119C4⋊C8×C151—41no—
120#103×C151—22no—
121#103×C151—22no—
122#103×C151—22no—
123#103×C151—22no—
124#103×C151—41no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—41no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—41no—
130#97×C151—22no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151D411yescharacteristic
137#95×C151D411yescharacteristic
138C24×C151—21no—
139C24×C151C2×D411yescharacteristic
140#41×C151—44no—
141#41×C151—44no—
142#41×C151—44no—
143#41×C151—44no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151C2×D412yes—
153C2×Q8×C151C2×D412yes—
154C2×Q8×C151#4112yes—
155C2×Q8×C151#4112yes—
156C2×D4×C151—24no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151#4112yes—
165C22×C4×C151—21no—
166C22×C4×C151—24no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—42no—
180C22×C4×C151—42no—
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2411yescharacteristic
187Q16×C151—28no—
188SD16×C151—44no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151C2×D412yes—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—42no—
212C4⋊C4×C151—42no—
213C4⋊C4×C151—42no—
214C4⋊C4×C151—42no—
215C4⋊C4×C151—42no—
216C4⋊C4×C151—81no—
217C4⋊C4×C151—81no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—41no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—81no—
224C22⋊C4×C151—81no—
225C22⋊C4×C151—81no—
226C22⋊C4×C151—81no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—42no—
232C42×C151—42no—
233C42×C151—42no—
234C23×C151—22no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—41no—
248C23×C151C22×D411yescharacteristic
249Q8×C151—22no—
250Q8×C151—22no—
251Q8×C151—22no—
252Q8×C151—22no—
253Q8×C151—22no—
254Q8×C151—41no—
255Q8×C151—41no—
256Q8×C151#12314yes—
257D4×C151—22no—
258D4×C151—22no—
259D4×C151—48no—
260D4×C151—41no—
261D4×C151—41no—
262C2×C4×C151—22no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—22no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
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—48no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
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#13712yes—
303C2×C4×C151C22×D411yescharacteristic
304C2×C4×C151C2×#4111yescharacteristic
305C2×C4×C151C2×#4111yescharacteristic
306C2×C4×C151C2×#4111yescharacteristic
307C2×C4×C151H(5,𝔽2)11yescharacteristic
308C2×C4×C151H(5,𝔽2)11yescharacteristic
309C8×C151—22no—
310C8×C151—41no—
311C8×C151—41no—
312C8×C151—41no—
313C22×C151—41no—
314C22×C151—42no—
315C22×C151—41no—
316C22×C151—42no—
317C22×C151—42no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—41no—
323C22×C151—81no—
324C22×C151—81no—
325C22×C151—81no—
326C22×C151—81no—
327C22×C151#52511yescharacteristic
328C22×C151D4211yescharacteristic
329C22×C151#54611yescharacteristic
330C22×C151C2×#13711yescharacteristic
331C22×C151#57511yescharacteristic
332C22×C151#57711yescharacteristic
333C22×C151#57711yescharacteristic
334C4×C151—24no—
335C4×C151—22no—
336C4×C151—41no—
337C4×C151—42no—
338C4×C151—41no—
339C4×C151—41no—
340C4×C151—41no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151—81no—
344C4×C151—81no—
345C4×C151—81no—
346C4×C151C2×#12311yescharacteristic
347C4×C151#53811yescharacteristic
348C4×C151#54611yescharacteristic
349C4×C151#55111yescharacteristic
350C2×C151—81no—
351C2×C151—82no—
352C2×C151#241811yescharacteristic
353C2×C151#311611yescharacteristic
354C2×C151#312511yescharacteristic
355C2×C151#327111yescharacteristic
356C2×C151#327811yescharacteristic
357C2×C151#331611yescharacteristic
358C2×C151#331711yescharacteristic
359#24924C15111yesmaximal, characteristic, direct product factor, Sylow
360C151#2492411yescharacteristic, direct product factor, Sylow
361C2×#452C2×C15111yescharacteristic
362C2×#441C2×C15111yescharacteristic, complemented
363#2423C2×C15111yescharacteristic, complemented
364#2341C2×C15111yescharacteristic
365#2094C2×C15111yescharacteristic, complemented
366#2077C2×C15111yescharacteristic, complemented
367#2055C2×C15111yescharacteristic, complemented
368#2035C2×C15111yescharacteristic, complemented
369#1936C2×C15111yescharacteristic, complemented
370#1924C2×C15111yescharacteristic, complemented
371#1880C2×C15111yescharacteristic, complemented
372#1878C2×C15111yescharacteristic, complemented
373#1865C2×C15111yescharacteristic, complemented
374#1803C2×C15111yescharacteristic, complemented
375#1788C2×C15111yescharacteristic
376C22×#41C22×C15111yescharacteristic
377C22×Q16C22×C15111yescharacteristic
378C22×SD16C22×C15111yescharacteristic
379C2×C22⋊Q8C22×C15111yescharacteristic
380C2×C4×Q8C22×C15111yescharacteristic
381C2×C4×Q8C22×C15111yescharacteristic
382C2×C4×Q8C22×C15111yescharacteristic
383#452—24no—
384#441—24no—
385C2×#106C22×C15111yescharacteristic
386C2×#106C22×C15111yescharacteristic
387C2×C4⋊C8C22×C15111yescharacteristic
388C2×#103C22×C15111yescharacteristic
389C2×#103C22×C15111yescharacteristic
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#102C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×#102C22×C15111yescharacteristic
396C2×C22⋊C8C22×C15111yescharacteristic
397C2×C22⋊C8C22×C15111yescharacteristic
398C2×#97C22×C15111yescharacteristic
399#399—21no—
400#398—21no—
401#391C22×C15111yescharacteristic
402#390—21no—
403#390—21no—
404#390C22×C15111yescharacteristic
405#390C22×C15111yescharacteristic
406#389C22×C15111yescharacteristic
407#388—21no—
408#387—21no—
409#384C22×C15111yescharacteristic
410#380—21no—
411#380C22×C15111yescharacteristic
412#380C22×C15111yescharacteristic
413C4×C22⋊C4—21no—
414C4×C22⋊C4C22×C15111yescharacteristic
415#340C22×C15111yescharacteristic
416#340C22×C15111yescharacteristic
417#340C22×C15111yescharacteristic
418#340C22×C15111yescharacteristic
419#336C22×C15111yescharacteristic
420#336C22×C15111yescharacteristic
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—41no—
426C2×#41—41no—
427C22×Q8C23×C15111yescharacteristic
428C22×Q8C23×C15111yescharacteristic
429C22×D4—21no—
430C22×D4C23×C15111yescharacteristic
431C23×C4—21no—
432C23×C4C23×C15111yescharacteristic
433C2×Q16—22no—
434C2×Q16—22no—
435C2×Q16D4×C15114yes—
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—41no—
439C22×C8C23×C15111yescharacteristic
440C22×C8C23×C15111yescharacteristic
441C22×C8C23×C15111yescharacteristic
442C22×C8C23×C15111yescharacteristic
443C22⋊Q8—22no—
444C22⋊Q8—41no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—41no—
449C4×Q8—41no—
450C4×Q8—41no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
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⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C15111yescharacteristic
471C2×C22⋊C4D4×C15111yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C23×C15111yescharacteristic
476C2×C42C23×C15111yescharacteristic
477#106—22no—
478#106—41no—
479C4⋊C8—41no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—22no—
484#103—41no—
485#102—22no—
486#102—22no—
487#102—41no—
488C22⋊C8—22no—
489C22⋊C8—41no—
490#97—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95D4×C15111yescharacteristic
497#95D4×C15111yescharacteristic
498C24—21no—
499C24C2×D4×C15111yescharacteristic
500#41—44no—
501#41—44no—
502#41—44no—
503#41—44no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8C2×D4×C15112yes—
513C2×Q8C2×D4×C15112yes—
514C2×Q8#41×C15112yes—
515C2×Q8#41×C15112yes—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4#41×C15112yes—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4C2×D4×C15111yescharacteristic
542C22×C4C2×D4×C15111yescharacteristic
543C22×C4C2×D4×C15111yescharacteristic
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C24×C15111yescharacteristic
547Q16—28no—
548SD16—44no—
549C2×C8—21no—
550C2×C8—21no—
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×C8C2×D4×C15112yes—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C22⋊C4—22no—
579C22⋊C4—41no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42—42no—
593C42—42no—
594C23—21no—
595C23—22no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23C22×D4×C15111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8#123×C15114yes—
617D4—22no—
618D4—22no—
619D4—48no—
620D4—41no—
621D4—41no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—48no—
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—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4#137×C15112yes—
663C2×C4C22×D4×C15111yescharacteristic
664C2×C4C2×#41×C15111yescharacteristic
665C2×C4C2×#41×C15111yescharacteristic
666C2×C4C2×#41×C15111yescharacteristic
667C2×C4H(5,𝔽2)×C15111yescharacteristic
668C2×C4H(5,𝔽2)×C15111yescharacteristic
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C22—41no—
674C22—42no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22#525×C15111yescharacteristic
688C22D42×C15111yescharacteristic
689C22#546×C15111yescharacteristic
690C22C2×#137×C15111yescharacteristic
691C22#575×C15111yescharacteristic
692C22#577×C15111yescharacteristic
693C22#577×C15111yescharacteristic
694C4—24no—
695C4—22no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4C2×#123×C15111yescharacteristic
707C4#538×C15111yescharacteristic
708C4#546×C15111yescharacteristic
709C4#551×C15111yescharacteristic
710C2—81no—
711C2—82no—
712C2#2418×C15111yescharacteristic
713C2#3116×C15111yescharacteristic
714C2#3125×C15111yescharacteristic
715C2#3271×C15111yescharacteristic
716C2#3278×C15111yescharacteristic
717C2#3316×C15111yescharacteristic
718C2#3317×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×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
3. #2423×C151C2semidirect
5. #2094×C151C2semidirect
6. #2077×C151C2semidirect
7. #2055×C151C2semidirect
8. #2035×C151C2semidirect
9. #1936×C151C2semidirect
10. #1924×C151C2semidirect
11. #1880×C151C2semidirect
12. #1878×C151C2semidirect
13. #1865×C151C2semidirect
14. #1803×C151C2semidirect
359. #24924C151direct (N × H)
360. C151#24924direct (N × H)
362. C2×#441C2×C151semidirect
363. #2423C2×C151semidirect
365. #2094C2×C151semidirect
366. #2077C2×C151semidirect
367. #2055C2×C151semidirect
368. #2035C2×C151semidirect
369. #1936C2×C151semidirect
370. #1924C2×C151semidirect
371. #1880C2×C151semidirect
372. #1878C2×C151semidirect
373. #1865C2×C151semidirect
374. #1803C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#452×C1512
C2×#441×C1512
#2423×C1512
#2341×C1512
#2094×C1512
#2077×C1512
#2055×C1512
#2035×C1512
#1936×C1512
#1924×C1512
#1880×C1512
#1878×C1512
#1865×C1512
#1803×C1512
#1788×C1512
#24924151