Finite Group Databasebeta

← C151×#24109 #50329034

Subgroups — C151×#24109 #50329034

Order 38656.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2C2×#485×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2485×C151C211yesmaximal, characteristic
5#2058×C151C211yesmaximal, characteristic, complemented
6#2057×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2035×C151C211yesmaximal, characteristic, complemented
9#1894×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic
11#1865×C151C211yesmaximal, characteristic, complemented
12#1863×C151C211yesmaximal, characteristic, complemented
13#1853×C151C211yesmaximal, characteristic, complemented
14#1852×C151C211yesmaximal, characteristic, complemented
15#1823×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17#554×C151—24no—
18#554×C151—24no—
19C2×C4⋊Q8×C151C2211yescharacteristic
20C2×#125×C151—21no—
21C2×C22⋊Q8×C151—21no—
22C2×C22⋊Q8×C151—21no—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×C22⋊Q8×C151C2211yescharacteristic
25C2×C4×Q8×C151C2211yescharacteristic
26C2×C4×D4×C151—21no—
27C2×C4×D4×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C22×C4⋊C4×C151C2211yescharacteristic
30C22×C4⋊C4×C151C2211yescharacteristic
31#485×C151—24no—
32#428×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#107×C151C2211yescharacteristic
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×#106×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46#397×C151—21no—
47#394×C151—21no—
48#389×C151C2211yescharacteristic
49#389×C151C2211yescharacteristic
50#388×C151—21no—
51#387×C151—21no—
52#380×C151C2211yescharacteristic
53#380×C151C2211yescharacteristic
54#380×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151—21no—
64C22×Q8×C151C2311yescharacteristic
65C22×D4×C151D411yescharacteristic
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C2×M16×C151—22no—
71C2×M16×C151—22no—
72C2×M16×C151—22no—
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C4⋊Q8×C151—22no—
78C4⋊Q8×C151—22no—
79#125×C151—28no—
80C22⋊Q8×C151—28no—
81C22⋊Q8×C151—28no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151D414yes—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C4×D4×C151—28no—
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91#117×C151—22no—
92#117×C151—22no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—22no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—22no—
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151D411yescharacteristic
105C2×C4⋊C4×C151D414yes—
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151D411yescharacteristic
120C2×C22⋊C4×C151D411yescharacteristic
121C2×C42×C151—21no—
122C2×C42×C151—21no—
123C2×C42×C151C2311yescharacteristic
124#107×C151—22no—
125#107×C151—22no—
126#107×C151—22no—
127#106×C151—22no—
128#106×C151—22no—
129#106×C151—22no—
130#103×C151—22no—
131#103×C151—22no—
132#103×C151—22no—
133#103×C151—22no—
134C22⋊C8×C151—22no—
135C22⋊C8×C151—22no—
136C22⋊C8×C151—22no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151—21no—
142C24×C151C2×D411yescharacteristic
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—81no—
151C2×Q8×C151—81no—
152C2×Q8×C151C2×D412yes—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—22no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—24no—
165C22×C4×C151—24no—
166C22×C4×C151—21no—
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—81no—
177C22×C4×C151—81no—
178C22×C4×C151—81no—
179C22×C4×C151—81no—
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D412yes—
184C22×C4×C151C2×D412yes—
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2411yescharacteristic
187M16×C151—28no—
188C2×C8×C151—21no—
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#4112yes—
199C2×C8×C151#4112yes—
200C4⋊C4×C151—24no—
201C4⋊C4×C151—24no—
202C4⋊C4×C151—24no—
203C4⋊C4×C151—24no—
204C4⋊C4×C151—24no—
205C4⋊C4×C151—24no—
206C4⋊C4×C151—22no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
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—42no—
219C4⋊C4×C151—81no—
220C4⋊C4×C151C2×D412yes—
221C4⋊C4×C151C2×D412yes—
222C4⋊C4×C151C2×D412yes—
223C22⋊C4×C151—24no—
224C22⋊C4×C151—24no—
225C22⋊C4×C151—22no—
226C22⋊C4×C151—22no—
227C22⋊C4×C151—42no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—81no—
230C22⋊C4×C151—81no—
231C42×C151—24no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—42no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151#12012yes—
248C23×C151#13712yes—
249C23×C151C22×D411yescharacteristic
250Q8×C151—22no—
251Q8×C151—22no—
252Q8×C151—41no—
253Q8×C151—41no—
254Q8×C151—84no—
255D4×C151—28no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—22no—
261C2×C4×C151—22no—
262C2×C4×C151—22no—
263C2×C4×C151—22no—
264C2×C4×C151—21no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
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—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
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—84no—
299C2×C4×C151—84no—
300C2×C4×C151#12012yes—
301C2×C4×C151#13712yes—
302C2×C4×C151C22×D411yescharacteristic
303C2×C4×C151C22×D411yescharacteristic
304C2×C4×C151C2×#4111yescharacteristic
305C2×C4×C151C2×#4111yescharacteristic
306C2×C4×C1512−1+411yescharacteristic
307C2×C4×C1512−1+411yescharacteristic
308C8×C151—22no—
309C8×C151—22no—
310C8×C151—41no—
311C8×C151—41no—
312C22×C151—22no—
313C22×C151—22no—
314C22×C151—22no—
315C22×C151—22no—
316C22×C151—22no—
317C22×C151—22no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—41no—
323C22×C151—41no—
324C22×C151—41no—
325C22×C151—41no—
326C22×C151C2×#12011yescharacteristic
327C22×C151#54711yescharacteristic
328C22×C151#54711yescharacteristic
329C22×C151C2×#13711yescharacteristic
330C22×C151C2×#13711yescharacteristic
331C22×C151#57611yescharacteristic
332C22×C151#57711yescharacteristic
333C4×C151—22no—
334C4×C151—22no—
335C4×C151—41no—
336C4×C151—42no—
337C4×C151—41no—
338C4×C151—42no—
339C4×C151—42no—
340C4×C151—42no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151—81no—
344C4×C151—81no—
345C4×C151#52511yescharacteristic
346C4×C151#53611yescharacteristic
347C4×C151#54711yescharacteristic
348C4×C151#54711yescharacteristic
349C2×C151—42no—
350C2×C151—42no—
351C2×C151#240611yescharacteristic
352C2×C151#300411yescharacteristic
353C2×C151#301211yescharacteristic
354C2×C151#334411yescharacteristic
355C2×C151#334611yescharacteristic
356C2×C151#335611yescharacteristic
357C2×C151#335711yescharacteristic
358#24109C15111yesmaximal, characteristic, direct product factor, Sylow
359C151#2410911yescharacteristic, direct product factor, Sylow
360C2×#554C2×C15111yescharacteristic
361C2×#485C2×C15111yescharacteristic, complemented
362C2×#428C2×C15111yescharacteristic, complemented
363#2485C2×C15111yescharacteristic
364#2058C2×C15111yescharacteristic, complemented
365#2057C2×C15111yescharacteristic, complemented
366#2036C2×C15111yescharacteristic, complemented
367#2035C2×C15111yescharacteristic, complemented
368#1894C2×C15111yescharacteristic, complemented
369#1870C2×C15111yescharacteristic
370#1865C2×C15111yescharacteristic, complemented
371#1863C2×C15111yescharacteristic, complemented
372#1853C2×C15111yescharacteristic, complemented
373#1852C2×C15111yescharacteristic, complemented
374#1823C2×C15111yescharacteristic, complemented
375C22×M16C22×C15111yescharacteristic
376#554—24no—
377#554—24no—
378C2×C4⋊Q8C22×C15111yescharacteristic
379C2×#125—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8C22×C15111yescharacteristic
383C2×C22⋊Q8C22×C15111yescharacteristic
384C2×C4×Q8C22×C15111yescharacteristic
385C2×C4×D4—21no—
386C2×C4×D4C22×C15111yescharacteristic
387C2×#117C22×C15111yescharacteristic
388C22×C4⋊C4C22×C15111yescharacteristic
389C22×C4⋊C4C22×C15111yescharacteristic
390#485—24no—
391#428—24no—
392C2×#107C22×C15111yescharacteristic
393C2×#107C22×C15111yescharacteristic
394C2×#107C22×C15111yescharacteristic
395C2×#106C22×C15111yescharacteristic
396C2×#106C22×C15111yescharacteristic
397C2×#106C22×C15111yescharacteristic
398C2×#103C22×C15111yescharacteristic
399C2×#103C22×C15111yescharacteristic
400C2×#103C22×C15111yescharacteristic
401C2×#103C22×C15111yescharacteristic
402C2×C22⋊C8C22×C15111yescharacteristic
403C2×C22⋊C8C22×C15111yescharacteristic
404C2×C22⋊C8C22×C15111yescharacteristic
405#397—21no—
406#394—21no—
407#389C22×C15111yescharacteristic
408#389C22×C15111yescharacteristic
409#388—21no—
410#387—21no—
411#380C22×C15111yescharacteristic
412#380C22×C15111yescharacteristic
413#380C22×C15111yescharacteristic
414#340C22×C15111yescharacteristic
415#340C22×C15111yescharacteristic
416#340C22×C15111yescharacteristic
417#340C22×C15111yescharacteristic
418#340C22×C15111yescharacteristic
419#340C22×C15111yescharacteristic
420#336C22×C15111yescharacteristic
421#336C22×C15111yescharacteristic
422C22×Q8—21no—
423C22×Q8C23×C15111yescharacteristic
424C22×D4D4×C15111yescharacteristic
425C23×C4—21no—
426C23×C4—21no—
427C23×C4C23×C15111yescharacteristic
428C23×C4C23×C15111yescharacteristic
429C2×M16—22no—
430C2×M16—22no—
431C2×M16—22no—
432C22×C8C23×C15111yescharacteristic
433C22×C8C23×C15111yescharacteristic
434C22×C8C23×C15111yescharacteristic
435C22×C8C23×C15111yescharacteristic
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438#125—28no—
439C22⋊Q8—28no—
440C22⋊Q8—28no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8D4×C15114yes—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×D4—28no—
448C4×D4—22no—
449C4×D4—22no—
450#117—22no—
451#117—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C15111yescharacteristic
464C2×C4⋊C4D4×C15114yes—
465C2×C4⋊C4C23×C15111yescharacteristic
466C2×C4⋊C4C23×C15111yescharacteristic
467C2×C4⋊C4C23×C15111yescharacteristic
468C2×C4⋊C4C23×C15111yescharacteristic
469C2×C4⋊C4C23×C15111yescharacteristic
470C2×C4⋊C4C23×C15111yescharacteristic
471C2×C4⋊C4C23×C15111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4D4×C15111yescharacteristic
479C2×C22⋊C4D4×C15111yescharacteristic
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C23×C15111yescharacteristic
483#107—22no—
484#107—22no—
485#107—22no—
486#106—22no—
487#106—22no—
488#106—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501C24C2×D4×C15111yescharacteristic
502C24C2×D4×C15111yescharacteristic
503C2×Q8—24no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—81no—
510C2×Q8—81no—
511C2×Q8C2×D4×C15112yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
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—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4C2×D4×C15111yescharacteristic
540C22×C4C2×D4×C15111yescharacteristic
541C22×C4C2×D4×C15111yescharacteristic
542C22×C4C2×D4×C15112yes—
543C22×C4C2×D4×C15112yes—
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C24×C15111yescharacteristic
546M16—28no—
547C2×C8—21no—
548C2×C8—21no—
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#41×C15112yes—
558C2×C8#41×C15112yes—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4C2×D4×C15112yes—
580C4⋊C4C2×D4×C15112yes—
581C4⋊C4C2×D4×C15112yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—24no—
591C42—21no—
592C42—21no—
593C42—42no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23#120×C15112yes—
607C23#137×C15112yes—
608C23C22×D4×C15111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613Q8—84no—
614D4—28no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
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—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4#120×C15112yes—
660C2×C4#137×C15112yes—
661C2×C4C22×D4×C15111yescharacteristic
662C2×C4C22×D4×C15111yescharacteristic
663C2×C4C2×#41×C15111yescharacteristic
664C2×C4C2×#41×C15111yescharacteristic
665C2×C42−1+4×C15111yescharacteristic
666C2×C42−1+4×C15111yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22C2×#120×C15111yescharacteristic
686C22#547×C15111yescharacteristic
687C22#547×C15111yescharacteristic
688C22C2×#137×C15111yescharacteristic
689C22C2×#137×C15111yescharacteristic
690C22#576×C15111yescharacteristic
691C22#577×C15111yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4#525×C15111yescharacteristic
705C4#536×C15111yescharacteristic
706C4#547×C15111yescharacteristic
707C4#547×C15111yescharacteristic
708C2—42no—
709C2—42no—
710C2#2406×C15111yescharacteristic
711C2#3004×C15111yescharacteristic
712C2#3012×C15111yescharacteristic
713C2#3344×C15111yescharacteristic
714C2#3346×C15111yescharacteristic
715C2#3356×C15111yescharacteristic
716C2#3357×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C151C2semidirect
3. C2×#428×C151C2semidirect
5. #2058×C151C2semidirect
6. #2057×C151C2semidirect
7. #2036×C151C2semidirect
8. #2035×C151C2semidirect
9. #1894×C151C2semidirect
11. #1865×C151C2semidirect
12. #1863×C151C2semidirect
13. #1853×C151C2semidirect
14. #1852×C151C2semidirect
15. #1823×C151C2semidirect
358. #24109C151direct (N × H)
359. C151#24109direct (N × H)
361. C2×#485C2×C151semidirect
362. C2×#428C2×C151semidirect
364. #2058C2×C151semidirect
365. #2057C2×C151semidirect
366. #2036C2×C151semidirect
367. #2035C2×C151semidirect
368. #1894C2×C151semidirect
370. #1865C2×C151semidirect
371. #1863C2×C151semidirect
372. #1853C2×C151semidirect
373. #1852C2×C151semidirect
374. #1823C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#485×C1512
C2×#428×C1512
#2485×C1512
#2058×C1512
#2057×C1512
#2036×C1512
#2035×C1512
#1894×C1512
#1870×C1512
#1865×C1512
#1863×C1512
#1853×C1512
#1852×C1512
#1823×C1512
#24109151