Finite Group Databasebeta

← C151×#25076 #50330001

Subgroups — C151×#25076 #50330001

Order 38656.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C151C211yesmaximal, characteristic, complemented
2C2×#459×C151C211yesmaximal, characteristic, complemented
3C2×#447×C151C211yesmaximal, characteristic, complemented
4C22×#102×C151C211yesmaximal, characteristic, complemented
5#2433×C151C211yesmaximal, characteristic, complemented
6#2361×C151C211yesmaximal, characteristic, complemented
7#2067×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#2041×C151C211yesmaximal, characteristic, complemented
10#2011×C151C211yesmaximal, characteristic, complemented
11#1982×C151C211yesmaximal, characteristic, complemented
12#1925×C151C211yesmaximal, characteristic, complemented
13#1879×C151C211yesmaximal, characteristic, complemented
14#1874×C151C211yesmaximal, characteristic, complemented
15#1850×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic, complemented
20C23×C8×C151C2211yescharacteristic
21C2×#127×C151C2211yescharacteristic
22C2×#127×C151C2211yescharacteristic
23C2×#121×C151C2211yescharacteristic
24C2×#121×C151C2211yescharacteristic
25C2×#120×C151—21no—
26C2×#120×C151—21no—
27C2×C4×D4×C151—21no—
28C2×C4×D4×C151C2211yescharacteristic, complemented
29C22×C4⋊C4×C151C2211yescharacteristic
30#466×C151—24no—
31#459×C151—24no—
32#447×C151—24no—
33C2×#107×C151C2211yescharacteristic, complemented
34C2×C4⋊C8×C151C2211yescharacteristic, complemented
35C2×C4⋊C8×C151C2211yescharacteristic, complemented
36C2×#102×C151—24no—
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic, complemented
44C2×#102×C151C2211yescharacteristic, complemented
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×C22⋊C8×C151C2211yescharacteristic
48#392×C151—21no—
49#392×C151—21no—
50#390×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
52#390×C151C2211yescharacteristic, complemented
53#389×C151C2211yescharacteristic, complemented
54#388×C151—21no—
55#386×C151—21no—
56#385×C151—21no—
57C4×C4⋊C4×C151C2211yescharacteristic, complemented
58C4×C22⋊C4×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61#336×C151C2211yescharacteristic, complemented
62#336×C151C2211yescharacteristic, complemented
63C25×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C22×D4×C151—21no—
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151—21no—
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—22no—
74C22×D4×C151—22no—
75C22×D4×C151—41no—
76C22×D4×C151—41no—
77C22×D4×C151C2311yescharacteristic
78C22×D4×C151C2311yescharacteristic
79C22×D4×C151C2311yescharacteristic
80C22×D4×C151C2311yescharacteristic
81C23×C4×C151—21no—
82C23×C4×C151—21no—
83C23×C4×C151C2311yescharacteristic
84C2×D8×C151—22no—
85C2×D8×C151—22no—
86C2×D8×C151—22no—
87C2×D8×C151—22no—
88C2×D8×C151—22no—
89C2×D8×C151—22no—
90C2×D8×C151—41no—
91C2×D8×C151—41no—
92C2×D8×C151—41no—
93C22×C8×C151—22no—
94C22×C8×C151—22no—
95C22×C8×C151—41no—
96C22×C8×C151C2311yescharacteristic
97C22×C8×C151C2311yescharacteristic
98C22×C8×C151C2311yescharacteristic
99C22×C8×C151C2311yescharacteristic
100#127×C151—22no—
101#127×C151—22no—
102#127×C151—41no—
103#127×C151—41no—
104#121×C151—22no—
105#121×C151—22no—
106#121×C151—22no—
107#121×C151D414yescomplemented
108#120×C151—44no—
109#120×C151—44no—
110C4×D4×C151—22no—
111C4×D4×C151—41no—
112C4×D4×C151—44no—
113C2×C4⋊C4×C151—22no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—41no—
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C4⋊C4×C151C2311yescharacteristic
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×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151D411yescharacteristic
131C2×C22⋊C4×C151D411yescharacteristic
132C2×C42×C151—21no—
133C2×C42×C151C2311yescharacteristic
134C2×C42×C151C2311yescharacteristic
135#107×C151—22no—
136C4⋊C8×C151—22no—
137C4⋊C8×C151—41no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142#102×C151—22no—
143#102×C151—22no—
144#102×C151—22no—
145#102×C151—22no—
146#102×C151—41no—
147#102×C151D414yescomplemented
148C22⋊C8×C151—22no—
149#95×C151—21no—
150#95×C151—21no—
151#95×C151D411yescharacteristic
152#95×C151D411yescharacteristic
153C24×C151—21no—
154C24×C151—21no—
155C24×C151—21no—
156C24×C151—21no—
157C24×C151—42no—
158C24×C151—42no—
159C24×C151—42no—
160C24×C151—42no—
161C24×C151—42no—
162C24×C151—81no—
163C24×C151—81no—
164C24×C151C2×D411yescharacteristic
165C2×D4×C151—28no—
166C2×D4×C151—24no—
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—21no—
178C2×D4×C151—21no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—44no—
189C2×D4×C151—44no—
190C2×D4×C151—42no—
191C2×D4×C151—42no—
192C2×D4×C151—44no—
193C2×D4×C151—42no—
194C2×D4×C151—42no—
195C2×D4×C151—42no—
196C2×D4×C151—42no—
197C2×D4×C151—42no—
198C2×D4×C151—42no—
199C2×D4×C151—42no—
200C2×D4×C151—42no—
201C2×D4×C151—42no—
202C2×D4×C151—42no—
203C2×D4×C151—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—42no—
207C2×D4×C151—81no—
208C2×D4×C151—81no—
209C2×D4×C151—81no—
210C2×D4×C151—81no—
211C2×D4×C151C2×D412yes—
212C2×D4×C151C2×D412yes—
213C2×D4×C151#4112yes—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—42no—
223C22×C4×C151—42no—
224C22×C4×C151—42no—
225C22×C4×C151—42no—
226C22×C4×C151—81no—
227C22×C4×C151—81no—
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D412yes—
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151#4112yes—
235C22×C4×C151C2411yescharacteristic
236D8×C151—44no—
237D8×C151—44no—
238D8×C151—44no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
245C2×C8×C151—21no—
246C2×C8×C151—21no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—44no—
251C2×C8×C151C2×D412yes—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151—21no—
255C4⋊C4×C151—21no—
256C4⋊C4×C151—21no—
257C4⋊C4×C151—21no—
258C4⋊C4×C151—42no—
259C4⋊C4×C151—42no—
260C4⋊C4×C151C2×D412yes—
261C4⋊C4×C151C2×D412yes—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—24no—
264C22⋊C4×C151—42no—
265C22⋊C4×C151—42no—
266C22⋊C4×C151—42no—
267C22⋊C4×C151—42no—
268C22⋊C4×C151—42no—
269C22⋊C4×C151—42no—
270C22⋊C4×C151—42no—
271C22⋊C4×C151—81no—
272C22⋊C4×C151D814yescomplemented
273C42×C151—21no—
274C42×C151—21no—
275C42×C151—21no—
276C42×C151—21no—
277C42×C151—42no—
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—21no—
282C23×C151—22no—
283C23×C151—22no—
284C23×C151—22no—
285C23×C151—48no—
286C23×C151—41no—
287C23×C151—41no—
288C23×C151—41no—
289C23×C151—41no—
290C23×C151—41no—
291C23×C151—41no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151—41no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151—41no—
308C23×C151—41no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—84no—
312C23×C151—84no—
313C23×C151—84no—
314C23×C151—84no—
315C23×C151—84no—
316C23×C151—84no—
317C23×C151#12112yes—
318C23×C151C2×D812yes—
319C23×C151AGL(1,ℤ/8)12yes—
320C23×C151C22×D411yescharacteristic
321D4×C151—22no—
322D4×C151—22no—
323D4×C151—22no—
324D4×C151—22no—
325D4×C151—22no—
326D4×C151—22no—
327D4×C151—48no—
328D4×C151—48no—
329D4×C151—41no—
330D4×C151—41no—
331D4×C151—41no—
332D4×C151—41no—
333D4×C151—41no—
334D4×C151—41no—
335D4×C151—41no—
336D4×C151—41no—
337D4×C151—41no—
338D4×C151—41no—
339D4×C151—84no—
340D4×C151—84no—
341D4×C151—84no—
342D4×C151—84no—
343D4×C151—84no—
344C2×C4×C151—21no—
345C2×C4×C151—21no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—22no—
351C2×C4×C151—22no—
352C2×C4×C151—22no—
353C2×C4×C151—22no—
354C2×C4×C151—22no—
355C2×C4×C151—21no—
356C2×C4×C151—22no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—84no—
373C2×C4×C151—84no—
374C2×C4×C151#12112yes—
375C2×C4×C151C2×D812yes—
376C2×C4×C151C2×D812yes—
377C2×C4×C151C22×D411yescharacteristic
378C2×C4×C151C22×D411yescharacteristic
379C2×C4×C151C2×#4111yescharacteristic
380C2×C4×C151C2×#4111yescharacteristic
381C2×C4×C151H(5,𝔽2)11yescharacteristic
382C2×C4×C151H(5,𝔽2)11yescharacteristic
383C8×C151—22no—
384C8×C151—41no—
385C8×C151—41no—
386C8×C151—41no—
387C22×C151—22no—
388C22×C151—22no—
389C22×C151—22no—
390C22×C151—22no—
391C22×C151—22no—
392C22×C151—22no—
393C22×C151—42no—
394C22×C151—42no—
395C22×C151—42no—
396C22×C151—42no—
397C22×C151—42no—
398C22×C151—42no—
399C22×C151—42no—
400C22×C151—42no—
401C22×C151—42no—
402C22×C151—816no—
403C22×C151—81no—
404C22×C151—81no—
405C22×C151—81no—
406C22×C151—81no—
407C22×C151—81no—
408C22×C151—81no—
409C22×C151—81no—
410C22×C151—81no—
411C22×C151—81no—
412C22×C151—81no—
413C22×C151—81no—
414C22×C151—81no—
415C22×C151—81no—
416C22×C151—81no—
417C22×C151—81no—
418C22×C151—81no—
419C22×C151—81no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151#45914yescomplemented
423C22×C151C2×#12111yescharacteristic
424C22×C151D4211yescharacteristic
425C22×C151#54611yescharacteristic
426C22×C151C22×D811yescharacteristic
427C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C151#57611yescharacteristic
429C22×C151#57711yescharacteristic
430C4×C151—22no—
431C4×C151—22no—
432C4×C151—22no—
433C4×C151—41no—
434C4×C151—42no—
435C4×C151—42no—
436C4×C151—41no—
437C4×C151—81no—
438C4×C151—81no—
439C4×C151#52511yescharacteristic
440C4×C151#53811yescharacteristic
441C4×C151D4211yescharacteristic
442C4×C151#54611yescharacteristic
443C2×C151—24no—
444C2×C151—82no—
445C2×C151—82no—
446C2×C151—82no—
447C2×C151—161no—
448C2×C151#242411yescharacteristic
449C2×C151C2×#45911yescharacteristic
450C2×C151#304511yescharacteristic
451C2×C151#326511yescharacteristic
452C2×C151D4×D811yescharacteristic
453C2×C151#329411yescharacteristic
454C2×C151#331811yescharacteristic
455#25076C15111yesmaximal, characteristic, direct product factor, Sylow
456C151#2507611yescharacteristic, direct product factor, Sylow
457C2×#466C2×C15111yescharacteristic, complemented
458C2×#459C2×C15111yescharacteristic, complemented
459C2×#447C2×C15111yescharacteristic, complemented
460C22×#102C2×C15111yescharacteristic, complemented
461#2433C2×C15111yescharacteristic, complemented
462#2361C2×C15111yescharacteristic, complemented
463#2067C2×C15111yescharacteristic, complemented
464#2054C2×C15111yescharacteristic, complemented
465#2041C2×C15111yescharacteristic, complemented
466#2011C2×C15111yescharacteristic, complemented
467#1982C2×C15111yescharacteristic, complemented
468#1925C2×C15111yescharacteristic, complemented
469#1879C2×C15111yescharacteristic, complemented
470#1874C2×C15111yescharacteristic, complemented
471#1850C2×C15111yescharacteristic, complemented
472C23×D4C22×C15111yescharacteristic
473C22×D8C22×C15111yescharacteristic
474C22×D8C22×C15111yescharacteristic
475C22×D8C22×C15111yescharacteristic, complemented
476C23×C8C22×C15111yescharacteristic
477C2×#127C22×C15111yescharacteristic
478C2×#127C22×C15111yescharacteristic
479C2×#121C22×C15111yescharacteristic
480C2×#121C22×C15111yescharacteristic
481C2×#120—21no—
482C2×#120—21no—
483C2×C4×D4—21no—
484C2×C4×D4C22×C15111yescharacteristic, complemented
485C22×C4⋊C4C22×C15111yescharacteristic
486#466—24no—
487#459—24no—
488#447—24no—
489C2×#107C22×C15111yescharacteristic, complemented
490C2×C4⋊C8C22×C15111yescharacteristic, complemented
491C2×C4⋊C8C22×C15111yescharacteristic, complemented
492C2×#102—24no—
493C2×#102C22×C15111yescharacteristic
494C2×#102C22×C15111yescharacteristic
495C2×#102C22×C15111yescharacteristic
496C2×#102C22×C15111yescharacteristic
497C2×#102C22×C15111yescharacteristic
498C2×#102C22×C15111yescharacteristic
499C2×#102C22×C15111yescharacteristic, complemented
500C2×#102C22×C15111yescharacteristic, complemented
501C2×#102C22×C15111yescharacteristic, complemented
502C2×#102C22×C15111yescharacteristic, complemented
503C2×C22⋊C8C22×C15111yescharacteristic
504#392—21no—
505#392—21no—
506#390C22×C15111yescharacteristic
507#390C22×C15111yescharacteristic
508#390C22×C15111yescharacteristic, complemented
509#389C22×C15111yescharacteristic, complemented
510#388—21no—
511#386—21no—
512#385—21no—
513C4×C4⋊C4C22×C15111yescharacteristic, complemented
514C4×C22⋊C4C22×C15111yescharacteristic
515#340C22×C15111yescharacteristic, complemented
516#340C22×C15111yescharacteristic, complemented
517#336C22×C15111yescharacteristic, complemented
518#336C22×C15111yescharacteristic, complemented
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C15111yescharacteristic
534C22×D4C23×C15111yescharacteristic
535C22×D4C23×C15111yescharacteristic
536C22×D4C23×C15111yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C15111yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C15111yescharacteristic
553C22×C8C23×C15111yescharacteristic
554C22×C8C23×C15111yescharacteristic
555C22×C8C23×C15111yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C15114yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C15111yescharacteristic
574C2×C4⋊C4C23×C15111yescharacteristic
575C2×C4⋊C4C23×C15111yescharacteristic
576C2×C4⋊C4C23×C15111yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C15111yescharacteristic
587C2×C22⋊C4D4×C15111yescharacteristic
588C2×C42—21no—
589C2×C42C23×C15111yescharacteristic
590C2×C42C23×C15111yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C15114yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C15111yescharacteristic
608#95D4×C15111yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C15111yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C15112yes—
668C2×D4C2×D4×C15112yes—
669C2×D4#41×C15112yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C15111yescharacteristic
685C22×C4C2×D4×C15111yescharacteristic
686C22×C4C2×D4×C15111yescharacteristic
687C22×C4C2×D4×C15112yes—
688C22×C4C2×D4×C15111yescharacteristic
689C22×C4C2×D4×C15111yescharacteristic
690C22×C4#41×C15112yes—
691C22×C4C24×C15111yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C15112yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C15112yes—
717C4⋊C4C2×D4×C15112yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C15114yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C15112yes—
774C23C2×D8×C15112yes—
775C23AGL(1,ℤ/8)×C15112yes—
776C23C22×D4×C15111yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C15112yes—
831C2×C4C2×D8×C15112yes—
832C2×C4C2×D8×C15112yes—
833C2×C4C22×D4×C15111yescharacteristic
834C2×C4C22×D4×C15111yescharacteristic
835C2×C4C2×#41×C15111yescharacteristic
836C2×C4C2×#41×C15111yescharacteristic
837C2×C4H(5,𝔽2)×C15111yescharacteristic
838C2×C4H(5,𝔽2)×C15111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22#459×C15114yescomplemented
879C22C2×#121×C15111yescharacteristic
880C22D42×C15111yescharacteristic
881C22#546×C15111yescharacteristic
882C22C22×D8×C15111yescharacteristic
883C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
884C22#576×C15111yescharacteristic
885C22#577×C15111yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4#525×C15111yescharacteristic
896C4#538×C15111yescharacteristic
897C4D42×C15111yescharacteristic
898C4#546×C15111yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2#2424×C15111yescharacteristic
905C2C2×#459×C15111yescharacteristic
906C2#3045×C15111yescharacteristic
907C2#3265×C15111yescharacteristic
908C2D4×D8×C15111yescharacteristic
909C2#3294×C15111yescharacteristic
910C2#3318×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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
1. C2×#466×C151C2semidirect
2. C2×#459×C151C2semidirect
3. C2×#447×C151C2semidirect
4. C22×#102×C151C2semidirect
5. #2433×C151C2semidirect
6. #2361×C151C2semidirect
7. #2067×C151C2semidirect
8. #2054×C151C2semidirect
9. #2041×C151C2semidirect
10. #2011×C151C2semidirect
11. #1982×C151C2semidirect
12. #1925×C151C2semidirect
13. #1879×C151C2semidirect
14. #1874×C151C2semidirect
15. #1850×C151C2semidirect
19. C22×D8×C151C22semidirect
28. C2×C4×D4×C151C22semidirect
33. C2×#107×C151C22semidirect
34. C2×C4⋊C8×C151C22semidirect
35. C2×C4⋊C8×C151C22semidirect
43. C2×#102×C151C22semidirect
44. C2×#102×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
52. #390×C151C22semidirect
53. #389×C151C22semidirect
57. C4×C4⋊C4×C151C22semidirect
59. #340×C151C22semidirect
60. #340×C151C22semidirect
61. #336×C151C22semidirect
62. #336×C151C22semidirect
107. #121×C151D4semidirect
147. #102×C151D4semidirect
272. C22⋊C4×C151D8semidirect
422. C22×C151#459semidirect
455. #25076C151direct (N × H)
456. C151#25076direct (N × H)
457. C2×#466C2×C151semidirect
458. C2×#459C2×C151semidirect
459. C2×#447C2×C151semidirect
460. C22×#102C2×C151semidirect
461. #2433C2×C151semidirect
462. #2361C2×C151semidirect
463. #2067C2×C151semidirect
464. #2054C2×C151semidirect
465. #2041C2×C151semidirect
466. #2011C2×C151semidirect
467. #1982C2×C151semidirect
468. #1925C2×C151semidirect
469. #1879C2×C151semidirect
470. #1874C2×C151semidirect
471. #1850C2×C151semidirect
475. C22×D8C22×C151semidirect
484. C2×C4×D4C22×C151semidirect
489. C2×#107C22×C151semidirect
490. C2×C4⋊C8C22×C151semidirect
491. C2×C4⋊C8C22×C151semidirect
499. C2×#102C22×C151semidirect
500. C2×#102C22×C151semidirect
501. C2×#102C22×C151semidirect
502. C2×#102C22×C151semidirect
508. #390C22×C151semidirect
509. #389C22×C151semidirect
513. C4×C4⋊C4C22×C151semidirect
515. #340C22×C151semidirect
516. #340C22×C151semidirect
517. #336C22×C151semidirect
518. #336C22×C151semidirect
563. #121D4×C151semidirect
603. #102D4×C151semidirect
728. C22⋊C4D8×C151semidirect
878. C22#459×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1512
C2×#459×C1512
C2×#447×C1512
C22×#102×C1512
#2433×C1512
#2361×C1512
#2067×C1512
#2054×C1512
#2041×C1512
#2011×C1512
#1982×C1512
#1925×C1512
#1879×C1512
#1874×C1512
#1850×C1512
#25076151