Finite Group Databasebeta

← C151×#22424 #50327349

Subgroups — C151×#22424 #50327349

Order 38656.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C151C211yesmaximal, characteristic
2C2×#435×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4C2×#416×C151C211yesmaximal, characteristic, complemented
5#2354×C151C211yesmaximal, characteristic, complemented
6#1983×C151C211yesmaximal, characteristic, complemented
7#1959×C151C211yesmaximal, characteristic, complemented
8#1894×C151C211yesmaximal, characteristic, complemented
9#1893×C151C211yesmaximal, characteristic, complemented
10#1875×C151C211yesmaximal, characteristic, complemented
11#1873×C151C211yesmaximal, characteristic, complemented
12#1802×C151C211yesmaximal, characteristic, complemented
13#1788×C151C211yesmaximal, characteristic, complemented
14#1786×C151C211yesmaximal, characteristic, complemented
15#1762×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic, complemented
20#546×C151—24no—
21#546×C151C418yescomplemented
22C2×#124×C151C2211yescharacteristic
23C2×#123×C151—21no—
24C2×C22⋊Q8×C151C2211yescharacteristic
25C2×#121×C151—21no—
26C2×#121×C151C2211yescharacteristic
27C2×#120×C151—21no—
28C2×C4×D4×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C2×#117×C151C2211yescharacteristic
31C2×#117×C151C2211yescharacteristic, complemented
32C22×C22⋊C4×C151—21no—
33#435×C151—24no—
34C2×C4⋊C8×C151C2211yescharacteristic, complemented
35#418×C151—24no—
36#416×C151—24no—
37C2×#103×C151C2211yescharacteristic, complemented
38C2×#103×C151C2211yescharacteristic, complemented
39C2×#103×C151C2211yescharacteristic, complemented
40C2×#103×C151C2211yescharacteristic, complemented
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×C22⋊C8×C151C2211yescharacteristic
50C2×C22⋊C8×C151C2211yescharacteristic, complemented
51C2×#97×C151C2211yescharacteristic, complemented
52#390×C151—21no—
53#388×C151—21no—
54#388×C151—21no—
55#384×C151C2211yescharacteristic, complemented
56#380×C151C2211yescharacteristic
57#380×C151C2211yescharacteristic, complemented
58C4×C4⋊C4×C151—21no—
59C4×C4⋊C4×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64C25×C151—21no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—41no—
69C2×#41×C151—41no—
70C2×#41×C151C2×C414yes—
71C22×Q8×C151C2311yescharacteristic
72C22×D4×C151—21no—
73C22×D4×C151—22no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—41no—
79C22×D4×C151—41no—
80C22×D4×C151C2×C414yes—
81C22×D4×C151D411yescharacteristic
82C22×D4×C151C2311yescharacteristic
83C22×D4×C151C2311yescharacteristic
84C23×C4×C151—21no—
85C23×C4×C151—21no—
86C23×C4×C151C2311yescharacteristic
87C23×C4×C151C2311yescharacteristic
88C2×M16×C151—22no—
89C2×M16×C151—22no—
90C2×M16×C151—41no—
91C22×C8×C151—22no—
92C22×C8×C151—22no—
93C22×C8×C151—41no—
94C22×C8×C151C2311yescharacteristic
95C22×C8×C151C2311yescharacteristic
96C22×C8×C151C2311yescharacteristic
97C22×C8×C151C2311yescharacteristic
98#124×C151—22no—
99#124×C151C2×C414yes—
100#123×C151—28no—
101C22⋊Q8×C151—22no—
102C22⋊Q8×C151C2×C414yes—
103#121×C151—22no—
104#121×C151—28no—
105#121×C151C2×C414yes—
106#120×C151—28no—
107C4×D4×C151—22no—
108C4×D4×C151C2×C414yes—
109C4×D4×C151C2×C414yes—
110C4×D4×C151D414yes—
111#117×C151—22no—
112#117×C151—22no—
113#117×C151—41no—
114#117×C151—41no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151D411yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C4⋊C4×C151C2311yescharacteristic
121C2×C4⋊C4×C151C2311yescharacteristic
122C2×C4⋊C4×C151C2311yescharacteristic
123C2×C4⋊C4×C151C2311yescharacteristic
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—28no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151D411yescharacteristic
135C2×C22⋊C4×C151D411yescharacteristic
136C2×C42×C151—21no—
137C2×C42×C151—21no—
138C2×C42×C151—21no—
139C2×C42×C151C2311yescharacteristic
140C4⋊C8×C151—22no—
141#103×C151—22no—
142#103×C151—22no—
143#103×C151—41no—
144#103×C151—41no—
145#102×C151—22no—
146#102×C151—22no—
147#102×C151—22no—
148#102×C151—22no—
149#102×C151—22no—
150#102×C151—41no—
151#102×C151—41no—
152#102×C151D414yescomplemented
153C22⋊C8×C151—22no—
154C22⋊C8×C151—22no—
155#97×C151—22no—
156#95×C151—21no—
157#95×C151—21no—
158#95×C151—21no—
159C24×C151—21no—
160C24×C151—21no—
161C24×C151—24no—
162C24×C151—42no—
163C24×C151—42no—
164C24×C151—42no—
165C24×C151—42no—
166C24×C151—81no—
167C24×C151—81no—
168C24×C151C2×D411yescharacteristic
169C24×C151C2×D411yescharacteristic
170#41×C151—28no—
171#41×C151—44no—
172#41×C151—44no—
173#41×C151—44no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151C22×C412yes—
180C2×D4×C151—28no—
181C2×D4×C151—24no—
182C2×D4×C151—24no—
183C2×D4×C151—24no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—44no—
193C2×D4×C151—44no—
194C2×D4×C151—44no—
195C2×D4×C151—41no—
196C2×D4×C151—41no—
197C2×D4×C151—42no—
198C2×D4×C151—42no—
199C2×D4×C151—42no—
200C2×D4×C151—42no—
201C2×D4×C151—81no—
202C2×D4×C151—81no—
203C2×D4×C151C22⋊C414yes—
204C2×D4×C151C22×C412yes—
205C2×D4×C151C22×C412yes—
206C2×D4×C151C2×D412yes—
207C2×D4×C151#4112yes—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—24no—
220C22×C4×C151—24no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—42no—
225C22×C4×C151—42no—
226C22×C4×C151—81no—
227C22×C4×C151—81no—
228C22×C4×C151C22×C412yes—
229C22×C4×C151C22×C412yes—
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D411yescharacteristic
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2×D412yes—
235C22×C4×C151C2×D412yes—
236C22×C4×C151C2411yescharacteristic
237M16×C151—44no—
238C2×C8×C151—21no—
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—44no—
250C2×C8×C151C2×D412yes—
251C4⋊C4×C151—24no—
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—21no—
259C4⋊C4×C151—21no—
260C4⋊C4×C151—42no—
261C4⋊C4×C151—81no—
262C4⋊C4×C151C22⋊C414yes—
263C4⋊C4×C151C22×C412yes—
264C4⋊C4×C151C2×D412yes—
265C22⋊C4×C151—24no—
266C22⋊C4×C151—24no—
267C22⋊C4×C151—24no—
268C22⋊C4×C151—24no—
269C22⋊C4×C151—24no—
270C22⋊C4×C151—42no—
271C22⋊C4×C151—42no—
272C22⋊C4×C151—81no—
273C22⋊C4×C151—81no—
274C22⋊C4×C151C22⋊C414yes—
275C22⋊C4×C151C22⋊C414yes—
276C42×C151—42no—
277C42×C151—42no—
278C42×C151—42no—
279C42×C151C22×C412yes—
280C42×C151C2×D412yes—
281C23×C151—22no—
282C23×C151—22no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—22no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—22no—
297C23×C151—48no—
298C23×C151—48no—
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—84no—
310C23×C151—84no—
311C23×C151—84no—
312C23×C151—84no—
313C23×C151—84no—
314C23×C151C2×C22⋊C412yes—
315C23×C151C2×C22⋊C412yes—
316C23×C151C22×D411yescharacteristic
317Q8×C151—22no—
318Q8×C151—22no—
319Q8×C151—41no—
320Q8×C151—41no—
321D4×C151—22no—
322D4×C151—22no—
323D4×C151—22no—
324D4×C151—22no—
325D4×C151—22no—
326D4×C151—44no—
327D4×C151—48no—
328D4×C151—48no—
329D4×C151—41no—
330D4×C151—41no—
331D4×C151—84no—
332D4×C151C4×D414yes—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—22no—
342C2×C4×C151—22no—
343C2×C4×C151—22no—
344C2×C4×C151—22no—
345C2×C4×C151—22no—
346C2×C4×C151—22no—
347C2×C4×C151—22no—
348C2×C4×C151—22no—
349C2×C4×C151—22no—
350C2×C4×C151—22no—
351C2×C4×C151—22no—
352C2×C4×C151—48no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
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—84no—
369C2×C4×C151C2×C22⋊C412yes—
370C2×C4×C151C2×C22⋊C412yes—
371C2×C4×C151C2×C22⋊C412yes—
372C2×C4×C151C2×C22⋊C412yes—
373C2×C4×C151C23×C411yescharacteristic
374C2×C4×C151C22×D411yescharacteristic
375C2×C4×C151C22×D411yescharacteristic
376C2×C4×C151C2×#4111yescharacteristic
377C2×C4×C151H(5,𝔽2)11yescharacteristic
378C2×C4×C151H(5,𝔽2)11yescharacteristic
379C8×C151—22no—
380C8×C151—41no—
381C8×C151—41no—
382C8×C151—41no—
383C22×C151—22no—
384C22×C151—22no—
385C22×C151—24no—
386C22×C151—22no—
387C22×C151—22no—
388C22×C151—22no—
389C22×C151—22no—
390C22×C151—42no—
391C22×C151—42no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—42no—
395C22×C151—41no—
396C22×C151—41no—
397C22×C151—42no—
398C22×C151—41no—
399C22×C151—41no—
400C22×C151—42no—
401C22×C151—41no—
402C22×C151—41no—
403C22×C151—42no—
404C22×C151—42no—
405C22×C151—42no—
406C22×C151—42no—
407C22×C151—816no—
408C22×C151—81no—
409C22×C151—81no—
410C22×C151—81no—
411C22×C151—81no—
412C22×C151C22×C22⋊C411yescharacteristic
413C22×C151D4211yescharacteristic
414C22×C151#54611yescharacteristic
415C22×C151#57511yescharacteristic
416C22×C151#57511yescharacteristic
417C22×C151#57611yescharacteristic
418C22×C151#57711yescharacteristic
419C4×C151—22no—
420C4×C151—22no—
421C4×C151—22no—
422C4×C151—22no—
423C4×C151—42no—
424C4×C151—42no—
425C4×C151—42no—
426C4×C151—81no—
427C4×C151—81no—
428C4×C151—81no—
429C4×C151C2×C4×D411yescharacteristic
430C4×C151#51811yescharacteristic
431C4×C151D4211yescharacteristic
432C4×C151#54611yescharacteristic
433C2×C151—42no—
434C2×C151—42no—
435C2×C151—44no—
436C2×C151—82no—
437C2×C151D4×C22⋊C411yescharacteristic
438C2×C151#289611yescharacteristic
439C2×C151#289711yescharacteristic
440C2×C151#326711yescharacteristic
441C2×C151#326811yescharacteristic
442C2×C151#331111yescharacteristic
443C2×C151#331911yescharacteristic
444#22424C15111yesmaximal, characteristic, direct product factor, Sylow
445C151#2242411yescharacteristic, direct product factor, Sylow
446C2×#546C2×C15111yescharacteristic
447C2×#435C2×C15111yescharacteristic, complemented
448C2×#418C2×C15111yescharacteristic, complemented
449C2×#416C2×C15111yescharacteristic, complemented
450#2354C2×C15111yescharacteristic, complemented
451#1983C2×C15111yescharacteristic, complemented
452#1959C2×C15111yescharacteristic, complemented
453#1894C2×C15111yescharacteristic, complemented
454#1893C2×C15111yescharacteristic, complemented
455#1875C2×C15111yescharacteristic, complemented
456#1873C2×C15111yescharacteristic, complemented
457#1802C2×C15111yescharacteristic, complemented
458#1788C2×C15111yescharacteristic, complemented
459#1786C2×C15111yescharacteristic, complemented
460#1762C2×C15111yescharacteristic, complemented
461C22×#41C22×C15111yescharacteristic
462C23×D4C22×C15111yescharacteristic
463C22×M16C22×C15111yescharacteristic
464C23×C8C22×C15111yescharacteristic, complemented
465#546—24no—
466#546C4×C15118yescomplemented
467C2×#124C22×C15111yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C22×C15111yescharacteristic
470C2×#121—21no—
471C2×#121C22×C15111yescharacteristic
472C2×#120—21no—
473C2×C4×D4C22×C15111yescharacteristic
474C2×C4×D4C22×C15111yescharacteristic
475C2×#117C22×C15111yescharacteristic
476C2×#117C22×C15111yescharacteristic, complemented
477C22×C22⋊C4—21no—
478#435—24no—
479C2×C4⋊C8C22×C15111yescharacteristic, complemented
480#418—24no—
481#416—24no—
482C2×#103C22×C15111yescharacteristic, complemented
483C2×#103C22×C15111yescharacteristic, complemented
484C2×#103C22×C15111yescharacteristic, complemented
485C2×#103C22×C15111yescharacteristic, complemented
486C2×#102C22×C15111yescharacteristic
487C2×#102C22×C15111yescharacteristic
488C2×#102C22×C15111yescharacteristic
489C2×#102C22×C15111yescharacteristic
490C2×#102C22×C15111yescharacteristic
491C2×#102C22×C15111yescharacteristic
492C2×#102C22×C15111yescharacteristic
493C2×#102C22×C15111yescharacteristic
494C2×C22⋊C8C22×C15111yescharacteristic
495C2×C22⋊C8C22×C15111yescharacteristic, complemented
496C2×#97C22×C15111yescharacteristic, complemented
497#390—21no—
498#388—21no—
499#388—21no—
500#384C22×C15111yescharacteristic, complemented
501#380C22×C15111yescharacteristic
502#380C22×C15111yescharacteristic, complemented
503C4×C4⋊C4—21no—
504C4×C4⋊C4C22×C15111yescharacteristic, complemented
505#340C22×C15111yescharacteristic, complemented
506#340C22×C15111yescharacteristic, complemented
507#340C22×C15111yescharacteristic, complemented
508#340C22×C15111yescharacteristic, complemented
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C15114yes—
516C22×Q8C23×C15111yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C15114yes—
526C22×D4D4×C15111yescharacteristic
527C22×D4C23×C15111yescharacteristic
528C22×D4C23×C15111yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C15111yescharacteristic
532C23×C4C23×C15111yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C23×C15111yescharacteristic
540C22×C8C23×C15111yescharacteristic
541C22×C8C23×C15111yescharacteristic
542C22×C8C23×C15111yescharacteristic
543#124—22no—
544#124C2×C4×C15114yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×C4×C15114yes—
548#121—22no—
549#121—28no—
550#121C2×C4×C15114yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×C4×C15114yes—
554C4×D4C2×C4×C15114yes—
555C4×D4D4×C15114yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C15111yescharacteristic
564C2×C4⋊C4C23×C15111yescharacteristic
565C2×C4⋊C4C23×C15111yescharacteristic
566C2×C4⋊C4C23×C15111yescharacteristic
567C2×C4⋊C4C23×C15111yescharacteristic
568C2×C4⋊C4C23×C15111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C15111yescharacteristic
580C2×C22⋊C4D4×C15111yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C15111yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103—41no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102—41no—
597#102D4×C15114yescomplemented
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C15111yescharacteristic
614C24C2×D4×C15111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C15112yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
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—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C15114yes—
649C2×D4C22×C4×C15112yes—
650C2×D4C22×C4×C15112yes—
651C2×D4C2×D4×C15112yes—
652C2×D4#41×C15112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C15112yes—
674C22×C4C22×C4×C15112yes—
675C22×C4C2×D4×C15111yescharacteristic
676C22×C4C2×D4×C15111yescharacteristic
677C22×C4C2×D4×C15111yescharacteristic
678C22×C4C2×D4×C15111yescharacteristic
679C22×C4C2×D4×C15112yes—
680C22×C4C2×D4×C15112yes—
681C22×C4C24×C15111yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C15112yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C15114yes—
708C4⋊C4C22×C4×C15112yes—
709C4⋊C4C2×D4×C15112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C15114yes—
720C22⋊C4C22⋊C4×C15114yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C15112yes—
725C42C2×D4×C15112yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C15112yes—
760C23C2×C22⋊C4×C15112yes—
761C23C22×D4×C15111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C15114yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4C2×C22⋊C4×C15112yes—
815C2×C4C2×C22⋊C4×C15112yes—
816C2×C4C2×C22⋊C4×C15112yes—
817C2×C4C2×C22⋊C4×C15112yes—
818C2×C4C23×C4×C15111yescharacteristic
819C2×C4C22×D4×C15111yescharacteristic
820C2×C4C22×D4×C15111yescharacteristic
821C2×C4C2×#41×C15111yescharacteristic
822C2×C4H(5,𝔽2)×C15111yescharacteristic
823C2×C4H(5,𝔽2)×C15111yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C15111yescharacteristic
858C22D42×C15111yescharacteristic
859C22#546×C15111yescharacteristic
860C22#575×C15111yescharacteristic
861C22#575×C15111yescharacteristic
862C22#576×C15111yescharacteristic
863C22#577×C15111yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C15111yescharacteristic
875C4#518×C15111yescharacteristic
876C4D42×C15111yescharacteristic
877C4#546×C15111yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C15111yescharacteristic
883C2#2896×C15111yescharacteristic
884C2#2897×C15111yescharacteristic
885C2#3267×C15111yescharacteristic
886C2#3268×C15111yescharacteristic
887C2#3311×C15111yescharacteristic
888C2#3319×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#546×C151C2
LCSG ▷ C2×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×#435×C151C2semidirect
3. C2×#418×C151C2semidirect
4. C2×#416×C151C2semidirect
5. #2354×C151C2semidirect
6. #1983×C151C2semidirect
7. #1959×C151C2semidirect
8. #1894×C151C2semidirect
9. #1893×C151C2semidirect
10. #1875×C151C2semidirect
11. #1873×C151C2semidirect
12. #1802×C151C2semidirect
13. #1788×C151C2semidirect
14. #1786×C151C2semidirect
15. #1762×C151C2semidirect
19. C23×C8×C151C22semidirect
21. #546×C151C4semidirect
31. C2×#117×C151C22semidirect
34. C2×C4⋊C8×C151C22semidirect
37. C2×#103×C151C22semidirect
38. C2×#103×C151C22semidirect
39. C2×#103×C151C22semidirect
40. C2×#103×C151C22semidirect
50. C2×C22⋊C8×C151C22semidirect
51. C2×#97×C151C22semidirect
55. #384×C151C22semidirect
57. #380×C151C22semidirect
59. C4×C4⋊C4×C151C22semidirect
60. #340×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #340×C151C22semidirect
152. #102×C151D4semidirect
444. #22424C151direct (N × H)
445. C151#22424direct (N × H)
447. C2×#435C2×C151semidirect
448. C2×#418C2×C151semidirect
449. C2×#416C2×C151semidirect
450. #2354C2×C151semidirect
451. #1983C2×C151semidirect
452. #1959C2×C151semidirect
453. #1894C2×C151semidirect
454. #1893C2×C151semidirect
455. #1875C2×C151semidirect
456. #1873C2×C151semidirect
457. #1802C2×C151semidirect
458. #1788C2×C151semidirect
459. #1786C2×C151semidirect
460. #1762C2×C151semidirect
464. C23×C8C22×C151semidirect
466. #546C4×C151semidirect
476. C2×#117C22×C151semidirect
479. C2×C4⋊C8C22×C151semidirect
482. C2×#103C22×C151semidirect
483. C2×#103C22×C151semidirect
484. C2×#103C22×C151semidirect
485. C2×#103C22×C151semidirect
495. C2×C22⋊C8C22×C151semidirect
496. C2×#97C22×C151semidirect
500. #384C22×C151semidirect
502. #380C22×C151semidirect
504. C4×C4⋊C4C22×C151semidirect
505. #340C22×C151semidirect
506. #340C22×C151semidirect
507. #340C22×C151semidirect
508. #340C22×C151semidirect
597. #102D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1512
C2×#435×C1512
C2×#418×C1512
C2×#416×C1512
#2354×C1512
#1983×C1512
#1959×C1512
#1894×C1512
#1893×C1512
#1875×C1512
#1873×C1512
#1802×C1512
#1788×C1512
#1786×C1512
#1762×C1512
#22424151