Finite Group Databasebeta

← C151×#22036 #50326961

Subgroups — C151×#22036 #50326961

Order 38656.

1162 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C151C211yesmaximal, characteristic, complemented
2C2×#407×C151C211yesmaximal, characteristic, complemented
3C4×#120×C151C211yesmaximal, characteristic
4#1955×C151C211yesmaximal, characteristic, complemented
5#1954×C151C211yesmaximal, characteristic, complemented
6#1924×C151C211yesmaximal, characteristic, complemented
7#1924×C151C211yesmaximal, characteristic, complemented
8#1924×C151C211yesmaximal, characteristic, complemented
9#1923×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1869×C151C211yesmaximal, characteristic, complemented
13#1851×C151C211yesmaximal, characteristic, complemented
14#1779×C151C211yesmaximal, characteristic, complemented
15#1753×C151C211yesmaximal, characteristic, complemented
16C24×C4×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic, complemented
20C2×#120×C151C411yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24#435×C151—24no—
25C2×C4⋊C8×C151C2211yescharacteristic, complemented
26C2×C4⋊C8×C151C2211yescharacteristic, complemented
27C2×C4⋊C8×C151C2211yescharacteristic, complemented
28#407×C151—24no—
29C2×C22⋊C8×C151C2211yescharacteristic
30C2×C22⋊C8×C151C2211yescharacteristic
31C2×C22⋊C8×C151C2211yescharacteristic
32C2×C22⋊C8×C151C2211yescharacteristic
33C2×C22⋊C8×C151C2211yescharacteristic
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic, complemented
40C2×C22⋊C8×C151C2211yescharacteristic, complemented
41C2×C22⋊C8×C151C2211yescharacteristic, complemented
42C2×#97×C151C2211yescharacteristic, complemented
43C2×#97×C151C2211yescharacteristic, complemented
44C2×C4×C8×C151C2211yescharacteristic, complemented
45#386×C151C411yescharacteristic
46#386×C151C411yescharacteristic
47#386×C151C411yescharacteristic
48#385×C151C411yescharacteristic
49#385×C151C411yescharacteristic
50#385×C151C411yescharacteristic
51#379×C151C411yescharacteristic
52C4×C22⋊C4×C151C2211yescharacteristic
53C4×C22⋊C4×C151C2211yescharacteristic
54C4×C22⋊C4×C151C2211yescharacteristic
55#336×C151C2211yescharacteristic, complemented
56#336×C151C2211yescharacteristic, complemented
57#336×C151C2211yescharacteristic, complemented
58#336×C151C2211yescharacteristic, complemented
59#336×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61C25×C151C2×C411yescharacteristic
62C22×D4×C151C2×C411yescharacteristic
63C22×D4×C151C2×C411yescharacteristic
64C22×D4×C151C2×C411yescharacteristic
65C23×C4×C151—22no—
66C23×C4×C151—22no—
67C23×C4×C151—41no—
68C23×C4×C151—41no—
69C23×C4×C151—41no—
70C23×C4×C151—41no—
71C23×C4×C151C2×C411yescharacteristic
72C23×C4×C151C2×C411yescharacteristic
73C23×C4×C151C2×C411yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C23×C4×C151C2311yescharacteristic
77C23×C4×C151C2311yescharacteristic
78C2×M16×C151—22no—
79C2×M16×C151—41no—
80C2×M16×C151—41no—
81C2×M16×C151—41no—
82C2×M16×C151—41no—
83C2×M16×C151D414yescomplemented
84C22×C8×C151—22no—
85C22×C8×C151—41no—
86C22×C8×C151—41no—
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91C22×C8×C151C2311yescharacteristic
92C22×C8×C151C2311yescharacteristic
93C22×C8×C151C2311yescharacteristic
94C22×C8×C151C2311yescharacteristic
95#120×C151—24no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C4×D4×C151—41no—
99C4×D4×C151—41no—
100C4×D4×C151—41no—
101C4×D4×C151—41no—
102C2×C4⋊C4×C151C2×C411yescharacteristic
103C2×C4⋊C4×C151C2×C411yescharacteristic
104C2×C4⋊C4×C151C2×C411yescharacteristic
105C2×C22⋊C4×C151C2×C411yescharacteristic
106C2×C22⋊C4×C151C2×C411yescharacteristic
107C2×C22⋊C4×C151C2×C411yescharacteristic
108C2×C22⋊C4×C151C2×C411yescharacteristic
109C2×C22⋊C4×C151C2×C411yescharacteristic
110C2×C22⋊C4×C151C2×C411yescharacteristic
111C2×C22⋊C4×C151C2×C411yescharacteristic
112C2×C22⋊C4×C151C2×C411yescharacteristic
113C2×C22⋊C4×C151C2×C411yescharacteristic
114C2×C22⋊C4×C151C2×C411yescharacteristic
115C2×C22⋊C4×C151C2×C411yescharacteristic
116C2×C22⋊C4×C151C2×C411yescharacteristic
117C2×C42×C151C2311yescharacteristic
118C2×C42×C151C2311yescharacteristic
119C2×C42×C151C2311yescharacteristic
120C4⋊C8×C151—22no—
121C4⋊C8×C151—41no—
122C4⋊C8×C151—41no—
123C22⋊C8×C151—22no—
124C22⋊C8×C151—22no—
125C22⋊C8×C151—22no—
126C22⋊C8×C151—22no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151—41no—
131C22⋊C8×C151—41no—
132C22⋊C8×C151—41no—
133C22⋊C8×C151—41no—
134C22⋊C8×C151—41no—
135C22⋊C8×C151—41no—
136#97×C151—22no—
137#97×C151—41no—
138C4×C8×C151—41no—
139#95×C151C2×C411yescharacteristic
140#95×C151C2×C411yescharacteristic
141#95×C151C2×C411yescharacteristic
142#95×C151C2×C411yescharacteristic
143#95×C151C2×C411yescharacteristic
144#95×C151C2×C411yescharacteristic
145C24×C151—22no—
146C24×C151—22no—
147C24×C151—22no—
148C24×C151—41no—
149C24×C151—41no—
150C24×C151—41no—
151C24×C151—41no—
152C24×C151C22×C411yescharacteristic
153C24×C151C22×C411yescharacteristic
154C24×C151C22×C411yescharacteristic
155C24×C151C22×C411yescharacteristic
156C2×D4×C151—22no—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—41no—
161C2×D4×C151—41no—
162C2×D4×C151—41no—
163C2×D4×C151—41no—
164C2×D4×C151M1614yescomplemented
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—22no—
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—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—41no—
191C22×C4×C151—41no—
192C22×C4×C151—41no—
193C22×C4×C151—41no—
194C22×C4×C151—41no—
195C22×C4×C151—41no—
196C22×C4×C151—44no—
197C22×C4×C151—44no—
198C22×C4×C151—44no—
199C22×C4×C151—44no—
200C22×C4×C151C22×C411yescharacteristic
201C22×C4×C151C22×C411yescharacteristic
202C22×C4×C151C22×C411yescharacteristic
203C22×C4×C151C22×C411yescharacteristic
204C22×C4×C151C22×C411yescharacteristic
205C22×C4×C151C22×C411yescharacteristic
206C22×C4×C151C22×C411yescharacteristic
207C22×C4×C151C22×C411yescharacteristic
208C22×C4×C151C22×C411yescharacteristic
209C22×C4×C151C22×C411yescharacteristic
210C22×C4×C151C2×D412yes—
211C22×C4×C151#4112yes—
212C22×C4×C151C2411yescharacteristic
213M16×C151—44no—
214M16×C151—44no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—44no—
238C2×C8×C151C2×D412yes—
239C2×C8×C151C2×D412yes—
240C4⋊C4×C151—22no—
241C4⋊C4×C151—41no—
242C4⋊C4×C151—41no—
243C22⋊C4×C151—22no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—41no—
250C22⋊C4×C151—41no—
251C22⋊C4×C151—41no—
252C22⋊C4×C151—41no—
253C22⋊C4×C151—41no—
254C22⋊C4×C151—41no—
255C42×C151—21no—
256C42×C151—21no—
257C42×C151—21no—
258C42×C151—21no—
259C42×C151—21no—
260C42×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—21no—
264C23×C151—21no—
265C23×C151—21no—
266C23×C151—21no—
267C23×C151—21no—
268C23×C151—21no—
269C23×C151—21no—
270C23×C151—21no—
271C23×C151—21no—
272C23×C151—21no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—21no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—44no—
286C23×C151—44no—
287C23×C151—44no—
288C23×C151—44no—
289C23×C151—44no—
290C23×C151—44no—
291C23×C151—44no—
292C23×C151C4×D412yes—
293C23×C151C2×M1612yes—
294C23×C151C2×M1612yes—
295C23×C151#13112yes—
296C23×C151C23×C411yescharacteristic
297D4×C151—44no—
298D4×C151—44no—
299D4×C151—44no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—22no—
307C2×C4×C151—22no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—21no—
330C2×C4×C151—21no—
331C2×C4×C151—21no—
332C2×C4×C151—44no—
333C2×C4×C151—44no—
334C2×C4×C151—44no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—41no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151C4×D412yes—
348C2×C4×C151C2×M1612yes—
349C2×C4×C151C22×D411yescharacteristic
350C2×C4×C151C2×#4111yescharacteristic
351C2×C4×C151H(5,𝔽2)11yescharacteristic
352C2×C4×C151H(5,𝔽2)11yescharacteristic
353C2×C4×C151H(5,𝔽2)11yescharacteristic
354C2×C4×C151H(5,𝔽2)11yescharacteristic
355C8×C151—22no—
356C8×C151—22no—
357C8×C151—41no—
358C8×C151—41no—
359C8×C151—41no—
360C8×C151—41no—
361C8×C151—41no—
362C8×C151—41no—
363C22×C151—22no—
364C22×C151—22no—
365C22×C151—22no—
366C22×C151—22no—
367C22×C151—22no—
368C22×C151—22no—
369C22×C151—22no—
370C22×C151—22no—
371C22×C151—22no—
372C22×C151—22no—
373C22×C151—22no—
374C22×C151—22no—
375C22×C151—416no—
376C22×C151—41no—
377C22×C151—41no—
378C22×C151—41no—
379C22×C151—41no—
380C22×C151—41no—
381C22×C151—41no—
382C22×C151—41no—
383C22×C151—41no—
384C22×C151—41no—
385C22×C151—41no—
386C22×C151—41no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151—41no—
392C22×C151C2×C4×D411yescharacteristic
393C22×C151#51811yescharacteristic
394C22×C151#51811yescharacteristic
395C22×C151C22×M1611yescharacteristic
396C22×C151C2×#13111yescharacteristic
397C22×C151#56811yescharacteristic
398C22×C151#56811yescharacteristic
399C4×C151—22no—
400C4×C151—22no—
401C4×C151—41no—
402C4×C151—41no—
403C4×C151—41no—
404C4×C151—41no—
405C4×C151—41no—
406C4×C151—41no—
407C4×C151—41no—
408C4×C151—41no—
409C4×C151#53411yescharacteristic
410C4×C151#53511yescharacteristic
411C4×C151#53811yescharacteristic
412C4×C151#53811yescharacteristic
413C2×C151—42no—
414C2×C151—42no—
415C2×C151—42no—
416C2×C151—42no—
417C2×C151#232111yescharacteristic
418C2×C151#293311yescharacteristic
419C2×C151D4×M1611yescharacteristic
420C2×C151#297311yescharacteristic
421C2×C151#297411yescharacteristic
422C2×C151#297611yescharacteristic
423C2×C151#297811yescharacteristic
424#22036C15111yesmaximal, characteristic, direct product factor, Sylow
425C151#2203611yescharacteristic, direct product factor, Sylow
426C2×#435C2×C15111yescharacteristic, complemented
427C2×#407C2×C15111yescharacteristic, complemented
428C4×#120C2×C15111yescharacteristic
429#1955C2×C15111yescharacteristic, complemented
430#1954C2×C15111yescharacteristic, complemented
431#1924C2×C15111yescharacteristic, complemented
432#1924C2×C15111yescharacteristic, complemented
433#1924C2×C15111yescharacteristic, complemented
434#1923C2×C15111yescharacteristic, complemented
435#1870C2×C15111yescharacteristic, complemented
436#1869C2×C15111yescharacteristic, complemented
437#1869C2×C15111yescharacteristic, complemented
438#1851C2×C15111yescharacteristic, complemented
439#1779C2×C15111yescharacteristic, complemented
440#1753C2×C15111yescharacteristic, complemented
441C24×C4C22×C15111yescharacteristic
442C22×M16C22×C15111yescharacteristic
443C22×M16C22×C15111yescharacteristic
444C23×C8C22×C15111yescharacteristic, complemented
445C2×#120C4×C15111yescharacteristic
446C2×C4×D4C22×C15111yescharacteristic
447C2×C4×D4C22×C15111yescharacteristic
448C2×C4×D4C22×C15111yescharacteristic
449#435—24no—
450C2×C4⋊C8C22×C15111yescharacteristic, complemented
451C2×C4⋊C8C22×C15111yescharacteristic, complemented
452C2×C4⋊C8C22×C15111yescharacteristic, complemented
453#407—24no—
454C2×C22⋊C8C22×C15111yescharacteristic
455C2×C22⋊C8C22×C15111yescharacteristic
456C2×C22⋊C8C22×C15111yescharacteristic
457C2×C22⋊C8C22×C15111yescharacteristic
458C2×C22⋊C8C22×C15111yescharacteristic
459C2×C22⋊C8C22×C15111yescharacteristic
460C2×C22⋊C8C22×C15111yescharacteristic
461C2×C22⋊C8C22×C15111yescharacteristic
462C2×C22⋊C8C22×C15111yescharacteristic
463C2×C22⋊C8C22×C15111yescharacteristic
464C2×C22⋊C8C22×C15111yescharacteristic, complemented
465C2×C22⋊C8C22×C15111yescharacteristic, complemented
466C2×C22⋊C8C22×C15111yescharacteristic, complemented
467C2×#97C22×C15111yescharacteristic, complemented
468C2×#97C22×C15111yescharacteristic, complemented
469C2×C4×C8C22×C15111yescharacteristic, complemented
470#386C4×C15111yescharacteristic
471#386C4×C15111yescharacteristic
472#386C4×C15111yescharacteristic
473#385C4×C15111yescharacteristic
474#385C4×C15111yescharacteristic
475#385C4×C15111yescharacteristic
476#379C4×C15111yescharacteristic
477C4×C22⋊C4C22×C15111yescharacteristic
478C4×C22⋊C4C22×C15111yescharacteristic
479C4×C22⋊C4C22×C15111yescharacteristic
480#336C22×C15111yescharacteristic, complemented
481#336C22×C15111yescharacteristic, complemented
482#336C22×C15111yescharacteristic, complemented
483#336C22×C15111yescharacteristic, complemented
484#336C22×C15111yescharacteristic, complemented
485#336C22×C15111yescharacteristic, complemented
486C25C2×C4×C15111yescharacteristic
487C22×D4C2×C4×C15111yescharacteristic
488C22×D4C2×C4×C15111yescharacteristic
489C22×D4C2×C4×C15111yescharacteristic
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4C2×C4×C15111yescharacteristic
497C23×C4C2×C4×C15111yescharacteristic
498C23×C4C2×C4×C15111yescharacteristic
499C23×C4C23×C15111yescharacteristic
500C23×C4C23×C15111yescharacteristic
501C23×C4C23×C15111yescharacteristic
502C23×C4C23×C15111yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16D4×C15114yescomplemented
509C22×C8—22no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8C23×C15111yescharacteristic
513C22×C8C23×C15111yescharacteristic
514C22×C8C23×C15111yescharacteristic
515C22×C8C23×C15111yescharacteristic
516C22×C8C23×C15111yescharacteristic
517C22×C8C23×C15111yescharacteristic
518C22×C8C23×C15111yescharacteristic
519C22×C8C23×C15111yescharacteristic
520#120—24no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—41no—
527C2×C4⋊C4C2×C4×C15111yescharacteristic
528C2×C4⋊C4C2×C4×C15111yescharacteristic
529C2×C4⋊C4C2×C4×C15111yescharacteristic
530C2×C22⋊C4C2×C4×C15111yescharacteristic
531C2×C22⋊C4C2×C4×C15111yescharacteristic
532C2×C22⋊C4C2×C4×C15111yescharacteristic
533C2×C22⋊C4C2×C4×C15111yescharacteristic
534C2×C22⋊C4C2×C4×C15111yescharacteristic
535C2×C22⋊C4C2×C4×C15111yescharacteristic
536C2×C22⋊C4C2×C4×C15111yescharacteristic
537C2×C22⋊C4C2×C4×C15111yescharacteristic
538C2×C22⋊C4C2×C4×C15111yescharacteristic
539C2×C22⋊C4C2×C4×C15111yescharacteristic
540C2×C22⋊C4C2×C4×C15111yescharacteristic
541C2×C22⋊C4C2×C4×C15111yescharacteristic
542C2×C42C23×C15111yescharacteristic
543C2×C42C23×C15111yescharacteristic
544C2×C42C23×C15111yescharacteristic
545C4⋊C8—22no—
546C4⋊C8—41no—
547C4⋊C8—41no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557C22⋊C8—41no—
558C22⋊C8—41no—
559C22⋊C8—41no—
560C22⋊C8—41no—
561#97—22no—
562#97—41no—
563C4×C8—41no—
564#95C2×C4×C15111yescharacteristic
565#95C2×C4×C15111yescharacteristic
566#95C2×C4×C15111yescharacteristic
567#95C2×C4×C15111yescharacteristic
568#95C2×C4×C15111yescharacteristic
569#95C2×C4×C15111yescharacteristic
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24C22×C4×C15111yescharacteristic
578C24C22×C4×C15111yescharacteristic
579C24C22×C4×C15111yescharacteristic
580C24C22×C4×C15111yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4M16×C15114yescomplemented
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4C22×C4×C15111yescharacteristic
626C22×C4C22×C4×C15111yescharacteristic
627C22×C4C22×C4×C15111yescharacteristic
628C22×C4C22×C4×C15111yescharacteristic
629C22×C4C22×C4×C15111yescharacteristic
630C22×C4C22×C4×C15111yescharacteristic
631C22×C4C22×C4×C15111yescharacteristic
632C22×C4C22×C4×C15111yescharacteristic
633C22×C4C22×C4×C15111yescharacteristic
634C22×C4C22×C4×C15111yescharacteristic
635C22×C4C2×D4×C15112yes—
636C22×C4#41×C15112yes—
637C22×C4C24×C15111yescharacteristic
638M16—44no—
639M16—44no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—44no—
663C2×C8C2×D4×C15112yes—
664C2×C8C2×D4×C15112yes—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C4×D4×C15112yes—
718C23C2×M16×C15112yes—
719C23C2×M16×C15112yes—
720C23#131×C15112yes—
721C23C23×C4×C15111yescharacteristic
722D4—44no—
723D4—44no—
724D4—44no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4C4×D4×C15112yes—
773C2×C4C2×M16×C15112yes—
774C2×C4C22×D4×C15111yescharacteristic
775C2×C4C2×#41×C15111yescharacteristic
776C2×C4H(5,𝔽2)×C15111yescharacteristic
777C2×C4H(5,𝔽2)×C15111yescharacteristic
778C2×C4H(5,𝔽2)×C15111yescharacteristic
779C2×C4H(5,𝔽2)×C15111yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—416no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22C2×C4×D4×C15111yescharacteristic
818C22#518×C15111yescharacteristic
819C22#518×C15111yescharacteristic
820C22C22×M16×C15111yescharacteristic
821C22C2×#131×C15111yescharacteristic
822C22#568×C15111yescharacteristic
823C22#568×C15111yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4#534×C15111yescharacteristic
835C4#535×C15111yescharacteristic
836C4#538×C15111yescharacteristic
837C4#538×C15111yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—42no—
842C2#2321×C15111yescharacteristic
843C2#2933×C15111yescharacteristic
844C2D4×M16×C15111yescharacteristic
845C2#2973×C15111yescharacteristic
846C2#2974×C15111yescharacteristic
847C2#2976×C15111yescharacteristic
848C2#2978×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC2×#120×C151C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C151C2semidirect
2. C2×#407×C151C2semidirect
4. #1955×C151C2semidirect
5. #1954×C151C2semidirect
6. #1924×C151C2semidirect
7. #1924×C151C2semidirect
8. #1924×C151C2semidirect
9. #1923×C151C2semidirect
10. #1870×C151C2semidirect
11. #1869×C151C2semidirect
12. #1869×C151C2semidirect
13. #1851×C151C2semidirect
14. #1779×C151C2semidirect
15. #1753×C151C2semidirect
19. C23×C8×C151C22semidirect
25. C2×C4⋊C8×C151C22semidirect
26. C2×C4⋊C8×C151C22semidirect
27. C2×C4⋊C8×C151C22semidirect
39. C2×C22⋊C8×C151C22semidirect
40. C2×C22⋊C8×C151C22semidirect
41. C2×C22⋊C8×C151C22semidirect
42. C2×#97×C151C22semidirect
43. C2×#97×C151C22semidirect
44. C2×C4×C8×C151C22semidirect
55. #336×C151C22semidirect
56. #336×C151C22semidirect
57. #336×C151C22semidirect
58. #336×C151C22semidirect
59. #336×C151C22semidirect
60. #336×C151C22semidirect
83. C2×M16×C151D4semidirect
164. C2×D4×C151M16semidirect
424. #22036C151direct (N × H)
425. C151#22036direct (N × H)
426. C2×#435C2×C151semidirect
427. C2×#407C2×C151semidirect
429. #1955C2×C151semidirect
430. #1954C2×C151semidirect
431. #1924C2×C151semidirect
432. #1924C2×C151semidirect
433. #1924C2×C151semidirect
434. #1923C2×C151semidirect
435. #1870C2×C151semidirect
436. #1869C2×C151semidirect
437. #1869C2×C151semidirect
438. #1851C2×C151semidirect
439. #1779C2×C151semidirect
440. #1753C2×C151semidirect
444. C23×C8C22×C151semidirect
450. C2×C4⋊C8C22×C151semidirect
451. C2×C4⋊C8C22×C151semidirect
452. C2×C4⋊C8C22×C151semidirect
464. C2×C22⋊C8C22×C151semidirect
465. C2×C22⋊C8C22×C151semidirect
466. C2×C22⋊C8C22×C151semidirect
467. C2×#97C22×C151semidirect
468. C2×#97C22×C151semidirect
469. C2×C4×C8C22×C151semidirect
480. #336C22×C151semidirect
481. #336C22×C151semidirect
482. #336C22×C151semidirect
483. #336C22×C151semidirect
484. #336C22×C151semidirect
485. #336C22×C151semidirect
508. C2×M16D4×C151semidirect
589. C2×D4M16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1512
C2×#407×C1512
C4×#120×C1512
#1955×C1512
#1954×C1512
#1924×C1512
#1923×C1512
#1870×C1512
#1869×C1512
#1851×C1512
#1779×C1512
#1753×C1512
#22036151