Finite Group Databasebeta

← C151×#22988 #50327913

Subgroups — C151×#22988 #50327913

Order 38656.

1050 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#436×C151C211yesmaximal, characteristic, complemented
2C2×#435×C151C211yesmaximal, characteristic, complemented
3C2×#435×C151C211yesmaximal, characteristic, complemented
4C2×#423×C151C211yesmaximal, characteristic, complemented
5C4×#121×C151C211yesmaximal, characteristic
6#1955×C151C211yesmaximal, characteristic, complemented
7#1940×C151C211yesmaximal, characteristic, complemented
8#1924×C151C211yesmaximal, characteristic, complemented
9#1923×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1870×C151C211yesmaximal, characteristic, complemented
12#1851×C151C211yesmaximal, characteristic, complemented
13#1850×C151C211yesmaximal, characteristic, complemented
14#1771×C151C211yesmaximal, characteristic, complemented
15#1749×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×#121×C151C411yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C22×C42×C151C2211yescharacteristic
25#436×C151—24no—
26#435×C151—24no—
27#435×C151—24no—
28#423×C151—24no—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×C4⋊C8×C151C2211yescharacteristic
32C2×C4⋊C8×C151C2211yescharacteristic
33C2×C4⋊C8×C151C2211yescharacteristic
34C2×C4⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×C22⋊C8×C151C2211yescharacteristic
41C2×C22⋊C8×C151C2211yescharacteristic
42C2×C22⋊C8×C151C2211yescharacteristic
43C2×#97×C151C2211yescharacteristic
44C2×#97×C151C2211yescharacteristic
45C2×#97×C151C2211yescharacteristic
46C2×C4×C8×C151C2211yescharacteristic
47#390×C151C411yescharacteristic
48#389×C151C411yescharacteristic
49#388×C151C411yescharacteristic
50#388×C151C411yescharacteristic
51#386×C151C411yescharacteristic
52#386×C151C411yescharacteristic
53#380×C151C411yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C22⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×D4×C151C2×C411yescharacteristic
64C22×D4×C151C2×C411yescharacteristic
65C22×D4×C151C2×C411yescharacteristic
66C23×C4×C151C2×C411yescharacteristic
67C23×C4×C151C2×C411yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C23×C4×C151C2311yescharacteristic
71C2×M16×C151—22no—
72C2×M16×C151—22no—
73C2×M16×C151—22no—
74C2×M16×C151—22no—
75C2×M16×C151—22no—
76C2×M16×C151—22no—
77C2×M16×C151—41no—
78C2×M16×C151—41no—
79C2×M16×C151—41no—
80C22×C8×C151—22no—
81C22×C8×C151—22no—
82C22×C8×C151—41no—
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91#121×C151—24no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C2×C4⋊C4×C151C2×C411yescharacteristic
99C2×C4⋊C4×C151C2×C411yescharacteristic
100C2×C4⋊C4×C151C2×C411yescharacteristic
101C2×C4⋊C4×C151C2×C411yescharacteristic
102C2×C4⋊C4×C151C2×C411yescharacteristic
103C2×C22⋊C4×C151C2×C411yescharacteristic
104C2×C22⋊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×C42×C151—22no—
114C2×C42×C151—22no—
115C2×C42×C151C2×C411yescharacteristic
116C2×C42×C151C2×C411yescharacteristic
117C2×C42×C151C2311yescharacteristic
118C2×C42×C151C2311yescharacteristic
119C2×C42×C151C2311yescharacteristic
120C2×C42×C151C2311yescharacteristic
121C4⋊C8×C151—22no—
122C4⋊C8×C151—22no—
123C4⋊C8×C151—22no—
124C4⋊C8×C151—22no—
125C4⋊C8×C151—22no—
126C4⋊C8×C151D414yescomplemented
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151—22no—
131C22⋊C8×C151—22no—
132C22⋊C8×C151—41no—
133C22⋊C8×C151—41no—
134C22⋊C8×C151D414yescomplemented
135#97×C151—22no—
136#97×C151—22no—
137#97×C151—22no—
138C4×C8×C151—22no—
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×C151C22×C411yescharacteristic
146C24×C151C22×C411yescharacteristic
147C24×C151C22×C411yescharacteristic
148C2×D4×C151—22no—
149C2×D4×C151—22no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—41no—
155C2×D4×C151—41no—
156C2×D4×C151—41no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
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—41no—
177C22×C4×C151—41no—
178C22×C4×C151—41no—
179C22×C4×C151C22×C411yescharacteristic
180C22×C4×C151C22×C411yescharacteristic
181C22×C4×C151C22×C411yescharacteristic
182C22×C4×C151C22×C411yescharacteristic
183C22×C4×C151C22×C411yescharacteristic
184C22×C4×C151C22×C411yescharacteristic
185C22×C4×C151C22×C411yescharacteristic
186C22×C4×C151C22×C411yescharacteristic
187C22×C4×C151C22×C411yescharacteristic
188C22×C4×C151C22×C411yescharacteristic
189C22×C4×C151C22×C411yescharacteristic
190C22×C4×C151C2×D412yes—
191C22×C4×C151#4112yes—
192C22×C4×C151C2411yescharacteristic
193M16×C151—44no—
194M16×C151—44no—
195M16×C151—44no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—44no—
217C2×C8×C151C2×D412yes—
218C2×C8×C151C2×D412yes—
219C2×C8×C151C2×D412yes—
220C2×C8×C151C2×D412yes—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—41no—
226C22⋊C4×C151—22no—
227C22⋊C4×C151—22no—
228C22⋊C4×C151—22no—
229C22⋊C4×C151—22no—
230C22⋊C4×C151—22no—
231C22⋊C4×C151—22no—
232C22⋊C4×C151—22no—
233C22⋊C4×C151—41no—
234C22⋊C4×C151—41no—
235C22⋊C4×C151M1614yescomplemented
236C42×C151—22no—
237C42×C151—22no—
238C42×C151—21no—
239C42×C151—21no—
240C42×C151—21no—
241C42×C151—21no—
242C42×C151—21no—
243C42×C151—21no—
244C42×C151C2×D412yes—
245C42×C151#4112yes—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—21no—
264C23×C151—21no—
265C23×C151C4×D412yes—
266C23×C151C2×M1612yes—
267C23×C151C23×C411yescharacteristic
268D4×C151—44no—
269D4×C151—44no—
270D4×C151—44no—
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—21no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—44no—
304C2×C4×C151—44no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151C4×D412yes—
314C2×C4×C151C4×D412yes—
315C2×C4×C151C4×D412yes—
316C2×C4×C151C2×M1612yes—
317C2×C4×C151C2×M1612yes—
318C2×C4×C151C22×D411yescharacteristic
319C2×C4×C151C22×D411yescharacteristic
320C2×C4×C151C2×#4111yescharacteristic
321C2×C4×C151C2×#4111yescharacteristic
322C2×C4×C151H(5,𝔽2)11yescharacteristic
323C2×C4×C1512−1+411yescharacteristic
324C8×C151—22no—
325C8×C151—22no—
326C8×C151—22no—
327C8×C151—22no—
328C8×C151—41no—
329C8×C151—41no—
330C8×C151—41no—
331C8×C151—41no—
332C22×C151—22no—
333C22×C151—22no—
334C22×C151—22no—
335C22×C151—22no—
336C22×C151—22no—
337C22×C151—22no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151—41no—
348C22×C151—41no—
349C22×C151—41no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151C2×C4×D411yescharacteristic
354C22×C151C2×C4×D411yescharacteristic
355C22×C151#52011yescharacteristic
356C22×C151C22×M1611yescharacteristic
357C22×C151#56811yescharacteristic
358C22×C151#56811yescharacteristic
359C22×C151#56811yescharacteristic
360C4×C151—22no—
361C4×C151—22no—
362C4×C151—22no—
363C4×C151—22no—
364C4×C151—22no—
365C4×C151—41no—
366C4×C151—41no—
367C4×C151—41no—
368C4×C151—41no—
369C4×C151—41no—
370C4×C151—41no—
371C4×C151D4211yescharacteristic
372C4×C151#54711yescharacteristic
373C4×C151#54811yescharacteristic
374C4×C151#55311yescharacteristic
375C2×C151—42no—
376C2×C151—42no—
377C2×C151—81no—
378C2×C151#236111yescharacteristic
379C2×C151#293011yescharacteristic
380C2×C151#293211yescharacteristic
381C2×C151D4×M1611yescharacteristic
382C2×C151D4×M1611yescharacteristic
383C2×C151#298911yescharacteristic
384C2×C151#299511yescharacteristic
385#22988C15111yesmaximal, characteristic, direct product factor, Sylow
386C151#2298811yescharacteristic, direct product factor, Sylow
387C2×#436C2×C15111yescharacteristic, complemented
388C2×#435C2×C15111yescharacteristic, complemented
389C2×#435C2×C15111yescharacteristic, complemented
390C2×#423C2×C15111yescharacteristic, complemented
391C4×#121C2×C15111yescharacteristic
392#1955C2×C15111yescharacteristic, complemented
393#1940C2×C15111yescharacteristic, complemented
394#1924C2×C15111yescharacteristic, complemented
395#1923C2×C15111yescharacteristic, complemented
396#1870C2×C15111yescharacteristic, complemented
397#1870C2×C15111yescharacteristic, complemented
398#1851C2×C15111yescharacteristic, complemented
399#1850C2×C15111yescharacteristic, complemented
400#1771C2×C15111yescharacteristic, complemented
401#1749C2×C15111yescharacteristic, complemented
402C22×M16C22×C15111yescharacteristic
403C22×M16C22×C15111yescharacteristic
404C22×M16C22×C15111yescharacteristic
405C23×C8C22×C15111yescharacteristic
406C2×#121C4×C15111yescharacteristic
407C2×C4×D4C22×C15111yescharacteristic
408C2×C4×D4C22×C15111yescharacteristic
409C2×C4×D4C22×C15111yescharacteristic
410C22×C42C22×C15111yescharacteristic
411#436—24no—
412#435—24no—
413#435—24no—
414#423—24no—
415C2×C4⋊C8C22×C15111yescharacteristic
416C2×C4⋊C8C22×C15111yescharacteristic
417C2×C4⋊C8C22×C15111yescharacteristic
418C2×C4⋊C8C22×C15111yescharacteristic
419C2×C4⋊C8C22×C15111yescharacteristic
420C2×C4⋊C8C22×C15111yescharacteristic
421C2×C22⋊C8C22×C15111yescharacteristic
422C2×C22⋊C8C22×C15111yescharacteristic
423C2×C22⋊C8C22×C15111yescharacteristic
424C2×C22⋊C8C22×C15111yescharacteristic
425C2×C22⋊C8C22×C15111yescharacteristic
426C2×C22⋊C8C22×C15111yescharacteristic
427C2×C22⋊C8C22×C15111yescharacteristic
428C2×C22⋊C8C22×C15111yescharacteristic
429C2×#97C22×C15111yescharacteristic
430C2×#97C22×C15111yescharacteristic
431C2×#97C22×C15111yescharacteristic
432C2×C4×C8C22×C15111yescharacteristic
433#390C4×C15111yescharacteristic
434#389C4×C15111yescharacteristic
435#388C4×C15111yescharacteristic
436#388C4×C15111yescharacteristic
437#386C4×C15111yescharacteristic
438#386C4×C15111yescharacteristic
439#380C4×C15111yescharacteristic
440C4×C4⋊C4C22×C15111yescharacteristic
441C4×C22⋊C4C22×C15111yescharacteristic
442C4×C22⋊C4C22×C15111yescharacteristic
443#336C22×C15111yescharacteristic
444#336C22×C15111yescharacteristic
445#336C22×C15111yescharacteristic
446#336C22×C15111yescharacteristic
447#336C22×C15111yescharacteristic
448#336C22×C15111yescharacteristic
449C22×D4C2×C4×C15111yescharacteristic
450C22×D4C2×C4×C15111yescharacteristic
451C22×D4C2×C4×C15111yescharacteristic
452C23×C4C2×C4×C15111yescharacteristic
453C23×C4C2×C4×C15111yescharacteristic
454C23×C4C23×C15111yescharacteristic
455C23×C4C23×C15111yescharacteristic
456C23×C4C23×C15111yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C2×M16—41no—
465C2×M16—41no—
466C22×C8—22no—
467C22×C8—22no—
468C22×C8—41no—
469C22×C8C23×C15111yescharacteristic
470C22×C8C23×C15111yescharacteristic
471C22×C8C23×C15111yescharacteristic
472C22×C8C23×C15111yescharacteristic
473C22×C8C23×C15111yescharacteristic
474C22×C8C23×C15111yescharacteristic
475C22×C8C23×C15111yescharacteristic
476C22×C8C23×C15111yescharacteristic
477#121—24no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C2×C4⋊C4C2×C4×C15111yescharacteristic
485C2×C4⋊C4C2×C4×C15111yescharacteristic
486C2×C4⋊C4C2×C4×C15111yescharacteristic
487C2×C4⋊C4C2×C4×C15111yescharacteristic
488C2×C4⋊C4C2×C4×C15111yescharacteristic
489C2×C22⋊C4C2×C4×C15111yescharacteristic
490C2×C22⋊C4C2×C4×C15111yescharacteristic
491C2×C22⋊C4C2×C4×C15111yescharacteristic
492C2×C22⋊C4C2×C4×C15111yescharacteristic
493C2×C22⋊C4C2×C4×C15111yescharacteristic
494C2×C22⋊C4C2×C4×C15111yescharacteristic
495C2×C22⋊C4C2×C4×C15111yescharacteristic
496C2×C22⋊C4C2×C4×C15111yescharacteristic
497C2×C22⋊C4C2×C4×C15111yescharacteristic
498C2×C22⋊C4C2×C4×C15111yescharacteristic
499C2×C42—22no—
500C2×C42—22no—
501C2×C42C2×C4×C15111yescharacteristic
502C2×C42C2×C4×C15111yescharacteristic
503C2×C42C23×C15111yescharacteristic
504C2×C42C23×C15111yescharacteristic
505C2×C42C23×C15111yescharacteristic
506C2×C42C23×C15111yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511C4⋊C8—22no—
512C4⋊C8D4×C15114yescomplemented
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—41no—
519C22⋊C8—41no—
520C22⋊C8D4×C15114yescomplemented
521#97—22no—
522#97—22no—
523#97—22no—
524C4×C8—22no—
525#95C2×C4×C15111yescharacteristic
526#95C2×C4×C15111yescharacteristic
527#95C2×C4×C15111yescharacteristic
528#95C2×C4×C15111yescharacteristic
529#95C2×C4×C15111yescharacteristic
530#95C2×C4×C15111yescharacteristic
531C24C22×C4×C15111yescharacteristic
532C24C22×C4×C15111yescharacteristic
533C24C22×C4×C15111yescharacteristic
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4C22×C4×C15111yescharacteristic
566C22×C4C22×C4×C15111yescharacteristic
567C22×C4C22×C4×C15111yescharacteristic
568C22×C4C22×C4×C15111yescharacteristic
569C22×C4C22×C4×C15111yescharacteristic
570C22×C4C22×C4×C15111yescharacteristic
571C22×C4C22×C4×C15111yescharacteristic
572C22×C4C22×C4×C15111yescharacteristic
573C22×C4C22×C4×C15111yescharacteristic
574C22×C4C22×C4×C15111yescharacteristic
575C22×C4C22×C4×C15111yescharacteristic
576C22×C4C2×D4×C15112yes—
577C22×C4#41×C15112yes—
578C22×C4C24×C15111yescharacteristic
579M16—44no—
580M16—44no—
581M16—44no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—44no—
603C2×C8C2×D4×C15112yes—
604C2×C8C2×D4×C15112yes—
605C2×C8C2×D4×C15112yes—
606C2×C8C2×D4×C15112yes—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—41no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4M16×C15114yescomplemented
622C42—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42C2×D4×C15112yes—
631C42#41×C15112yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23C4×D4×C15112yes—
652C23C2×M16×C15112yes—
653C23C23×C4×C15111yescharacteristic
654D4—44no—
655D4—44no—
656D4—44no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4C4×D4×C15112yes—
700C2×C4C4×D4×C15112yes—
701C2×C4C4×D4×C15112yes—
702C2×C4C2×M16×C15112yes—
703C2×C4C2×M16×C15112yes—
704C2×C4C22×D4×C15111yescharacteristic
705C2×C4C22×D4×C15111yescharacteristic
706C2×C4C2×#41×C15111yescharacteristic
707C2×C4C2×#41×C15111yescharacteristic
708C2×C4H(5,𝔽2)×C15111yescharacteristic
709C2×C42−1+4×C15111yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22C2×C4×D4×C15111yescharacteristic
740C22C2×C4×D4×C15111yescharacteristic
741C22#520×C15111yescharacteristic
742C22C22×M16×C15111yescharacteristic
743C22#568×C15111yescharacteristic
744C22#568×C15111yescharacteristic
745C22#568×C15111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4D42×C15111yescharacteristic
758C4#547×C15111yescharacteristic
759C4#548×C15111yescharacteristic
760C4#553×C15111yescharacteristic
761C2—42no—
762C2—42no—
763C2—81no—
764C2#2361×C15111yescharacteristic
765C2#2930×C15111yescharacteristic
766C2#2932×C15111yescharacteristic
767C2D4×M16×C15111yescharacteristic
768C2D4×M16×C15111yescharacteristic
769C2#2989×C15111yescharacteristic
770C2#2995×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC2×#121×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×#436×C151C2semidirect
2. C2×#435×C151C2semidirect
3. C2×#435×C151C2semidirect
4. C2×#423×C151C2semidirect
6. #1955×C151C2semidirect
7. #1940×C151C2semidirect
8. #1924×C151C2semidirect
9. #1923×C151C2semidirect
10. #1870×C151C2semidirect
11. #1870×C151C2semidirect
12. #1851×C151C2semidirect
13. #1850×C151C2semidirect
14. #1771×C151C2semidirect
15. #1749×C151C2semidirect
126. C4⋊C8×C151D4semidirect
134. C22⋊C8×C151D4semidirect
235. C22⋊C4×C151M16semidirect
385. #22988C151direct (N × H)
386. C151#22988direct (N × H)
387. C2×#436C2×C151semidirect
388. C2×#435C2×C151semidirect
389. C2×#435C2×C151semidirect
390. C2×#423C2×C151semidirect
392. #1955C2×C151semidirect
393. #1940C2×C151semidirect
394. #1924C2×C151semidirect
395. #1923C2×C151semidirect
396. #1870C2×C151semidirect
397. #1870C2×C151semidirect
398. #1851C2×C151semidirect
399. #1850C2×C151semidirect
400. #1771C2×C151semidirect
401. #1749C2×C151semidirect
512. C4⋊C8D4×C151semidirect
520. C22⋊C8D4×C151semidirect
621. C22⋊C4M16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#436×C1512
C2×#435×C1512
C2×#423×C1512
C4×#121×C1512
#1955×C1512
#1940×C1512
#1924×C1512
#1923×C1512
#1870×C1512
#1851×C1512
#1850×C1512
#1771×C1512
#1749×C1512
#22988151