Finite Group Databasebeta

← C151×#22471 #50327396

Subgroups — C151×#22471 #50327396

Order 38656.

1424 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C151C211yesmaximal, characteristic
2C2×#435×C151C212yesmaximal, complemented
3#1985×C151C212yesmaximal, complemented
4#1870×C151C212yesmaximal, complemented
5#1869×C151C212yesmaximal, complemented
6#1817×C151C211yesmaximal, characteristic, complemented
7#1817×C151C211yesmaximal, characteristic, complemented
8#1797×C151C211yesmaximal, characteristic, complemented
9#1749×C151C211yesmaximal, characteristic, complemented
10#1728×C151C211yesmaximal, characteristic, complemented
11C2×#336×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C411yescharacteristic
13C22×M16×C151C2212yes—
14C23×C8×C151C2212yes—
15C4×#41×C151—28no—
16C2×C4×Q8×C151C411yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18C2×C4×D4×C151C411yescharacteristic
19C2×C4×D4×C151C411yescharacteristic
20C2×C4×D4×C151C411yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151C411yescharacteristic
25C2×#117×C151C411yescharacteristic
26C2×#117×C151C411yescharacteristic
27C22×C42×C151C2211yescharacteristic
28C22×C42×C151C2211yescharacteristic
29C22×C42×C151C2211yescharacteristic
30#435×C151—28no—
31C2×C4⋊C8×C151C2212yes—
32C2×C22⋊C8×C151C2212yes—
33C2×C22⋊C8×C151C2212yes—
34C2×C22⋊C8×C151C2212yes—
35C2×C22⋊C8×C151C2212yes—
36C2×#97×C151C2212yes—
37#336×C151C2212yes—
38#336×C151C2212yes—
39#336×C151C2212yes—
40#336×C151C2212yes—
41#336×C151C2211yescharacteristic
42#336×C151C2211yescharacteristic
43#336×C151C2211yescharacteristic
44#336×C151C2211yescharacteristic
45C2×#41×C151—24no—
46C2×#41×C151—24no—
47C2×#41×C151—24no—
48C22×Q8×C151C2×C411yescharacteristic
49C22×D4×C151C2×C411yescharacteristic
50C22×D4×C151C2×C411yescharacteristic
51C22×D4×C151C2×C411yescharacteristic
52C23×C4×C151C2×C411yescharacteristic
53C23×C4×C151C2×C411yescharacteristic
54C23×C4×C151C2×C411yescharacteristic
55C23×C4×C151C2×C411yescharacteristic
56C23×C4×C151C2×C411yescharacteristic
57C23×C4×C151C2×C411yescharacteristic
58C23×C4×C151C2311yescharacteristic
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2311yescharacteristic
61C2×M16×C151—24no—
62C2×M16×C151—24no—
63C2×M16×C151—42no—
64C22×C8×C151—24no—
65C22×C8×C151—24no—
66C22×C8×C151—42no—
67C22×C8×C151C2312yes—
68C22×C8×C151C2312yes—
69C22×C8×C151C2312yes—
70C22×C8×C151C2312yes—
71C4×Q8×C151—24no—
72C4×Q8×C151—24no—
73C4×D4×C151—24no—
74C4×D4×C151—24no—
75C4×D4×C151—24no—
76C4×D4×C151—24no—
77C4×D4×C151—24no—
78C4×D4×C151D418yes—
79#117×C151—24no—
80#117×C151—24no—
81#117×C151—24no—
82C2×C4⋊C4×C151C2×C411yescharacteristic
83C2×C4⋊C4×C151C2×C411yescharacteristic
84C2×C4⋊C4×C151C2×C411yescharacteristic
85C2×C4⋊C4×C151C2×C411yescharacteristic
86C2×C4⋊C4×C151C2×C411yescharacteristic
87C2×C4⋊C4×C151C2×C411yescharacteristic
88C2×C22⋊C4×C151C2×C411yescharacteristic
89C2×C22⋊C4×C151C2×C411yescharacteristic
90C2×C22⋊C4×C151C2×C411yescharacteristic
91C2×C22⋊C4×C151C2×C411yescharacteristic
92C2×C22⋊C4×C151C2×C411yescharacteristic
93C2×C22⋊C4×C151C2×C411yescharacteristic
94C2×C42×C151—24no—
95C2×C42×C151—24no—
96C2×C42×C151—24no—
97C2×C42×C151C2×C411yescharacteristic
98C2×C42×C151C2×C411yescharacteristic
99C2×C42×C151C2×C411yescharacteristic
100C2×C42×C151C2×C411yescharacteristic
101C2×C42×C151C2×C411yescharacteristic
102C2×C42×C151C2×C411yescharacteristic
103C2×C42×C151C2311yescharacteristic
104C2×C42×C151C2311yescharacteristic
105C2×C42×C151C2311yescharacteristic
106C2×C42×C151C2311yescharacteristic
107C4⋊C8×C151—24no—
108C22⋊C8×C151—24no—
109C22⋊C8×C151—24no—
110C22⋊C8×C151—24no—
111C22⋊C8×C151—42no—
112#97×C151—24no—
113C24×C151C22×C411yescharacteristic
114C24×C151C22×C411yescharacteristic
115C24×C151C22×C411yescharacteristic
116#41×C151—232no—
117C2×Q8×C151—22no—
118C2×Q8×C151—22no—
119C2×Q8×C151—22no—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—22no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151C22⋊C414yes—
128C2×D4×C151M1614yescomplemented
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—41no—
154C22×C4×C151—41no—
155C22×C4×C151—41no—
156C22×C4×C151M1614yescomplemented
157C22×C4×C151C22×C411yescharacteristic
158C22×C4×C151C22×C411yescharacteristic
159C22×C4×C151C22×C411yescharacteristic
160C22×C4×C151C22×C411yescharacteristic
161C22×C4×C151C22×C411yescharacteristic
162C22×C4×C151C22×C411yescharacteristic
163C22×C4×C151C22×C411yescharacteristic
164C22×C4×C151C22×C411yescharacteristic
165C22×C4×C151C22×C411yescharacteristic
166C22×C4×C151C22×C411yescharacteristic
167C22×C4×C151C22×C411yescharacteristic
168C22×C4×C151C2×D414yes—
169C22×C4×C151C2×D414yes—
170C22×C4×C151C2411yescharacteristic
171M16×C151—48no—
172C2×C8×C151—22no—
173C2×C8×C151—22no—
174C2×C8×C151—22no—
175C2×C8×C151—22no—
176C2×C8×C151—22no—
177C2×C8×C151—22no—
178C2×C8×C151—22no—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C2×C8×C151—22no—
183C2×C8×C151—48no—
184C2×C8×C151#4114yescomplemented
185C4⋊C4×C151—22no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151C22⋊C414yes—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—22no—
194C22⋊C4×C151—22no—
195C22⋊C4×C151C22⋊C414yes—
196C22⋊C4×C151C22⋊C414yes—
197C42×C151—22no—
198C42×C151—22no—
199C42×C151—22no—
200C42×C151—22no—
201C42×C151—22no—
202C42×C151—22no—
203C42×C151—22no—
204C42×C151—22no—
205C42×C151—22no—
206C42×C151C2×D414yes—
207C23×C151—21no—
208C23×C151—21no—
209C23×C151—21no—
210C23×C151—21no—
211C23×C151—21no—
212C23×C151—21no—
213C23×C151—21no—
214C23×C151—21no—
215C23×C151—21no—
216C23×C151—21no—
217C23×C151—21no—
218C23×C151—21no—
219C23×C151—21no—
220C23×C151—21no—
221C23×C151—21no—
222C23×C151—21no—
223C23×C151C2×C22⋊C412yes—
224C23×C151C2×C22⋊C412yes—
225C23×C151C2×M1612yes—
226C23×C151C2×M1612yes—
227C23×C151C2×M1612yes—
228C23×C151C23×C411yescharacteristic
229Q8×C151—28no—
230D4×C151—28no—
231D4×C151—28no—
232D4×C151—28no—
233C2×C4×C151—28no—
234C2×C4×C151—28no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—28no—
252C2×C4×C151—24no—
253C2×C4×C151—24no—
254C2×C4×C151—24no—
255C2×C4×C151—24no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—44no—
266C2×C4×C151—44no—
267C2×C4×C151—44no—
268C2×C4×C151—42no—
269C2×C4×C151—42no—
270C2×C4×C151C2×C22⋊C412yes—
271C2×C4×C151C2×C22⋊C412yes—
272C2×C4×C151C2×C22⋊C412yes—
273C2×C4×C151C2×C22⋊C412yes—
274C2×C4×C151C2×M1612yes—
275C2×C4×C151C2×M1612yes—
276C2×C4×C151C2×M1612yes—
277C2×C4×C151#13112yes—
278C2×C4×C151C22×D412yes—
279C2×C4×C151C2×#4112yes—
280C2×C4×C151H(5,𝔽2)11yescharacteristic
281C2×C4×C1512−1+411yescharacteristic
282C8×C151—24no—
283C8×C151—42no—
284C8×C151—42no—
285C8×C151—42no—
286C22×C151—22no—
287C22×C151—22no—
288C22×C151—22no—
289C22×C151—22no—
290C22×C151—22no—
291C22×C151—22no—
292C22×C151—22no—
293C22×C151—22no—
294C22×C151—22no—
295C22×C151—22no—
296C22×C151—22no—
297C22×C151—22no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—41no—
301C22×C151—41no—
302C22×C151—41no—
303C22×C151—41no—
304C22×C151—41no—
305C22×C151—41no—
306C22×C151#40714yes—
307C22×C151C22×C22⋊C411yescharacteristic
308C22×C151C4×#4111yescharacteristic
309C22×C151#52011yescharacteristic
310C22×C151C22×M1611yescharacteristic
311C22×C151C22×M1611yescharacteristic
312C22×C151C2×#13111yescharacteristic
313C22×C151#56811yescharacteristic
314C4×C151—22no—
315C4×C151—22no—
316C4×C151—22no—
317C4×C151—22no—
318C4×C151—22no—
319C4×C151—22no—
320C4×C151—22no—
321C4×C151—22no—
322C4×C151—41no—
323C4×C151—41no—
324C4×C151—41no—
325C4×C151#54612yes—
326C4×C151#54712yes—
327C2×C151—24no—
328C2×C151—42no—
329C2×C151—42no—
330C2×C151#233911yescharacteristic
331C2×C151C2×#40711yescharacteristic
332C2×C151#288011yescharacteristic
333C2×C151#296511yescharacteristic
334C2×C151#297011yescharacteristic
335C2×C151#298911yescharacteristic
336C2×C151#299011yescharacteristic
337#22471C15111yesmaximal, characteristic, direct product factor, Sylow
338C151#2247111yescharacteristic, direct product factor, Sylow
339C2×C4×#41C2×C15111yescharacteristic
340C2×#435C2×C15112yescomplemented
341#1985C2×C15112yescomplemented
342#1870C2×C15112yescomplemented
343#1869C2×C15112yescomplemented
344#1817C2×C15111yescharacteristic, complemented
345#1817C2×C15111yescharacteristic, complemented
346#1797C2×C15111yescharacteristic, complemented
347#1749C2×C15111yescharacteristic, complemented
348#1728C2×C15111yescharacteristic, complemented
349C2×#336C2×C15111yescharacteristic, complemented
350C22×#41C4×C15111yescharacteristic
351C22×M16C22×C15112yes—
352C23×C8C22×C15112yes—
353C4×#41—28no—
354C2×C4×Q8C4×C15111yescharacteristic
355C2×C4×Q8C22×C15111yescharacteristic
356C2×C4×D4C4×C15111yescharacteristic
357C2×C4×D4C4×C15111yescharacteristic
358C2×C4×D4C4×C15111yescharacteristic
359C2×C4×D4C22×C15111yescharacteristic
360C2×C4×D4C22×C15111yescharacteristic
361C2×C4×D4C22×C15111yescharacteristic
362C2×#117C4×C15111yescharacteristic
363C2×#117C4×C15111yescharacteristic
364C2×#117C4×C15111yescharacteristic
365C22×C42C22×C15111yescharacteristic
366C22×C42C22×C15111yescharacteristic
367C22×C42C22×C15111yescharacteristic
368#435—28no—
369C2×C4⋊C8C22×C15112yes—
370C2×C22⋊C8C22×C15112yes—
371C2×C22⋊C8C22×C15112yes—
372C2×C22⋊C8C22×C15112yes—
373C2×C22⋊C8C22×C15112yes—
374C2×#97C22×C15112yes—
375#336C22×C15111yescharacteristic
376#336C22×C15111yescharacteristic
377#336C22×C15111yescharacteristic
378#336C22×C15112yes—
379#336C22×C15112yes—
380#336C22×C15112yes—
381#336C22×C15112yes—
382#336C22×C15111yescharacteristic
383C2×#41—24no—
384C2×#41—24no—
385C2×#41—24no—
386C22×Q8C2×C4×C15111yescharacteristic
387C22×D4C2×C4×C15111yescharacteristic
388C22×D4C2×C4×C15111yescharacteristic
389C22×D4C2×C4×C15111yescharacteristic
390C23×C4C2×C4×C15111yescharacteristic
391C23×C4C2×C4×C15111yescharacteristic
392C23×C4C2×C4×C15111yescharacteristic
393C23×C4C2×C4×C15111yescharacteristic
394C23×C4C2×C4×C15111yescharacteristic
395C23×C4C2×C4×C15111yescharacteristic
396C23×C4C23×C15111yescharacteristic
397C23×C4C23×C15111yescharacteristic
398C23×C4C23×C15111yescharacteristic
399C2×M16—24no—
400C2×M16—24no—
401C2×M16—42no—
402C22×C8—24no—
403C22×C8—24no—
404C22×C8—42no—
405C22×C8C23×C15112yes—
406C22×C8C23×C15112yes—
407C22×C8C23×C15112yes—
408C22×C8C23×C15112yes—
409C4×Q8—24no—
410C4×Q8—24no—
411C4×D4—24no—
412C4×D4—24no—
413C4×D4—24no—
414C4×D4—24no—
415C4×D4—24no—
416C4×D4D4×C15118yes—
417#117—24no—
418#117—24no—
419#117—24no—
420C2×C4⋊C4C2×C4×C15111yescharacteristic
421C2×C4⋊C4C2×C4×C15111yescharacteristic
422C2×C4⋊C4C2×C4×C15111yescharacteristic
423C2×C4⋊C4C2×C4×C15111yescharacteristic
424C2×C4⋊C4C2×C4×C15111yescharacteristic
425C2×C4⋊C4C2×C4×C15111yescharacteristic
426C2×C22⋊C4C2×C4×C15111yescharacteristic
427C2×C22⋊C4C2×C4×C15111yescharacteristic
428C2×C22⋊C4C2×C4×C15111yescharacteristic
429C2×C22⋊C4C2×C4×C15111yescharacteristic
430C2×C22⋊C4C2×C4×C15111yescharacteristic
431C2×C22⋊C4C2×C4×C15111yescharacteristic
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42C2×C4×C15111yescharacteristic
436C2×C42C2×C4×C15111yescharacteristic
437C2×C42C2×C4×C15111yescharacteristic
438C2×C42C2×C4×C15111yescharacteristic
439C2×C42C2×C4×C15111yescharacteristic
440C2×C42C2×C4×C15111yescharacteristic
441C2×C42C23×C15111yescharacteristic
442C2×C42C23×C15111yescharacteristic
443C2×C42C23×C15111yescharacteristic
444C2×C42C23×C15111yescharacteristic
445C4⋊C8—24no—
446C22⋊C8—24no—
447C22⋊C8—24no—
448C22⋊C8—24no—
449C22⋊C8—42no—
450#97—24no—
451C24C22×C4×C15111yescharacteristic
452C24C22×C4×C15111yescharacteristic
453C24C22×C4×C15111yescharacteristic
454#41—232no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4C22⋊C4×C15114yes—
466C2×D4M16×C15114yescomplemented
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4M16×C15114yescomplemented
495C22×C4C22×C4×C15111yescharacteristic
496C22×C4C22×C4×C15111yescharacteristic
497C22×C4C22×C4×C15111yescharacteristic
498C22×C4C22×C4×C15111yescharacteristic
499C22×C4C22×C4×C15111yescharacteristic
500C22×C4C22×C4×C15111yescharacteristic
501C22×C4C22×C4×C15111yescharacteristic
502C22×C4C22×C4×C15111yescharacteristic
503C22×C4C22×C4×C15111yescharacteristic
504C22×C4C22×C4×C15111yescharacteristic
505C22×C4C22×C4×C15111yescharacteristic
506C22×C4C2×D4×C15114yes—
507C22×C4C2×D4×C15114yes—
508C22×C4C24×C15111yescharacteristic
509M16—48no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—48no—
522C2×C8#41×C15114yescomplemented
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4C22⋊C4×C15114yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4C22⋊C4×C15114yes—
534C22⋊C4C22⋊C4×C15114yes—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42C2×D4×C15114yes—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23C2×C22⋊C4×C15112yes—
562C23C2×C22⋊C4×C15112yes—
563C23C2×M16×C15112yes—
564C23C2×M16×C15112yes—
565C23C2×M16×C15112yes—
566C23C23×C4×C15111yescharacteristic
567Q8—28no—
568D4—28no—
569D4—28no—
570D4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—28no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4C2×C22⋊C4×C15112yes—
609C2×C4C2×C22⋊C4×C15112yes—
610C2×C4C2×C22⋊C4×C15112yes—
611C2×C4C2×C22⋊C4×C15112yes—
612C2×C4C2×M16×C15112yes—
613C2×C4C2×M16×C15112yes—
614C2×C4C2×M16×C15112yes—
615C2×C4#131×C15112yes—
616C2×C4C22×D4×C15112yes—
617C2×C4C2×#41×C15112yes—
618C2×C4H(5,𝔽2)×C15111yescharacteristic
619C2×C42−1+4×C15111yescharacteristic
620C8—24no—
621C8—42no—
622C8—42no—
623C8—42no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22#407×C15114yes—
645C22C22×C22⋊C4×C15111yescharacteristic
646C22C4×#41×C15111yescharacteristic
647C22#520×C15111yescharacteristic
648C22C22×M16×C15111yescharacteristic
649C22C22×M16×C15111yescharacteristic
650C22C2×#131×C15111yescharacteristic
651C22#568×C15111yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4#546×C15112yes—
664C4#547×C15112yes—
665C2—24no—
666C2—42no—
667C2—42no—
668C2#2339×C15111yescharacteristic
669C2C2×#407×C15111yescharacteristic
670C2#2880×C15111yescharacteristic
671C2#2965×C15111yescharacteristic
672C2#2970×C15111yescharacteristic
673C2#2989×C15111yescharacteristic
674C2#2990×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC22×#41×C151C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C151C2semidirect
3. #1985×C151C2semidirect
4. #1870×C151C2semidirect
5. #1869×C151C2semidirect
6. #1817×C151C2semidirect
7. #1817×C151C2semidirect
8. #1797×C151C2semidirect
9. #1749×C151C2semidirect
10. #1728×C151C2semidirect
11. C2×#336×C151C2semidirect
128. C2×D4×C151M16semidirect
156. C22×C4×C151M16semidirect
184. C2×C8×C151#41semidirect
337. #22471C151direct (N × H)
338. C151#22471direct (N × H)
340. C2×#435C2×C151semidirect
341. #1985C2×C151semidirect
342. #1870C2×C151semidirect
343. #1869C2×C151semidirect
344. #1817C2×C151semidirect
345. #1817C2×C151semidirect
346. #1797C2×C151semidirect
347. #1749C2×C151semidirect
348. #1728C2×C151semidirect
349. C2×#336C2×C151semidirect
466. C2×D4M16×C151semidirect
494. C22×C4M16×C151semidirect
522. C2×C8#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C1512
C2×#435×C1512
#1985×C1512
#1870×C1512
#1869×C1512
#1817×C1512
#1797×C1512
#1749×C1512
#1728×C1512
C2×#336×C1512
#22471151