Finite Group Databasebeta

← C151×#22870 #50327795

Subgroups — C151×#22870 #50327795

Order 38656.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic
2C2×C4×D8×C151C211yesmaximal, characteristic, complemented
3C22×#102×C151C211yesmaximal, characteristic, complemented
4#2361×C151C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
6#1970×C151C211yesmaximal, characteristic, complemented
7#1934×C151C211yesmaximal, characteristic, complemented
8#1925×C151C211yesmaximal, characteristic, complemented
9#1893×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1862×C151C211yesmaximal, characteristic, complemented
13#1852×C151C211yesmaximal, characteristic, complemented
14C4×#102×C151C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×C4×D4×C151—21no—
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic, complemented
25C22×C4⋊C4×C151C2211yescharacteristic
26C22×C22⋊C4×C151—21no—
27#447×C151C418yescomplemented
28C4×D8×C151—24no—
29C2×#107×C151C2211yescharacteristic, complemented
30C2×#107×C151C2211yescharacteristic, complemented
31C2×#102×C151—24no—
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic, complemented
39C2×#102×C151C2211yescharacteristic, complemented
40C2×C22⋊C8×C151C2211yescharacteristic
41C2×C4×C8×C151C2211yescharacteristic, complemented
42C2×C4×C8×C151C2211yescharacteristic, complemented
43#390×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic, complemented
46#389×C151C2211yescharacteristic, complemented
47#388×C151—21no—
48#386×C151—21no—
49#386×C151—21no—
50#386×C151—21no—
51#385×C151—21no—
52#380×C151C2211yescharacteristic
53#379×C151—21no—
54C4×C4⋊C4×C151C2211yescharacteristic, complemented
55C4×C22⋊C4×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#340×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61#336×C151C2211yescharacteristic, complemented
62C25×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151—22no—
65C22×D4×C151—21no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—41no—
69C22×D4×C151—41no—
70C22×D4×C151C2×C414yescomplemented
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C22×D4×C151C2311yescharacteristic
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151—21no—
77C23×C4×C151—21no—
78C23×C4×C151C2311yescharacteristic
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C2×D8×C151—41no—
82C2×D8×C151—41no—
83C2×D8×C151C2×C414yescomplemented
84C2×D8×C151C2×C414yescomplemented
85C22×C8×C151—22no—
86C22×C8×C151—22no—
87C22×C8×C151—41no—
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91C22×C8×C151C2311yescharacteristic
92#121×C151—22no—
93#121×C151C2×C414yescomplemented
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—41no—
98C4×D4×C151—41no—
99C4×D4×C151—41no—
100C4×D4×C151—44no—
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—41no—
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—44no—
122C2×C22⋊C4×C151D411yescharacteristic
123C2×C22⋊C4×C151D411yescharacteristic
124C2×C42×C151—21no—
125C2×C42×C151C2311yescharacteristic
126C2×C42×C151C2311yescharacteristic
127#107×C151—22no—
128#107×C151—41no—
129#102×C151—22no—
130#102×C151—22no—
131#102×C151—22no—
132#102×C151—22no—
133#102×C151—41no—
134#102×C151C2×C414yescomplemented
135#102×C151C2×C414yescomplemented
136#102×C151D414yescomplemented
137C22⋊C8×C151C2×C414yescomplemented
138C4×C8×C151—22no—
139C4×C8×C151—41no—
140#95×C151—21no—
141#95×C151—21no—
142#95×C151—21no—
143#95×C151D411yescharacteristic
144#95×C151D411yescharacteristic
145C24×C151—21no—
146C24×C151—21no—
147C24×C151—21no—
148C24×C151—24no—
149C24×C151—42no—
150C24×C151—42no—
151C24×C151—42no—
152C24×C151—42no—
153C24×C151—81no—
154C24×C151—81no—
155C24×C151C2×D411yescharacteristic
156C2×D4×C151—28no—
157C2×D4×C151—24no—
158C2×D4×C151—24no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—44no—
173C2×D4×C151—44no—
174C2×D4×C151—44no—
175C2×D4×C151—42no—
176C2×D4×C151—42no—
177C2×D4×C151—42no—
178C2×D4×C151—42no—
179C2×D4×C151C22×C412yes—
180C2×D4×C151C22×C412yes—
181C2×D4×C151C22×C412yes—
182C2×D4×C151C2×D412yes—
183C2×D4×C151#4112yes—
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—21no—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—42no—
196C22×C4×C151—42no—
197C22×C4×C151—42no—
198C22×C4×C151—42no—
199C22×C4×C151—42no—
200C22×C4×C151—42no—
201C22×C4×C151—81no—
202C22×C4×C151—81no—
203C22×C4×C151—81no—
204C22×C4×C151—81no—
205C22×C4×C151C22×C412yes—
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151#4112yes—
212C22×C4×C151C2411yescharacteristic
213D8×C151—28no—
214D8×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—44no—
225C2×C8×C151C22×C412yes—
226C2×C8×C151C22×C412yes—
227C2×C8×C151C2×D412yes—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151—21no—
234C4⋊C4×C151—21no—
235C4⋊C4×C151—21no—
236C4⋊C4×C151—42no—
237C4⋊C4×C151—42no—
238C4⋊C4×C151C22×C412yes—
239C4⋊C4×C151C2×D412yes—
240C22⋊C4×C151—22no—
241C22⋊C4×C151—24no—
242C22⋊C4×C151—42no—
243C22⋊C4×C151—42no—
244C22⋊C4×C151—42no—
245C22⋊C4×C151—42no—
246C22⋊C4×C151—42no—
247C22⋊C4×C151—42no—
248C22⋊C4×C151—42no—
249C22⋊C4×C151—81no—
250C22⋊C4×C151—81no—
251C22⋊C4×C151—81no—
252C22⋊C4×C151D814yescomplemented
253C42×C151—21no—
254C42×C151—21no—
255C42×C151—21no—
256C42×C151—21no—
257C42×C151—42no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—22no—
263C23×C151—22no—
264C23×C151—22no—
265C23×C151—22no—
266C23×C151—22no—
267C23×C151—48no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151—41no—
277C23×C151—41no—
278C23×C151—41no—
279C23×C151—41no—
280C23×C151—41no—
281C23×C151—41no—
282C23×C151—41no—
283C23×C151—41no—
284C23×C151—48no—
285C23×C151—84no—
286C23×C151—84no—
287C23×C151—84no—
288C23×C151—84no—
289C23×C151—84no—
290C23×C151C4×D412yes—
291C23×C151C2×D812yes—
292C23×C151#13512yes—
293C23×C151C22×D411yescharacteristic
294D4×C151—22no—
295D4×C151—22no—
296D4×C151—22no—
297D4×C151—22no—
298D4×C151—22no—
299D4×C151—22no—
300D4×C151—22no—
301D4×C151—48no—
302D4×C151—48no—
303D4×C151—41no—
304D4×C151—41no—
305D4×C151—41no—
306D4×C151—41no—
307D4×C151C4×D414yescomplemented
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—22no—
315C2×C4×C151—22no—
316C2×C4×C151—22no—
317C2×C4×C151—22no—
318C2×C4×C151—22no—
319C2×C4×C151—21no—
320C2×C4×C151—22no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—84no—
340C2×C4×C151—84no—
341C2×C4×C151—84no—
342C2×C4×C151—84no—
343C2×C4×C151C4×D412yes—
344C2×C4×C151C2×D812yes—
345C2×C4×C151C2×D812yes—
346C2×C4×C151C23×C411yescharacteristic
347C2×C4×C151C22×D411yescharacteristic
348C2×C4×C151C2×#4111yescharacteristic
349C2×C4×C151C2×#4111yescharacteristic
350C2×C4×C151H(5,𝔽2)11yescharacteristic
351C2×C4×C151H(5,𝔽2)11yescharacteristic
352C8×C151—22no—
353C8×C151—22no—
354C8×C151—22no—
355C8×C151—41no—
356C22×C151—22no—
357C22×C151—22no—
358C22×C151—22no—
359C22×C151—22no—
360C22×C151—22no—
361C22×C151—22no—
362C22×C151—24no—
363C22×C151—42no—
364C22×C151—42no—
365C22×C151—42no—
366C22×C151—42no—
367C22×C151—42no—
368C22×C151—42no—
369C22×C151—42no—
370C22×C151—42no—
371C22×C151—42no—
372C22×C151—42no—
373C22×C151—42no—
374C22×C151—42no—
375C22×C151—816no—
376C22×C151—81no—
377C22×C151—81no—
378C22×C151—81no—
379C22×C151—81no—
380C22×C151—81no—
381C22×C151—81no—
382C22×C151—81no—
383C22×C151—81no—
384C22×C151C4×D814yescomplemented
385C22×C151C2×C4×D411yescharacteristic
386C22×C151D4211yescharacteristic
387C22×C151#54611yescharacteristic
388C22×C151C22×D811yescharacteristic
389C22×C151C2×#13511yescharacteristic
390C22×C151#57611yescharacteristic
391C22×C151#57711yescharacteristic
392C4×C151—22no—
393C4×C151—22no—
394C4×C151—22no—
395C4×C151—42no—
396C4×C151—42no—
397C4×C151—41no—
398C4×C151—41no—
399C4×C151—81no—
400C4×C151—81no—
401C4×C151—81no—
402C4×C151C2×C4×D411yescharacteristic
403C4×C151#51811yescharacteristic
404C4×C151#54611yescharacteristic
405C4×C151#55111yescharacteristic
406C2×C151—24no—
407C2×C151—44no—
408C2×C151—82no—
409C2×C151—82no—
410C2×C151#235811yescharacteristic
411C2×C151C2×C4×D811yescharacteristic
412C2×C151#294611yescharacteristic
413C2×C151D4×D811yescharacteristic
414C2×C151#328211yescharacteristic
415C2×C151#329411yescharacteristic
416C2×C151#329711yescharacteristic
417#22870C15111yesmaximal, characteristic, direct product factor, Sylow
418C151#2287011yescharacteristic, direct product factor, Sylow
419C2×#447C2×C15111yescharacteristic
420C2×C4×D8C2×C15111yescharacteristic, complemented
421C22×#102C2×C15111yescharacteristic, complemented
422#2361C2×C15111yescharacteristic, complemented
423D4×C22⋊C4C2×C15111yescharacteristic, complemented
424#1970C2×C15111yescharacteristic, complemented
425#1934C2×C15111yescharacteristic, complemented
426#1925C2×C15111yescharacteristic, complemented
427#1893C2×C15111yescharacteristic, complemented
428#1879C2×C15111yescharacteristic, complemented
429#1879C2×C15111yescharacteristic, complemented
430#1862C2×C15111yescharacteristic, complemented
431#1852C2×C15111yescharacteristic, complemented
432C4×#102C2×C15111yescharacteristic, complemented
433C8×C22⋊C4C2×C15111yescharacteristic, complemented
434C23×D4C22×C15111yescharacteristic
435C22×D8C22×C15111yescharacteristic
436C22×D8C22×C15111yescharacteristic
437C23×C8C22×C15111yescharacteristic
438C2×#121C22×C15111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C15111yescharacteristic
441C2×C4×D4C22×C15111yescharacteristic
442C2×C4×D4C22×C15111yescharacteristic, complemented
443C22×C4⋊C4C22×C15111yescharacteristic
444C22×C22⋊C4—21no—
445#447C4×C15118yescomplemented
446C4×D8—24no—
447C2×#107C22×C15111yescharacteristic, complemented
448C2×#107C22×C15111yescharacteristic, complemented
449C2×#102—24no—
450C2×#102C22×C15111yescharacteristic
451C2×#102C22×C15111yescharacteristic
452C2×#102C22×C15111yescharacteristic
453C2×#102C22×C15111yescharacteristic
454C2×#102C22×C15111yescharacteristic
455C2×#102C22×C15111yescharacteristic
456C2×#102C22×C15111yescharacteristic, complemented
457C2×#102C22×C15111yescharacteristic, complemented
458C2×C22⋊C8C22×C15111yescharacteristic
459C2×C4×C8C22×C15111yescharacteristic, complemented
460C2×C4×C8C22×C15111yescharacteristic, complemented
461#390C22×C15111yescharacteristic
462#390C22×C15111yescharacteristic
463#390C22×C15111yescharacteristic, complemented
464#389C22×C15111yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—21no—
468#386—21no—
469#385—21no—
470#380C22×C15111yescharacteristic
471#379—21no—
472C4×C4⋊C4C22×C15111yescharacteristic, complemented
473C4×C22⋊C4C22×C15111yescharacteristic
474#340C22×C15111yescharacteristic, complemented
475#340C22×C15111yescharacteristic, complemented
476#340C22×C15111yescharacteristic, complemented
477#340C22×C15111yescharacteristic, complemented
478#336C22×C15111yescharacteristic, complemented
479#336C22×C15111yescharacteristic, complemented
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4C2×C4×C15114yescomplemented
489C22×D4C23×C15111yescharacteristic
490C22×D4C23×C15111yescharacteristic
491C22×D4C23×C15111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C15111yescharacteristic
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—41no—
500C2×D8—41no—
501C2×D8C2×C4×C15114yescomplemented
502C2×D8C2×C4×C15114yescomplemented
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8C23×C15111yescharacteristic
507C22×C8C23×C15111yescharacteristic
508C22×C8C23×C15111yescharacteristic
509C22×C8C23×C15111yescharacteristic
510#121—22no—
511#121C2×C4×C15114yescomplemented
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—41no—
516C4×D4—41no—
517C4×D4—41no—
518C4×D4—44no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4C23×C15111yescharacteristic
524C2×C4⋊C4C23×C15111yescharacteristic
525C2×C4⋊C4C23×C15111yescharacteristic
526C2×C4⋊C4C23×C15111yescharacteristic
527C2×C4⋊C4C23×C15111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4D4×C15111yescharacteristic
541C2×C22⋊C4D4×C15111yescharacteristic
542C2×C42—21no—
543C2×C42C23×C15111yescharacteristic
544C2×C42C23×C15111yescharacteristic
545#107—22no—
546#107—41no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102C2×C4×C15114yescomplemented
553#102C2×C4×C15114yescomplemented
554#102D4×C15114yescomplemented
555C22⋊C8C2×C4×C15114yescomplemented
556C4×C8—22no—
557C4×C8—41no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C15111yescharacteristic
562#95D4×C15111yescharacteristic
563C24—21no—
564C24—21no—
565C24—21no—
566C24—24no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24C2×D4×C15111yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4C22×C4×C15112yes—
598C2×D4C22×C4×C15112yes—
599C2×D4C22×C4×C15112yes—
600C2×D4C2×D4×C15112yes—
601C2×D4#41×C15112yes—
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—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4C22×C4×C15112yes—
624C22×C4C2×D4×C15111yescharacteristic
625C22×C4C2×D4×C15111yescharacteristic
626C22×C4C2×D4×C15111yescharacteristic
627C22×C4C2×D4×C15111yescharacteristic
628C22×C4C2×D4×C15111yescharacteristic
629C22×C4#41×C15112yes—
630C22×C4C24×C15111yescharacteristic
631D8—28no—
632D8—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—44no—
643C2×C8C22×C4×C15112yes—
644C2×C8C22×C4×C15112yes—
645C2×C8C2×D4×C15112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4C22×C4×C15112yes—
657C4⋊C4C2×D4×C15112yes—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C22⋊C4D8×C15114yescomplemented
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—48no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23C4×D4×C15112yes—
709C23C2×D8×C15112yes—
710C23#135×C15112yes—
711C23C22×D4×C15111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4C4×D4×C15114yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4C4×D4×C15112yes—
762C2×C4C2×D8×C15112yes—
763C2×C4C2×D8×C15112yes—
764C2×C4C23×C4×C15111yescharacteristic
765C2×C4C22×D4×C15111yescharacteristic
766C2×C4C2×#41×C15111yescharacteristic
767C2×C4C2×#41×C15111yescharacteristic
768C2×C4H(5,𝔽2)×C15111yescharacteristic
769C2×C4H(5,𝔽2)×C15111yescharacteristic
770C8—22no—
771C8—22no—
772C8—22no—
773C8—41no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—816no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C4×D8×C15114yescomplemented
803C22C2×C4×D4×C15111yescharacteristic
804C22D42×C15111yescharacteristic
805C22#546×C15111yescharacteristic
806C22C22×D8×C15111yescharacteristic
807C22C2×#135×C15111yescharacteristic
808C22#576×C15111yescharacteristic
809C22#577×C15111yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C2×C4×D4×C15111yescharacteristic
821C4#518×C15111yescharacteristic
822C4#546×C15111yescharacteristic
823C4#551×C15111yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—82no—
828C2#2358×C15111yescharacteristic
829C2C2×C4×D8×C15111yescharacteristic
830C2#2946×C15111yescharacteristic
831C2D4×D8×C15111yescharacteristic
832C2#3282×C15111yescharacteristic
833C2#3294×C15111yescharacteristic
834C2#3297×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C2×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
2. C2×C4×D8×C151C2semidirect
3. C22×#102×C151C2semidirect
4. #2361×C151C2semidirect
5. D4×C22⋊C4×C151C2semidirect
6. #1970×C151C2semidirect
7. #1934×C151C2semidirect
8. #1925×C151C2semidirect
9. #1893×C151C2semidirect
10. #1879×C151C2semidirect
11. #1879×C151C2semidirect
12. #1862×C151C2semidirect
13. #1852×C151C2semidirect
14. C4×#102×C151C2semidirect
15. C8×C22⋊C4×C151C2semidirect
24. C2×C4×D4×C151C22semidirect
27. #447×C151C4semidirect
29. C2×#107×C151C22semidirect
30. C2×#107×C151C22semidirect
38. C2×#102×C151C22semidirect
39. C2×#102×C151C22semidirect
41. C2×C4×C8×C151C22semidirect
42. C2×C4×C8×C151C22semidirect
45. #390×C151C22semidirect
46. #389×C151C22semidirect
54. C4×C4⋊C4×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #340×C151C22semidirect
60. #336×C151C22semidirect
61. #336×C151C22semidirect
70. C22×D4×C151C2×C4semidirect
83. C2×D8×C151C2×C4semidirect
84. C2×D8×C151C2×C4semidirect
93. #121×C151C2×C4semidirect
134. #102×C151C2×C4semidirect
135. #102×C151C2×C4semidirect
136. #102×C151D4semidirect
137. C22⋊C8×C151C2×C4semidirect
252. C22⋊C4×C151D8semidirect
307. D4×C151C4×D4semidirect
384. C22×C151C4×D8semidirect
417. #22870C151direct (N × H)
418. C151#22870direct (N × H)
420. C2×C4×D8C2×C151semidirect
421. C22×#102C2×C151semidirect
422. #2361C2×C151semidirect
423. D4×C22⋊C4C2×C151semidirect
424. #1970C2×C151semidirect
425. #1934C2×C151semidirect
426. #1925C2×C151semidirect
427. #1893C2×C151semidirect
428. #1879C2×C151semidirect
429. #1879C2×C151semidirect
430. #1862C2×C151semidirect
431. #1852C2×C151semidirect
432. C4×#102C2×C151semidirect
433. C8×C22⋊C4C2×C151semidirect
442. C2×C4×D4C22×C151semidirect
445. #447C4×C151semidirect
447. C2×#107C22×C151semidirect
448. C2×#107C22×C151semidirect
456. C2×#102C22×C151semidirect
457. C2×#102C22×C151semidirect
459. C2×C4×C8C22×C151semidirect
460. C2×C4×C8C22×C151semidirect
463. #390C22×C151semidirect
464. #389C22×C151semidirect
472. C4×C4⋊C4C22×C151semidirect
474. #340C22×C151semidirect
475. #340C22×C151semidirect
476. #340C22×C151semidirect
477. #340C22×C151semidirect
478. #336C22×C151semidirect
479. #336C22×C151semidirect
488. C22×D4C2×C4×C151semidirect
501. C2×D8C2×C4×C151semidirect
502. C2×D8C2×C4×C151semidirect
511. #121C2×C4×C151semidirect
552. #102C2×C4×C151semidirect
553. #102C2×C4×C151semidirect
554. #102D4×C151semidirect
555. C22⋊C8C2×C4×C151semidirect
670. C22⋊C4D8×C151semidirect
725. D4C4×D4×C151semidirect
802. C22C4×D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
C2×C4×D8×C1512
C22×#102×C1512
#2361×C1512
D4×C22⋊C4×C1512
#1970×C1512
#1934×C1512
#1925×C1512
#1893×C1512
#1879×C1512
#1862×C1512
#1852×C1512
C4×#102×C1512
C8×C22⋊C4×C1512
#22870151