Finite Group Databasebeta

← C151×#24136 #50329061

Subgroups — C151×#24136 #50329061

Order 38656.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C151C211yesmaximal, characteristic, complemented
2C2×#478×C151C211yesmaximal, characteristic, complemented
3C2×#442×C151C211yesmaximal, characteristic, complemented
4#2537×C151C211yesmaximal, characteristic, complemented
5#2034×C151C211yesmaximal, characteristic, complemented
6#2033×C151C211yesmaximal, characteristic, complemented
7#1999×C151C211yesmaximal, characteristic, complemented
8#1999×C151C211yesmaximal, characteristic, complemented
9#1992×C151C211yesmaximal, characteristic, complemented
10#1955×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1853×C151C211yesmaximal, characteristic, complemented
15#1802×C151C211yesmaximal, characteristic, complemented
16C22×D8×C151C2211yescharacteristic
17#553×C151—24no—
18#553×C151—24no—
19C2×#126×C151—21no—
20C2×#125×C151C2211yescharacteristic
21C2×#123×C151—21no—
22C2×#121×C151—21no—
23C2×#121×C151—21no—
24C2×#121×C151C2211yescharacteristic
25C2×#121×C151C2211yescharacteristic
26C2×#121×C151C2211yescharacteristic
27C2×#121×C151C2211yescharacteristic
28C2×C4×D4×C151—21no—
29C2×C4×D4×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151C2211yescharacteristic
33C22×C4⋊C4×C151C2211yescharacteristic
34#478×C151—24no—
35#442×C151—24no—
36C2×#107×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×#106×C151C2211yescharacteristic
39C2×C4⋊C8×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic
49C2×C22⋊C8×C151C2211yescharacteristic
50C2×#97×C151C2211yescharacteristic
51#394×C151—21no—
52#394×C151—21no—
53#384×C151C2211yescharacteristic
54#380×C151—21no—
55#380×C151C2211yescharacteristic
56#380×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C22×D4×C151D411yescharacteristic
68C22×D4×C151C2311yescharacteristic
69C22×D4×C151C2311yescharacteristic
70C23×C4×C151—21no—
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C2×D8×C151—22no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82#126×C151—28no—
83#125×C151—22no—
84#125×C151D414yescomplemented
85#123×C151—28no—
86#121×C151—28no—
87#121×C151—22no—
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93#121×C151—41no—
94#121×C151—41no—
95#121×C151—44no—
96C4×D4×C151—28no—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102C4×D4×C151D414yescomplemented
103#117×C151—22no—
104#117×C151—22no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—22no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151D411yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151D411yescharacteristic
129C2×C22⋊C4×C151D411yescharacteristic
130C2×C42×C151—21no—
131C2×C42×C151C2311yescharacteristic
132#107×C151—22no—
133#106×C151—22no—
134#106×C151—22no—
135C4⋊C8×C151—22no—
136#102×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—41no—
141#102×C151—41no—
142C22⋊C8×C151—22no—
143C22⋊C8×C151—22no—
144C22⋊C8×C151—41no—
145C22⋊C8×C151—41no—
146#97×C151—22no—
147#95×C151—21no—
148#95×C151—21no—
149C24×C151—21no—
150C24×C151—21no—
151C24×C151C2×D411yescharacteristic
152C24×C151C2×D411yescharacteristic
153C2×D4×C151—24no—
154C2×D4×C151—22no—
155C2×D4×C151—24no—
156C2×D4×C151—22no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
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—41no—
168C2×D4×C151—42no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151—42no—
174C2×D4×C151—81no—
175C2×D4×C151—81no—
176C2×D4×C151—81no—
177C2×D4×C151—81no—
178C2×D4×C151C2×D412yes—
179C2×D4×C151#4112yes—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—24no—
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—21no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—24no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—42no—
201C22×C4×C151—42no—
202C22×C4×C151—42no—
203C22×C4×C151—81no—
204C22×C4×C151—81no—
205C22×C4×C151—81no—
206C22×C4×C151—81no—
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2411yescharacteristic
212D8×C151—28no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
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#4112yes—
225C4⋊C4×C151—24no—
226C4⋊C4×C151—24no—
227C4⋊C4×C151—24no—
228C4⋊C4×C151—22no—
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—21no—
237C4⋊C4×C151—21no—
238C4⋊C4×C151—42no—
239C4⋊C4×C151—81no—
240C4⋊C4×C151C2×D412yes—
241C4⋊C4×C151C2×D412yes—
242C4⋊C4×C151C2×D412yes—
243C22⋊C4×C151—24no—
244C22⋊C4×C151—24no—
245C22⋊C4×C151—24no—
246C22⋊C4×C151—24no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—42no—
250C22⋊C4×C151—42no—
251C22⋊C4×C151—42no—
252C22⋊C4×C151—42no—
253C22⋊C4×C151—42no—
254C42×C151—24no—
255C42×C151C2×D412yes—
256C42×C151C2×D412yes—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—22no—
264C23×C151—21no—
265C23×C151—22no—
266C23×C151—21no—
267C23×C151—21no—
268C23×C151—21no—
269C23×C151—21no—
270C23×C151—21no—
271C23×C151—21no—
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×C151AGL(1,ℤ/8)12yes—
285C23×C151C22×D411yescharacteristic
286D4×C151—22no—
287D4×C151—22no—
288D4×C151—22no—
289D4×C151—22no—
290D4×C151—44no—
291D4×C151—48no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—84no—
297D4×C151—84no—
298D4×C151—84no—
299C2×C4×C151—21no—
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—21no—
307C2×C4×C151—22no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
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—84no—
336C2×C4×C151—84no—
337C2×C4×C151—84no—
338C2×C4×C151#12012yes—
339C2×C4×C151#12012yes—
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C22×D411yescharacteristic
342C2×C4×C151C2×#4111yescharacteristic
343C2×C4×C151C2×#4111yescharacteristic
344C2×C4×C151H(5,𝔽2)11yescharacteristic
345C2×C4×C1512−1+411yescharacteristic
346C8×C151—22no—
347C8×C151—41no—
348C8×C151—41no—
349C8×C151—41no—
350C22×C151—22no—
351C22×C151—22no—
352C22×C151—22no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—41no—
356C22×C151—41no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—42no—
361C22×C151—42no—
362C22×C151—41no—
363C22×C151—42no—
364C22×C151—42no—
365C22×C151—41no—
366C22×C151—41no—
367C22×C151—42no—
368C22×C151—41no—
369C22×C151—42no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151—81no—
377C22×C151—81no—
378C22×C151C2×#12011yescharacteristic
379C22×C151#54611yescharacteristic
380C22×C151#54711yescharacteristic
381C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C151#57511yescharacteristic
383C22×C151#57611yescharacteristic
384C22×C151#57711yescharacteristic
385C4×C151—22no—
386C4×C151—22no—
387C4×C151—41no—
388C4×C151—41no—
389C4×C151—42no—
390C4×C151—42no—
391C4×C151—42no—
392C4×C151—81no—
393C4×C151—81no—
394C4×C151—81no—
395C4×C151#52511yescharacteristic
396C4×C151#53711yescharacteristic
397C4×C151#54811yescharacteristic
398C4×C151#55011yescharacteristic
399C2×C151—42no—
400C2×C151—81no—
401C2×C151—82no—
402C2×C151—82no—
403C2×C151#240711yescharacteristic
404C2×C151#300611yescharacteristic
405C2×C151#301211yescharacteristic
406C2×C151#330711yescharacteristic
407C2×C151#331811yescharacteristic
408C2×C151#334511yescharacteristic
409C2×C151#334711yescharacteristic
410#24136C15111yesmaximal, characteristic, direct product factor, Sylow
411C151#2413611yescharacteristic, direct product factor, Sylow
412C2×#553C2×C15111yescharacteristic, complemented
413C2×#478C2×C15111yescharacteristic, complemented
414C2×#442C2×C15111yescharacteristic, complemented
415#2537C2×C15111yescharacteristic, complemented
416#2034C2×C15111yescharacteristic, complemented
417#2033C2×C15111yescharacteristic, complemented
418#1999C2×C15111yescharacteristic, complemented
419#1999C2×C15111yescharacteristic, complemented
420#1992C2×C15111yescharacteristic, complemented
421#1955C2×C15111yescharacteristic, complemented
422#1875C2×C15111yescharacteristic, complemented
423#1874C2×C15111yescharacteristic, complemented
424#1854C2×C15111yescharacteristic, complemented
425#1853C2×C15111yescharacteristic, complemented
426#1802C2×C15111yescharacteristic, complemented
427C22×D8C22×C15111yescharacteristic
428#553—24no—
429#553—24no—
430C2×#126—21no—
431C2×#125C22×C15111yescharacteristic
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C15111yescharacteristic
436C2×#121C22×C15111yescharacteristic
437C2×#121C22×C15111yescharacteristic
438C2×#121C22×C15111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C15111yescharacteristic
441C2×C4×D4C22×C15111yescharacteristic
442C2×C4×D4C22×C15111yescharacteristic
443C2×#117C22×C15111yescharacteristic
444C22×C4⋊C4C22×C15111yescharacteristic
445#478—24no—
446#442—24no—
447C2×#107C22×C15111yescharacteristic
448C2×#106C22×C15111yescharacteristic
449C2×#106C22×C15111yescharacteristic
450C2×C4⋊C8C22×C15111yescharacteristic
451C2×#102C22×C15111yescharacteristic
452C2×#102C22×C15111yescharacteristic
453C2×#102C22×C15111yescharacteristic
454C2×#102C22×C15111yescharacteristic
455C2×#102C22×C15111yescharacteristic
456C2×#102C22×C15111yescharacteristic
457C2×C22⋊C8C22×C15111yescharacteristic
458C2×C22⋊C8C22×C15111yescharacteristic
459C2×C22⋊C8C22×C15111yescharacteristic
460C2×C22⋊C8C22×C15111yescharacteristic
461C2×#97C22×C15111yescharacteristic
462#394—21no—
463#394—21no—
464#384C22×C15111yescharacteristic
465#380—21no—
466#380C22×C15111yescharacteristic
467#380C22×C15111yescharacteristic
468#340C22×C15111yescharacteristic
469#340C22×C15111yescharacteristic
470#340C22×C15111yescharacteristic
471#340C22×C15111yescharacteristic
472#340C22×C15111yescharacteristic
473#340C22×C15111yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C15111yescharacteristic
479C22×D4C23×C15111yescharacteristic
480C22×D4C23×C15111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C15111yescharacteristic
485C23×C4C23×C15111yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C15111yescharacteristic
490C22×C8C23×C15111yescharacteristic
491C22×C8C23×C15111yescharacteristic
492C22×C8C23×C15111yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C15114yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C15114yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C15111yescharacteristic
524C2×C4⋊C4C23×C15111yescharacteristic
525C2×C4⋊C4C23×C15111yescharacteristic
526C2×C4⋊C4C23×C15111yescharacteristic
527C2×C4⋊C4C23×C15111yescharacteristic
528C2×C4⋊C4C23×C15111yescharacteristic
529C2×C4⋊C4C23×C15111yescharacteristic
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⋊C4D4×C15111yescharacteristic
540C2×C22⋊C4D4×C15111yescharacteristic
541C2×C42—21no—
542C2×C42C23×C15111yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C15111yescharacteristic
563C24C2×D4×C15111yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C15112yes—
590C2×D4#41×C15112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
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—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C15111yescharacteristic
619C22×C4C2×D4×C15111yescharacteristic
620C22×C4C2×D4×C15111yescharacteristic
621C22×C4C2×D4×C15111yescharacteristic
622C22×C4C24×C15111yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8#41×C15112yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C15112yes—
652C4⋊C4C2×D4×C15112yes—
653C4⋊C4C2×D4×C15112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C15112yes—
667C42C2×D4×C15112yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C15112yes—
696C23C22×D4×C15111yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C15112yes—
750C2×C4#120×C15112yes—
751C2×C4C22×D4×C15111yescharacteristic
752C2×C4C22×D4×C15111yescharacteristic
753C2×C4C2×#41×C15111yescharacteristic
754C2×C4C2×#41×C15111yescharacteristic
755C2×C4H(5,𝔽2)×C15111yescharacteristic
756C2×C42−1+4×C15111yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C15111yescharacteristic
790C22#546×C15111yescharacteristic
791C22#547×C15111yescharacteristic
792C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
793C22#575×C15111yescharacteristic
794C22#576×C15111yescharacteristic
795C22#577×C15111yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4#525×C15111yescharacteristic
807C4#537×C15111yescharacteristic
808C4#548×C15111yescharacteristic
809C4#550×C15111yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2#2407×C15111yescharacteristic
815C2#3006×C15111yescharacteristic
816C2#3012×C15111yescharacteristic
817C2#3307×C15111yescharacteristic
818C2#3318×C15111yescharacteristic
819C2#3345×C15111yescharacteristic
820C2#3347×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×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
1. C2×#553×C151C2semidirect
2. C2×#478×C151C2semidirect
3. C2×#442×C151C2semidirect
4. #2537×C151C2semidirect
5. #2034×C151C2semidirect
6. #2033×C151C2semidirect
7. #1999×C151C2semidirect
8. #1999×C151C2semidirect
9. #1992×C151C2semidirect
10. #1955×C151C2semidirect
11. #1875×C151C2semidirect
12. #1874×C151C2semidirect
13. #1854×C151C2semidirect
14. #1853×C151C2semidirect
15. #1802×C151C2semidirect
84. #125×C151D4semidirect
102. C4×D4×C151D4semidirect
410. #24136C151direct (N × H)
411. C151#24136direct (N × H)
412. C2×#553C2×C151semidirect
413. C2×#478C2×C151semidirect
414. C2×#442C2×C151semidirect
415. #2537C2×C151semidirect
416. #2034C2×C151semidirect
417. #2033C2×C151semidirect
418. #1999C2×C151semidirect
419. #1999C2×C151semidirect
420. #1992C2×C151semidirect
421. #1955C2×C151semidirect
422. #1875C2×C151semidirect
423. #1874C2×C151semidirect
424. #1854C2×C151semidirect
425. #1853C2×C151semidirect
426. #1802C2×C151semidirect
495. #125D4×C151semidirect
513. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1512
C2×#478×C1512
C2×#442×C1512
#2537×C1512
#2034×C1512
#2033×C1512
#1999×C1512
#1992×C1512
#1955×C1512
#1875×C1512
#1874×C1512
#1854×C1512
#1853×C1512
#1802×C1512
#24136151