Finite Group Databasebeta

← C151×#23580 #50328505

Subgroups — C151×#23580 #50328505

Order 38656.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C151C211yesmaximal, characteristic, complemented
2C2×#442×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic, complemented
4#2324×C151C211yesmaximal, characteristic, complemented
5#2059×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#2025×C151C211yesmaximal, characteristic, complemented
10#2011×C151C211yesmaximal, characteristic, complemented
11#1999×C151C211yesmaximal, characteristic, complemented
12#1999×C151C211yesmaximal, characteristic, complemented
13#1762×C151C211yesmaximal, characteristic, complemented
14C4×#102×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C22×D8×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18#540×C151—24no—
19#540×C151—24no—
20C2×#127×C151C2211yescharacteristic
21C2×#125×C151C2211yescharacteristic
22C2×#123×C151—21no—
23C2×#123×C151—21no—
24C2×#121×C151—21no—
25C2×#121×C151—21no—
26C2×#121×C151C2211yescharacteristic
27C2×#121×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151C2211yescharacteristic
33#442×C151—24no—
34C4×D8×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×#97×C151C2211yescharacteristic
48C2×C4×C8×C151C2211yescharacteristic
49#390×C151—21no—
50#390×C151C2211yescharacteristic
51#389×C151C2211yescharacteristic
52#388×C151—21no—
53#386×C151—21no—
54#385×C151—21no—
55#380×C151C2211yescharacteristic
56C4×C4⋊C4×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C22×D4×C151—21no—
68C22×D4×C151C2311yescharacteristic
69C22×D4×C151C2311yescharacteristic
70C22×D4×C151C2311yescharacteristic
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C23×C4×C151—21no—
74C23×C4×C151C2311yescharacteristic
75C2×D8×C151—22no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C2×D8×C151—22no—
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85#127×C151—22no—
86#127×C151—22no—
87#125×C151—22no—
88#125×C151—22no—
89#123×C151—28no—
90#123×C151—28no—
91#121×C151—28no—
92#121×C151—28no—
93#121×C151—22no—
94#121×C151—22no—
95#121×C151—22no—
96#121×C151—22no—
97#121×C151—22no—
98#121×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102C4×D4×C151—22no—
103C4×D4×C151D414yescomplemented
104C4×D4×C151D414yescomplemented
105#117×C151—22no—
106#117×C151—22no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151D411yescharacteristic
111C2×C4⋊C4×C151D411yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
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×C151D411yescharacteristic
127C2×C22⋊C4×C151D411yescharacteristic
128C2×C42×C151—21no—
129C2×C42×C151C2311yescharacteristic
130C2×C42×C151C2311yescharacteristic
131#107×C151—22no—
132#106×C151—22no—
133#102×C151—22no—
134#102×C151—22no—
135#102×C151—22no—
136#102×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—22no—
141C22⋊C8×C151—22no—
142C22⋊C8×C151—22no—
143#97×C151—22no—
144C4×C8×C151—22no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151—21no—
149C24×C151—21no—
150C24×C151—21no—
151C24×C151C2×D411yescharacteristic
152C2×D4×C151—24no—
153C2×D4×C151—24no—
154C2×D4×C151—24no—
155C2×D4×C151—24no—
156C2×D4×C151—24no—
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—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—81no—
173C2×D4×C151—81no—
174C2×D4×C151—81no—
175C2×D4×C151—81no—
176C2×D4×C151—81no—
177C2×D4×C151—81no—
178C2×D4×C151—81no—
179C2×D4×C151—81no—
180C2×D4×C151—81no—
181C2×D4×C151—81no—
182C2×D4×C151C2×D412yes—
183C2×D4×C151C2×D412yes—
184C2×D4×C151#4112yes—
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—24no—
195C22×C4×C151—24no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—42no—
199C22×C4×C151—81no—
200C22×C4×C151—81no—
201C22×C4×C151—81no—
202C22×C4×C151—81no—
203C22×C4×C151—81no—
204C22×C4×C151—81no—
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2411yescharacteristic
211D8×C151—28no—
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#4112yes—
224C2×C8×C151#4112yes—
225C4⋊C4×C151—24no—
226C4⋊C4×C151—24no—
227C4⋊C4×C151—22no—
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—81no—
237C4⋊C4×C151C2×D412yes—
238C4⋊C4×C151C2×D412yes—
239C4⋊C4×C151#4112yes—
240C22⋊C4×C151—24no—
241C22⋊C4×C151—24no—
242C22⋊C4×C151—24no—
243C22⋊C4×C151—24no—
244C22⋊C4×C151—24no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—42no—
248C22⋊C4×C151—81no—
249C22⋊C4×C151—81no—
250C22⋊C4×C151—81no—
251C42×C151—21no—
252C42×C151—21no—
253C42×C151—81no—
254C42×C151C2×D412yes—
255C42×C151C2×D412yes—
256C23×C151—22no—
257C23×C151—22no—
258C23×C151—21no—
259C23×C151—22no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—21no—
264C23×C151—21no—
265C23×C151—21no—
266C23×C151—41no—
267C23×C151—41no—
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×C151C22×D411yescharacteristic
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—22no—
288D4×C151—22no—
289D4×C151—22no—
290D4×C151—22no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—84no—
298D4×C151—84no—
299D4×C151—84no—
300D4×C151—84no—
301D4×C151—84no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—22no—
310C2×C4×C151—22no—
311C2×C4×C151—21no—
312C2×C4×C151—22no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
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—84no—
335C2×C4×C151—84no—
336C2×C4×C151—84no—
337C2×C4×C151#12012yes—
338C2×C4×C151#12012yes—
339C2×C4×C151C22×D411yescharacteristic
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C2×#4111yescharacteristic
342C2×C4×C151C2×#4111yescharacteristic
343C2×C4×C151C2×#4111yescharacteristic
344C2×C4×C151C2×#4111yescharacteristic
345C8×C151—22no—
346C8×C151—22no—
347C8×C151—41no—
348C8×C151—41no—
349C22×C151—41no—
350C22×C151—42no—
351C22×C151—41no—
352C22×C151—42no—
353C22×C151—41no—
354C22×C151—42no—
355C22×C151—42no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—42no—
362C22×C151—42no—
363C22×C151—41no—
364C22×C151—42no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151—81no—
368C22×C151—81no—
369C22×C151—81no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151—81no—
377C22×C151C2×#12011yescharacteristic
378C22×C151#52511yescharacteristic
379C22×C151#53211yescharacteristic
380C22×C151#57611yescharacteristic
381C22×C151#57611yescharacteristic
382C22×C151#57611yescharacteristic
383C22×C151#57711yescharacteristic
384C4×C151—22no—
385C4×C151—22no—
386C4×C151—42no—
387C4×C151—41no—
388C4×C151—41no—
389C4×C151—42no—
390C4×C151—41no—
391C4×C151—42no—
392C4×C151—81no—
393C4×C151—81no—
394C4×C151#52511yescharacteristic
395C4×C151#52511yescharacteristic
396C4×C151#53211yescharacteristic
397C4×C151#53211yescharacteristic
398C2×C151—81no—
399C2×C151—82no—
400C2×C151—82no—
401C2×C151—82no—
402C2×C151#238811yescharacteristic
403C2×C151#300811yescharacteristic
404C2×C151#301211yescharacteristic
405C2×C151#311911yescharacteristic
406C2×C151#312211yescharacteristic
407C2×C151#317611yescharacteristic
408C2×C151#317911yescharacteristic
409#23580C15111yesmaximal, characteristic, direct product factor, Sylow
410C151#2358011yescharacteristic, direct product factor, Sylow
411C2×#540C2×C15111yescharacteristic, complemented
412C2×#442C2×C15111yescharacteristic, complemented
413C2×C4×D8C2×C15111yescharacteristic, complemented
414#2324C2×C15111yescharacteristic, complemented
415#2059C2×C15111yescharacteristic, complemented
416#2041C2×C15111yescharacteristic, complemented
417#2034C2×C15111yescharacteristic, complemented
418#2033C2×C15111yescharacteristic, complemented
419#2025C2×C15111yescharacteristic, complemented
420#2011C2×C15111yescharacteristic, complemented
421#1999C2×C15111yescharacteristic, complemented
422#1999C2×C15111yescharacteristic, complemented
423#1762C2×C15111yescharacteristic, complemented
424C4×#102C2×C15111yescharacteristic, complemented
425#1750C2×C15111yescharacteristic, complemented
426C22×D8C22×C15111yescharacteristic
427C22×D8C22×C15111yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C15111yescharacteristic
431C2×#125C22×C15111yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C15111yescharacteristic
437C2×#121C22×C15111yescharacteristic
438C2×#121C22×C15111yescharacteristic
439C2×C4×D4C22×C15111yescharacteristic
440C2×C4×D4C22×C15111yescharacteristic
441C2×C4×D4C22×C15111yescharacteristic
442C2×#117C22×C15111yescharacteristic
443#442—24no—
444C4×D8—24no—
445C2×#107C22×C15111yescharacteristic
446C2×#106C22×C15111yescharacteristic
447C2×#102C22×C15111yescharacteristic
448C2×#102C22×C15111yescharacteristic
449C2×#102C22×C15111yescharacteristic
450C2×#102C22×C15111yescharacteristic
451C2×#102C22×C15111yescharacteristic
452C2×#102C22×C15111yescharacteristic
453C2×#102C22×C15111yescharacteristic
454C2×#102C22×C15111yescharacteristic
455C2×C22⋊C8C22×C15111yescharacteristic
456C2×C22⋊C8C22×C15111yescharacteristic
457C2×#97C22×C15111yescharacteristic
458C2×C4×C8C22×C15111yescharacteristic
459#390—21no—
460#390C22×C15111yescharacteristic
461#389C22×C15111yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C15111yescharacteristic
466C4×C4⋊C4C22×C15111yescharacteristic
467#340C22×C15111yescharacteristic
468#340C22×C15111yescharacteristic
469#340C22×C15111yescharacteristic
470#340C22×C15111yescharacteristic
471#336C22×C15111yescharacteristic
472#336C22×C15111yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C15111yescharacteristic
479C22×D4C23×C15111yescharacteristic
480C22×D4C23×C15111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C15111yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C15111yescharacteristic
492C22×C8C23×C15111yescharacteristic
493C22×C8C23×C15111yescharacteristic
494C22×C8C23×C15111yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C15114yescomplemented
514C4×D4D4×C15114yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C15111yescharacteristic
521C2×C4⋊C4D4×C15111yescharacteristic
522C2×C4⋊C4C23×C15111yescharacteristic
523C2×C4⋊C4C23×C15111yescharacteristic
524C2×C4⋊C4C23×C15111yescharacteristic
525C2×C4⋊C4C23×C15111yescharacteristic
526C2×C4⋊C4C23×C15111yescharacteristic
527C2×C22⋊C4—21no—
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⋊C4D4×C15111yescharacteristic
537C2×C22⋊C4D4×C15111yescharacteristic
538C2×C42—21no—
539C2×C42C23×C15111yescharacteristic
540C2×C42C23×C15111yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C15111yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
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—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C15112yes—
593C2×D4C2×D4×C15112yes—
594C2×D4#41×C15112yes—
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—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C15111yescharacteristic
616C22×C4C2×D4×C15111yescharacteristic
617C22×C4C2×D4×C15111yescharacteristic
618C22×C4C2×D4×C15111yescharacteristic
619C22×C4C2×D4×C15111yescharacteristic
620C22×C4C24×C15111yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
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#41×C15112yes—
634C2×C8#41×C15112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C15112yes—
648C4⋊C4C2×D4×C15112yes—
649C4⋊C4#41×C15112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C15112yes—
665C42C2×D4×C15112yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C15111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
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—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C15112yes—
748C2×C4#120×C15112yes—
749C2×C4C22×D4×C15111yescharacteristic
750C2×C4C22×D4×C15111yescharacteristic
751C2×C4C2×#41×C15111yescharacteristic
752C2×C4C2×#41×C15111yescharacteristic
753C2×C4C2×#41×C15111yescharacteristic
754C2×C4C2×#41×C15111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C15111yescharacteristic
788C22#525×C15111yescharacteristic
789C22#532×C15111yescharacteristic
790C22#576×C15111yescharacteristic
791C22#576×C15111yescharacteristic
792C22#576×C15111yescharacteristic
793C22#577×C15111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4#525×C15111yescharacteristic
805C4#525×C15111yescharacteristic
806C4#532×C15111yescharacteristic
807C4#532×C15111yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2#2388×C15111yescharacteristic
813C2#3008×C15111yescharacteristic
814C2#3012×C15111yescharacteristic
815C2#3119×C15111yescharacteristic
816C2#3122×C15111yescharacteristic
817C2#3176×C15111yescharacteristic
818C2#3179×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C151C2semidirect
2. C2×#442×C151C2semidirect
3. C2×C4×D8×C151C2semidirect
4. #2324×C151C2semidirect
5. #2059×C151C2semidirect
6. #2041×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #2025×C151C2semidirect
10. #2011×C151C2semidirect
11. #1999×C151C2semidirect
12. #1999×C151C2semidirect
13. #1762×C151C2semidirect
14. C4×#102×C151C2semidirect
15. #1750×C151C2semidirect
103. C4×D4×C151D4semidirect
104. C4×D4×C151D4semidirect
409. #23580C151direct (N × H)
410. C151#23580direct (N × H)
411. C2×#540C2×C151semidirect
412. C2×#442C2×C151semidirect
413. C2×C4×D8C2×C151semidirect
414. #2324C2×C151semidirect
415. #2059C2×C151semidirect
416. #2041C2×C151semidirect
417. #2034C2×C151semidirect
418. #2033C2×C151semidirect
419. #2025C2×C151semidirect
420. #2011C2×C151semidirect
421. #1999C2×C151semidirect
422. #1999C2×C151semidirect
423. #1762C2×C151semidirect
424. C4×#102C2×C151semidirect
425. #1750C2×C151semidirect
513. C4×D4D4×C151semidirect
514. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1512
C2×#442×C1512
C2×C4×D8×C1512
#2324×C1512
#2059×C1512
#2041×C1512
#2034×C1512
#2033×C1512
#2025×C1512
#2011×C1512
#1999×C1512
#1762×C1512
C4×#102×C1512
#1750×C1512
#23580151