Finite Group Databasebeta

← C151×#23938 #50328863

Subgroups — C151×#23938 #50328863

Order 38656.

1308 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C151C211yesmaximal, characteristic, complemented
2C2×#452×C151C211yesmaximal, characteristic, complemented
3C2×#449×C151C211yesmaximal, characteristic
4#2297×C151C211yesmaximal, characteristic, complemented
5#2026×C151C211yesmaximal, characteristic, complemented
6#2025×C151C211yesmaximal, characteristic, complemented
7#2015×C151C211yesmaximal, characteristic, complemented
8#2012×C151C211yesmaximal, characteristic, complemented
9#1880×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1877×C151C211yesmaximal, characteristic, complemented
13#1875×C151C211yesmaximal, characteristic, complemented
14#1873×C151C211yesmaximal, characteristic, complemented
15#1817×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×SD16×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic
21#529×C151—24no—
22#529×C151—24no—
23C2×#126×C151—21no—
24C2×#125×C151C2211yescharacteristic
25C2×#124×C151C2211yescharacteristic
26C2×#123×C151—21no—
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×D4×C151—21no—
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151—21no—
33C2×#117×C151C2211yescharacteristic
34C22×C42×C151C2211yescharacteristic
35#452×C151—24no—
36#449×C151—24no—
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47#391×C151C2211yescharacteristic
48#391×C151C2211yescharacteristic
49#390×C151C2211yescharacteristic
50#390×C151C2211yescharacteristic
51#386×C151—21no—
52#386×C151—21no—
53C4×C22⋊C4×C151—21no—
54C4×C22⋊C4×C151—21no—
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—41no—
68C2×#41×C151—41no—
69C22×Q8×C151C2311yescharacteristic
70C22×Q8×C151C2311yescharacteristic
71C22×D4×C151—21no—
72C22×D4×C151—21no—
73C22×D4×C151C2311yescharacteristic
74C22×D4×C151C2311yescharacteristic
75C23×C4×C151—21no—
76C23×C4×C151—21no—
77C23×C4×C151D411yescharacteristic
78C23×C4×C151D411yescharacteristic
79C23×C4×C151C2311yescharacteristic
80C2×Q16×C151—22no—
81C2×Q16×C151—22no—
82C2×Q16×C151—41no—
83C2×SD16×C151—22no—
84C2×SD16×C151—22no—
85C2×SD16×C151—22no—
86C2×SD16×C151—22no—
87C2×SD16×C151—41no—
88C2×SD16×C151—41no—
89C2×D8×C151—22no—
90C2×D8×C151—22no—
91C2×D8×C151—41no—
92C22×C8×C151C2311yescharacteristic
93C22×C8×C151C2311yescharacteristic
94C22×C8×C151C2311yescharacteristic
95C22×C8×C151C2311yescharacteristic
96#126×C151—28no—
97#125×C151—22no—
98#125×C151—22no—
99#124×C151—22no—
100#124×C151—22no—
101#123×C151—28no—
102C22⋊Q8×C151—22no—
103C22⋊Q8×C151D414yes—
104#121×C151—22no—
105#121×C151D414yes—
106C4×Q8×C151—22no—
107C4×Q8×C151—22no—
108C4×D4×C151—28no—
109C4×D4×C151—22no—
110C4×D4×C151—22no—
111#117×C151—28no—
112#117×C151—41no—
113#117×C151—41no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C4⋊C4×C151C2311yescharacteristic
121C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C42×C151—22no—
133C2×C42×C151—22no—
134C2×C42×C151—21no—
135C2×C42×C151—21no—
136C2×C42×C151D411yescharacteristic
137C2×C42×C151D411yescharacteristic
138C2×C42×C151C2311yescharacteristic
139C2×C42×C151C2311yescharacteristic
140#103×C151—22no—
141#103×C151—22no—
142#103×C151—41no—
143#103×C151—41no—
144#102×C151—22no—
145#102×C151—22no—
146#102×C151—41no—
147#102×C151—41no—
148C22⋊C8×C151—22no—
149C22⋊C8×C151—22no—
150#95×C151—21no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—21no—
154C24×C151—21no—
155C24×C151—21no—
156C24×C151C2×D411yescharacteristic
157#41×C151—44no—
158#41×C151—44no—
159#41×C151—44no—
160#41×C151—44no—
161C2×Q8×C151—21no—
162C2×Q8×C151—21no—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151—21no—
167C2×Q8×C151—21no—
168C2×Q8×C151—21no—
169C2×Q8×C151—21no—
170C2×Q8×C151—21no—
171C2×Q8×C151C2×D412yes—
172C2×Q8×C151#4112yes—
173C2×D4×C151—24no—
174C2×D4×C151—24no—
175C2×D4×C151—21no—
176C2×D4×C151—21no—
177C2×D4×C151—21no—
178C2×D4×C151—21no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—42no—
186C2×D4×C151—42no—
187C2×D4×C151—42no—
188C2×D4×C151—42no—
189C2×D4×C151C2×D412yes—
190C2×D4×C151#4112yes—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—24no—
196C22×C4×C151—24no—
197C22×C4×C151—22no—
198C22×C4×C151—22no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—22no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—41no—
207C22×C4×C151—41no—
208C22×C4×C151—41no—
209C22×C4×C151—42no—
210C22×C4×C151—42no—
211C22×C4×C151—42no—
212C22×C4×C151—42no—
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151C2×D411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D412yes—
218C22×C4×C151C2×D412yes—
219C22×C4×C151C2×D411yescharacteristic
220C22×C4×C151C2411yescharacteristic
221Q16×C151—44no—
222SD16×C151—44no—
223SD16×C151—44no—
224D8×C151—44no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C4⋊C4×C151—24no—
238C4⋊C4×C151—24no—
239C4⋊C4×C151—24no—
240C4⋊C4×C151—24no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151C2×D412yes—
248C4⋊C4×C151C2×D412yes—
249C22⋊C4×C151—24no—
250C22⋊C4×C151—24no—
251C22⋊C4×C151—24no—
252C22⋊C4×C151—24no—
253C22⋊C4×C151—24no—
254C22⋊C4×C151—42no—
255C22⋊C4×C151—42no—
256C22⋊C4×C151—42no—
257C22⋊C4×C151—42no—
258C22⋊C4×C151—42no—
259C42×C151—24no—
260C42×C151—22no—
261C42×C151—22no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151—21no—
265C42×C151—21no—
266C42×C151—42no—
267C23×C151—21no—
268C23×C151—21no—
269C23×C151—21no—
270C23×C151—21no—
271C23×C151—21no—
272C23×C151—21no—
273C23×C151—22no—
274C23×C151—22no—
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—41no—
285C23×C151—41no—
286C23×C151—41no—
287C23×C151#12012yes—
288C23×C151C22×D411yescharacteristic
289Q8×C151—22no—
290Q8×C151—22no—
291Q8×C151—22no—
292Q8×C151—22no—
293Q8×C151—41no—
294Q8×C151—41no—
295Q8×C151—41no—
296Q8×C151—41no—
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—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—22no—
312C2×C4×C151—22no—
313C2×C4×C151—22no—
314C2×C4×C151—22no—
315C2×C4×C151—22no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—22no—
320C2×C4×C151—22no—
321C2×C4×C151—22no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—44no—
329C2×C4×C151—48no—
330C2×C4×C151—48no—
331C2×C4×C151—44no—
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—41no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151#12012yes—
347C2×C4×C151#13512yes—
348C2×C4×C151C22×D411yescharacteristic
349C2×C4×C151C22×D411yescharacteristic
350C2×C4×C151C2×#4111yescharacteristic
351C2×C4×C151C2×#4111yescharacteristic
352C2×C4×C151H(5,𝔽2)11yescharacteristic
353C2×C4×C151H(5,𝔽2)11yescharacteristic
354C8×C151—41no—
355C8×C151—41no—
356C8×C151—41no—
357C8×C151—41no—
358C22×C151—22no—
359C22×C151—22no—
360C22×C151—22no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—42no—
366C22×C151—42no—
367C22×C151—42no—
368C22×C151—42no—
369C22×C151—42no—
370C22×C151—42no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151—81no—
377C22×C151—81no—
378C22×C151—81no—
379C22×C151C2×#12011yescharacteristic
380C22×C151#52511yescharacteristic
381C22×C151#53511yescharacteristic
382C22×C151C2×#13511yescharacteristic
383C22×C151#57511yescharacteristic
384C22×C151#57511yescharacteristic
385C22×C151#57511yescharacteristic
386C4×C151—22no—
387C4×C151—22no—
388C4×C151—42no—
389C4×C151—42no—
390C4×C151—41no—
391C4×C151—42no—
392C4×C151—41no—
393C4×C151—41no—
394C4×C151—42no—
395C4×C151—81no—
396C4×C151—81no—
397C4×C151#54611yescharacteristic
398C4×C151#54611yescharacteristic
399C4×C151#54611yescharacteristic
400C4×C151#54611yescharacteristic
401C2×C151—42no—
402C2×C151—82no—
403C2×C151—82no—
404C2×C151#240411yescharacteristic
405C2×C151#300211yescharacteristic
406C2×C151#300511yescharacteristic
407C2×C151#310211yescharacteristic
408C2×C151#311111yescharacteristic
409C2×C151#321211yescharacteristic
410C2×C151#321911yescharacteristic
411#23938C15111yesmaximal, characteristic, direct product factor, Sylow
412C151#2393811yescharacteristic, direct product factor, Sylow
413C2×#529C2×C15111yescharacteristic, complemented
414C2×#452C2×C15111yescharacteristic, complemented
415C2×#449C2×C15111yescharacteristic
416#2297C2×C15111yescharacteristic, complemented
417#2026C2×C15111yescharacteristic, complemented
418#2025C2×C15111yescharacteristic, complemented
419#2015C2×C15111yescharacteristic, complemented
420#2012C2×C15111yescharacteristic, complemented
421#1880C2×C15111yescharacteristic, complemented
422#1879C2×C15111yescharacteristic, complemented
423#1878C2×C15111yescharacteristic, complemented
424#1877C2×C15111yescharacteristic, complemented
425#1875C2×C15111yescharacteristic, complemented
426#1873C2×C15111yescharacteristic, complemented
427#1817C2×C15111yescharacteristic, complemented
428C22×#41C22×C15111yescharacteristic
429C22×Q16C22×C15111yescharacteristic
430C22×SD16C22×C15111yescharacteristic
431C22×SD16C22×C15111yescharacteristic
432C22×D8C22×C15111yescharacteristic
433#529—24no—
434#529—24no—
435C2×#126—21no—
436C2×#125C22×C15111yescharacteristic
437C2×#124C22×C15111yescharacteristic
438C2×#123—21no—
439C2×C22⋊Q8C22×C15111yescharacteristic
440C2×#121C22×C15111yescharacteristic
441C2×C4×Q8C22×C15111yescharacteristic
442C2×C4×D4—21no—
443C2×C4×D4C22×C15111yescharacteristic
444C2×#117—21no—
445C2×#117C22×C15111yescharacteristic
446C22×C42C22×C15111yescharacteristic
447#452—24no—
448#449—24no—
449C2×#103C22×C15111yescharacteristic
450C2×#103C22×C15111yescharacteristic
451C2×#103C22×C15111yescharacteristic
452C2×#103C22×C15111yescharacteristic
453C2×#102C22×C15111yescharacteristic
454C2×#102C22×C15111yescharacteristic
455C2×#102C22×C15111yescharacteristic
456C2×#102C22×C15111yescharacteristic
457C2×C22⋊C8C22×C15111yescharacteristic
458C2×C22⋊C8C22×C15111yescharacteristic
459#391C22×C15111yescharacteristic
460#391C22×C15111yescharacteristic
461#390C22×C15111yescharacteristic
462#390C22×C15111yescharacteristic
463#386—21no—
464#386—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467#340C22×C15111yescharacteristic
468#340C22×C15111yescharacteristic
469#340C22×C15111yescharacteristic
470#340C22×C15111yescharacteristic
471#336C22×C15111yescharacteristic
472#336C22×C15111yescharacteristic
473#336C22×C15111yescharacteristic
474#336C22×C15111yescharacteristic
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—41no—
480C2×#41—41no—
481C22×Q8C23×C15111yescharacteristic
482C22×Q8C23×C15111yescharacteristic
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C23×C15111yescharacteristic
486C22×D4C23×C15111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4D4×C15111yescharacteristic
490C23×C4D4×C15111yescharacteristic
491C23×C4C23×C15111yescharacteristic
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—41no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C22×C8C23×C15111yescharacteristic
505C22×C8C23×C15111yescharacteristic
506C22×C8C23×C15111yescharacteristic
507C22×C8C23×C15111yescharacteristic
508#126—28no—
509#125—22no—
510#125—22no—
511#124—22no—
512#124—22no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8D4×C15114yes—
516#121—22no—
517#121D4×C15114yes—
518C4×Q8—22no—
519C4×Q8—22no—
520C4×D4—28no—
521C4×D4—22no—
522C4×D4—22no—
523#117—28no—
524#117—41no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4C23×C15111yescharacteristic
531C2×C4⋊C4C23×C15111yescharacteristic
532C2×C4⋊C4C23×C15111yescharacteristic
533C2×C4⋊C4C23×C15111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C42—21no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—21no—
548C2×C42D4×C15111yescharacteristic
549C2×C42D4×C15111yescharacteristic
550C2×C42C23×C15111yescharacteristic
551C2×C42C23×C15111yescharacteristic
552#103—22no—
553#103—22no—
554#103—41no—
555#103—41no—
556#102—22no—
557#102—22no—
558#102—41no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566C24—21no—
567C24—21no—
568C24C2×D4×C15111yescharacteristic
569#41—44no—
570#41—44no—
571#41—44no—
572#41—44no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C15112yes—
584C2×Q8#41×C15112yes—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4C2×D4×C15112yes—
602C2×D4#41×C15112yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4C2×D4×C15111yescharacteristic
626C22×C4C2×D4×C15111yescharacteristic
627C22×C4C2×D4×C15111yescharacteristic
628C22×C4C2×D4×C15111yescharacteristic
629C22×C4C2×D4×C15112yes—
630C22×C4C2×D4×C15112yes—
631C22×C4C2×D4×C15111yescharacteristic
632C22×C4C24×C15111yescharacteristic
633Q16—44no—
634SD16—44no—
635SD16—44no—
636D8—44no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4C2×D4×C15112yes—
660C4⋊C4C2×D4×C15112yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C42—24no—
672C42—22no—
673C42—22no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23#120×C15112yes—
700C23C22×D4×C15111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—44no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—44no—
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—41no—
758C2×C4#120×C15112yes—
759C2×C4#135×C15112yes—
760C2×C4C22×D4×C15111yescharacteristic
761C2×C4C22×D4×C15111yescharacteristic
762C2×C4C2×#41×C15111yescharacteristic
763C2×C4C2×#41×C15111yescharacteristic
764C2×C4H(5,𝔽2)×C15111yescharacteristic
765C2×C4H(5,𝔽2)×C15111yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C15111yescharacteristic
792C22#525×C15111yescharacteristic
793C22#535×C15111yescharacteristic
794C22C2×#135×C15111yescharacteristic
795C22#575×C15111yescharacteristic
796C22#575×C15111yescharacteristic
797C22#575×C15111yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—81no—
808C4—81no—
809C4#546×C15111yescharacteristic
810C4#546×C15111yescharacteristic
811C4#546×C15111yescharacteristic
812C4#546×C15111yescharacteristic
813C2—42no—
814C2—82no—
815C2—82no—
816C2#2404×C15111yescharacteristic
817C2#3002×C15111yescharacteristic
818C2#3005×C15111yescharacteristic
819C2#3102×C15111yescharacteristic
820C2#3111×C15111yescharacteristic
821C2#3212×C15111yescharacteristic
822C2#3219×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#529×C151C2semidirect
2. C2×#452×C151C2semidirect
4. #2297×C151C2semidirect
5. #2026×C151C2semidirect
6. #2025×C151C2semidirect
7. #2015×C151C2semidirect
8. #2012×C151C2semidirect
9. #1880×C151C2semidirect
10. #1879×C151C2semidirect
11. #1878×C151C2semidirect
12. #1877×C151C2semidirect
13. #1875×C151C2semidirect
14. #1873×C151C2semidirect
15. #1817×C151C2semidirect
411. #23938C151direct (N × H)
412. C151#23938direct (N × H)
413. C2×#529C2×C151semidirect
414. C2×#452C2×C151semidirect
416. #2297C2×C151semidirect
417. #2026C2×C151semidirect
418. #2025C2×C151semidirect
419. #2015C2×C151semidirect
420. #2012C2×C151semidirect
421. #1880C2×C151semidirect
422. #1879C2×C151semidirect
423. #1878C2×C151semidirect
424. #1877C2×C151semidirect
425. #1875C2×C151semidirect
426. #1873C2×C151semidirect
427. #1817C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1512
C2×#452×C1512
C2×#449×C1512
#2297×C1512
#2026×C1512
#2025×C1512
#2015×C1512
#2012×C1512
#1880×C1512
#1879×C1512
#1878×C1512
#1877×C1512
#1875×C1512
#1873×C1512
#1817×C1512
#23938151